Computational and Information Science: First International Symposium, CIS 2004, Shanghai, China, December 16-18, 2004, Proceedings

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos New York University, NY, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

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Jun Zhang Ji-Huan He Yuxi Fu (Eds.)

Computational and Information Science First International Symposium, CIS 2004 Shanghai, China, December 16-18, 2004 Proceedings

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Volume Editors Jun Zhang University of Kentucky, Department of Computer Science 773 Anderson Hall, Lexington, KY 40506-0046, USA E-mail: [email protected] Ji-Huan He Donghua University, College of Science 1882 Yan-an Xilu Road, Shanghai 200051, China E-mail: [email protected] Yuxi Fu Shanghai Jiaotong University, Department of Computer Science 1954 Hua Shan Road, Shanghai 200030, China E-mail: [email protected]

Library of Congress Control Number: 2004116721 CR Subject Classification (1998): D, F, G, H, I ISSN 0302-9743 ISBN 3-540-24127-2 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2004 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 11368984 06/3142 543210

Preface

The 2004 International Symposium on Computational and Information Sciences (CIS 2004) aimed at bringing researchers in the area of computational and information sciences together to exchange new ideas and to explore new ground. The goal of the conference was to push the application of modern computing technologies to science, engineering, and information technologies to a new level of sophistication and understanding. The initial idea to organize such a conference with a focus on computation and applications was originated by Dr. Jun Zhang, during his visit to China in August 2003, in consultation with a few friends, including Dr. Jing Liu at the Chinese Academy of Sciences, Dr. Jun-Hai Yong at Tsinghua University, Dr. Geng Yang at Nanjing University of Posts and Communications, and a few others. After several discussions with Dr. Ji-Huan He, it was decided that Donghua University would host CIS 2004. CIS 2004 attempted to distinguish itself from other conferences in its emphasis on participation rather than publication. A submitted paper was only reviewed with the explicit understanding that, if accepted, at least one of the authors would attend and present the paper at the conference. It is our belief that attending conferences is an important part of one’s academic career, through which academic networks can be built that may benefit one’s academic life in the long run. We also made every effort to support graduate students in attending CIS 2004. In addition to set reduced registration fees for full-time graduate students, we awarded up to three prizes for to the Best Student Papers at CIS 2004. Students whose papers were selected for awards were given cash prizes, plus a waiver of registration fees. We received approximately 450 papers. All papers were reviewed by anonymous referees, members of the Scientific Committee, and the Co-chairs. Eventually 190 papers were selected for publication in the CIS 2004 proceedings. Papers were submitted by authors from 21 different countries and areas, symbolizing the true international nature of this symposium. Many people did a lot of work to make CIS 2004 possible. We are unable to recount their names one by one. Most of them helped CIS 2004 in the form of reviewing some submitted papers. Their time and efforts spent on making CIS 2004 successful is greatly appreciated. Special thanks are due to Laurence T. Yang for help in the proceedings publication negotiation with Springer, and to Dr. Jeonghwa Lee for categorizing the accepted papers. The CIS 2004 Scientific Committee was co-chaired by Drs. Jun Zhang, JiHuan He, and Yuxi Fu. Dr. Zhang was responsible for the overall organization of the conference, including forming the scientific committee, inviting the keynote speakers, calling for papers, handling most of the submitted papers, contacting the publishers, and preparing the final publications. Dr. He was responsible for

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organizing the local committee, applying for initial funding, arranging the conference site, handling some of the submitted papers, and collecting registration fees. Dr. Fu was mainly responsible for external funding and industrial sponsorship. CIS 2004 was jointly sponsored by Donghua University, Shanghai Jiaotong University, and the Laboratory for High Performance Scientific Computing and Computer Simulation at the University of Kentucky. We would like to thank the institutions for their generous support. September 2004 Jun Zhang CIS 2004 Co-chair

Organizing Committee International Scientific Committee Michael Berry, University of Tennessee, USA Xue-Bin Chi, Chinese Academy of Sciences, China Mehdi Dehghan, Amirkabir University of Technology, Iran Tony Drummond, Lawrence Berkeley National Laboratory, USA Yuxi Fu, Shanghai Jiaotong University, China (Co-chair) George Gravvanis, Hellenic Open University, Greece Qingping Guo, Wuhan University of Technology, China Murli M. Gupta, George Washington University, USA Ji-Huan He, Donghua University, China (Co-chair) Katica (Stevanovic) Hedrih, University of Nis, Yogoslavia Zhongxiao Jia, Tsinghua University, China Hai Jin, Huazhong University of Science and Technology, China Sangbae Kim, Hannam University, South Korea Wai Lam, City University of Hong Kong, China Ming-Lu Li, Shanghai Jiaotong University, China Ming-Chih Lai, National Chiao Tung University, Taiwan Zhongze Li, Chinese Academy of Sciences, China Jing Liu, Chinese Academy of Sciences, China Guang Meng, Shanghai Jiaotong University, China Zeyao Mo, IAPCM, China Kengo Nakajima, University of Tokyo, Japan Jun Ni, University of Iowa, USA Mohamed Othman, University Putra Malaysia, Malaysia Yi Pan, Georgia State University, USA Haesun Park, University of Minnesota, USA Padma Raghavan, Pennsylvania State University, USA Dinggang Shen, University of Pennsylvania, USA Pengcheng Shi, University of Science and Technology, Hong Kong, China Jie Wang, Nanjing University of Technology, China Wei Wang, University of North Carolina-Chapel Hill, USA Dexuan Xie, University of Wisconsin-Milwaukee, USA Geng Yang, Nanjing University of Posts and Communications, China Laurence Tianruo Yang, St. Francis Xavier University, Canada Jun-Hai Yong, Tsinghua University, China Jae Heon Yun, Chungbuk National University, South Korea Xiaodong Zhang, National Science Foundation, USA Jennifer J. Zhao, University of Michigan-Dearborn, USA Hong Zhu, Fudan University, China Jianping Zhu, University of Akron, USA Jun Zhang, University of Kentucky, USA (Co-chair) Albert Zomaya, University of Sydney, Australia

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Local Organizing Committee Guang Meng, Shanghai Jiaotong University, China (Chair) Juan Zhang, Donghua University, China (Secretary-General) Yu-Qin Wan, Donghua University, China (Secretary) Hong-Mei Liu, Donghua University, China (Secretary)

Referees Many people spent their valuable time on reviewing the submitted papers. We would like to thank them for their help. The following is an incomplete list of CIS 2004 referees: Gulsah Altun, Woo Jeong Bae, Deng Cai, Jiaheng Cao, Ke Chen, Kefei Chen, Wufan Chen, Yan Qiu Chen, Fuhua Cheng, Kwang-Hyun Cho, Bong Kyun Choi, Soo-Mi Choi, Se-Hak Chun, Larry Davis, Chris Ding, Yiming Ding, Yongsheng Ding, Yi Dong, Donglei Du, Hassan Ebrahimirad, Pingzhi Fan, Minrui Fei, Zongming Fei, Xiaobing Feng, Tongxiang Gu, Klaus Guerlebeck, Karimi Hamidreza, Young S. Han, Jianmin He, Yoshiaki Hoshino, Lei Hu, Qiangsheng Hua, Haining Huang, Maolin Huang, Xiaodi Huang, Ryu Ishikawa, Christopher Jaynes, N. Jeyanthi, Hao Ji, Yi Jiang, Hai Jin, Tao Jin, Yong-keun Jin, Han Jing, Jiwu Jing, Michael A. Jones, Jan Kaminsky, Oya Kalipsiz, Jiten Chandra Kalita, Ning Kang, Sung Ha Kang, Yun-Jeong Kang, Samir Karaa, Cheol-Ki Kim, Heechern Kim, Hyun Sook Kim, Jaekwon Kim, Kyungsoo Kim, Min Hyung Kim, Sangbae Kim, Yongdeok Kim, Wonha Kim, Andrew Klapper, Myeong-Cheol Ko, Oh-Woog Kwon, Sungho Kwon, Young Ha Kwon, Wai Lam, Zhiling Lan, Dong Hoon Lee, Eun-Joo Lee, Hong Joo Lee, Hyung-Woo Lee, Jeonghwa Lee, Kun Lee, Guido Lemos, Beibei Li, C.C. Li, Guojun Li, Jiguo Li, Minglu Li, Shuyu Li, Rui Liao, Chunxu Liu, Haifeng Liu, Huafeng Liu, Jundong Liu, Caicheng Lu, Liuming Lu, Linzhang Lu, RongXing Lu, Aarao Lyra, Kaveh Madani, D. Manivannan, Timo Mantere, R.K. Mohanty, Mohammad Reza Mostavi, Juggapong Natwichai, Michael K. Ng, Jun Ni, DaeHun Nyang, Mohamed Othman, Yi Pan, Hyungjun Park, Soon Young Park, Bingnan Pei, Dehu Qi, Ilkyeun Ra, Moh’d A. Radaideh, Chotirat Ann Ratanamahatana, John A. Rose, Hossein Rouhani, Chi Shen, Dinggang Shen, Wensheng Shen, Dongil Shin, Taeksoo Shin, Yeong Gil Shin, Bo Sun, Dalin Tang, Jason Teo, R. Thandeeswaran, Haluk Topcuoglu, Bruno Torresani, Changhe Tu, Jie Wang, Morgan Wang, Yong Wang, Xin Wang, Yu-Ping Wang, Zheng Wang, Ziqiang Wang, Yimin Wei, Yimin Wen, M. Victor Wickerhauser, Yilei Wu, Nong Xiao, Shuting Xu, Yinlong Xu, Yun Xu, Geng Yang, Huaiping Yang, Ruigang Yang, Yun Yang, Leslie Ying, Jun-Hai Yong, Kyung Hyun Yoon, Yijiao Yu, Yao Yuan, Yu-Feng Zang, Yiqiang Zhan, Naixiao Zhang, Yanning Zhang, Yufang Zhang, Yuqing Zhang, Jennifer Jing Zhao, Hongjun Zheng, Kun Zhou, Hong Zhu, Jianping Zhu, Qiaoming Zhu, Albert Zomaya

Table of Contents High Performance Computing and Algorithms High Order Finite Difference Schemes for the Solution of Elliptic PDEs Pierluigi Amodio, Ivonne Sgura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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An Algorithm for Optimal Tuning of Fuzzy PID Controllers on Precision Measuring Device Jia Lu, Yunxia Hu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A Grid Portal Model Based on Security and Storage Resource Proxy Quan Zhou, Geng Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Optimal Designs of Directed Double-Loop Networks Bao-Xing Chen, Wen-Jun Xiao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A QoS-Based Access and Scheduling Algorithm for Wireless Multimedia Communications Bin Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Feedforward Wavelet Neural Network and Multi-variable Functional Approximation Jing Zhao, Wang Chen, Jianhua Luo . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The Distributed Wavelet-Based Fusion Algorithm Rajchawit Sarochawikasit, Thitirat Wiyarat, Tiranee Achalakul . . . . . .

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Alternating Direction Finite Element Method for a Class of Moving Boundary Problems Xu-Zheng Liu, Xia Cui, Jun-Hai Yong, Jia-Guang Sun . . . . . . . . . . . . .

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Binomial-Tree Fault Tolerant Routing in Dual-Cubes with Large Number of Faculty Nodes Yaming Li, Shietung Peng, Wanming Chu . . . . . . . . . . . . . . . . . . . . . . . .

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The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) Method for Diffusion Equation J. Sulaiman, M.K. Hasan, M. Othman . . . . . . . . . . . . . . . . . . . . . . . . . . .

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An Effective Compressed Sparse Preconditioner for Large Scale Biomolecular Simulations Dexuan Xie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A Study on Lower Bound of Direct Proportional Length-Based DNA Computing for Shortest Path Problem Zuwairie Ibrahim, Yusei Tsuboi, Osamu Ono, Marzuki Khalid . . . . . . .

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Key Management for Secure Multicast Using the RingNet Hierarchy Guojun Wang, Lin Liao, Jiannong Cao, Keith C.C. Chan . . . . . . . . . .

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Open Middleware-Based Infrastructure for Context-Aware in Pervasive Computing Xianggang Zhang, Jun Liao, Jinde Liu . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Boundary Integral Simulation of the Motion of Highly Deformable Derops in a Viscous Flow with Spontaneous Marangoni Effect Wei Gu, Olga Lavrenteva, Avinoam Nir . . . . . . . . . . . . . . . . . . . . . . . . . .

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Solving Separable Nonlinear Equations with Jacobians of Rank Deficiency One Yun-Qiu Shen, Tjalling J. Ypma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Optimal Capacity Expansion Arc Algorithm on Networks Yuhua Liu, Shengsheng Yu, Jingzhong Mao, Peng Yang . . . . . . . . . . . . . 105 Solving Non-linear Finite Difference Systems by Normalized Approximate Inverses George A. Gravvanis, Konstantinos M. Giannoutakis . . . . . . . . . . . . . . . 111 An Adaptive Two-Dimensional Mesh Refinement Method for the Problems in Fluid Engineering Zhenquan Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 High Order Locally One-Dimensional Method for Parabolic Problems Samir Karaa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Networked Control System Design Accounting for Delay Information Byung In Park, Oh Kyu Kown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Eidon: Real-time Performance Evaluation Approach for Distributed Programs Based on Capacity of Communication Links Yunfa Li, Hai Jin, Zongfen Han, Chao Xie, Minna Wu . . . . . . . . . . . . . 136 Approximate Waiting Time Analysis of Burst Queue at an Edge in Optical Burst-Switched Networks SuKyoung Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

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A Balanced Model Reduction for T-S Fuzzy Systems with Uncertain Time Varying Parameters Seog-Hwan Yoo, Byung-Jae Choi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Genetic Algorithms with Stochastic Ranking for Optimal Channel Assignment in Mobile Communications Lipo Wang, Wen Gu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 A MPLS-Based Micro-mobility Supporting Scheme in Wireless Internet SuKyoung Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 A Novel RBF Neural Network with Fast Training and Accurate Generalization Lipo Wang, Bing Liu, Chunru Wan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Basic Mathematical Properties of Multiparty Joint Authentication in Grids Hui Liu, Minglu Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 GA Based Adaptive Load Balancing Approach for a Distributed System SeongHoon Lee, DongWoo Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 A Novel Approach to Load Balancing Problem Chuleui Hong, Wonil Kim, Yeongjoon Kim . . . . . . . . . . . . . . . . . . . . . . . . 188 Asynchronous Distributed Genetic Algorithm for Optimal Channel Routing Wonil Kim, Chuleui Hong, Yeongjoon Kim . . . . . . . . . . . . . . . . . . . . . . . . 194 High-Level Language and Compiler for Reconfigurable Computing Fu San Hiew, Kah Hoe Koay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 A Parallel Algorithm for the Biorthogonal Wavelet Transform Without Multiplication HyungJun Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Algorithms for Loosely Constrained Multiple Sequence Alignment Bin Song, Feng-feng Zhou, Guo-liang Chen . . . . . . . . . . . . . . . . . . . . . . . 213 Application of the Hamiltonian Circuit Latin Square to the Parallel Routing Algorithm on 2-Circulant Networks Yongeun Bae, Chunkyun Youn, Llyong Chung . . . . . . . . . . . . . . . . . . . . . 219 A Distributed Locking Protocol Jaechun No, Sung Soon Park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

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A Study on the Efficient Parallel Block Lanczos Method Sun Kyung Kim, Tae Hee Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Performance Evaluation of Numerical Integration Methods in the Physics Engine Jong-Hwa Choi, Dongkyoo Shin, Won Heo, Dongil Shin . . . . . . . . . . . . 238 A Design and Analysis of Circulant Preconditioners Ran Baik, Sung Wook Baik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 An Approximation Algorithm for a Queuing Model with Bursty Heterogeneous Input Processes Sugwon Hong, Tae-Sun Chung, Yeonseung Ryu, Hyuk Soo Jang, Chung Ki Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Improved Adaptive Modulation and Coding of MIMO with Selection Transmit Diversity Systems Young-hwan You, Min-goo Kang, Ou-seb Lee, Seung-il Sonh, Tae-won Jang, Hyoung-kyu Song, Dong-oh Kim and Kwa-seop Lim . . 258 Design of a Cycle-Accurate User-Retargetable Instruction-Set Simulator Using Process-Based Scheduling Scheme Hoonmo Yang, Moonkey Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 An Authentication Scheme Based Upon Face Recognition for the Mobile Environment Yong-Guk Kim, Taekyoung Kwon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 A Survey of Load Balancing in Grid Computing Yawei Li, Zhiling Lan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Fractal Tiling with the Extended Modular Group Rui-song Ye, Yu-ru Zou, Jian Lu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Shelling Algorithm in Solid Modeling Dong-Ming Yan, Hui Zhang, Jun-Hai Yong, Yu Peng, Jia-Guang Sun

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Load and Performance Balancing Scheme for Heterogeneous Parallel Processing Tae-Hyung Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 A Nonlinear Finite Difference Scheme for Solving the Nonlinear Parabolic Two-Step Model Weizhong Dai, Teng Zhu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

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Analysis on Networked-Induced Delays in Networked Learning Based Control Systems Li Lixiong, Fei Minrui, Zhou Xiaobing . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 A New Boundary Preserval and Noise Removal Method Combining Gibbs Random Field with Anisotropic-Diffusion Guang Tian, Fei-hu Qi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 The Geometric Constraint Solving Based on Mutative Scale Chaos Genetic Algorithm Cao Chunhong, Li Wenhui . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Genetic Algorithm Based Neuro-fuzzy Network Adaptive PID Control and Its Applications Dongqing Feng, Lingjiao Dong, Minrui Fei, Tiejun Chen . . . . . . . . . . . 330 Formalizing the Environment View of Process Equivalence Yuxi Fu, Xiaoju Dong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 A Scalable and Reliable Mobile Agent Computation Model Liu Yong, Xu Congfu, Wu Zhaohui, Pan Yunhe . . . . . . . . . . . . . . . . . . . 346 Building Grid Monitoring System Based on Globus Toolkit: Architecture and Implementation Kejing He, Shoubin Dong, Ling Zhang, Binglin Song . . . . . . . . . . . . . . . 353 History Information Based Optimization of Additively Decomposed Function with Constraints Qingsheng Ren, Jin Zeng, Feihu Qi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 An Efficient Multiple-Constraints QoS Routing Algorithm Based on Nonlinear Path Distance Xiaolong Yang, Min Zhang, Keping Long . . . . . . . . . . . . . . . . . . . . . . . . . 365 The Early and Late Congruences for Asymmetric χ
= -Calculus Farong Zhong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Improvement of the Resolution Ratio of the Seismic Record by Balanced Biorthogonal Multi-wavelet Transform Wenzhang He, Aidi Wu, Guoxiang Song . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Computer Modeling and Simulations Formally Specifying T Cell Cytokine Networks with B Method Shengrong Zou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

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Three-Dimensional Motion Analysis of the Right Ventricle Using an Electromechanical Biventricular Model Ling Xia, Meimei Huo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Growing RBF Networks for Function Approximation by A DE-Based Method Junhong Liu, Saku Kukkonen, Jouni Lampinen . . . . . . . . . . . . . . . . . . . . 399 Dual-Source Backoff for Enhancing Language Models Sehyeong Cho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 Use of Simulation Technology for Prediction of Radiation Dose in Nuclear Power Plant Yoon Hyuk Kim, Won Man Park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 A Numerical Model for Estimating Pedestrian Delays at Signalized Intersections in Developing Cities Qingfeng Li, Zhaoan Wang, Jianguo Yang . . . . . . . . . . . . . . . . . . . . . . . . 419 Feature Selection with Particle Swarms Yu Liu, Zheng Qin, Zenglin Xu, Xingshi He . . . . . . . . . . . . . . . . . . . . . . . 425 Influence of Moment Arms on Lumbar Spine Subjected to Follower Loads Kyungsoo Kim, Yoon Hyuk Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Monte Carlo Simulation of the Effects of Large Blood Vessels During Hyperthermia Zhong-Shan Deng, Jing Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 A Delimitative and Combinatorial Algorithm for Discrete Optimum Design with Different Discrete Sets Lianshuan Shi, Heng Fu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 A New Algebraic-Based Geometric Constraint Solving Approach: Path Tracking Homotopy Iteration Method Li Wenhui, Cao Chunhong, Yi Wan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 A BioAmbients Based Framework for Chain-Structured Biomolecules Modelling Cheng Fu, Zhengwei Qi, Jinyuan You . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Stability of Non-autonomous Delayed Cellular Neural Networks Qiang Zhang, Dongsheng Zhou, Xiaopeng Wei . . . . . . . . . . . . . . . . . . . . . 460 Allometric Scaling Law for Static Friction of Fibrous Materials Yue Wu, Yu-Mei Zhao, Jian-Yong Yu, Ji-Huan He . . . . . . . . . . . . . . . . . 465

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Flexible Web Service Composition Based on Interface Matching Shoujian Yu, Ruiqiang Guo, Jiajin Le . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 Representation of the Signal Transduction with Aberrance Using Ipi Calculus Min Zhang, Guoqiang Li, Yuxi Fu, Zhizhou Zhang, Lin He . . . . . . . . . . 477 The Application of Nonaffine Network Structural Model in Sine Pulsating Flow Field Juan Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

Biological and Medical Informatics Microcalcifications Detection in Digital Mammogram Using Morphological Bandpass Filters Ju Cheng Yang, Jin Wook Shin, Gab Seok Yang, Dong Sun Park . . . . 492 Peptidomic Pattern Analysis and Taxonomy of Amphibian Species Huiru Zheng, Piyush C Ojha, Stephen McClean, Norman D Black, John G Hughes, Chris Shaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 Global and Local Shape Analysis of the Hippocampus Based on Level-of-Detail Representations Jeong-Sik Kim, Soo-Mi Choi, Yoo-Joo Choi, Myoung-Hee Kim . . . . . . 504 Vascular Segmentation Using Level Set Method Yongqiang Zhao, Lei Zhang, Minglu Li . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Brain Region Extraction and Direct Volume Rendering of MRI Head Data Yong-Guk Kim, Ou-Bong Gwun, Ju-Whan Song . . . . . . . . . . . . . . . . . . . 516 Text Retrieval Using Sparsified Concept Decomposition Matrix Jing Gao, Jun Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 Knowledge-Based Search Engine for Specific 3D Models Dezhi Liu, Anshuman Razdan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530 Robust TSK Fuzzy Modeling Approach Using Noise Clustering Concept for Function Approximation Kyoungjung Kim, Kyu Min Kyung, Chang-Woo Park, Euntai Kim, Mignon Park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

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Helical CT Angiography of Aortic Stent Grafting: Comparison of Three-Dimensional Rendering Techniques Zhonghua Sun, Huiru Zheng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 A New Fuzzy Penalized Likelihood Method for PET Image Reconstruction Zhou Jian, Shu Huazhong, Luo Limin, Zhu Hongqing . . . . . . . . . . . . . . . 550 Interactive GSOM-Based Approaches for Improving Biomedical Pattern Discovery and Visualization Haiying Wang, Francisco Azuaje, Norman Black . . . . . . . . . . . . . . . . . . . 556 Discontinuity-Preserving Moving Least Squares Method Huafeng Liu, Pengcheng Shi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 Multiscale Centerline Extraction of Angiogram Vessels Using Gabor Filters Nong Sang, Qiling Tang, Xiaoxiao Liu, Wenjie Weng . . . . . . . . . . . . . . 570 Improved Adaptive Neighborhood Pre-processing for Medical Image Enhancement Du-Yih Tsai, Yongbum Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 On the Implementation of a Biologizing Intelligent System Byung-Jae Choi, Paul P. Wang, Seong Hwan Yoo . . . . . . . . . . . . . . . . . . 582 Computerized Detection of Liver Cirrhosis Using Wave Pattern of Spleen in Abdominal CT Images Won Seong, June-Sik Cho, Seung-Moo Noh, Jong-Won Park . . . . . . . . 589 Automatic Segmentation Technique Without User Modification for 3D Visualization in Medical Images Won Seong, Eui-Jeong Kim, Jong-Won Park . . . . . . . . . . . . . . . . . . . . . . 595 Adaptive Setreo Brain Images Segmentation Based on the Weak Membrane Model Yonghong Shi, Feihu Qi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601 PASL: Prediction of the Alpha-Helix Transmembrane by Pruning the Subcellular Location Young Joo Seol, Hyun Suk Park, Seong-Joon Yoo . . . . . . . . . . . . . . . . . . 607 Information Processing in Cognitive Science Sung-Kwan Je, Jae-Hyun Cho, Kwang-Baek Kim . . . . . . . . . . . . . . . . . . 613

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Reconstruction of Human Anatomical Models from Segmented Contour Lines Byeong-Seok Shin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619 Efficient Perspective Volume Visualization Method Using Progressive Depth Refinement Byeong-Seok Shin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625 Proteomic Pattern Classification Using Bio-markers for Prostate Cancer Diagnosis Jung-Ja Kim, Young-Ho Kim, Yonggwan Won . . . . . . . . . . . . . . . . . . . . 631 Deterministic Annealing EM and Its Application in Natural Image Segmentation Jonghyun Park, Wanhyun Cho, Soonyoung Park . . . . . . . . . . . . . . . . . . . 639 The Structural Classes of Proteins Predicted by Multi-resolution Analysis Jing Zhao, Peiming Song, Linsen Xie, Jianhua Luo . . . . . . . . . . . . . . . . 645 A Brief Review on Allometric Scaling in Biology Ji-Huan He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652 On He Map (River Map) and the Oldest Scientific Management Method Ji-Huan He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 A Novel Feature Selection Approach and Its Application Gexiang Zhang, Weidong Jin, Laizhao Hu . . . . . . . . . . . . . . . . . . . . . . . . . 665 Applying Fuzzy Growing Snake to Segment Cell Nuclei in Color Biopsy Images Min Hu, XiJian Ping, Yihong Ding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672 Evaluation of Morphological Reconstruction, Fast Marching and a Novel Hybrid Segmentation Method Jianfeng Xu, Lixu Gu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678

Data and Information Sciences Utilizing Staging Tables in Data Integration to Load Data into Materialized Views Ahmed Ejaz, Revett Kenneth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685 HMMs for Anomaly Intrusion Detection Ye Du, Huiqiang Wang, Yonggang Pang . . . . . . . . . . . . . . . . . . . . . . . . . . 692

XVIII Table of Contents

String Matching with Swaps in a Weighted Sequence Hui Zhang, Qing Guo, Costas S. Iliopoulos . . . . . . . . . . . . . . . . . . . . . . . . 698 Knowledge Maintenance on Data Streams with Concept Drifting Juggapong Natwichai, Xue Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 A Correlation Analysis on LSA and HAL Semantic Space Models Xin Yan, Xue Li, Dawei Song . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711 Discretization of Multidimensional Web Data for Informative Dense Regions Discovery Edmond H. Wu, Michael K. Ng, Andy M. Yip, Tony F. Chan . . . . . . . 718 A Simple Group Diffie-Hellman Key Agreement Protocol Without Member Serialization Xukai zou and Byrar Ramamurthy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Increasing the Efficiency of Support Vector Machine by Simplifying the Shape of Separation Hypersurface Yiqiang Zhan, Dinggang Shen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732 Implementation of the Security System for Instant Messengers Sangkyun Kim, Choon Seong Leem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Communication in Awareness Reaching Consensus Without Acyclic Condition Ken Horie, Takashi Matsuhisa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 A High-Availability Webserver Cluster Using Multiple Front-Ends Jongbae Moon, Yongyoon Cho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752 An Intelligent System for Passport Recognition Using Enhanced RBF Network Kwang-Baek Kim, Young-Ju Kim, Am-Suk Oh . . . . . . . . . . . . . . . . . . . . 762 A Distributed Knowledge Extration Data Mining Algorithm Jiang B. Liu, Umadevi Thanneru, Daizhan Cheng . . . . . . . . . . . . . . . . . 768 Image Retrieval Using Dimensionality Reduction Ke Lu, Xiaofei He, Jiazhi Zeng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775 Three Integration Methods for a Component-Based NetPay Vendor System Xiaoling Dai, John Grundy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782

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A Case Study on the Real-Time Click Stream Analysis System Sangkyun Kim, Choon Seong Leem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 788 Mining Medline for New Possible Relations of Concepts Wei Huang, Yoshiteru Nakamori, Shouyang Wang, Tieju Ma . . . . . . . . 794 Two Phase Approach for Spam-Mail Filtering Sin-Jae Kang, Sae-Bom Lee, Jong-Wan Kim, In-Gil Nam . . . . . . . . . . 800 Dynamic Mining for Web Navigation Patterns Based on Markov Model Jiu Jun Chen, Ji Gao, Jun Hu, Bei Shui Liao . . . . . . . . . . . . . . . . . . . . . 806 Component-Based Recommendation Agent System for Efficient Email Inbox Management Ok-Ran Jeong, Dong-Sub Cho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812 Information Security Based on Fourier Plane Random Phase Coding and Optical Scanning Kyu B. Doh, Kyeongwha Kim, Jungho Ohn, Ting-C Poon . . . . . . . . . . . 819 Simulation on the Interruptible Load Contract Jianxue Wang, Xifan Wang, Tao Du . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825 Consistency Conditions of the Expert Rule Set in the Probabilistic Pattern Recognition Marek W. Kurzynski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 An Agent Based Supply Chain System with Neural Network Controlled Processes Murat Ermis, Ozgur Koray Sahingoz, Fusun Ulengin . . . . . . . . . . . . . . . 837 Retrieval Based on Combining Language Models with Clustering Hua Huo, Boqin Feng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 Lightweight Mobile Agent Authentication Scheme for Home Network Environments Jae-gon Kim, Gu Su Kim, Young Ik Eom . . . . . . . . . . . . . . . . . . . . . . . . . 853 Dimensional Reduction Effects of Feature Vectors by Coefficients of Determination Jong-Wang Kim, Byung-Kon Hwang, Sin-Jae Kim, Young-Cheol Oh . 860 A Modular k-Nearest Neighbor Classification Method for Massively Parallel Text Categorization Hai Zhao, Bao-Liang Lu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867

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Avatar Behavior Representation and Control Technique: A Hierarchical Scripts Approach Jae-Kyung Kim, Won-Sung Sohn, Soon-Bum Lim, Yoon-Chul Choy . . 873 Analyzing iKP Security in Applied Pi Calculus Yonggen Gu, Guoqiang Li, Yuxi Fu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 General Public Key m-out-of-n Oblivious Transfer Zhide Chen, Hong Zhu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888 Determining Optimal Decision Model for Support Vector Machine by Genetic Algorithm Syng-Yup Ohn, Ha-Nam Nguyen, Dong Seong Kim, Jong Sou Park . . 895 A Mobile Application of Client-Side Personalization Based on WIPI Platform SangJun Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 An Agent Based Privacy Preserving Mining for Distributed Databases Sung Wook Baik, Jerzy Bala, Daewoong Rhee . . . . . . . . . . . . . . . . . . . . . 910 Geometrical Analysis for Assistive Medical Device Design Taeseung D. Yoo, Eunyoung Kim, Daniel K. Bogen, JungHyun Han . . 916 Hybrid Genetic Algorithms and Case-Based Reasoning Systems Hyunchul Ahn, Kyoung-jae Kim, Ingoo Han . . . . . . . . . . . . . . . . . . . . . . . 922 Pap´ılio Cryptography Algorithm Frederiko Stenio de Ara´ ujo, Karla Darlene Nempomuceno Ramos, Benjam´ın Ren´e Callejas Bedregal, Ivan Saraiva Silva . . . . . . . . . . . . . . . 928 A Parallel Optical Computer System for Large Dadatbase and Knowledge Based Systems Jong Whoa Na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934 Transaction Processing in Partially Replicated Databases Misook Bae, Buhyun Hwang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 940 Giving Temporal Order to News Corpus Hiroshi Uejima, Takao Miura, Isamu Shioya . . . . . . . . . . . . . . . . . . . . . . 947 Semantic Role Labeling Using Maximum Entropy Kwok Cheung Lan, Kei Shiu Ho, Robert Wing Pong Luk, Hong Va Leong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954

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An Instance Learning Approach for Automatic Semantic Annotation Wang Shu, Chen Enhong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 962 Interpretable Query Projection Learning Yiqiu Han, Wai Lam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 969 Improvements to Collaborative Filtering Systems Fu Lee Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975 Looking Up Files in Peer-to-Peer Using Hierarchical Bloom Filters Kohei Mitsuhashi, Takao Miura, Isamu Shioya . . . . . . . . . . . . . . . . . . . . 982 Application of Web Service in Web Mining Beibei Li, Jiajin Le . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 989 A Collaborative Work Framework for Joined-Up E-Government Web Services Liuming Lu, Guojin Zhu, Jiaxun Chen . . . . . . . . . . . . . . . . . . . . . . . . . . . 995 A Novel Method for Eye Features Extraction Zhonglong Zheng, Jie Yang, Meng Wang, Yonggang Wang . . . . . . . . . . 1002 A Q-Based Framework for Demand Bus Simulation Zhiqiang Liu, Cheng Zhu, Huanye Sheng, Peng Ding . . . . . . . . . . . . . . . 1008 A Revision for Gaussian Mixture Density Decomposition Algorithm Xiaobing Yang, Fansheng Kong, Bihong Liu . . . . . . . . . . . . . . . . . . . . . . . 1014 Discretization of Continuous Attributes in Rough Set Theory and Its Application Gexiang Zhang, Laizhao Hu, Weidong Jin . . . . . . . . . . . . . . . . . . . . . . . . . 1020 Fast Query Over Encrypted Character Data in Database Zheng-Fei Wang, Jing Dai, Wei Wang, Bai-Le Shi . . . . . . . . . . . . . . . . . 1027 Factoring-Based Proxy Signature Schemes with Forward-Security Zhenchuan Chai, Zhenfu Cao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034 A Method of Acquiring Ontology Information from Web Documents Lixin Han, Guihai Chen, Li Xie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1041 Adopting Ontologies and Rules in Web Searching Services He Hu, Xiao-yong Du . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047 An Arbitrated Quantum Message Signature Scheme Xin L¨ u, Deng-Guo Feng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054

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Fair Tracing Without Trustees for Multiple Banks Chen Lin, Xiaoqin Huang, Jinyuan You . . . . . . . . . . . . . . . . . . . . . . . . . . 1061 SVM Model Selection with the VC Bound Huaqing Li, Shaoyu Wang, Feihu Qi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067

Computational Graphics and Visualization Unbalanced Hermite Interpolation with Tschirnhausen Cubics Jun-Hai Yong, Hua Su . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072 An Efficient Iterative Optimization Algorithm for Imaging Thresholding Liju Dong, Ge Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1079 Computing the Sign of a Dot Product Sum Yong-Kang Zhu, Jun-Hai Yong, Guo-Qin Zheng . . . . . . . . . . . . . . . . . . . 1086 Bilateral Filter for Meshes Using New Predictor Yu-Shen Liu, Pi-Qiang Yu, Jun-Hai Yong, Hui Zhang, Jia-Guang Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093 Scientific Computing on Commodity Graphics Hardware Ruigang Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1100 FIR Filtering Based Image Stabilization Mechanism for Mobile Video Appliances Pyung Soo Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106 p-Belief Communication Leading to a Nash Equilibrium Takashi Matsuhisa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114 Color Image Vector Quantization Using an Enhanced Self-Organizing Neural Network Kwang Baek-Kim, Abhijit S. Pandya . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1121 Alternate Pattern Fill Xiao-Xin Zhang, Jun-Hai Yong, Lie-Hang Gong, Guo-Qin Zheng, Jia-Guang Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127 A Boundary Surface Based Ray Casting Using 6-Depth Buffers Ju-Whan Song, Ou-Bong Gwun, Seung-Wan Kim, Yong-Guk Kim . . . 1134 Adaptive Quantization of DWT-Based Stereo Residual Image Coding Han-Suh Koo, Chang-Sung Jeong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1141

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Finding the Natural Problem in the Bayer Dispersed Dot Method with Genetic Algorithm Timo Mantere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148 Real-Time Texture Synthesis with Patch Jump Maps Bin Wang, Jun-Hai Yong, Jia-Guang Sun . . . . . . . . . . . . . . . . . . . . . . . . 1155 Alternation of Levels-of-Detail Construction and Occlusion Culling for Terrain Rendering Hyung Sik Yoon, Moon-Ju Jung, JungHyun Han . . . . . . . . . . . . . . . . . . . 1161 New Algorithms for Feature Description, Analysis and Recognition of Binary Image Contours Donggang Yu, Wei Lai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1168 A Brushlet-Based Feature Set Applied to Texture Classification Tan Shan, Xiangrong Zhang, Licheng Jiao . . . . . . . . . . . . . . . . . . . . . . . . 1175 An Image Analysis System for Tongue Diagnosis in Traditional Chinese Medicine Yonggang Wang, Yue Zhou, Jie Yang, Qing Xu . . . . . . . . . . . . . . . . . . . . 1181 3D Mesh Fairing Based on Lighting and Geometric Conditions for Interactive Smooth Rendering Seung-Man Kim, Kwan H. Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187 Up to Face Extrusion Algorithm for Generating B-rep Solid Yu Peng, Hui Zhang, Jun-Hai Yong, Jia-Guang Sun . . . . . . . . . . . . . . . 1195 Adaptive Model-Based Multi-person Tracking Kyoung-Mi Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1201 A Novel Noise Modeling for Object Detection Using Uncalibrated Difference Image Joungwook Park, Kwan H. Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1208 Fast and Accurate Half Pixel Motion Estimation Using the Property of Motion Vector MiGyoung Jung, GueeSang Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216 An Efficient Half Pixel Motion Estimation Algorithm Based on Spatial Correlations HyoSun Yoon, GueeSang Lee, YoonJeong Shin . . . . . . . . . . . . . . . . . . . . . 1224 Multi-step Subdivision Algorithm for Chaikin Curves Ling Wu, Jun-Hai Yong, You-Wei Zhang, Li Zhang . . . . . . . . . . . . . . . . 1232

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Imaging Electromagnetic Field Using SMP Image Guo Wei, Chai Jianyun, Tang Zesheng . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239 Support Vector Machine Approach for Partner Selection of Virtual Enterprises Jie Wang, Weijun Zhong, Jun Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1247

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255

High Order Finite Difference Schemes for the Solution of Elliptic PDEs
Pierluigi Amodio1 and Ivonne Sgura2 1

2

Dipartimento di Matematica, Universit` a degli Studi di Bari, 70125 Bari, Italy [email protected] Dipartimento di Matematica, Universit` a degli Studi di Lecce, 73100 Lecce, Italy [email protected]

Abstract. We solve nonlinear elliptic PDEs by stable finite difference schemes of high order on a uniform meshgrid. These schemes have been introduced in [1] in the class of Boundary Value Methods (BVMs) to solve two-point Boundary Value Problems (BVPs) for second order ODEs and are high order generalizations of classical finite difference schemes for the first and second derivatives. Numerical results for a minimal surface problem and for the Gent model in nonlinear elasticity are presented. Keywords: Finite differences, Boundary Value Methods, Elliptic PDEs.

1

Introduction

Let us consider a two-dimensional nonlinear elliptic PDE formulated as:
−div(M (|∇u|)∇u) = λ, (x, y) ∈ Ω, u(x, y) = g(x, y) on ∂Ω

(1)

where Ω = [x0 , xf ] × [y0 , yf ], λ ∈ IR, | · | stands for the Euclidean norm in IR2 , div is the divergence operator and M (·) is sufficiently regular in its argument. Problems of this kind describe, for example, mathematical models for elastomers and soft tissues (see e.g. [2]) and are usually solved by finite elements and mixedfinite element techniques (see e.g. [3]). In this paper, we propose to solve (1) by stable finite difference schemes of high order on a regular domain with uniform meshgrid. The main idea is the application in more spatial dimensions of the new classes of Boundary Value Methods (BVMs) introduced in [1] to solve twopoint BVPs for second order ODEs. For this reason, in the first part of the paper we report on these formulae and their main properties. In the second part, we show how these schemes can be applied along each space dimension and then combined to solve an elliptic PDE. We show the performance of these techniques on a minimal surface problem and on the Gent model in nonlinear elasticity.


Work supported by GNCS and MIUR (60% project). The work of I. S. was partially supported by the Progetto Giovani Ricercatori Universit` a di Lecce-MIUR 2001/2002.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1–6, 2004. c Springer-Verlag Berlin Heidelberg 2004


2

2

P. Amodio and I. Sgura

Numerical Approximation for the ODE Case

Let us consider the nonlinear two-point BVP f (x, y, y  , y  ) = 0,

x ∈ [x0 , xf ],

y(x0 ) = y0 ,

y(xf ) = yf ,

(2)

and the discretization of the interval [x0 , xf ] by means of a constant stepsize h = (xf − x0 )/(n + 1) such that xi = x0 + ih, i = 0, . . . , n + 1, xn+1 ≡ xf . To approximate the derivatives in (2), we consider the following k − 1 finite difference schemes on a non-compact (long) stencil of k + 1 points y  (xi ) ≈

k−s 1  (s) α yi+j , h2 j=−s j+s

y  (xi ) ≈

k−s 1  (s) β yi+j , h j=−s j+s

s = 1, . . . , k − 1, (3)

such that each formula requires s initial values and k − s final values. For all (s) (s) s, the coefficients αj+s and βj+s have to be calculated in order to attain the maximum possible order k. We note that, if k = 2, then s = 1 and the obtained formulae correspond to the traditional central differences to approximate the second and the first derivatives [4]. For order k > 2, we can define higher order approximation schemes to solve (2) such that all the formulae in (3) need to be used. In fact, by following the approach of the BVMs, first introduced in [5], for each derivative we select one scheme among the k−1 in (3) by fixing the number s = s¯ of initial conditions to be required. This scheme is called main method and it is used to approximate each derivative at the points xi , for i = s¯, . . . , n + s¯ − k + 1. The formulae for s = 1, . . . , s¯ − 1 are used to approximate the derivatives in the first s¯ − 1 points and the formulae for s = s¯ + 1, . . . , k − 1 are used for the approximation in the last k − s¯ − 1 points of the interval. We remark that high order finite difference schemes on non-compact stencils typically present complicated numerical formulations near boundaries (see e.g. [6]) that can reduce the global order of approximation. For this reason, compact schemes aimed at achieving higher accuracy without extra points have been preferred in many applications (see e.g. [7]). In [1] new classes of BVMs of even order have been defined to discretize the derivatives in (2). For the second derivative it has been proved that the coeffi(i) (k−i) cients in (3) satisfy the symmetry property αj = αk−j , for i = 1, . . . , k − 1, j = 0, . . . , k. Therefore, by imposing s¯ = k/2 a generalization of the central differences formulae is obtained. For example, if k = 4 the following approximations are obtained:   5 1 1 1 y  (x1 ) ≈ h12 11 12 y0 − 3 y1 + 2 y2 + 3 y3 − 12 y4 , y  (xi ) ≈ y  (xn ) ≈

1 h2 1 h2



1 − 12 yi−2 + 43 yi−1 − 52 yi + 43 yi+1 −



1 12 yi+2

1 − 12 yn−3 + 13 yn−2 + 12 yn−1 − 53 yn +



i = 2, . . . , n − 1,

,

11 12 yn+1



.

High Order Finite Difference Schemes for the Solution of Elliptic PDEs

3

Similarly, the coefficients for the approximation of the first derivative satisfy (k−i) = −βk−j , for i = 1, . . . , k − 1, j = 0, . . . , k. In [1] three different schemes of even order have been considered. They correspond to high order extensions of the classical backward, forward and central difference schemes. For this reason, they have been called Generalized Backward Differentiation Formulae (GBDFs) (see also [5]), Generalized Forward Differentiation Formulae (GFDFs) and Extended Central Difference Formulae (ECDFs), respectively. For example, if k = 4 we have the formulae   1 yi+3 , i = 1, . . . , ρ − 1, y  (xi ) ≈ h1 − 14 yi−1 − 56 yi + 32 yi+1 − 12 yi+2 + 12 (i) βj

y  (xi ) ≈

1 h

y  (xi ) ≈

1 h

 

1 12 yi−2

− 23 yi−1 + 23 yi+1 −

1 12 yi+2



i = ρ, . . . , σ − 1,

,

 1 − 12 yi−3 + 12 yi−2 − 32 yi−1 + 56 yi + 14 yi+1 ,

i = σ, . . . , n.

where the following values of (ρ, σ) characterize the method GBDF: (n − 1, n);

ECDF: (2, n);

GFDF: (2, 3).

In the rest of this paper the combinations of the generalized central differences for the second derivative with the above three classes of methods for the first derivative will be called D2GBDFs, D2ECDFs and D2GFDFs. If Y = [y1 , y2 , . . . , yn ]T is the unknown vector and Y (x) = [y(x1 ), . . . , y(xn )]T is the vector of the exact solution, we have the following approximations Y  (x) ≈

1  AY , h2

Y  (x) ≈

1  BY , h

 and B  are the n × (n + 2) matrices containing where Y = [y0 , Y T , yf ]T , and A the coefficients of all the schemes used for the approximation. A conditioning analysis on the linear test problem y  − 2γy  + µy = 0 is reported in [1]. The main result is that, for µ < 0, the D2ECDFs yield well conditioned matrices for all γ ∈ IR and for all h, whereas the D2GBDFs and D2GFDFs require the stepsize restrictions described in Table 1. Note that the well-conditioning regions become wider for increasing orders. Table 1. Stepsize restrictions required to obtain well-conditioning method

γ0 no restr. h ≤ q/γ

order q

4

6

8

1 17/12 16/9

In [1] many numerical examples on second order ODE-BVPs show that these schemes have good convergence properties also for nonlinear problems.

4

3

P. Amodio and I. Sgura

Application to Elliptic PDEs

Since elliptic problems in two or more dimensions usually present both second order, first order and mixed partial derivatives, it seems to be a good idea to apply the above schemes along each space variable and to combine them to have an overall finite difference method of high order. In the following twodimensional examples we discretize the rectangular domain [x0 , xf ] × [y0 , yf ] by means of different stepsizes hx = (xf − x0 )/(n + 1) and hy = (yf − y0 )/(m + 1). The discrete solution in the internal points is set in the unknown vector U = (U1 , U2 , . . . , Um )T , Uj = (u1j , . . . unj ) where uij ≈ u(xi , yj ). Therefore, the m ⊗ B n )U , following approximations are considered: Uxy (x, y) ≈ hx1hy (B Uxx (x, y) ≈

1  n )U , (Im ⊗ A h2x

Uyy (x, y) ≈

Ux (x, y) ≈

1  n )U , (Im ⊗ B hx

Uy (x, y) ≈

1  , (Am ⊗ In )U h2y 1   (Bm ⊗ In )U hy

r and B r are the same matrices of dimension where Ir = [0r , Ir , 0r ], 0r ∈ IRr , A  r × (r + 2) defined in Section 2, and U contains also the boundary values 1 , . . . , U m+1 )T ,  = (U 0 , U U

i = (u0j , . . . un+1,j ). U

Both the examples proposed in this section are nonlinear and their discretization yields a nonlinear discrete problem that we solve by the Picard’s iteration: ˜ (p+1) = f (U (p) ), ∆U

p = 0, 1, . . . ,

U (0) given,

(4)

where f (U (p) ) contains the nonlinear terms, Ar is a square quasi-Toeplitz band matrix with bandwidth k + 1 (k order of the method), obtained by eliminating r , and ∆˜ = 1 (Im ⊗ An ) + 1 (Am ⊗ In ) ∈ IRm·n × the first and last column of A h2x h2y m·n IR approximates the Laplace operator. Numerical experiments show that the considered approach could be effective when the solution is smooth. Otherwise a continuation strategy with respect to the parameter in the PDE is needed. The linear system at each step is solved by means of a direct solver and the stopping ˜ (p+1) − f (U (p) ) ≤ tol, for a criteria used are U (p+1) − U (p)  ≤ tol and ∆U fixed tolerance tol. The numerical results are reported only for the D2GBDFs and D2ECDFs, since D2GFDFs exhibit results very similar to the D2GBDFs. 3.1

A Minimal Surface Problem

This problem is obtained by setting  M (|∇u|) = ( 1 + |∇u|2 )−1

and λ = 0,

and can be formulated as (1 + u2y )uxx − 2ux uy uxy + (1 + u2x )uyy = 0.

High Order Finite Difference Schemes for the Solution of Elliptic PDEs

5

This is a well known elliptic problem and it is usually solved by means of finite element methods.   cos(y−0.5) We consider an example with the exact solution u(x, y) = log cos(x−0.5) and Dirichlet boundary conditions on the square domain Ω = [0, 1] × [0, 1]. The problem is solved starting in (4) from U (0) ≡ 0 and using hx = hy , that is m = n. The convergence behaviour and the order estimates are given in Table 2. Table 2. Minimal surface problem - Convergence behavior (tol = 1e-13) method n

3.2

error

order 4 rate iterat.

error

order 6 rate iterat.

error

order 8 rate iterat.

D2GBDF 9 4.65e-06 19 2.63e-07 4.15 39 1.09e-08 4.60

21 21 21

4.59e-07 9.73e-09 5.56 1.26e-10 6.27

20 20 20

6.83e-08 6.35e-10 6.75 2.67e-12 7.89

19 19 19

D2ECDF 9 4.63e-06 19 2.69e-07 4.11 39 1.14e-08 4.56

17 17 17

4.58e-07 9.66e-09 5.57 1.24e-10 6.28

17 17 17

6.83e-08 6.34e-10 6.75 2.67e-12 7.89

17 17 17

The Gent Model in Nonlinear Elasticity

The Gent model is used in nonlinear elasticity to describe the anti-plane shear deformations for a class of isotropic and incompressible hyperelastic rubber-like materials [2]. To investigate the mechanical response of the material the PDE (1) has to be solved with −1 M (|∇u|) = µ(1 − Jm |∇u|2 )−1 ,

µ > 0,

Jm > 0,

−1 for (x, y) ∈ Ω = [0, L] × [0, 1] and u(x, y) = 0 for (x, y) ∈ δΩ. If α = Jm , the equation (1) is equivalent to the following expression:

[1 + α(u2x − u2y )]uxx + [1 − α(u2x − u2y )]uyy + 4αux uy uxy =

λ [1 − α(u2x + u2y )]2 . µ

For increasing values of the parameter λ > 0 an interior localization occurs that represents the zone of fracture of the material. We consider two applications with L = 1 and L = 4. In the first case the localization is at the point (0.5, 0.5) and the solution is a downward cone that, for increasing values of λ, tends to an up-side down pyramid. If the rectangular domain is considered, the localization is along the line (x, 0.5) and, in addition, boundary layers appear in the y-direction. We set Jm = 97.2, µ = 1 and we solve both cases for λ = 50 by using hx = hy . To achieve convergence a continuation technique starting from λ = 10 has been used. In Tables 3–4 we report the meshsizes, the number of Picard iterations occurred (with tol = 10−10 ) along the continuation and an error estimate calculated with respect to the solution obtained by the method of order 8 in the same class and on the same mesh. We emphasize that the two methods behave

6

P. Amodio and I. Sgura Table 3. Gent problem with λ = 50 on a square domain

n m

D2GBDF6 error iterates

D2ECDF6 error iterates

19 19 5.37e-3 (10-50-30) 5.19e-3 (10-47-27) 39 39 7.99e-5 (10-47-20) 7.85e-5 (10-48-20) 79 79 1.34e-5 (10-48-14) 1.33e-5 (10-48-14) Table 4. Gent problem with λ = 50 on a rectangular domain

n m

error

D2GBDF6 iterates

error

D2ECDF6 iterates

9 39 1.87e-1 (14-56-257-134) 1.87e-1 (14-49-179-124) 19 79 5.87e-3 (14-53-146-103) 5.64e-3 (15-52-142-105) 39 159 8.29e-5 (15-52-143-85) 8.13e-5 (15-52-142-85)

similarly, but the continuation strategy is required to obtain the convergence of the D2GBDF. As a general comment, we can conclude that the new schemes introduced in the ODE framework seem to be very promising also to solve elliptic PDEs accurately. Future developments of this research concern the approximation with variable stepsize, a suitable strategy of mesh variation and numerical comparisons with compact finite difference schemes (see e.g. [7]).

References 1. Amodio, P., Sgura, I.: High order finite difference schemes for the solution of second order BVPs. J. Comput. Appl. Math. (2004) in press. 2. Horgan, C., Saccomandi, G., Sgura, I.: A two-point boundary-value problem for the axial shear of hardening isotropic incompressible nonlinearly elastic materials. SIAM J. Appl. Math. 62 (2002) 1712–1727 3. Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer Series in Comput. Math. 23, Springer-Verlag, Berlin (1994) 4. Ascher, U., Mattheij, R., Russell, R.: Numerical Solution of Boundary Value Problems for ODEs. Classics in Applied Mathematics 13, SIAM, Philadelphia (1995) 5. Brugnano, L., Trigiante, D.: Solving ODEs by Linear Multistep Initial and Boundary Value Methods. Gordon & Breach, Amsterdam (1998) 6. Fornberg, B., Ghrist, M.: Spatial finite difference approximations for wave–type equations. SIAM J. Numer. Anal. 37 (1999) 105–130 7. Ge, L., Zhang, J.: Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients. J. Comput. Appl. Math. 143 (2002) 9–27

An Algorithm for the Optimal Tuning of Fuzzy PID Controllers on Precision Measuring Device Jia Lu and Yunxia Hu Department of Computer Science and Information System, University of Phoenix, 5050 NW 125 Avenue, Coral Springs, FL 33076, U.S.A. [email protected]

Abstract. A new computability methodology was proposed for the fuzzy proportional integral derivative (PID) controllers based on the theoretical fuzzy analysis and the downhill simplex optimization. The paper analyzes the algorithm of downhill simplex searching of the optimization objective functions. The input and objective function of downhill factors were selected for constructing optimal decision rules for the fuzzy logic controller. An optimizer was built around the simplex algorithm that it minimized a simplex within an Ndimensional. The sampling rate is 0.1 and the controllers are implemented under a 0.5 second time delay. The simulation confirmed the viability of the algorithm in its effectiveness of the adaptive fuzzy logic controller.

1 Introduction There have been a number of proposed methods in tuning fuzzy logic control [1] [2]. Genetic algorithms are searching algorithm to optimize the rule table of conventional fuzzy logic controller [3]. Genetic algorithm tuning is to design coding scheme, which refers to select tuning parameters and encode them into a bit-string representation [4]. However, the genetic algorithm is attempting to describe some system an engineer faces the fact that all processes and events in the system cannot be fully described and identified. This is why approximate algorithms are always needed to determine for industrial and medical fields. In addition to the controller structure design, another important issue is parameter tuning. There exist some problems to obtain optimal parameters due to lack of the information between a model and its real system. Downhill simplex searching algorithm was used for multi-dimension optimization problems such as quantitative analysis of convergence beam electron diffraction. Downhill is a local optimization algorithm that can be used to find the nearest local minimum as soon as possible [5]. The downhill simplex algorithm was chosen in this research for optimizing the design of fuzzy logic controllers. It determined the control decision for the process and played a key role in the fuzzy logic controller. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 7–12, 2004. © Springer-Verlag Berlin Heidelberg 2004

8

J. Lu and Y. Hu

2 Algorithm Searching 2.1 Searching Space An easy way we used was to set up a simplex for starting with an initial starting point P0, and the other N initial points. The downhill simplex method now takes a series of steps, but the most steps just moving the point of the simplex where the function is largest through the opposite face of the simplex to a lower point. When combined with other operations, the simplex was used to change direction on encountering a valley at an angle and contract in the neighborhood of a minimum. The three vertices of the polytope are denoted by Pl, Pa, Ph, and their function are fl, fa and fh respectively. The indices are selected as fl < fa < fh. The object was to search a point at which the function value is minimum. The best point can be used as the conjugate point of the worst point. A line is connected between point Pl and Pa, and let Ph be the middle point bisecting the line segment. A line is connected between Ph and Pa, such as the point Pr satisfies Ph Pa = Pa Pr. The point Pr lies on the segment Ph Pa is the conjugate point of Pr . Therefore, fr is the objective value of point Pr. If fr ≥ fa, the new point Pr goes far from the worst point Ph. Therefore, the size of the search step needs to be decreased slightly. A point Ps is selected between Ph and Pr. If fr < fa, the new point Pr is really much better than the worst point Ph. The new point Pe can be chosen in the extension line of the Ph and Pr. If fe ≤ fr, then the new point Pe can be chosen as Ps, otherwise, Pr will be Ps. 2.2 Searching for Fuzzy PID Controller Combining the downhill simplex searching algorithm with the µ-law surface tuning of fuzzy lookup table, we setup tuning parameters the fuzzy PID controller. The number of dimensions in the downhill simplex algorithm is determined by the number of tuning parameters. A set of parameters was constructed a point in the downhill simplex algorithm for the fuzzy PID controller. In order to start a downhill simplex searching, N+1 points were used. Let all the points be represented by Pi, where i = 1… N+1 and the worst point is PN+1. If 0 y, h ≥ x. Furthermore if the sufficient and necessary conditions are satisfied, then L(n; l, h, x, y) is realized by a unique directed doubleloop network G(n; 1, s), where s ≡ αl −βl (mod n), and αy +βh = 1 for some integers α, β. Lemma 3. [2] Suppose that  L(n; l, h, x, y) is an L-shape tile. Let z0 = |x − y|. Then d(L(n; l, h, x, y)) ≥ 3n − 0.75z02 +0.5z0 − 2.

3

Main Results

For any given positive integer n, we can get d(n) by using the following algorithm: For s = 2 to n2−1, calculate the diameter of G(n; 1, s) by using the algorithm given in [12].

By using the above algorithm, we can find s0 ∈ {2, 3, · · · ,  n2  − 1} such that the digraph G(n; 1, s0 ) has the minimum diameter. As d(n; 1, n+1−s)=d(n; 1, s) (Theorem 7 [1] ), we have d(n) = d(n; 1, s0 ). With the aid of a computer and by using the above algorithm, we have the following Lemma 4. Lemma 4. When n ≤ 300000, we have d(n) ≤ lb(n) + 4 and only 27 integers such that d(n) = lb(n) + 4. These 27 4-tight optimal double-loop networks are G(53749; 1, 985), G(64729; 1, 394), G(69283; 1, 1764), G(94921; 1, 515), G(101467; 1, 2438), G(103657; 1, 528), G(142441; 1, 635), G(147649; 1, 617), G(159076; 1, 676), G(196435; 1, 746), G(200507; 1, 3532), G(210488; 1, 6696),

22

B.-X. Chen and W.-J. Xiao

G(225109; 1, 5650), G(226131; 1, 7632), G(235171; 1, 791), G(236671; 1, 6374), G(244909; 1, 13376), G(253882; 1, 964), G(256507; 1, 963), G(260941; 1, 8969), G(266281; 1, 875), G(267107; 1, 858), G(271681; 1, 3063), G(279827; 1, 5363), G(281939; 1, 851), G(284431; 1, 869), G(291883; 1, 881). The former 4 4-tight optimal double-loop networks were reported in [14]. By Lemma 4 we can prove the following Theorem 1. Theorem 1. Suppose that n is k-tight optimal. If an L-shape tile L(n; l, h, x, y) is k-tight, then |x − y| ≤ 2k + 6. By Lemma 2 and Theorem 1 we have the following Lemma 5. Lemma 5. Suppose that n = 3t2 + At + B ∈ Ii (t) and n is k-tight optimal. Let l = 2t + a, h = 2t + b, x = t + a + b − i − k, y = t + a + b − i − k + z, where 0 ≤ z ≤ 2k + 6. Then a k-tight L-shape tile L(n; l, h, x, y)( or L(n; l, h, y, x)) is realizable if and only if the indeterminate equation (1) has an integer solution (a0 , b0 ) and 2t + a0 > t + a0 + b0 − i − k + z ≥ 0, 2t + b0 ≥ t + a0 + b0 − i − k ≥ 0, gcd(2t + b0 , t + a0 + b0 − i − k + z) = 1 (or 2t + a0 > t + a0 + b0 − i − k ≥ 0, 2t + b0 ≥ t + a0 + b0 − i − k + z ≥ 0, gcd(2t + b0 , t + a0 + b0 − i − k) = 1). (a + b − i − k)(a + b − i − k + z) − ab + (A + z − 2i − 2k)t + B = 0

(1)

Theorem 2. Let H(k, z, t) = (i + k)2 − (i + k)z + z 2 + 3[(2i + 2k − A − z)t − B]. The indeterminate equation (1) has an integer solution if and only if there exist two nonnegative integers s and m such that 4H(k, z, t) = s2 + 3m2 . If 4H(k, z, t) can be represented as s2 + 3m2 , where s, m ∈ Z + , then the following four pairs are solutions of the indeterminate equation (1) and at least two of them are integer solutions: , b = j+s−3m ; (2) a = (1) a = j+s+3m 6 6 j−s+3m j−s−3m (3) a = , b = ; (4) a = 6 6 where j = 4i + 4k − 2z.

j+s−3m , 6 j−s−3m , 6

b= b=

j+s+3m ; 6 j−s+3m ; 6

From Theorem 2 we know that the following Algorithm 1 can find out all integer solutions of the indeterminate equation (1). Algorithm 1: Suppose that t, A, B, i, k, z are given integers. In the following we will find out all integer solutions of the equation (1). Step 1: H := 4(i + k)2 − 4(i + k)z + 4z 2 + 12[(2i + 2k − A − z)t − B]; Step 2: √if H ≥ 0 then s :=  H; do while s≥0 m :=  (H − s2 )/3 ; if H == s2 + 3m2 then Find out integer pairs in the four pairs of Theorem 2; endif s := s − 1; enddo endif

Optimal Designs of Directed Double-Loop Networks

23

Note that √ the running time complexity of the algorithm 1 is determined by the value of H and the value of H is mainly determined by √ √ 12∗(2i+2k−A−z)t. Thus the running time complexity of the algorithm 1 is O( kt), i.e., O( kn0.25 ). So from Theorem 2 we get the following Theorem 3. Theorem 3. For any given integers t, A, B, i, k, z, Algorithm 1 can find out all integer solutions of the indeterminate equation (1). The running time complexity √ of the algorithm 1 is O( kn0.25 ). For any given positive integer n (n ≥ 5), the following Algorithm 2 will find out a k-tight optimal double-loop network G(n; 1, s). Algorithm 2: For any given positive integer n (n ≥ 5), we will find out a k-tight optimal double-loop network G(n; 1, s). Step 1: Given n, calculate t, A, B, i such that n = 3t2 + At + B ∈ Ii (t). Let k := 0; Step 2: Do while .t. z := 0; Do while z y ≥ 0, l > y and gcd(y, h
) = 1) or (l > y ≥ 0, h > x ≥ 0, h ≥ y and gcd(x, h − x) = 1) then L(n; l, h, x, y) or L(n; l, h, y, x) is realizable; goto step 3; endif z := z + 1; enddo k := k + 1; enddo Step 3: For a realizable L-shape tile L(n; l0 , h0 , x0 , y0 ) we just found, we can find out two integers α and β such that αy0 + β(h0 − y0 ) = 1. Let s ≡ αl0 − β(l0 − x0 ) (mod n). Then we get G(n; 1, s), which is a k-tight optimal double-loop network.

Theorem 4. For any given positive integer n (n ≥ 5), Algorithm 2 can find out a k-tight optimal double-loop network G(n; 1, s). The running time complexity of Algorithm 2 is O(k 2.5 n0.25 log n). With the aid of a computer and by using Algorithm 2, we find out that there are 153 5-tight optimal integers when n ≤ 10000000. They are 417289, 526429, 858157, 1302637, 1368379, 1498333, 1507507, 1562149, 1624085, 1648837, 1820047, 1832749, 1913203, 1940597, 2226769, 2366981, 2511661, 2551397, 2773321, 2828101, 3147077, 3225553, 3349743, 3504857, 3509749, 3545867, 3863273, 4029797, 4032493, 4226743, 4269343, 4282909, 4379069, 4457293, 4472131, 4475545, 4494557, 4550419,

1572187, 2063833, 2886739, 3586741, 4333223, 4564933,

1585333, 2143921, 2926097, 3630413, 4335347, 4565153,

1620149, 2205637, 3130549, 3649189, 4343606, 4800031,

24

B.-X. Chen and W.-J. Xiao

4803541, 5605427, 5921329, 6533653, 7117013, 7617121, 8102293, 8568124, 8871373, 9247505, 9478977,

4916373, 4943467, 5080441, 5100967, 5134069, 5284307, 5637901, 5670869, 5683259, 5702509, 5759077, 5809849, 5989249, 6005741, 6062029, 6110827, 6350429, 6390793, 6575167, 6605357, 6666961, 6704059, 6835893, 6920707, 7272697, 7276777, 7295053, 7302173, 7315269, 7425289, 7631221, 7667467, 7675253, 7705783, 7733041, 7823495, 8104009, 8124297, 8305807, 8351836, 8375197, 8408707, 8600936, 8639023, 8659213, 8679027, 8686149, 8727733, 9029681, 9055117, 9097969, 9155057, 9197197, 9197749, 9279149, 9279413, 9309497, 9344659, 9393953, 9394393, 9607633, 9697471, 9739907, 9859849, 9870097, 9881161.

5458921, 5892629, 6473537, 6921077, 7541929, 7824149, 8467493, 8823511, 9204749, 9470143,

5560873, 5899027, 6505839, 6921565, 7593397, 8011667, 8550321, 8849477, 9231617, 9472057,

There are only 3 6-tight optimal integers when n ≤ 10000000. They are 7243747, 8486867, 9892013.

References [1] Hwang, F. K., Xu, Y. H.: Double loop networks with minimum delay. Discrete Mathematics, 66(1987) 109-118 [2] Li, Q., Xu, J. M., Zhang, Z. L.: Infinite families of optimal double loop networks. Science in China (Series A), 23(1993) 9:979-992 (in Chinese) [3] Xu, J. M.: Designing of optimal double loop networks. Science in China (Series E), 29(1999) 3: 272-278 (in Chinese) [4] Liu, H. P., Yang, Y. X. , Hu, M. Z.: On the construction of tight double loop networks. Practising & Theory in System Engineering, 12 (2001) 72-75 (in Chinese) [5] Shen Jian, Li Qiao: Two theorems on double loop networks. Journal of China University of Science and Technology, 25 (1995) 2:127-132 [6] Esque, P., Aguilo, F., Fiol, M. A.: Double commutative-step digraphs with minimum diameters. Discrete Mathematics, 114 (1993) 147-157 [7] Aguilo, F., Fiol, M. A.: An efficient algorithm to find optimal double loop networks. Discrete Mathematics, 138 (1995) 15-29 [8] Erdos, P., Hsu, D. F.: Distributed loop networks with minimum transmission delay. Theoretical Computer Science, 100 (1992) 223-241 [9] Mukhopadhyaya, K., Sinha, B. P.: Fault-tolerant routing in distributed loop networks. IEEE Trans. on Comput., 44 (1995)12:1452-1456 [10] Chen, Z. X., Jin, P.: On the [+1]-link-prior shortest path and optimal routing for double-loop networks. Journal of computer research & development, 38 (2001)7: 788-792 (in Chinese) [11] Wong, C. K., Coppersmith, D.: A combinatorial problem related to multimodule memory organizations. J. ACM 21 (1974) 392-402 [12] Ying, C., Hwang, F. K.: Diameters of weighted double loop networks. Journal of Algorithm, 9 (1988) 401-410 [13] Shen Jian, Li Qiao: Two theorems on double loop networks. Journal of China University of Science and Technology, 25 (1995) 2:127-132 [14] Xu, J. M., Liu, Q.: One infinite family of 4-tight optimal double loop networks. Science in China (Series A), 33 (2003)1:71-74 [15] Rodseth, O. J.: Weighted multi-connected loop networks. Disc. Math., 148 (1996) 161-173

A QoS-Based Access and Scheduling Algorithm for Wireless Multimedia Communications Bin Wang Depart. of Radio Engineering, Southeast University, Nanjing, P. R. of China [email protected]

Abstract. In this paper, an overview of existing MAC scheduling algorithms is briefly presented. Then considerations concerning QoS of wireless communication are discussed. In order to improve the QoS of wireless communication, we proposed a new QoS-based algorithm for wireless access and scheduling in centralized network where all traffics are controlled by the base station. The algorithm uses TDMA in the radio air interface, but it can also be adapted to other access methods, such as CDMA. Finally, the simulation is performed to show the QoS guarantee with the new algorithm.

1 Introduction The media access algorithms can be classified into two categories: centralized and distributed[1]. Distributed algorithm is the contention-based protocol, where the access to media depends on the contention of each station, while the centralized algorithm assigns the access opportunity to the station according to the access request. To meet QoS requirements in wireless applications, the distributed algorithms such as EDCF adopt the idea of traffic categories[3]. The traffic with higher priority is assigned with more media share by reducing the probability of the lower priority traffic access. Although the EDCF can meet the QoS requirements statistically, it cannot strictly provide QoS guarantee. What’s more, the QoS of the real-time traffic keeps decreasing as more traffics join the contention. It is found that distributed algorithms are not suitable to strictly guarantee QoS requirements, so the traditional time-stamp based algorithms such as EDD[5] and WFQ[6] cannot be used. Comparatively, centralized protocols perform better than distributed ones from the QoS point of view. In the centralized network, BS(Base Station) selects from all applicants according to their queue length and traffic priority indicated in their access requests, PCF [2] and HCF [4] are such kind of algorithms which can meet QoS requirements in some degree, but still cannot guarantee strictly time-bounded traffic. To solve the problems mentioned above, we proposed a QoS-based access and scheduling algorithm to enhance the QoS performance in wireless multimedia network. The algorithm absorbs the merits of both centralized and distributed algorithms to serve real-time and non-real-time traffics with different QoS priorities [7]. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 25–31, 2004. © Springer-Verlag Berlin Heidelberg 2004

26

B. Wang

This paper is organized as following. Section 2 introduces the main idea and principle of our algorithm. Section 3 describes our access and scheduling algorithm in detail. Section 4 presents some simulation results. Section 5 gives some conclusions.

2 Radio Resource Management for Multimedia Communications The criteria for classification of different QoS includes: throughput, BER, acceptable delay, acceptable delay jitter. However, from users’ point of view, the main concern is the sensitiveness of the traffic delay[8]. Thus, the QoS can also be categorized into classes: background, interactive, streaming and conversational. In this algorithm, we categorize the streaming and conversational classes into realtime services, which are provided with higher guarantee compared to the non-realtime traffics such as the web browsing of interactive class and email of background classes. As depicted in the figure 1, traffics are arranged in periodic super frames, and each super frame can be divided into three parts, access period, real-time service transmit period and best-effort service transmit period.

Fig. 1. The structure of the resource arrangement in time

All traffics are managed by the BS. The downlink traffics(from BS to MS) are directly sent to MS in compound frames(data and polling parts), while the uplink traffics(from the MS to BS) have to wait until the BS polls them. Because real-time services have demanding requirements on time delay, we have to assign them fixed time slots and scan them periodically. The difficulties of the scheduling algorithm are how to poll the MS in time to guarantee the QoS of real-time traffics while at the same time to reduce the overhead of polling as much as possible, in other words, to reduce the chance of polling idle MSs. This problem will be solved by the algorithm proposed in the next section. We adopt the best-effort policy to serve non-real-time traffics in the round-robin manner.

A QoS-Based Access and Scheduling Algorithm

27

3 QoS-Based Access and Scheduling Algorithm 3.1 Access Algorithm If only the best-effort traffics are supported by the system, the module of access control is not necessary. But in order to guarantee specific QoS requirement under limited system capacity, the module controlling the new arriving access requests is required. We all have the suffering of unbearable delay when we watch online TV, the fact is that the required output of the port overweighs the output the system can afford, so no one can get desired service quality from it. The problem comes from the lackness of protection mechanism for the QoS of the ongoing traffic. In other words, we need the mechanism allowing the system to reject new access request before the QoS requirements of the ongoing traffics and the newly arrived traffics cannot be longer satisfied. In our algorithm whether the access can be accepted is determined by two factors: service QoS requirement and current traffic load of the system (Figure 2).

Output

Input specific QoS service request

access control

current traffic load

new setting for the scheduling

current traffic adjust

Fig. 2. Access control system

The duty of the beacon in our algorithm is of no difference to the regular one, it maintains the synchronization of local timers of the MSs and delivers protocol related parameters. Upon receiving the beacon frame, the MSs that want to initiate new traffics start the access requests. The collision of the access requests can be avoided to some extent by the slotted ALOHA. Access requests can be classified accordingly into real-time and non-real-time ones. After successfully receiving the access request frames, all the non-real-time access requests are accepted. The requests of real-time traffic, however, have to be checked whether the current system capacity can accommodate them. If it is big enough, the requested traffic will be activated by the subsequently polling. Otherwise, the BS access control module will deny the request. 3.2 Scheduling Algorithm With the protection mechanism of the access control, we can schedule the accepted traffics efficiently. To each newly accepted traffic, resources are assigned. The traffic in higher QoS class has the priority to be served first. In the same QoS class, the traffic accepted earlier has higher priority than later ones. The interactions of different modules are presented in Figure 3.

28

B. Wang new service request

access control

load control

beacon traffic class 1

class N

real-time traffic

class N+1

class N+M

non-real-time traffic

priority

receive

transmit

Fig. 3. QoS-based MAC access and scheduling algorithm

To real-time or say time-bounded traffics, traffic delay must be strictly controlled. The bearable delay of certain QoS class can be calculated by T i = L i / R i , where L i is the length of the packet transmitted, and R i is the average bit rate of the traffic, i.e., the length of the frame transmitted each time is 128Bytes, while the realtime traffic rate is 64Kbps, so the period of this QoS class traffic is 128×8 = 8ms. 128×1000 Each class of real-time traffic has its own Ti and our algorithm picks the greatest common divisor of all the Ti as the period of the super frame. In summary, the whole access and scheduling algorithm can be described as: 1. Once new service requests arrive, all the best-effort service requests are accepted. To real-time service requests, the access control module has to check the current traffic load of the system to see whether the left channel capacity can accommodate the new traffic with required QoS, if the QoS requirement of the new access request cannot be met, the access is denied. 2. If the real-time service access request has been accepted, the system will assign the appropriate type of channel(time slot in fact) to the new connection. In this algorithm, the system creates a new queue in the requested QoS class, the scheduling and load control functions are adjusted accordingly. 3. Real-time traffics with the highest QoS class are served first. As to the traffic MSi (ith mobile station), the algorithm detects whether there are downlink frames for MSi or the period of the traffic Ti has expired. If Ti has expired, BS will poll the MSi. If meantime there are downlink frame for the MSi, the polling frame is made into a compound frame. Otherwise, the traffic with lower priority is served. 4. After finishing real-time traffics, the time slots left in the super frame are allocated among the non-real-time traffics. 5. The assignment of left time slots among non-real-time traffic depends on the QoS classes of the non-real-time traffic, which is similar to the operation of the realtime traffics, the traffics with higher level of QoS are served first. In the same class, traffics are served by the mechanism of first-in-first-serve, which is implemented by a cyclic array. So the traffic is not served this super frame will have a relatively higher priority in the subsequent ones.

A QoS-Based Access and Scheduling Algorithm

29

The beacon frame is used to trigger access requests from MS, MSs compete in the subsequent uplink slots for access using the slotted ALOHA.

4 Simulation To evaluate the performance of the access and scheduling algorithm we proposed, we set up a simulation model depicted in Figure 4 based on OPNET simulator.

Fig. 4. The scenario for simulation

This scenario consists of 8 entities--one BS and 7 MSs, and MSs can be classified into 3 classes as shown in Figure 4, where the QoS class 1 represents 64kbps duplex voice traffic and the QoS class 2 represents 128kbps downlink video stream, and both classes belong to real-time traffics. The QoS class 3 represents the non-real-time traffic. In each class, the MS with the lower sequence number has higher priority. Table 1. Simulation parameters for whole system Propagation delay Processing delay Length of simulation running Data rate Duty cycle

6us 0us 6hours 1Mbps 16ms

Table 2. Simulation parameters for each MS QoS class MS0 MS1 MS2 MS3 MS4 MS5 MS6

1 1 2 2 3 3 3

Li

(bytes) 128 128 512 512 128 128 128

Ri

(kbps) 64 64 128 128 ~ ~ ~

Ti (ms) 16 16 32 32 ~ ~ ~

Starting time(ms) 6 17 33 49 65 71 87

30

B. Wang

The parameters for system simulation can be seen in Table 1 and the simulation parameters for each MS are listed in Table 2. By simulation, the average delays, maximum delays and delay variances of real-time traffics are shown in Table 3. Table 3. Simulation results for real-time traffic

Average delays( ms ) Maximum delays( ms ) Delay variances( ms 2 ) Packets transmitted in time

MS0 5.1 8.9 3.3 100%

MS1 7.3 11.7 3.8 100%

MS2 18.1 24.3 7.7 100%

MS3 19.3 26.5 10.4 100%

The results of simulations in Table 3 show that the both average delays and maximum delays of the real-time traffics are all within the limit of service requirements(the delays are all lower than the required traffic period Ti with the comparison of Table 2 and Table 3), and the percentages of packets transmitted in time also convince the efficiency of our algorithm. Table 4. Simulation results for non-real-time traffic

Average delays( ms ) Average throughput(kbps)

MS4 63.6 16.1

MS5 63.9 16.0

MS6 63.8 16.0

Table 4 shows that the real-time traffics grab most of the bandwidth from nonreal-time traffics to guarantee its QoS, and the share of the remaining time slots among non-real-time traffics is fair, which can be seen from average delays and throughput.

5 Conclusions In this paper, we proposed a QoS-based access and scheduling algorithm for wireless multimedia communications in packet-switched network. The main focus of the paper is to suppress the delays of the real-time traffics under the required QoS limit. The algorithm triggers the real-time traffic by events of either downlink traffic arrival or traffic bearable delay expiration. The non-real-time traffics are transmitted at the rest bandwidth(time slots), the scheduling of non-real-time traffics adopts the round-robbin algorithm. Moreover, we adopted the access control mechanism to secure the QoS requirements of real-time traffics by denying the new traffic request which cannot be satisfied and could undermine the quality of existing traffics.

A QoS-Based Access and Scheduling Algorithm

31

References 1. Ramjee, P.,Marina, R: Technology Trends in Wireless Communications. Artech House 2. Wireless LAN Medium Access Control and Physical Layer Specifications. IEEE 802.11 standard, 1999. 3. Stefan, M., Sunghyun: IEEE 802.11e Wireless LAN for Quality of Service 4. H.L. Truong, i: The IEEE 802.11e MAC for Quality of Service in Wireless LANs 5. Alan, D: Analysis and Simulation of a Fair Queueing Algorithm. Proc. ACM SigComm’89 6. Duan-Shin, L: Weighted Fair Queueing and Compensation Techniques for Wireless Packet Switched Networks. IEEE Trans. on Vehicular Tech. on 10/29/03. 7. Habetha, J: 802.11a versus HiperLAN/2 –A Comparison of Decentralized and Centralized MAC Protocols for Multihop Ad Hoc Radio Networks. 8. P. Coverdale: Itu-T Study Group 12: Multimedia QoS requirements from a user perspective. Workshop on QoS and user perceived transmission quality in evolving networks, Oct 2001.

Feedforward Wavelet Neural Network and Multi-variable Functional Approximation1 Jing Zhao1,2 , Wang Chen3, and Jianhua Luo1 1 Biomedical

Engineering Department, School of Life Science and Technology, Shanghai Jiaotong University, Shanghai 200240, P.R. China [email protected] 2 Basic Department, 3 Department of Automation, Logistical Engineering University, Chongqing 400016, P.R. China

Abstract. In this paper, a novel WNN, multi-input and multi-output feedforward wavelet neural network is constructed. In the hidden layer, wavelet basis functions are used as activate function instead of the sigmoid function of feedforward network. The training formulas based on BP algorithm are mathematically derived and training algorithm is presented. A numerical experiment is given to validate the application of this wavelet neural network in multivariable functional approximation.

1 Introduction Artificial neural network is a kind of mathematical model simulating the structural and functional features of brain neuron network of mankind and having the ability of selfmodification. Neural network has the ability of approximating any function at the fuzzy, noisy and non-linear conditions [1]. But it has its own deficiency such as slow convergence speed and getting local minimum value. On the other hand, just as Fourier series, wavelet series has the ability of functional approximation. Furthermore, wavelet transformation is a good tool for time-frequency localization. It could characterize non-stationary signal locally and self-adaptively. In 1992, Zhang Qinghua and Benveniste presented the concept of wavelet neural network (WNN) by integrating wavelet analysis with neural network [2]. Combining the localization feature of wavelet transform and the self-modification function of neural network, WNN selfadaptively modifies the parameters of basis wavelets through training. So it could overcome the backwards of neural network and could approximate functions more rapidly and efficiently. The WNN proposed by Zhang Qinghua is a mono-output network and the activate function of the output layer is a linear function. In this paper, we present a novel WNN, a multi-input and multi-output feedforward wavelet neural 1

This work is supported by 863 Project of China (No.2002AA234021) and 973 Project of China (No. 2002CB512800).

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 32–37, 2004. © Springer-Verlag Berlin Heidelberg 2004

Feedforward Wavelet Neural Network and Multi-variable Functional Approximation

33

network. In addition, a nonlinear function, sigmoid function is chosen as activate function of the output layer. This makes WNN has stronger approximation functions.

2 The Structure of Wavelet Neural Network For a BP neural network with only one hidden layer of neurons, using basis wavelets as its activate functions of hidden layer, we get a multi-input and multi-output wavelet neural networks in Fig. 1. This WNN has m, p, n nodes in the input layer, hidden layer and output layer respectively. Its structural parameters are following: Connection matrix between input layer and hidden layer: W (1) = ( w (jk1) ) p×m Connection matrix between hidden layer and output layer: W ( 2 ) = ( wij( 2 ) ) n× p Bias vector of the hidden layer neurons: Θ (1) = (θ 1(1) ,θ 2(1) ,...θ p(1) ) Bias vector of the output layer neurons: Θ

( 2)

= (θ 1( 2 ) ,θ 2( 2 ) ,...θ n( 2 ) )

Fig. 1. The Structure of Wavelet Neural Network

Suppose the activate functions of the hidden layer neurons are a group of basis wavelets. This means the activate function of the jth node in the hidden layer is:

ψa

j ,b j

(t ) =

1 aj

ψ(

t − bj aj

)

j = 1,2,..., p

(1)

in which the mother wavelet ψ (t ) is localized both in time and frequency and could be chosen as different function according to the feature of the problem. According to the desire of the problem, the activate function of the output layer neurons could be chose as linear function or sigmoid function. In this paper, f(t) is chosen as sigmoid function.

34

J. Zhao, W. Chen, and J. Luo

So the parameters of the wavelet neural network in Fig. 1 are:

(W (1) , W ( 2 ) , Θ (1) , Θ ( 2 ) , a1 , " , a p , b1 , " , b p ) These parameters could be adjusted through training.

3 Training Formulas Derivation for WNN Backpropagation method is the most frequently used technique for training a feedforward network. It involves two passes through the network, a forward pass and a backward pass. The forward pass generates the network’s output activities and the backward pass involves propagating the error initially found in the output nodes back through the network to assign errors to each node that contributed to the initial error. Once all the errors are assigned, the weights are changed so as to minimize these errors. Since the WNN in Fig. 1 is derived from a feedforward neural network, we use backpropagation method to train this network. For the WNN in Fig. 1, when the input vector is X = ( x1 , x 2 , ", x m ) , we get the output of the jth node in hidden layer: m

ψ a ,b (∑ w(jk1) xk −θ j(1) ) = ψ a ,b (net(j1) ) = j

j

j

k =1

in which net (j1) =

m

∑w

(1) jk

j

1 aj

ψ(

net(j1) − b j aj

x k − θ (j1)

)

(2)

(3)

k =1

The output of the ith node of output layer is: p

y i = f (∑ wij( 2 )ψ a j ,b j (net (j1) ) − θ i( 2) ) = f (net i( 2 ) ) ,

(4)

j =1

p

where net i( 2 ) = ∑ wij( 2 )ψ a ,b (net (j1) ) − θ i( 2 ) j j

(5)

j =1

From equation (4) we get the output vector of the WNN: Y = ( y1 , y 2 , " , y n ) . Suppose we have Q training samples. For each sample q, the desired output vector is Dq = ( d q , d q 2 , " d qn ) , the output vector of the WNN is Yq = ( y q1 , y q 2 , " , y qn ) 1 . With these Q training samples, we train the WNN through batch learning process. Then the main goal of the network is to minimize the total error E of each output node i over all training samples q:

E=

1 Q n ∑∑ (d qi − y qi ) 2 2 q =1 i =1

(6)

From equations (2)−(6), we could deduce the partial derivatives of the error E to each parameter as following.

Feedforward Wavelet Neural Network and Multi-variable Functional Approximation Q ∂E = − (d qi − y qi ) ⋅ y qi ⋅ (1 − y qi ) ⋅ψ a j ,b j (netqj(1) ) ∑ (2) ∂wij q =1 Q n ∂E −1 (1) ( 2) = − a j ∑[ψ ' a j ,b j (netqj ) ⋅ xqk ⋅ ∑ (d qi − y qi ) ⋅ y qi ⋅ (1 − y qi ) ⋅ wij ] (1) ∂w jk q =1 i =1

Q ∂E = ∑ (d qi − y qi ) ⋅ y qi ⋅ (1 − y qi ) ( 2) ∂θ i q =1

35

(7)

(8)

(9)

Q n ∂E = ∑ [ψ ' a j ,b j (net qj(1) ) ⋅ ∑ (d qi − y qi ) ⋅ y qi ⋅ (1 − y qi ) ⋅ wij( 2) ] (1) ∂θ j q =1 i =1

−1 netqj(1) −bj ∂E Q aj = ∑{[ ψaj ,bj (netqj(1) ) + ψ'aj ,bj (netqj(1) )] 2 ∂aj q=1 2 aj

(10)

(11)

n

⋅ ∑(dqi − yqi) ⋅ yqi ⋅ (1− yqi) ⋅ w ij(2) } i=1

Q n ∂E = a −j 1 ∑ [ψ ' a j ,b j (net qj(1) )∑ (d qi − y qi ) ⋅ y qi ⋅ (1 − y qi ) ⋅ wij( 2 ) ] ∂b j q =1 i =1

where

ψ 'a

j ,b j

1

(net (j1) ) =

aj

ψ '(

net (j1) − b j aj

(12)

).

In order to speed convergence and avoid vibration, we use backpropagation algorithm with momentum. Suppose learning rate is η and momentum is α ( 0 < α < 1) , we get adjusting formulas for network parameters as following:

wij( 2 ) (t + 1) = wij( 2 ) (t ) − η

∂E + α [ wij( 2 ) (t ) − wij( 2 ) (t − 1)] ∂wij( 2 )

(13)

w (jk1) (t + 1) = w (jk1) (t ) − η

∂E + α [ w (jk1) (t ) − w (jk1) (t − 1)] ∂w (jk1)

(14)

∂E + α [θ i( 2 ) (t ) − θ i( 2 ) (t − 1)] ∂θ i( 2 ) ∂E θ j(1) (t + 1) = θ (j1) (t ) − η (1) + α [θ j(1) (t ) − θ j(1) (t − 1)] ∂θ j

θ i( 2 ) (t + 1) = θ i( 2) (t ) − η

(15) (16)

a j (t + 1) = a j (t ) − η

∂E + α [ a j (t ) − a j (t − 1)] ∂a j

(17)

b j (t + 1) = b j (t ) − η

∂E + α [b j (t ) − b j (t − 1)] ∂b j

(18)

36

J. Zhao, W. Chen, and J. Luo

4 Algorithm for WNN Training From the discussion above, we get algorithm for training the WNN in Fig. 1 as following: (1) Initializing network parameters: For each parameter, give a little random number

as its initial value; (2) Supplying training sample set: Give input vectors X q = ( x q1 , x q 2 , " , x qm ) and desired output vectors D q = ( d q1 , d q 2 , " d qn ) , q=1,2,…Q; (3) Self-training of the network: Compute network outputs according to current

network parameters and input vectors in training sample set: p

y qi = f (∑ wij( 2 )ψ a j ,b j (net qj(1) ) − θ i( 2 ) ) = f (net qi( 2 ) ) , q = 1,2,…Q; j =1

(4) Computing the error: Compute the error between network outputs and desired

outputs over all training samples q:

E=

1 Q n ∑∑ (d qi − y qi ) 2 2 q =1 i =1

If E is less than ε , the little positive number given in advance, stop network training. Otherwise, go to (5). (5) Computing gradient vectors: Compute the partial derivatives of the error E to each parameter according to equations (7) ~ (12). (6) Modifying network parameters: Modify network parameters according to equations (13)~(18). Go to (2).

5 Numerical Example Approximate the function f ( x, y ) = ( x + y )e 0.5 x , x ∈ [0,1], y ∈ [0,2.5] . The sample data set is composed of 400 input-output pairs. A WNN of 2 nodes in input layer, 30 nodes in hidden layer and 1 node in output layer is constructed. The activate function of the jth node in the hidden layer is:

ψa

j ,b j

(t ) =

1 aj

ψ(

t − bj aj

)

j = 1,2,...,30

in which the mother wavelet ψ (t ) is chosen as Mexican Hat wavelet:

ψ (t ) = (1 − t 2 )e − t

2

/2

The activate function of the output layer neurons is chosen as sigmoid function:

f (t ) =

1 1 + e −t

After 300 times of iteration, the final mean square error is 0.0557.

Feedforward Wavelet Neural Network and Multi-variable Functional Approximation

37

To compare with the performance of this WNN, we construct another standard neural network (NN) with the same structure. The only difference is the activate function of the hidden layer of the standard neural network is sigmoid function. After 300 times of iteration, the final mean square error of this standard neural network is 0.2996. In Fig 2, we give the original function with 400 input-out pairs and the approximated function with 1600 input-output pairs respectively by WNN and NN. The proposed WNN has better performance from Fig. 2.

Mesh figure of 400 training samples

Mesh figure of 1600 testing samples by WNN

Mesh figure of 1600 testing samples by NN Fig. 2. Mesh Figures of the Original Function and the Approximated Function

References 1. Cybenko, G.: Approximation by Superpositions of a Sigmoid Function. Math of Control. Signals and Systems. 2 (1989) 303-314 2. Zhang, Q., Benveniste, A.: Wavelet Networks. IEEE Trans. on NN. 3 (1992) 889-898 3. Zhang, Q.: Using Wavelet Network in Nonparametric Estimation. IEEE Trans Neural Networks 2 (1997) 227-236 4. Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Regional Series in Applied Mathematics. Philadelphia PA: SIAM (1992)

The Distributed Wavelet-Based Fusion Algorithm Rajchawit Sarochawikasit, Thitirat Wiyarat, and Tiranee Achalakul Department of Computer Engineering, King Mongkut’s University of Technology, Thonburi, Bangkok 10140, Thailand {raj, tiranee}@cpe.kmutt.ac.th, [email protected]

Abstract. This paper describes a distributed algorithm for use in the analysis of the multi-spectral satellite images. The algorithm combines the spatialfrequency wavelet transform and the maximum selection fusion algorithm. It fuses a multi-spectral image set into a single high quality achromatic image that suits the human visual system. The algorithm operates on a distributed collection of computers that are connected through LAN. A scene of Chiangmai, Thailand, taken from the Landsat ETM+ sensor is used to assess the algorithm image quality, performance and scalability.

1 Introduction Multi-spectral image fusion is the process of combining images from different wavelengths to produce a unified image, removing the need for frame by frame evaluation to extract important information. Image fusion can be accomplished using a wide variety of techniques that include pixel, feature, and decision level algorithms [3]. At the pixel level, raw pixels can be fused using image arithmetic, band-ratio methods [8], wavelet transforms [6], maximum contrast selection techniques [7], and/or the principal/independent component transforms [2], [5]. At the feature level, raw images can be transformed into a representation of objects, such as image segments, shapes, or object orientations [4]. Finally, at the decision level, images can be processed individually and an identity declaration is used to fuse the results [4]. Many image fusion techniques in recent literatures often utilize the multiscaledecomposition-based methods. The methods generally involve transformation of each source image from the spatial domain to other domains, such as frequency or spatial-frequency domains. The composite representation is then constructed using a wide variety of fusion rules, and the final fused image can be obtained by taking an inverse transformation. Several multi-scale transforms provide both spatial and frequency domain localization. However, we chose to study the wavelet transform as it provides a more compact representation, separates spatial orientation in different bands, and efficiently de-correlates interesting attributes in the original image. Our fusion algorithm is based on a variation of the Daubechies discrete wavelet transform [9] and the implementation of the maximum coefficient fusion system. From the experiments, we found that the DWT introduced a relatively complete set of embedded information with little noise and also relatively efficient in computing. The wavelet theory is used as a mathematical foundation to produce coefficient components for each source image. Then, a composite representation is constructed, J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 38–43, 2004. © Springer-Verlag Berlin Heidelberg 2004

The Distributed Wavelet-Based Fusion Algorithm

39

based on the maximum absolute coefficient selection. The model is capable of joining the composite discrete wavelet, supporting the sharpness and brightness changes, edges and lines boundaries or even feature in the image set. In our approach, the coefficients are associated with one another in the same scale, which can be called a single-scale grouping scheme. The fusion algorithm can be described in Fig. 1. The 2-level decomposition of Mallat’s Algorithm for DWT is utilized in our work. The DWT is applied recursively over the spatial data. Each input image will be decomposed and down-sampled using the low pass and high pass digital FIR filters. First, the row of the input image is convolved, and the column is then down-sampled to obtain two sub-images whose horizontal resolutions are reduced by a factor of 2. Both sub-images are then filtered and down-sampled into four output images producing high-high, high-low, low-high, and low-low bands.

Original Multi-spectral Images

DWT

Activity Level Measurement

Coefficient Grouping and Combining

Fused Image

Fig. 1. The fusion algorithm

The activity level is then measured. The level reflects the energy in the space between the coefficients. Our work employed the coefficient-based activity (CBA). The technique considers each coefficient separately. After the decomposition process, we obtain a set of coefficients in several decomposition levels. We, then, experimented with the single-scale grouping method [10], which joining the coefficients from the same decomposition scale. After achieving the approximate coefficients and the group of detail coefficients, we create the resulting image by fusing multiple components using the maximum selection rule. Let In be the coefficient matrix that represents the original image of frame n. Ihn represents the high frequency components, and Iln represents the low frequency components. Gn denotes the gradient of the high frequency component Ihn., Gn = gradient(Ihn). The fused coefficient of all high frequency components, Fh, can be calculated as shown in the following code fragment. The fused coefficient of all low frequency components, Fl, can be calculated as l

follows: Fl = max( I n ).

Using the fused components of the low and the high

frequency coefficients, the resulting image can then be generated by taking the inverse transform of both fused components. max = 0 for ( i = 0; i < n ; i++) if (Gmax < Gi) max =h i ; Fh = I max; To demonstrate the algorithm, it was applied to an 8-band multi-spectral image collected with the Landsat Satellite. These images correspond to the mixture of urban and foliated area taken at wavelengths between 0.45 and 12.5 micron. Fig. 2

40

R. Sarochawikasit, T. Wiyarat, and T. Achalakul

shows a single multi-spectral image via a representative sample of frames picked from the 8 spectral bands. Notice that the band on the left shows significant contrast on the forestry and road systems. However, since this image is hidden in a data set, an automated method is required to extract the information without frameby-frame inspection.

Fig. 2. The Landsat ETM+ of Chiangmai, Thailand

Fig. 3 shows the resulting fused image obtained through our algorithm. Notice that the image quality, especially the contrast level and the image details are visibly enhanced compared to the original images. The result suggests that the fusion system is capable of summarizing most of the important information and put it into the resulting image. The calculated SNR values are all above 40 db, which states the minimal information loss in the resulting image. The wavelet transform has high computational costs because it involves pixel convolution. The performance requirement discourages the use of our algorithm in real-time applications. To improve performance, we explored a concurrent algorithm employing low-cost, commercial-off-the-shelf computers connected using a standard LAN.

Fig. 3. The resulting image

2 Concurrent Algorithms The concurrent algorithm decomposes each image frame into sub-images, which can be operated on relatively independently. Each sub-image consists of a set of pixels.

The Distributed Wavelet-Based Fusion Algorithm

41

The allocation of sub-images to processors is managed through a variant of the manager/worker technique. This strategy employs a manager thread that performs the above decomposition, and distributes sub-cubes to a set of worker threads. Each worker performs relatively independent components of the overall image transformation. A manager thread coordinates the actions of the workers, gathers partial results from them, and assembles the final resulting image. The main abstract code of the algorithm is shown in Program 1 and is executed at every processor on the network. The manager and workers are executed as independent threads with a single thread per processor. The manager abstract code is shown below in Program 2. The manager thread serves primarily to synchronize and accumulate partial results from the workers. The manager loads original image frames and then distributes them to a set of workers (line 4&5). It also synchronizes the calculation by making sure that the partial results are received from all workers before moving on to the next stage in the algorithm. When the partial results are returned (line 6), the manager applies the maximum selection rule (stated in the previous section) to form a fused coefficient set (line 7&8). The fused coefficient set is then divided into subsets (line 9) and the subsets are distributed once again to perform the inverse transformation (line 10&11). The final result is assembled after all the workers send back the partial results (line 12) and then is displayed (line 13). Each worker thread waits for the manager to send its part of image (line 1). Once the sub-image arrives, the convolution is performed to filter and to down sample the sub-image using Mallat’s Algorithm (line 2). The activity level measurement and the coefficient single-scale grouping are then performed (line 3&4). The resulting coefficient matrix is sent back to the manager to be fused (line 5). The worker then waits for its next set of data (line 6). Once received, it applies the inverse wavelet transform to convert the coefficient set back to the spatial domain (line 7). The results are sent to the manager for displaying (line 8). main() { p = getMyProcessorId() if(p == 0) { numSubImages = getNumSubImages(numWorker, numPixel) manager(numSubimages, numWorkers) } foreach remaining available processor worker(); } manager(numSubImages, numWorkers) { 1 coeffCube = [][] 2 coeffFused = [] 3 finalImage = [] 4 foreach worker i { 5 send (i, aSubImage) 6 coefficientMatrix [i] = recv(i) } 7 coeffCube = build (coeffMatrix []) 8 coeffFused = maxSelection(coeffCube) 9 subCoefficient = sizeof(coeffFused) / numWorkers 10 foreach worker i { 11 send(i, aSubCoefficient)

R. Sarochawikasit, T. Wiyarat, and T. Achalakul

42

12

finalImage = merge (finalImage, recv (i)) }

13 }

display(finalImage)

worker(numSubImages, numWorkers) { 1 aSubImage = recv (manager) 2 coeffMatrix = convolve(aSubImage) 3 coeffMatrix = activityMeasure(coeffMatrix) 4 coeffMatrix = coeffGrouping(coeffMatrix) 5 send (manager, coeffMatrix) 6 subCoefficient = recv(manager) 7 subImage = inverseTransform(subCoefficient) 8 send (manager, subImage) }

3 Performance Evaluations In this section we study the algorithms scaling properties. The performance of the algorithm when generating the results presented in section 1 was measured on a networked workstations of eight nodes. Each node is a Silicon Graphics O2 running at 300 MHz with a RAM of 128 MB. Fig. 4 shows the speed up gained as a function of the number of processors, plotted against the ideal speedup. 1000

Log T

100

Excution Time Ideal Time 10

1 1

2

4

8

Nodes

Fig. 4. Performance To reduce the communication overheads, the next version of the concurrent code will add granularity as another variable. We suspect that by adjusting the granularity, we will be able to find the optimum grain size for the data set. Communication and computation overlapping concept can be utilized and thus reduce the effect of the overheads. Applying the dynamic load balancing should also help as the load can be transferred to faster processors introducing the best system utilization.

4 Conclusion This paper has described an image fusion model and its concurrent algorithm based on the wavelet transform. The algorithm has been applied to the 8-band Landsat

The Distributed Wavelet-Based Fusion Algorithm

43

ETM+ data set. The experiments demonstrated acceptable results in terms of performance and scalability. A more complete experimental and analytical study is in progress. In addition, we are currently exploring the concept of dynamic load balancing to speedup the concurrent algorithm. We expect that by fine-tuning the concurrent code, the algorithm will enable real-time satellite image fusion for land use classification application.

References 1. Chandy L. M., Taylor S., An Introduction to Parallel Programming, Jones and Bartlett publishers, Boston, 1992. 2. Gonzales R. and R. Woods, “Digital Image Processing”, Addison-Wesley Publishing Company, pp 81 – 125, 1993. 3. Hall D.L., Mathematical Techniques in multisensor Data Fusion, Artech House Inc., Boston, 1992. 4. Hall D.L, "An Introduction to Multisensor Data Fusion," Proceedings of the IEEE, Vol. 85, No. 1, January 1997, pp. 6-23. 5. Lee T., Independent Component Analysis: Theory and Applications, kluwer Academic Publishers, Boston, 1998.Li H., Manjunath B. A., Mitra S. K., "Multisensor Image Fusion Using the Wavelet Transform," Graphical Models and Image Processing, Vol. 57, No. 3, May 1995, pp. 235-245. 6. Li H., B.S. Manjunath, S.K. Mitra, "Multisensor Image Fusion Using the Wavelet Transform", Graphical Models and Image Processing, vol. 57, No. 3, pp. 235-245, 1995. 7. Peli T., K. Ellis, and R. Stahl, “Multi-Spectral Image Fusion for Visual Display”, SPIE vol. 3719 Sensor Fusion: Architectures, Algorithms, and Applications III, Orlando, FL, pp. 359-368, April 1999. 8. Richards J. A., and Jai X., Remote Sensing Digital Image Analysis: An Introduction, New York, NY: Springer, 1998. 9. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C 2nd edn., (Cambridge University Press, Cambridge, 1995). 10. Zhang Z. and R.S. Blum,”A Categorization of Multiscale-decomposition-based Image Fusion Schemes with a Performance Study for a Digital Camera Application”, Proceedings of the IEEE, pp. 1315-1328, August 1999.

Alternating Direction Finite Element Method for a Class of Moving Boundary Problems Xu-Zheng Liu1 , Xia Cui2 , Jun-Hai Yong3 , and Jia-Guang Sun3 1

Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China 2 Laboratory of Computational Physics, Institute of Applied Physics Computational Mathematics, Beijing, 100088, P.R. China 3 School of Software, Tsinghua University, Beijing, 100084, P.R. China

Abstract. An alternating direction finite element scheme for a class of moving boundary problems is studied. Using coordinate transformations of the spatial variants, a new domain independent of the time is obtained and an ADFE scheme on the new domain is proposed. Then the unique solvability of the approximation scheme is proved, and optimal H 1 and L2 norm space estimates and O((∆t)2 ) estimate for the temporal variant are obtained.

1

Introduction

In many problems in science and engineering, the locations of one or more of the domain boundaries are not fixed. Solutions of these problems require the tracking of moving boundaries. The moving boundaries that are not only irregular but also changing during the computation present a challenge to many numerical methods. In spite of this difficulty, there are still many research works on these problems [1] [2]. Usually most of the numerical procedures need fairly heavy computation for the multi-dimensional moving boundary problems. Alternating direction (AD) method is an efficient way to deal with multi-dimensional problems, because it can reduce such complex problems to a series of simple onedimensional problems, hence greatly eliminate the calculation. However, to our best knowledge, in spite of the obvious merit of the AD method, there is still no related study on applying it to the numerical simulation for multi-dimensional moving boundary problems. A probable reason for this phenomenon may come from the fact that the irregularity and persistent variation of the boundary bring much difficulty to the practical realization of the AD algorithm. In fact, for a variety class of moving boundary problems, AD procedure is feasible. In this paper, we will consider the AD method for a class of moving boundary problems. For those problems, firstly coordinate transformations are used to change the practical domain to a fixed one which is called as computational domain. The boundaries of this computational domain are independent of time. Then AD calculations are done on the computational domain. During the calculation J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 44–50, 2004. c Springer-Verlag Berlin Heidelberg 2004


ADFE Method for a Class of Moving Boundary Problems

45

procedure, the corresponding evaluations can be turned back to the original domain whenever and wherever needed. To obtain numerical solutions with high precision, herein, we use ADFE (Alternating Direction Finite Element) method for the AD simulation, because it keeps both the the advantages of AD method (efficiency) and FE method (high accuracy). ADFE method is first developed by Douglas et al [3] in 1971, and many related publications can be found since then [4]. The idea of coordinate transformations extends from [5], where Lesiant P. and Touzani R. study one-dimensional Stefan problem. Moreover, this strategy of the paper may be extended to more general numerical schemes, such as ADFD (Alternating Direction Finite Difference), etc., as long as they are efficient to solve the derived problems after the coordinate transformation procedure. Consider the moving boundary problem written as: ut (X, t) − ∇ · (a(X, t, u)∇u(X, t)) 2
bi (X, t, u) ∂u(X,t) = f (X, t, u), + ∂xi

X ∈ Ω(t) ⊂ R2 , t ∈ J,

u(X, 0) = u0 (X), u(X, t) = 0,

X ∈ Ω(0) ⊂ R2 , t = 0, X ∈ ∂Ω(t), t ∈ J,

i=1

(1.1)

where Ω(t) = {X = (x1 , x2 ), xi ∈ (si,1 (t), si,2 (t)), i = 1, 2)}, J = [0, T ]. The given functions f , u0 are assumed to be properly smooth functions. The boundary functions si,j (t)(i, j = 1, 2) and their first derivatives s˙ i,j (t)(i, j = 1, 2) are continuous. Additionally the two boundary functions si,1 (t), si,2 (t) (i = 1, 2) of Ω(t) do not intersect with each other. The remaining part of the paper is organized as follows. An ADEF scheme for (1.1) is proposed in Section 2, corresponding approximation and stability properties are derived in Section 3, hence the convergence of the scheme is obtained. Further discussion is presented in the last section. Here and below, K will be a generic positive constant and may be different each time it is used.  is an arbitrary small constant. Denote (φ, ψ)t = 11  s2,2 (t)  s1,2 (t) ˙ φψ dx1 dx2 , (φ, ψ) = 0 0 φψdy1 dy2 , φ(t) = dφ(t) dt , and Dφ = s2,1 (t) s1,1 (t) ∂2φ ∂y1 ∂y2 .

Divide [0, T ] into L small equal intervals, define the timestep ∆t =

and tn = n∆t. Let φnt = φt |t=tn , φn (ψ) = φ(Y, tn , ψ), ∂t φn = n+1

n

n−1

n+1

n

+φ and dt φn = φ ∆t−φ . Hence ∂t φn = ∂tt φn = φ −2φ (∆t)2 this relation is useful in the future estimate.

2

n+1

φ

∆t n 2 ∂tt φ

+

T L,

n−1

−φ , 2∆t n−1 dt φ ,

ADFE Schemes

Firstly, the variational formulation of (1.1) can be described as: Finding u ∈ L2 (J, H01 (Ω(t))) with ut ∈ L2 (J, H −1 (Ω(t))) such that (ut , v)t − (a(X, t, u)∇u(X, t), ∇v)t 2
+ (bi (X, t, u) ∂u(X,t) ∂xi , v)t = (f (X, t, u), v)t ,

∀v ∈ H01 (Ω(t)), t ∈ J,

(u(X, 0), v)t = (u0 , v)0 ,

∀v ∈ H01 (Ω(0)).

i=1

(2.1)

46

X.-Z. Liu et al. x −s

(t)

i,1 Secondly, we introduce the coordinate transformations: yi = si,2i(t)−s i,1 (t) (i = 1, 2), namely, xi = si,1 (t)+(si,2 (t)−si,1 (t))yi (i = 1, 2), then yi ∈ (0, 1), and ˆ = (0, 1)×(0, 1). Denote Y = (y1 , y2 ), u ˆ= the domain Ω(t) is transformed into Ω u ˆ(Y, t) = u(X, t), a ˆ(ˆ u) = a ˆ(Y, t, u ˆ) = a(X, t, u), ˆbi (ˆ u) = ˆbi (Y, t, u ˆ) = bi (X, t, u) a ˆ(ˆ u) (i = 1, 2), fˆ(ˆ u) = fˆ(Y, t, u ˆ) = f (X, t, u). Set pi (ˆ u) = pi (Y, t, u ˆ) = (si,2 (t)−s 2, i,1 (t))

ˆ

s˙

s˙

(t)

(t)−s˙

(t)

u) bi (ˆ i,1 i,1 u) = qi (Y, t, u ˆ) = si,2 (t)−s − si,2 (t)−s − si,2 yi (i = 1, 2). The qi (ˆ i,1 (t) i,1 (t) i,2 (t)−si,1 (t) variational formulation (2.1) is equivalent to: ˆ u ˆ such that Finding u ˆ ∈ L2 (J, H01 (Ω)), ˆt ∈ L2 (J, H −1 (Ω))

(ˆ ut , vˆ) − +

2
i=1

2
i=1

(Y,t) ∂ v ((pi (Y, t, u ˆ) ∂ uˆ∂y , ∂yˆi ) i

(Y,t) qi (Y, t, u ˆ) ∂ uˆ∂y , vˆ) = (fˆ(Y, t, u ˆ), vˆ), i

ˆ ∀ˆ v ∈ H01 (Ω),

(2.2)

ˆ ∀ˆ v ∈ H01 (Ω).

(ˆ u(Y, 0), vˆ) = (ˆ u0 , vˆ)0 ,

ˆ into M1 × M2 small equal intervals and denote h1 = 1/M1 , h2 = Divide Ω i 1/M2 , h = max{h1 , h2 }. Let µi = span{γ1i (yi ), γ2i (yi ), ..., γM (yi )} ⊂ H01 ([0, 1]) i (i = 1, 2) be the one dimensional k degree finite element space along the ˆn = the tensor finite element space µ = µ1 ⊗ µ2 . Let U direction
n 1 yi . Define ˆ ) = pi (Y, tn , U ˆ n ), q n (U ˆ ) = qi (Y, tn , U ˆ n ) (i = 1, 2), Γ γ (y1 )γ 2 (y2 ), pn (U i,j n

i,j i

j

i

i

ˆ ) = f (Y, tn , U ˆ n ). Denote p∗ as an upper bound for the functions p1 and p2 , f (U let λ be a properly selected positive constant and satisfy the inequality λ > 14 p∗ , then we propose an alternating direction discrete scheme of (2.2): ˆ n ∈ µ satisfies Finding U 2 2 ˆ n , vˆ) +
(pn (U ˆ ) ∂ Uˆ n , ∂ vˆ ) +
(q n (U ˆ ) ∂ Uˆ n , vˆ) (∂t U i i ∂yi ∂yi ∂yi i=1

i=1

ˆ n+1 − 2U ˆn + U ˆ n−1 ), ∇ˆ +λ(∇(U v) 2 3 n ˆ ˆ ), vˆ), +2λ (∆t) (D∂tt U , Dˆ v ) = (f n (U 0 ˆ u0 , vˆ), (U , vˆ) = (ˆ


(2.3) ∀ˆ v ∈ µ, ∀ˆ v ∈ µ.


Set Cirs = (γri (yi ), γsi (yi )), Airs = ((γri (yi )) , (γsi (yi )) ), for r, s = 1, ..., Mi ; let Ci = (Cirs )r,s , Ai = (Airs )r,s be Mi × Mi matrices (i = 1, 2). Equivalently, (2.3) can be rewritten into a vector form which will give a clear hint of alternating direction: (C1 + 2λ∆tA1 ) ⊗ (C2 + 2λ∆tA2 )(Γ n+1 − 2Γ n + Γ n−1 ) = 2∆tΨ n , where, Ψ n = −

2
i=1

ˆn

ˆ ) ∂ U , ∂ vˆ )+ (pni (U ∂yi ∂yi

2


(2.4)

ˆn

ˆ n−1 , vˆ), ˆ ) ∂ U , vˆ)+(f n (U ˆ ), vˆ)−(dt U (qin (U ∂yi

i=1

Γ n+1 is the unknown vector. Noticing that Ci and Ai are independent of time, thus (2.4) only needs to be decomposed once at each time step. Therefore, the calculation is highly economical.

ADFE Method for a Class of Moving Boundary Problems

3

47

Approximation and Stability Properties

We define the Ritz Projector of the solution u ˆ in space µ as u ˜, where u ˜ satisfies 2 2

∂(ˆ u−˜ u) ∂ v ∂(ˆ u −˜ u ) (pi (ˆ u) ∂yi , ∂yˆi ) + (qi (ˆ u) ∂yi , vˆ) + κ(ˆ u−u ˜, vˆ) = 0, ∀ˆ v ∈ µ, (3.1) i=1

i=1

and κ is a proper positive constant. Set u ˆ−u ˜ = η, then similar as [6], we can get the following approximation property: ηt L2 (L2 ) + ηL∞ (L2 ) + hηL∞ (H 1 ) = O(hk+1 ).

(3.2)

Denote ξ = u ˜ − U , then u ˆ − U = η + ξ . Subtracting (2.3) from (2.2), and noting the equality (3.1), we derive the error equation: n

n

ˆn

n

ˆn

n

n

3 

2 n  v ˆ ) ∂ξ , ∂ˆ Lni =: (∂t ξ n , vˆ) + [ (pni (U ) + λ(∇(ξ n+1 − 2ξ n + ξ n−1 ), ∇ˆ v )] ∂y ∂y i i i=1 i=1

v) +2λ2 (∆t)3 (D∂tt ξ n , Dˆ = (∂t u ˆn − u ˆnt −

2 

∂u ˜n  n ˆ ∂ξ n − qi (U ) ∂yi ∂yi i=1 2

ˆ )] [qin (ˆ u) − qin (U

i=1

ˆ )] − ∂t η n + κη n , vˆ) − +[f n (ˆ u) − f n (U

2 

˜n ∂ˆ v ˆ )] ∂ u ([pni (ˆ u) − pni (U , ) ∂yi ∂yi i=1

+[λ(∆t)2 (∇∂tt u ˆn , ∇ˆ v ) + 2λ2 (∆t)3 (D∂tt u ˜n , Dˆ v )] =:

3 

Rin .

(3.3)

i=1

Taking vˆ = ∂t ξ n as a test function, multiplying (3.3) by 2∆t and summing for n = 1, 2, ..., N − 1, and estimating the derived terms one by one, we show for the left hand, there are 2∆t

N −1 

Ln1 = 2∆t

n=1

2∆t

N −1 

N −1 

∂t ξ n 2 ,

(3.4)

n=1

Ln2 = 2∆t

n=1

N −1  2  n=1 i=1

+

N −1 

ˆ ) − 2λ] ([pni (U

∂ξ n ∂(∂t ξ n ) , ) ∂yi ∂yi

N λ(∇ξ n+1 2 − ∇ξ n−1 2 ) =: LN 2,1 + L2,2 .

(3.5)

n=1 N 2 N −1 2 Obviously, LN  ) − λ(∇ξ 1 2 − ∇ξ 0 2 ). Using 2,2 = λ(∇ξ  − ∇ξ summation by parts, the following estimate holds: 1 N −1 ˆ (U ) − 2λL∞ (∇ξ N −1 2 + ∇ξ N 2 ) LN 2,1 ≤ 2 p N −1 (3.6) ˆ ) − 2λL∞ (∇ξ 0 2 + ∇ξ 1 2 ) + K∆t
∇ξ n 2 , + 12 p0 (U n=1

ˆ ) − 2λL∞ = max{pl (U ˆ ) − 2λL∞ , pl (U ˆ ) − 2λL∞ }(l = N − 1, 0). where pl (U 1 2 Next, noticing that ∂tt ξ n = (dt ξ n − dt ξ n−1 )/∆t, ∂t ξ n = (dt ξ n + dt ξ n−1 )/2, we get the equality

48

X.-Z. Liu et al.

2∆t

N
−1 n=1

Ln3 = 2λ2 (∆t)3 (Ddt ξ N −1 2 − Ddt ξ 0 2 ).

(3.7)

Now, we turn our attention to each Rin on the right side and obtain 2∆t

N −1 

R1n ≤ K[(∆t)4 + η2L2 (L2 ) + ηt 2L2 (L2 ) ]

n=1

+K∆t

N −1 

ξ n 21 + ∆t

n=1

|2∆t

N −1 

N −1 

∂t ξ n 2 .

(3.8)

n=1

R2n | ≤ K[ξ 1 21 + ξ 0 21 + η 1 2 + η 0 2 + η2L2 (L2 ) + ηt 2L2 (L2 ) ]

n=1

+K∆t

N −1 

ξ n 21 + [∇ξ N 2 + ∆t

n=1

|2∆t

N −1 

N −1 

∂t ξ n 2 ],

(3.9)

n=1

R3n | ≤ K[(∆t)4 + ∇ξ 0 2 + ∇ξ 1 2 ]

n=1

+K∆t

N −1 

∇ξ n 2 + [∇ξ N 2 + ∇ξ N −1 2 ].

(3.10)

n=1

Combining relations (3.4)-(3.10) and noting λ > 14 p∗ , then using Grownwall’s lemma, we deduce ∆t

N −1 

∂t ξ n 2 + ξ N 21 + ξ N −1 21 + (∆t)3 Ddt ξ N −1 2

n=1 4

≤ K[(∆t) +η2L∞ (L2) +ηt 2L2 (L2 ) +ξ 0 21 +ξ 1 21 +(∆t)3 Ddt ξ 0 2]. (3.11) Summarizing (3.11) and (3.2), we can obtain the following approximation result. Theorem 1. For λ > 14 p∗, if ξ 0 1 + ξ 1 1 + (∆t)3/2  Ddt ξ 0  = O(hk+1 + (∆t)2 )

(3.12)

satisfies, then for the ADFE scheme (2.3), there is ˆ L∞ (L2 ) + hˆ ˆ L∞ (H 1 ) = O(hk+1 + (∆t)2 ), ˆ )t L2 (L2 ) + ˆ u−U u−U (ˆ u−U e.g. discrete L∞ (L2 ) and L∞ (H 1 ) approximation norm are all optimal on the computational domain. ˆ n in (2.3), and using an analogous reasoning Taking the test function vˆ = ∂t U procedure, we get the stability result on the computational domain.

ADFE Method for a Class of Moving Boundary Problems

49

Theorem 2. Under the same condition of theorem 1, we have ∆t

N
−1 n=1

ˆ N 2 + ∇U ˆ N −1 2 ˆ n 2 + ∇U ∂t U

N −1 ˆ 0 2 + ∆t
f n (U ˆ 0 2 + U ˆ 1 2 + (∆t)3 Ddt U ˆ )2 ]. ≤ K[ U 1 1 n=1

From Theorem 1 and Theorem 2, we can conclude the ADFE scheme (2.3) is uniquely solvable and has optimal H 1 and L2 norm convergence properties on the computational domain. Since the coordinate transformations are inverse between the computational domain and the practical domain, by using the equivalent norm property (Lemma 2.2 in [5]), we can obtain the same conclusion for the corresponding approximation solution U and the exact solution u of (2.1) on the practical domain.

4

Discussion

To start the procedure (2.3), we need to define perfect initial values to satisfy ˆ0 = u (3.12). In fact, this condition is easy to fulfill. For example, letting U ˜0 , 0 1 1 ˆ ˆ ˆ 1 as ˆ 2 = U +U , and defining U denoting U 2 2


1

ˆ

1

ˆ 2 ) ∂ U 2 , ∂ vˆ ) + (pi (U ∂yi ∂yi

i=1

2
i=1

1

ˆ

1

1

1

ˆ 2 ) ∂ U 2 , vˆ) + κ(U ˆ 2 , vˆ) = (fˆ(U ˆ 2 ), vˆ), (qi (U ∂yi

∀ˆ v ∈ µ.

will be a feasible choice. By transforming the domain with perfect coordinate transformations, the ADFE method can be applied to solve a class of moving boundary problems. The idea can be easily extended to 3D problems. For certain more complicated boundaries whose functions are dependent on both the temporal and the spatial variants with enough smoothness, this strategy can also be considered. Of course, after the coordinate transformations, any natural efficient numerical procedure, such as ADFD, etc., can also be discussed to solve moving boundary problems which will appear in the future paper. For more complex problems, more detailed considerations are necessary.

Acknowledgement The project is supported by Hi-Tech Research and Development Program of China (863 Project)(2003AA4Z1010) and National Key Basic Research Project of China (973 Project)(2002CB312106).

References 1. Zhao, Y. and Forhad, A.: A general method for simulation of fluid flows with moving and compliant boundaries on unstructured grids. Computer Methods in Applied Mechanics and Engineering 192 (2003) 4439–4466

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2. Cui, X.: The finite element methods for the parabolic integro-differential equation in 2-dimensional time-dependent domain. Numerical Mathematics, A Journal of Chinese Universities 21 (1999) 228–235 3. Douglas, J. and Dupont, T.: Alternating-direction galerkin methods on rectangles. In Hubbard, B., ed.: Proceedings of Symposium on Numerical Solution of Partial Differential Equation II. (1971) 133–214 4. Cui, X.: Adfe method with high accuracy for nonlinear parabolic integro-differential system with nonlinear boundary conditions. Acta Mathematica Scientia 22B (2002) 473–483 5. Lesaint, P. and Touzani, R.: Approximation of the heat equation in a variable domain with application to the stefan problem. SIAM Journal on Numerical Analysis 26 (1989) 366–379 6. Ciarlet, P.: The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam (1978)

Binomial-Tree Fault Tolerant Routing in Dual-Cubes with Large Number of Faulty Nodes Yamin Li1 , Shietung Peng1 , and Wanming Chu2 2

1 Department of Computer Science, Hosei University, Tokyo 184-8584 Japan Department of Computer Hardware, University of Aizu, Fukushima 965-8580 Japan

Abstract. A dual-cube DC(m) has m + 1 links per node where m is the degree of a cluster (m-cube), and one extra link is used for connection between clusters. The dual-cube mitigates the problem of increasing number of links in the large-scale hypercube network while keeps most of the topological properties of the hypercube network. In this paper, we propose efficient algorithms for finding a nonfaulty routing path between any two nonfaulty nodes in the dual-cube with a large number of faulty nodes. A node v ∈ DC(m) is called k-safe if v has at least k nonfaulty neighbors. The DC(m) is called k-safe if every node in DC(m) is k-safe. The first algorithm presented in this paper is an off-line algorithm that uses global information of faulty status. It finds a nonfaulty path of length at most d(s, t) + O(k 2 ) in O(|F | + m) time for any two nonfaulty nodes s and t in the k-safe DC(m) with number of faulty nodes |F | < 2k (m + 1 − k), where 0 ≤ k ≤ m/2. The second algorithm is an online algorithm that uses local information only. It can find a faultfree path with high probability in an arbitrarily faulty dual-cube with unbounded number of faulty nodes.

1

Introduction

As the size of computer networks increases continuously, the node failures are inevitable. Routing in computer networks with faults has been more important and has attracted considerable attention in the last decade. Hypercube is a popular network studied by researchers and adopted in many implementations of parallel computer systems, such as Intel iPSC, the nCUBE, the Connection Machine CM-2, and the SGI’s Origin 2000 and Origin 3000. Previous research has shown that a hypercube can tolerate a constant fraction of faulty nodes. For example, Najjar et al[1] demonstrated that for the 10-cube, 33 percent of nodes can fail and the network can still remain connected with a probability of 99 percent. Gu and Peng[2] proposed off-line routing algorithms for a k-safe n-cube with up to 2k (n − k) − 1 faulty nodes, where a node u is k-safe if u has at least k nonfaulty neighbor nodes, and an n-cube is k-safe if all nodes in the cube are k-safe. Chen et al[3] also proposed a distributed routing algorithm in hypercube with large amount of faulty nodes based on local subcube-connectivity. A dual-cube DC(m)[4, 5] is an undirected graph on the node set {0, 1}2m+1 and there is a link between two nodes u = (u0 u1 . . . um um+1 . . . u2m ) and v = J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 51–56, 2004. c Springer-Verlag Berlin Heidelberg 2004


52

Y. Li, S. Peng, and W. Chu

(v0 v1 . . . vm vm+1 . . . v2m ) if and only if the following conditions are satisfied: 1) u and v differ exactly in one bit position i, 2) if 1 ≤ i ≤ m then u0 = v0 = 1 and 3) if m + 1 ≤ i ≤ 2m then u0 = v0 = 0. We use (u : v) to denote a link connecting nodes u and v, and (u → v) or (v1 : v2 : . . . : vr ) to denote a path or a cycle. For a node u = (u1 . . . un ), u(i) denotes the node (u1 . . . ui−1 ui ui+1 . . . un ), where ui is the logical negation of ui . The set of neighbors of a subgraph T in G is denoted as N (T ) = {v|(w : v) ∈ E(G), w ∈ V (T ), v ∈V (T )}.

2

Fault Tolerant Routing Algorithm for k-Safe Dual-Cube

We first briefly introduce the algorithm for the fault-tolerant routing in k-safe hypercubes[2]. Given a k-safe n-cube Hn , a set of faulty nodes F with |F | < 2k (n − k), and two nonfaulty nodes s and t, the idea of finding a fault-free path s → t is as follows. First, partition Hn along dimension i into two (n − 1)-cubes, 0 1 0 1 and Hn−1 , such that s and t are separated, say s ∈ Hn−1 and t ∈ Hn−1 . Hn−1 1 1 Assume that |F ∩ Hn−1 | ≤ |F |/2. Then, we want to route s to Hn−1 by a fault-free path of length at most k + 2. This can be done by first constructing a fault-free k-binomial tree with root s Tk (s) in Hn . Since Hn is k-safe the Tk (s) 1 =∅ or u(i) is nonfaulty, where u ∈ Tk (s), then s can be found. If Tk (s) ∩ Hn−1 1 is routed to Hn−1 . Otherwise, since |F | < 2k (n − k) there exists a u ∈ N (Tk (s)) 1 such that u and u(i) are nonfaulty. Therefore, we can route s to s ∈ Hn−1 .  1 1 The fault-free path s → t in Hn−1 can be found recursively since Hn−1 is 1 (k − 1)-safe and |F ∩ Hn−1 | < 2k−1 ((n − 1) − (k − 1)). The recursion halts when k = 0. In this case, |F | < n and a fault-free path s → t of length at most d(s, t) + 2 can be found in O(n) time[6]. The fault-free path s → s of length at most k + 2 can be found in O(|F |) time. Since at most half of the faulty nodes are
involved in the next recursion. The time complexity of the algorithm k−1 T (n) = i=0 O(|F |/2i ) + O(n) = O(|F | + n). The length of the path, L(k), satisfies the equation L(k) ≤ L(k − 1) + (k + 2) if k > 0, and L(0) ≤ d(s, t) + 2. From this, L(k) = d(s, t) + O(k 2 ). The algorithm described above is denoted as Hypercube Routing(Hn , s, t, k, F, P ), where P is the fault-free path s → t in Hn . A dual-cube DC(m) is k-safe if every node in DC(m) is k-safe. We present an algorithm for finding a fault-free path s → t in a k-safe DC(m) with number of faulty nodes |F | < 2k (m − k + 1). First, we describe two key techniques for the design of the algorithm. The first one is called virtual cube. Given two distinct clusters of the same class in DC(m), say Cs and Ct are of class 0, the virtual (m + 1)-cube V Hm+1 = Cs ∪ Ct ∪ {(u : v)|u ∈ Cs , v ∈ Ct , and ui = vi for all i, m + 1 ≤ i ≤ 2m}. We call the edge (u : v) virtual edge. A virtual edge in V Hm+1 corresponds to a path (u → v) in DC(m), and (s → t) = (s → u : u = u(0) → v  = v (0) : v → t), where (u → v  ) is a path of length at most m in Cu
, a cluster of class 1. The 2m paths in DC(m) corresponding to the 2m virtual edges in V Hm+1 are disjoint. The virtual edge (u : v) is nonfaulty if nodes u, v, u , and v  are nonfaulty and

Binomial-Tree Fault Tolerant Routing in Dual-Cubes

53

|F ∩ Cu
| < 2k−1 (m − k + 1). If the virtual edge is nonfaulty then since Cu
is a (k − 1)-safe m-cube, a fault-free path u → v in DC(m) can be found. Finding all faulty virtual edge takes at most O(|F |) time. The second one is a technique to find a fault-free path s → u : u = u(0) of length at most k + 2, where path s → u is a path in Cs under the condition that DC(m) is k-safe and |F | < 2k (m − k + 1). The path s → u can be found by constructing a fault-free k-binomial-tree Tk (s) in Cs , and then considering the nodes in N (Tk (s)). Algorithm 1 (Binomial Tree Routing(DC(m), s, F, P )) Input: DC(m), a nonfaulty node s, and a set of faulty nodes F with |F | < 2k (m − k + 1) Output: a fault-free path P = (s → u : u
) of length at most k + 2 begin P = ∅; find a fault-free (k − 1)-binomial tree Tk−1 (s) in Cs ; if there exists a nonfaulty u
for u ∈ Tk−1 (s) then P = P ∪ (s → u : u
); else find a fault-free k-binomial tree Tk (s) = Tk−1 (s) ∪ {(u : u(i) )|u ∈ Tk−1 (s)}, where u(i) is nonfaulty, and i =ij , 1 ≤ j ≤ r, the dimensions used for the path s → u in Tk−1 ; find a node u ∈ N (Tk (s)) ∩ Cs such that u and u
are nonfaulty; P = P ∪ (s → w : u : u
), where s → w is a path in Tk (s); end

The details is depicted by Algorithm 1. The next lemma shows that Binomial Tree Routing algorithm is correct. Lemma 1. For 0 ≤ k ≤ m/2, and a nonfaulty node s in a k-safe DC(m) with number of faulty nodes |F | < 2k (m − k + 1), the fault-free path (s → u : u ) of length at most k + 2 can be found in O(|F | + m) time. Proof: From Binomial Tree Routing algorithm, since DC(m) is k-safe we know that either a fault-free Tk (s) in Cs is found or there exists a nonfaulty node w ∈ Tk−1 (s) such that w is nonfaulty. In the letter case, let w = u and it is done. So, we assume that Tk (s) is found and for every w in Tk (s), w is faulty. It was known that for Tk (s) in an m-cube, we have |N (Tk (s))| ≥ 2k (m − k) ([6]). Since Cs is an m-cube and there are at most |F | − 2k < 2k (mk + 1) − 2k = 2k mk faulty nodes in Cs , there exists a node u ∈ N (Tk (s)) such that u and u are nonfaulty. The main idea of the proposed algorithm is to route s to Ct if s and t are in different clusters and |F ∩ Cs | ≥ |F ∩ Ct |. This can be done using the similar idea of Algorithm 1 and is shown in Algorithm 2, Cluster Routing. The next lemma shows that the algorithm is correct.

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Y. Li, S. Peng, and W. Chu

Algorithm 2 (Cluster Routing(DC(m), s, t, F, P )) Input: a k-safe DC(m), nodes s and t, Cs and Ct are of the same class, and a set of faulty nodes F with |F | < 2k (m − k + 1) and |F ∩ Cs | ≥ |F ∩ Ct | Output: a fault-free path P = (s → u → v), where v ∈ Ct and u → v is the path corresponding to virtual edge (u : v) begin P = ∅; find a fault-free (k − 1)-binomial tree Tk−1 (s) in Cs if there is a u ∈ Tk−1 (s) such that u
is nonfaulty then if virtual edge (u : v) is nonfaulty then P = (s → u → v), (u → v) is a fault-free path in DC(m) else find a fault-free (k − 1)-binomial tree Tk−1 (u
) in Cu
; find a nonfaulty w ∈ N (Tk−1 (u
)) ∩ Cu
such that virtual edge (u = w
: v) is nonfaulty; P = (s → w : u → v), u → v is a fault-free path in DC(m) else find a fault-free k-binomial tree Tk (s) by extending Tk−1 (s); find a nonfaulty u ∈ N (Tk (s)) ∩ Cs such that virtual edge (u : v) is nonfaulty; P = (s → u → v), u → v is a fault-free path in DC(m); end

Lemma 2. For 0 ≤ k ≤ m/2, and nonfaulty nodes s and t in a k-safe DC(m) with number of faulty nodes |F | < 2k (m − k + 1), the fault-free path (s → u → v) can be found in O(|F | + m) time, where (s → u) is a path in Cs and (u → v) is the path corresponding to virtual edge (u : v). Proof: We divide the proof into two cases. Case 1: Tk (s) is in Cs . Since |N (TK (s))| ≥ 2k (m − k + 1) we can find a nonfaulty virtual edge (u : v), u ∈ N (Tk (s)). Then we are done. Case 2: there exists u ∈ Tk−1 (s) such that u is nonfaulty and virtual edge is faulty. In this case, we should try to route u to Ct using a fault-free (k−1)-binomial tree in Cu
. From Cluster Routing algorithm, since the paths that route u ∈ N (Tk−1 (s)) to Ct and the path that route w ∈ N (Tk−1 (u )) to Ct are disjoint and there are totally 2k (m − k + 1) disjoint paths, we claim that a fault-free path that route s to Ct does exist. The algorithm that constructs s → t is shown in Algorithm 3. Theorem 1. For 0 ≤ k ≤ m/2, and two nonfaulty nodes s and t in in a k-safe DC(m) with number of faulty nodes |F | < 2k (m−k +1), the fault-free path s → t of length at most d(s, t) + O(k 2 ) can be found in O(|F | + m) time. Proof: The correctness of the DualCube Routing algorithm follows easily from Binomial Tree Routing, Cluster Routing, and Hypercube Routing algorithms. The Length of the path L(s, t) and time complexity of the algorithm T (m) are shown below for Case 1. The other cases follows easily from the algorithm. L(s, t) ≤ (k + 2) + (d(u , v  ) + 1) + (d(v, t) + O(k 2 )). Since d(u , v  ) + d(v, t) ≤ d(s, t) + d(s, u) = d(s, t) + k + 1, we have L(s, t) = d(s, t) + O(k 2 ). The time is O(|F |) for Binomial Tree Routing; O(m) for finding path u → v; and O(|F |+m) for Hypercube Routing. Therefore, the running time T (m) = O(|F | + m).

Binomial-Tree Fault Tolerant Routing in Dual-Cubes

55

Algorithm 3 (DualCube Routing(DC(m), s, t, k, F, P )) Input: DC(m), nonfaulty nodes s and t, and a set of faulty nodes F with |F | < 2k (m − k + 1) Output: a fault-free path P = (s → t) begin P = ∅; Case 1: Cs =Ct and class id(s) = class id(t) Cluster Routing(DC(m), s, F, P ); Hypercube Routing(Ct , v, t, k − 1, F ∩ Ct , P
); P = P ∪ P
; Case 2: class id(s) =class id(t) Binomial Tree Routing(DC(m), s, F, P ); if Cu
= Ct then Hypercube Routing(Ct , u
, t, k − 1, P ); else find a fault-free path P
= (u
→ t) as in Case 1; P = P ∪ P
; Case 3: Cs = Ct if |F ∩ Cs | < 2k−1 (m − (k − 1)) then Hypercube Routing(Cs , s, t, k − 1, P ); else Binomial Tree Routing(DC(m), s, F, P ); Binomial Tree Routing(DC(m), t, F, P
); find a fault-free path P
= (u
s → u
t ) as in Case 1; P = P ∪ P
∪ (u
s → u
t ); end

3

A Practical Fault-Tolerant Routing Algorithm

The proposed algorithm in the previous section requires that the dual-cube is ksafe. In reality, the chance that the dual-cube will not be k-safe increases when the number of faulty nodes grows. We propose an efficient routing algorithm for the fault-tolerant routing in dual-cube containing a large number of faulty nodes and dual-cube may not be k-safe. In general, without k-safe property, the fault-free k-binomial tree Tk (s) might not exist and the routing algorithm might fail to find the fault-free path s → t although the fault-free path does exist. However, for practical reasons, it is interesting to design an efficient algorithm that find a fault-free path s → t using only local information of fault status in the dual-cube with a large number of faulty nodes. The proposed algorithm for fault tolerant routing in an arbitrary faulty dualcube is distributed and local-information-based. The algorithm is similar to algorithm 3. However, the new algorithm doesn’t calculate F while route s to cluster Ct , and it uses binomial trees of increasing size starting with 0-binomial tree, a tree of single node. If the algorithm fails to find a fault-free path s → u → v then it tries 1-binomial tree and so on until either a fault-free path is found or the k-binomial tree cannot be constructed. Due to the page limitation, we will not present the details of our algorithm in this draft. The simulations for this

Y. Li, S. Peng, and W. Chu

100 90

180 160

80 70 60 50 40 30 20 10 0

m m m m m

= = = = =

9 8 7 6 5

Extra path e (%)

Rate of successful routing ps (%)

56

140 120

m m m m m

= = = = =

5 6 7 8 9

100 80 60 40 20 0

0

10 20 30 40 50 Probability of node failures pf (%)

Fig. 1. Successful routing rate

0 10 20 30 40 50 Probability of node failures pf (%)

Fig. 2. Path length (%)

algorithm have been conducted with uniformly distribution of faulty nodes in DC(m) for m = 5, 6, 7, 8 and 9. The results for successful routing v.s. the node failure rate are shown in Figure 1. It can be seen from the figure that the successful routing rate is very high (> 90%) if the node failure rate is less than 30%. The successful routing rate drop more deeply when the node failure rate is beyond 30%. However, we can say that in most cases, the successful routing rates are still larger than 50% with the node failure rates up to 50%. As for the length of the routing path, we show the results in Figure 2. From the figure, we can say that the fault-free paths found by our algorithm are very close to the minimum paths in most of the cases. The experimental data show that the proposed algorithm performs well in an arbitrarily faulty dual-cubes with possible very large set of faulty nodes.

References 1. Najjar, W., Gaudiot, J.L.: Network resilience: A measure of network fault tolerance. IEEE Transactions on Computers 39 (1990) 174–181 2. Gu, Q.P., Peng, S.: Unicast in hypercubes with large number of faulty nodes. IEEE Transactions on Parallel and Distributed Systems 10 (1999) 964–975 3. Chen, J., Wang, G., Chen, S.: Locally subcube-connected hypercube networks: Theoretical analysis and experimental results. IEEE Transactions on Computers 51 (2002) 530–540 4. Li, Y., Peng, S.: Dual-cubes: a new interconnection network for high-performance computer clusters. In: Proceedings of the 2000 International Computer Symposium, Workshop on Computer Architecture, ChiaYi, Taiwan (2000) 51–57 5. Li, Y., Peng, S., Chu, W.: Efficient collective communications in dual-cube. The Journal of Supercomputing 28 (2004) 71–90 6. Gu, Q.P., Peng, S.: Optimal algorithms for node-to-node fault tolerant routing in hypercubes. The Computer Journal 39 (1996) 626–629

The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) Method for Diffusion Equation J. Sulaiman1 , M.K. Hasan2 , and M. Othman3 1

School of Science and Technology, Universiti Malaysia Sabah, Locked Bag 2073, 88999 Kota Kinabalu, Sabah 2 Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D.E. 3 Department of Communication Tech. and Network, Faculty of Computer Science and Info. Tech., Universiti Putra Malaysia, 43400 Serdang, Selangor D.E., Malaysia [email protected]

Abstract. The primary goal of this paper is to apply the Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for solving one-dimensional diffusion problems. The formulation of the HSIADE method is also derived. Some numerical experiments are conducted that to verify the HSIADE method is more efficient than the Full-Sweep method.

1

Introduction

The half-sweep iterative method is introduced by Abdullah [1] via the Explicit Decoupled Group (EDG) iterative method to solve two-dimensional Poisson equations. The further application of this method to solve partial differential equations can be found via Ibrahim & Abdullah [4], Yousif & Evans [6], and Abdullah & Ali [2]. Based on this method, the concept of the half-sweep method is applied onto the Iterative Alternating Decomposition Explicit (IADE) method. This is an excellent technique for solving system of linear equations, and it is one of the twostep iterative methods. In this paper, combination of both methods will result in the Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method. Other IADE methods include the Reduced Iterative Alternating Decomposition Explicit (RIADE) method (Sahimi & Khatim [5]). To show the effectiveness of the HSIADE method, let us consider the onedimensional diffusion equation as given by ∂U ∂2U =α 2 , ∂t ∂ x

a ≤ x ≤ b, and 0 ≤ t ≤ T,

(1)

subject to the initial condition and U (x, t) = g1 (x), a ≤ x ≤ b the boundary conditions J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 57–63, 2004. c Springer-Verlag Berlin Heidelberg 2004


58

J. Sulaiman, M.K. Hasan, and M. Othman

U (a, t) = g2 (t), U (b, t) = g3 (t),


0 ≤ t ≤ T,

which α is a diffusion parameter. Before describing formulation of the finite difference approximation equation in case of the full- and half-sweep iterative over the problem (1), we assume the solution domain (1) can be uniformly divided into (n + 1) and M subintervals in the x and t directions. The subintervals in the x and t directions are denoted by ∆x and ∆t respectively which are uniform and defined as  ∆x = h = (b−a) m = n + 1, m (2) −0) ∆t = (TM .

h

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

9

10

11

12

13

14

15

16

a:

2h

0

1

2

3

4

5

6

7

8

b:

Fig. 1. a and b shows the distribution of uniformly points at any t level for the fulland half- sweep cases, respectively

2

The Half-Sweep Finite Difference Approximation

According to Figure 1 in the previous section, the finite grid networks provide a guide for formulation the full- and half-sweep finite difference approximation equations for the problem (1). Here, implementations of the full- or half-sweep iterative involve the • type of node points only. It is obvious that the implementation of the half-sweep iterative method just involves half of whole inner points as shown in Figure 1b compared with the full-sweep iterative method. Then the approximated solution at remaining points can be computed directly, see Abdullah [1], Ibrahim & Abdullah [4], Yousif & Evans [6]. By using the central difference and Crank-Nicolson approaches, the full- and half-sweep finite difference approximation equations can generally be stated as

The Half-Sweep Iterative Alternating Decomposition Explicit Method

59

β − β1 Ui−p,j+1 + β2 Ui,j+1 − β1 Ui+p,j+1 = fi,j

(3)

where

  α∆t α∆t α∆t , β , β = 1 + = 1 − 2 3 2(ph)2 (ph)2 (ph)2 = β1 Ui−p,j + β3 Ui,j + β1 Ui+p,j

β1 = β fi,j

The values of p which correspond to 1 and 2 represent the full- and half-sweep cases respectively. The equation (3), considered at the j + 1 time level, generates a system of linear equation as follows Aβ U βj+1 = fjβ

(4)

where coefficient matrix Aβ is given by ⎡

β2 −β1 ⎢ −β1 β2 −β1 ⎢ ⎢ −β1 β2 −β1 ⎢ ⎢ .. .. .. ⎢ . . . ⎢ ⎣ −β1 β2 −β1 −β1 β2

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

.

m (m p −p)×( p −p)

Moreover, the full- and half sweeps Gauss-Seidel (FGS and HGS) methods acts as the control methods of numerical results.

3

The HSIADE Method

In developing of formulations of the full- and half-sweep IADE methods namely FSIADE and HSIADE respectively, let us consider the system of equation (4) in case of p = 1, 2. Hence, the scheme of the IADE method using the MitchellFairweather variant (Sahimi & Khatim [5]) can be expressed as 1

(rI + G1 )U (k+ 2 ) = (rI − gG2 )U (k) + f 1 (rI + G2 )U (k+1) = (rI − gG1 )U (k+ 2 ) + gf

(5)

where r, k and I represent as an acceleration parameter, the k iteration and an identity matrix respectively and the relation of g and r is given by g = (6 + r)/6. In fact formulations of the FSIADE and HSIADE methods are to assume that the coefficient matrix, A of the system (6) can be written generally as 1 A = G1 + G2 − G1 G2 6

(6)

60

J. Sulaiman, M.K. Hasan, and M. Othman

where ⎤

⎡

1 0 ⎢ a1p 1 ⎢ ⎢ a2p ⎢ G1 = ⎢ ⎢ ⎢ ⎣

0 1 0 .. .. .. . . . m 0 a p −3p 1 a mp −2p 1

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ m (m p −1)×( p −1)

⎤

⎡

e1p h1p ⎢ 0 e2p ⎢ ⎢ 0 ⎢ G2 = ⎢ ⎢ ⎢ ⎣

and

h2p e3p h3p .. .. .. . . . 0 e mp −2p h mp −2p 0 e mp −1p

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

.

m (m p −1)×( p −1)

The scheme of the FSIADE and HSIADE onto the system (6) methods can be shown by determining values of G1 and G2 matrixes as follow 6 (β2 − 1) 5 6 −6β1 , ei = 6 hi = − β1 , ai = 5 6 − ei 6 1 ei+p = (β2 + ai hp − 1) 5 6 e1p =

(7)

for i = 1p, 2p, . . . , m p − 2p. The FSIADE and HSIADE algorithms at level k + 1/2 and level k + 1 are explicitly implemented by using the equations (8) and (9) along points in interval [a, b] until the specified convergence criterion is satisfied. 1. At level (k + 1/2) (k+1/2)

Ui

=

 1

(k+1/2) (k) (k) −ai−p Ui−p + si Ui + wi Ui+p + fi d

(8)

for i = 1p, 2p, . . . , m p − 1p where d = 1 + r, a0 = wm = 0, sj = r − gej , wj = −guj , ∀j = 1p, 2p, . . . , m p − p. 2. At level (k + 1) (k+1)

Ui

=

 1

(k+1/2) (k+1/2) (k+1) vi−p Ui−p + sUi + gfi − hi Ui+p di

(9)

m for i = m p − 1p, p − 2p, . . . , 2p, p where di = r + ei , v0 = um = 0, s = m r − g, vj = −gaj , ∀j = m p − 1p, p − 2p, . . . , p.

The Half-Sweep Iterative Alternating Decomposition Explicit Method

61

Table 1. Comparisons of no. of iteration, exe. time and max. absolute errors of the methods No. of iterations Grid size 64 128 256 512 FGS 204 691 2315 7491 FSIADE (r = 0.6) 40 152 537 1823 FSIADE (r=opt) 39 80 384 618 HGS 62 204 691 2315 HSIADE (r = 0.6) 29 40 152 537 HSIADE (r=opt) 25 39 80 384 Execution time (seconds) Grid size Methods 64 128 256 512 FGS 0.22 1.32 9.23 63.88 FSIADE (r = 0.6) 0.11 0.49 5.11 26.42 FSIADE (r=opt) 0.06 0.39 3.73 12.96 HGS 0.06 0.22 1.48 9.40 HSIADE (r = 0.6) 0.05 0.11 0.50 6.54 HSIADE (r=opt) 0.00 0.11 0.44 5.27 Maximum Absolute Errors Grid size Methods 64 128 256 512 FGS 3.3e-7 4.7e-7 7.4e-7 1.7e-6 FSIADE (r = 0.6) 3.1e-7 4.0e-7 4.7e-7 6.6e-7 FSIADE (r=opt) 4.1e-7 4.1e-7 4.8e-7 7.9e-7 HGS 7.9e-9 3.3e-7 4.7e-7 7.4e-7 HSIADE (r = 0.6) 4.1e-9 3.1e-7 4.0e-7 4.6e-7 HSIADE (r=opt) 4.0e-9 3.1e-7 3.9e-7 4.1e-7 Methods

4

1024 2048 22653 55466 5965 18372 800 1528 7491 22653 1823 5965 618 800

1024 456.76 189.83 34.99 63.83 24.88 14.50

2048 3106.91 1455.54 136.71 459.67 336.20 38.56

1024 5.7e-6 1.4e-6 3.3e-7 1.7e-6 6.6e-7 4.1e-7

2048 2.2e-5 4.4e-6 4.7e-7 5.7e-6 1.4e-6 4.1e-7

Numerical Experiments

To verify the efficiency of the implementation of the HSIADE scheme as derived in equation (5), which is based on the approximation equation (3), some numerical experiments are conducted to solve the one-dimensional diffusion equation as follows ∂2U ∂U = 2 , ∂t ∂ x

0 ≤ x ≤ 1, 0 ≤ t ≤ 1.

(10)

The initial and boundary conditions and exact solution of the problem (10) is given by 2

U (x, t) = e−π t sin(πx), 0 ≤ x ≤ 1, 0 ≤ t ≤ 1. All results of numerical experiments, which were gained from implementations of the FGS, HGS, FSIADE and HSIADE methods have been recorded in

62

J. Sulaiman, M.K. Hasan, and M. Othman 20000 FSIADE (r=0.6) FSIADE (r=opt)

No. of iterations

15000

HSIADE (r=opt)

10000

5000

0 64

128

256

512

1024

2048

Grid size

Fig. 2. Number of iterations versus grid size of the FSIADE and HSIADE methods

1600 FSIADE (r=0.6) 1400 FSIADE (r=opt)

Exec. time (seconds)

1200

HSIADE (r=opt)

1000

800

600

400

200

0 64

128

256

512

1024

2048

Grid size

Fig. 3. Execution time (seconds) versus grid size of the FSIADE and HSIADE methods

Table 1. In implementations mentioned above, the convergence test considered the tolerance error  = 10−10 . Figures 2 and 3 show number of iterations and execution time against grid size respectively.

5

Summary

By referring onto Table 1 and it has shown in Figure 2 that number of iterations decreased by 37.50-95.64% and 2.50-91.68% respectively correspond to

The Half-Sweep Iterative Alternating Decomposition Explicit Method

63

the HSIADE (r optimum) and FSIADE (r optimum) methods compared with the FSIADE (r = 0.6) method. In addition, the execution time against the grid size of both the HSIADE (r optimum) and FSIADE (r optimum) methods are much faster about 77.55-100% and 20.40-90.61% respectively than the FSIADE method, see Figure 3. The whole results show that the HSIADE method is much better in terms of a number of iterations and the execution time than the FSIADE method. This is because the computational complexity of the HSIADE method is nearly 50% of the IADE method.

References 1. Abdullah, A.R.: The Four Explicit Decoupled Group (EDG) Method: A Fast Poisson Solver. Intern. Journal of Computers Mathematics, 38 (1991) 61–70. 2. Abdullah, A.R., Ali, N.H.M.: A Comparative Study of Parallel Strategies for the Solution of Elliptic PDE’s. Parallel Algorithms and Aplications, 10 (1996) 93–103. 3. Evans, D.J., Sahimi, M.S., : The Alternating Group Explicit iterative method (AGE) to solve parabolic and hyperbolic partial differential equations. Ann. Rev. Num. Fluid Mechanic and Heat Trans., 2 (1988) 283-389. 4. Ibrahim, A., Abdullah, A.R., : Solving the two-dimensional diffusion equation by the four point explicit decoupled group (EDG) iterative method. International Journal Computer Mathematics, 58 (1995) 253-256. 5. Sahimi, M.S., Khatim, M. : The Reduced Iterative Alternating Decomposition Explicit (RIADE) Method for the Diffusion Equation. Pertanika J. Sci. & Technol., 9(1) (2001) 13-20. 6. Yousif, W. S., Evans, D. J. : Explicit De-coupled Group iterative methods and their implementations. Parallel Algorithms and Applications, 7 (2001) 53-71.

An Effective Compressed Sparse Preconditioner for Large Scale Biomolecular Simulations
Dexuan Xie Department of Mathematical Sciences, University of Wisconsin, Milwaukee, WI 53201-0413, USA [email protected]

Abstract. The natural preconditioner defined by local potentials is effective in the truncated Newton method for minimizing large scale biomolecular potential energy functions. This paper extends its definition, and proposes an algorithm for generating the sparse pattern of the preconditioner from the primary structure of a molecular system with N atoms. It shows that the implementation of the new compressed sparse preconditioner requires only a linear order of N memory locations.

1

Introduction

The natural preconditioner M defined by local potentials [7] can significantly improve the convergence and performance of the CHARMM version of TNPACK (the truncated Newton program package [6]) for minimizing the potential energy function of a biomolecular system with N atoms [3, 8–10]. Here CHARMM is one widely-used molecular mechanics and dynamics program [1]. While the truncated Newton (TN) method is a second derivative minimization method [2], it can be simply modified into a first derivative method by using a finite difference approximation to the product of the Hessian matrix (i.e., the second derivative of the potential function) with a vector. Thus, the total memory requirement of TNPACK can be reduced to a linear order of N if the preconditioner M can be formulated in a compress format by a linear order of N memory locations. If so, the size of a biomolecular system that TNPACK can be applied to will be sharply increased. However, since the sparse pattern of M is extremely irregular, which varies with molecular systems, it is difficult to compress M without employing a full 3N × 3N matrix. How to formulate a compressed M by a linear order of N memory locations has been an open problem for a long time. This paper solves this problem and extends the definition of the preconditioner using the spherical cutoff approach to improve the efficiency of the preconditioner for a biomolecular system containing a large number of water molecules. Note that a sparse Hessian matrix has been programmed in CHARMM in a


This work was supported by the National Science Foundation through grant DMS0241236, and, in part, by the Graduate School Research Committee Award (343267101-4) of the University of Wisconsin-Milwaukee.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 64–70, 2004. c Springer-Verlag Berlin Heidelberg 2004


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special compress format (which will be referred to as the CHARMM compress format for clarity) [4]. Hence, a new scheme is first developed to generate the sparse pattern of the preconditioner from the primary structure of a biomolecular system, along with a given spherical cutoff condition, and express it in the CHARMM compress format. With such a sparse pattern, the preconditioner is then defined as a compressed sparse Hessian matrix so that the program routines for evaluating the preconditioner can be easily created by adapting the current CHARMM program routines. Finally, the compressed preconditioner is converted from the CHARMM compress format to the YSMP (Yale Sparse Matrix Package [5]) compress format, resulting in the compressed sparse preconditioner suitable for TNPACK. It is shown that the new compressed preconditioner can be formulated and evaluated in a linear order of N memory locations. The remainder of this paper is organized as follows. Section 2 defines the new natural preconditioner. Section 3 expresses the compressed preconditioner in both CHARMM and YSMP formats. Section 4 describes a scheme for formulating the sparse pattern of the preconditioner directly from the primary structure of a molecular system. Section 5 presents a scheme for converting the CHARMM compress format to the YSMP compress format. Numerical results will be reported in the subsequent paper.

2

The New Definition of the Natural Preconditioner

Let E(X) be a biomolecular potential energy function with X = (X1 , X2 , . . . , XN ), where Xi = (xi , yi , zi ) denotes the position of atom i for i = 1, 2, . . . , N . An important task in biomolecular simulations is to find a minimum point of E(X) over the 3N dimensional space, which often leads to a feasible conformation of the molecular system. In general, E includes the local potential Elocal , the van der Waals potential energy, and the Coulomb potential energy. Elocal is defined as the sum of the bond length, bond angle, and torsional potential terms. See [1] for a detail description of the biomolecular potential energy function. With a given Elocal and a given nonnegative value of η, the sparse pattern set P is introduced as below: ∂ 2 Elocal (X)
= 0 or Xi − Xj 2 ≤ η for i < j, i, j = 1, 2, . . . , N }, ∂Xi ∂Xj (1)
where Xi − Xj 2 = (xi − xj )2 + (yi − yj )2 + (zi − zj )2 . The natural preconditioner is a sparse N × N symmetric block matrix M defined by M = (Mij )N i,j=1 with block entry Mij as given below: P = {(i, j)|

 Mij =

∂ 2 E(X) ∂Xi ∂Xj

if (i, j) ∈ P for i ≤ j, 0 otherwise

and Mij = Mji

where i, j = 1, 2, . . . , N , 0 denotes a 3 × 3 matrix of zero, and

for i > j,

(2)

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⎡ ∂ 2 E(X) ⎢ =⎢ ⎣ ∂Xi ∂Xj

∂2E ∂2E ∂2E ∂xi ∂xj ∂xi ∂yj ∂xi ∂zj ∂2E ∂2E ∂2E ∂yi ∂xj ∂yi ∂yj ∂yi ∂zj ∂2E ∂2E ∂2E ∂zi ∂xj ∂zi ∂yj ∂zi ∂zj

⎤ ⎥ ⎥. ⎦

(3)

In [7], M was defined as the Hessian matrix of Elocal . Clearly, replacing Elocal by E and adding the cutoff condition Xi − Xj 2 ≤ η in the definition of M in (1) and (2) can significantly improve the approximation of the preconditioner to the Hessian matrix of E. Hence, the new preconditioner is expected to be more effective than the traditional one in [7] for TNPACK. The preconditioner M is very sparse. It has only a linear order of N nonzero entries. In fact, each local potential term of Elocal involves at most three bond connections, and the value of η is small (a default value of η in TNPACK is 4 ˚ A). Hence, the total number of nonzero block entries on each row of M is a small fixed number. Thus, M has only a linear order of N nonzero entries.

3

The Preconditioner in Two Compress Formats

In this section, the preconditioner is compressed in the CHARMM and YSMP formats, respectively. For clarity, the ith row of the upper triangle part of M is assumed to have ni + 1 nonzero block entries Mij with column indices j = i, νi1 , νi2 , . . . , νi,ni satisfying i < νi1 < νi2 < . . . < νini and ni ≥ 0 for i = 1, 2, . . . , N.

(4)

Thus, the sparse pattern set P can be rewritten as P = {(i, j)|j = i, νi1 , νi2 , . . . , νi,ni satisfying (4) for i = 1, 2, . . . , N }.

(5)

The block entry Mij is also denoted by ⎡

⎤ mµ,ν mµ,ν+1 mµ,ν+2 Mij = ⎣ mµ+1,ν mµ+1,ν+1 mµ+1,ν+2 ⎦ , mµ+2,ν mµ+2,,ν+1 mµ+2,ν+2 where µ = 3i − 2 and ν = 3j − 2 for i, j = 1, 2, . . . , N . It is only needed to store the upper triangle part of M since M is symmetric. In the CHARMM compress format, a sparse matrix is stored into two integer arrays C and P and one real array M, where M holds the nonzero entries of M , C the column indices of the nonzero block entries in M, and P the position of the column index νi1 in C for i = 1, 2, . . . , N. For the preconditioner M with the sparse pattern set P given in (5), the three arrays M, C and P can be found as below: C = (ν11 , ν12 , . . . , ν1,n1 , ν21 , ν22 , . . . , ν2,n2 , . . . , νN 1 , νN 2 , . . . , νN,nN ),

(6)

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P = (P(1), P(2), . . . , P(N )) with the ith component P(i) being defined by P(1) = 1

and P(i) = 1 +

i−1

nk

for i = 2, 3, . . . , N,

(7)

k=1

and M = (R(1), R(2), . . . , R(N )) with R(i) holding the ni + 1 nonzero block entries of row i in the form R(i) = (D(i), U(i, νi1 ), U(i, νi2 ), . . . , U(i, νini )). Here D(i) holds the upper triangle part of Mii , and U(i, j) the 9 entries of Mij with i < j in a row by row pattern. In terms of C and P, the column index νij and number ni are expressed as νi,j = C(P(i) + j − 1) and ni = P(i + 1) − P(i),

(8)

where j = 1, 2, . . . , ni , and i = 1, 2, . . . , N . In the YSMP compress format, a sparse matrix is stored into two integer arrays IA and JA and one real array A, where A holds the nonzero entries of the matrix in a row-wise fashion, JA the column indices of the entries of A, and IA is a pointer vector in which the ith entry IA(i) points to the location of the first nonzero entry of the i-th row of the matrix in vector A. If A(k) = mij , where mij is the first nonzero entry of the i-th row, then IA(i) and JA(k) are defined by IA(i) = k and JA(k) = j. Clearly, the difference IA(i + 1) − IA(i) indicates the total number of nonzero entries in the ith row of M , and the nonzero entries of the ith row of M can be expressed by A(IA(i)), A(IA(i) + 1), . . . , A(IA(i + 1) − 1), while their column indices by JA(IA(i)), JA(IA(i) + 1), . . . , JA(IA(i + 1) − 1), where i = 1, 2, . . . , n, and IA(n + 1) = IA(n) + 1. For the natural preconditioner M , there are ni + 1 nonzero block entries in the ith row of the upper triangle part of M , and each block entry is a 3 × 3 matrix. Hence, for each value of i for i = 1, 2, . . . , N , the corresponding three rows of M have labelling indices 3i − 2, 3i − 1 and 3i, and contain 3ni + 3, 3ni + 2 and 3ni + 1 nonzero entries, respectively. Thus, the compressed M by the YSMP compress format can be easily obtained.

4

Formulation of the Sparse Pattern Arrays C and P

The primary structure of a molecular system is described as a list of pairs (ζk , ηk ) for k = 1, 2, . . . , Nb in CHARMM, where ζk and ηk denote the labelling indices of the two end atoms of bond k, and Nb the total number of bonds. For a given

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bond list, the sparse pattern arrays C and P can be generated by using the following scheme: It is clear that comparing the two atomic indices of each bond with the index of a given atom can identify all the atoms that share one bond with the given atom. Suppose that for i = 1, 2, . . . , N , there exist li such atoms with labelling indices µi,1 , µi,2 , . . . , µi,li . Then, these indices can be held by vector J as below: J (I(i) + k − 1) = µi,k

for k = 1, 2, . . . , li , and i = 1, 2, . . . , N,

(9)

i−1 where I(1) = 1, and I(i) = k=1 lk for i = 2, 3, . . . , N. Since I(i) points to the position of µi,1 in vector J , li can be expressed by li = I(i) − I(i − 1) for i = 1, 2, . . . , N. By using J and I, the sparse pattern arrays C and P are formulated in four steps for each given atom, say atom i, where 1 ≤ i ≤ N . In Step 1, find li atoms with indices µi,1 , µi,2 , . . . , µi,li that share one bond with atom i from J and I. If there exists µi,j > i with 1 ≤ j ≤ li , then µi,j is selected as a new entry of C. In Step 2, for each selected atom from Step 1, say atom k, find lk atoms with indices µk,1 , µk,2 , . . . , µk,lk that share one bond with atom k from J and I. If there exists µk,j > i with 1 ≤ j ≤ lk , then µk,j is selected as a new entry of C. In Step 3, for each selected atom in Step 2, say atom t, similarly find the atoms that share one bond with atom t and have indices more than i from J and I. Clearly, such selected atoms connect to atom i through three bonds. Hence, their indices become new entries of C. Finally, in Step 4, the indices of atoms satisfying the cutoff condition are selected as new entries of C if η
= 0. To ensure that the indices {νij } satisfy (4), in each step of selecting the ith entry of C, the repeated indices between P(i) and P(i + 1) − 1 are excluded. The above scheme can be implemented in a linear order of N memory locations. In fact, both I and P size N + 1, and the sizes of

Nare vectors of N l and J and C can be found to be i=1 i i=1 ni , respectively. Set Cmax = max{max1≤i≤N ni , max1≤i≤N li }. Clearly, Cmax is a constant much less than N . A default value of Cmax is set as 180 in TNPACK. Hence, the sizes of J and C are estimated as Cmax N . Therefore, the total number of integers required to formulate the sparse pattern arrays C and P are estimated as 2(N + 1 + Cmax N ) ≈ 2(Cmax + 1)N = O(N ).

5

Switch the CHARMM Format to the YSMP Format

Since TNPACK uses the YSMP compress format to store the preconditioner M , a scheme is needed to switch the CHARMM format (M, C, P) to the YSMP format (A, IA, JA). It is easy to obtain IA and JA from C and P since the involved numbers {µi,j } and {ni } can be produced directly from formula (8) when the sparse pattern arrays C and P are available.

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Clearly, the sparse pattern of M remains the same in the whole minimization process because it is defined according to the bond list. Hence, the formulation of the sparse pattern (IA, JA) or (C, P) is carried out only at the initial step of TN iterations. After the pattern (IA, JA) is produced, the memory locations of the four integer arrays I, J , C, and P can be released immediately. To switch M to A, two additional pointer arrays, ξ and ζ, are introduced as below. Set their ith components ξ(i) and ζ(i) to store the positions of mµµ and mµν in the vector M, respectively, where µ = 3i − 2 and ν = 3νi,τ − 2 for τ = 1, 2, . . . , ni , and i = 1, 2, . . . , N. ξ(i) and ζ(i) can be found as below: ξ(1) = 1,

and ξ(i) = 9ni−1 + ξ(i − 1) + 6

for i = 2, 3, . . . , N,

ζ(i) = ξ(i) + 9(τ − 1) + 6 for τ = 1, 2, . . . , ni , i = 1, 2, . . . , N.

(10) (11)

In terms of ξ and ζ, the nonzero entry array A can be produced directly from M by the following expressions: A(IA(µ) + k) = M(ξ(i) + k), A(IA(µ + 1) + 1) = M(ξ(i) + 4),

A(IA(µ + 1)) = M(ξ(i) + 3), A(IA(µ + 2)) = M(ξ(i) + 5),

A(IA(µ) + 3j + k + 1) = M(ζ(i) + k), A(IA(µ + 1) + 3j + k) = M(ζ(i) + k + 3), A(IA(µ + 2) + 3j + k − 1) = M(ζ(i) + k + 6), where k = 0, 1, 2, µ = 3i − 2, j = 1, 2, . . . , ni , and i = 1, 2, . . . , N .

N Both M and A have the same size, which can be found by 6N + 9 i=1 ni , and estimated by (9 max ni + 6)N ≤ 9Cmax N = O(N ). 1≤i≤N

Hence, the formulation of A from M requires only a linear order of N memory locations.

References 1. Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S. Karplus, M.: CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J. Comp. Chem., 4 (1983) 187-217. 2. Dembo, R. S., Steihaug, T.: Truncated-Newton algorithms for large-scale unconstrained optimization. Math. Prog., 26 (1983) 190-212. 3. Derreumaux, P., Zhang, G., Brooks, B., Schlick, T.: A truncated-Newton method adapted for CHARMM and biomolecular applications. J. Comp. Chem., 15 (1994) 532-552. 4. Perahia, D., Mouawad, L.: Computation of low-frequency normal modes in macromolecules: improvements to the method of diagonalization in a mixed basis and application to hemoglobin. Computers & Chemistry, 19 (1995) 241-245.

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5. Schultz, M. H., Eisenstat, S. C., Sherman, A. H.: Algorithms and data structures for sparse symmetric Gaussian elimination. SIAM J. Sci. Statist. Comput., 2 (1981) 225-237. 6. Schlick, T., Fogelson, A.: TNPACK — A truncated Newton minimization package for large-scale problems: I. Algorithm and usage. ACM Trans. Math. Softw., 14 (1992) 46-70. 7. Schlick, T., Overton, M. L.: A powerful truncated Newton method for potential energy functions. J. Comp. Chem., 8 (1987) 1025-1039. 8. Xie, D., Schlick, T.: Efficient implementation of the truncated-Newton algorithm for large-scale chemistry applications. SIAM J. OPT., 10 (1999) 132-154. 9. Xie, D., Schlick, T.: Remark on Algorithm 702—The updated truncated Newton minimization package. ACM Trans. on Math. Software, 25 (1999) 108-122. 10. Xie, D., Schlick, T.: A more lenient stopping rule for line search algorithms. Optimization Methods and Software, 17 (2002) 683-700.

A Study on Lower Bound of Direct Proportional Length-Based DNA Computing for Shortest Path Problem Zuwairie Ibrahim1, Yusei Tsuboi 1, Osamu Ono1, and Marzuki Khalid2 1

Institute of Applied DNA Computing, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki-shi, Kanagawa-ken, Japan 214-8571 {zuwairie, ono, tsuboi}@isc.meiji.ac.jp 2 Center for Artificial Intelligence and Robotics (CAIRO), Universiti Teknologi Malaysia, Jalan Semarak, 54100, Kuala Lumpur, Malaysia [email protected]

Abstract. Previously, we proposed a direct proportional length-based DNA computing approach for weighted graph problem. The approach has been proposed essentially to overcome the shortcoming of constant proportional length-based DNA computing approach. However, by using this approach, the minimum weight of edges that can be encoded is limited. Hence, in this paper, the lower bound, in term of minimum weight that can be encoded by direct proportional length-based DNA computing is analyzed. Also, the parameters contribute to the lower bound are investigated in order to identify the relation between those parameters and the lower bound of the direct proportional length-based DNA computing approach.

1 Introduction A constant proportional length-based DNA computing specifically proposed for solving Traveling Salesman Problem (TSP) has been proposed by Narayanan and Zorbalas [4]. A constant increase of DNA strands is encoded according to the actual length of the distance. A drawback of this method is that, there is a possibility of an occurrence of concatenated DNA strands of two distances which could be longer than the DNA strand of the longest distance that has been encoded. This may lead to errors in computing the shortest path [3]. This scheme, however, has not been realized by any laboratory experiment. Due to drawbacks in implementation, the constant proportional length-based DNA computing has not yet been implemented in any laboratory experiment. Thus, with the aim to solve the limitation of the constant-proportional length-based approach, by improving the previously proposed encoding style in [3], a direct proportional length-based DNA computing approach has been proposed [2]. The computation can be carried out in vitro by using the same computing architecture as Adleman [1]. In this approach, the cost of an edge is encoded as a direct-proportional length oligonucleotides, or oligos for short. As a result, during the computation, the important information is the length of the DNA duplex. Since this will result in numerous numbers of J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 71–76, 2004. © Springer-Verlag Berlin Heidelberg 2004

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combinations, by using the standard bio-molecular laboratory operations, it is possible to extract the optimal combination which represents a solution to the problem. However, we realized that there arises a drawback of direct proportional lengthbased DNA computing. The minimum weight of edges can be handled is limited. In other words, there is a lower bound in term of the weight of edges can be encoded by oligos. At first, the direct proportional length-based approach will be presented. At the end of this paper, the relation between those parameters and the lower bound, is studied. It is expected that this study will give some impacts and considerations when the laboratory experiment will be carried out soon, in future.

2 Direct Proportional Length-Based DNA Computing As the shortest path problem is chosen as a benchmark, the input to this problem is a weighted, directed graph G = ( V, E,ω ), a start node u and an end node v. The output of the shortest path problem is a ( u , υ ) path with the smallest cost. In the case given in Figure 1, if u is V1 and υ is V5, the cost for the shortest path will be given as 27 and the optimal path is clearly shown as V1 – V2 – V5.

Fig. 1. Example showing a weighted directed graph G = (V, E) with the shortest path shown as V 1 - V3 - V4 - V 5

If the directed graph shown in Figure 3 is considered. Let n be the total number of nodes in the graph. The DNA sequences correspond to all nodes and its complements are designed. Let Vi (i= 1, 2, … , n) and Vi (i= 1, 2, … , n) be the β-mer (β is an even number) DNA sequences correspond to the ith node in the graph and its complement respectively. If β = 20, by using the available software for DNA sequence design, DNASequenceGenerator [5], the DNA sequences Vi is designed and listed in Table 1.

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The complement, the GC contents (GC%), and melting temperature (Tm) of each sequence are shown as well. In Table 1, Vi can be separated into Via and Vib where Via is defined as half-5-end and Vib is defined as half-3-end of Vi. Table 1. DNA sequences for nodes. The melting temperature, Tm are calculated based on Sugimoto nearest neighbor thermodynamic parameter (Sugimoto et al., 1996)

20-mer sequences (5’-3’)

Node (Vi)

Via

Vib

V1

TATGCTCATT

TGCATTTTGA

V2

CAGGAGCGTC

TGAGAGCGAG

V3

TACCGGATCG

ACCGGCTAAG

V4

TCGTCCAAGG

GAGGCTTCTC

V5

GCTATATTGC

GCTGGATGTG

20-mer complement sequences (5’-3’) TCAAAATGCA AATGAGCATA CTCGCTCTCA GACGCTCCTG CTTAGCCGGT CGATCCGGTA GAGAAGCCTC CCTTGGACGA CACATCCAGC GCAATATAGC

GC% Tm (ºC)

30

46.13

65

58.58

60

55.12

60

54.46

50

52.16

We introduce three rules to synthesize oligos for each edge in the graph as follows: (i) If there is a connection between V1 to Vj, synthesize the oligo for edge as

V1 (β) + W1j (ωα- 3β/2) + Vja (β/2)

(1)

(ii) If there is a connection between Vi to Vj, where i ≠ 1, j ≠ n, synthesize the oligo

for edge as Vib (β/2) + Wij (ωα- β) + Vja (β/2)

(2)

(iii) If there is a connection between Vi to Vn, synthesize the oligo for edge as

Vib (β/2) + Win (ωα- 3β/2) + Vn (β)

(3)

The synthesized oligos consist of three segments. The number of DNA bases for each segment is shown in parenthesis, α is direct proportional factor, β is the length of the node sequences, and ‘+’ represents the join. Wij denotes the DNA sequences representing a cost between node Vi and Vj. As such, if α=1, for an edge from Vi to Vj, due to the synthesized rules, the DNA sequences for distance or costs, Wij are designed using the DNASequenceGenerator [5] and the results are listed as shown in Table 2. Table 3 on the other hand lists all the synthesized oligos based on the proposed synthesis rules. The complement oligos of each node and cost are synthesized as well.

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Table 2. DNA sequences for costs. Melting temperature, Tm are calculated based on Sugimoto nearest neighbor thermodynamic parameter (Sugimoto et al., 1996)

Cost, Wij

DNA sequences (5’-3’)

W13 W45

GAAGTGTACGTTAGGCTGCT AAAGGTCGTCTTTGAACGAG AAAGGCCCTCTTTTAACGAA GTCCTGTACT AAAGCCCGTCGGTTAAGCAA GTAGTTTACGCTGCGTCATT GCGTTGTTGCGAGGCATGTGGAGAA TTGATCGCTTTCGTGCATAACTGGG CAGCATCGTAGTAGAGCTAGTATCG AACTG ATAAGTAACG GAGGGGGCTC AAAGCTCGTC GTTTAAGGAAGTAC GGTACTATGCGTGATTTGGAGGTGGA

W34 W24 W25 W12 W23

Length GC% Tm (ºC) 20 20

50 45

51.59 50.34

30

43

60.45

40

48

69.47

50

52

74.08

50

50

72.19

50

46

70.91

Table 3. DNA sequences for edges

Edge

DNA sequences (5’-3’)

V1 – W13 – V3a

TATGCTCATTTGCATTTTGAGAAGTGTAC GTTAGGCTGCTTACCGGATCG

V4b – W45 – V5

GAGGCTTCTCAAAGGTCGTCTTTGAACGA GGCTATATTGC GCTGGATGTG

V3b – W34 – V4a

ACCGGCTAAGAAAGGCCCTCTTTTAACGA AGTCCTGTACT TCGTCCAAGG

V2b – W24 – V4a

TGAGAGCGAGAAAGCCCGTCGGTTAAGCAA GTAGTTTACG CTGCGTCATT TCGTCCAAGG

V2b – W23 – V3a

V2b – W25 – V5

V1 – W12 – V2a

TGAGAGCGAGAAAGCTCGTCGTTTAAGGAA GTACGGTACTATGCGTGATTTGGAGGTGGA TACCGGATCG TGAGAGCGAGGCGTTGTTGCGAGGCATGT GGAGAATTGATCGCTTTCGTGCATAACTGG GGCTATATTGCGCTGGATGTG TATGCTCATTTGCATTTTGACAGCATCGTA GTAGAGCTAGTATCGAACTGATAAGTAACG GAGGGGGCTCCAGGAGCGTC

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Then, all the synthesized oligos are poured into a test tube for initial pool generation. The generation of an initial pool solution is based on the hybridization/ligation method. In fact, the hybridization/ligation method for initial pool generation has been introduced firstly by Adleman (Adleman, 1994) in order to solve HPP. If the shortest path V1 - V3 - V4 - V5 is emphasized, Figure 2 clearly shows which kinds of oligos are important for the generation of this path. However, the unwanted combinations are also generated in the same manner. At this stage, an initial pool of solution has been produced and it is time to filter out the optimal combinations among the vast alternative combinations of the problem. Unlike conventional filtering, this process is not merely throwing away the unwanted DNA duplex but rather copying the target DNA duplex exponentially by using the incredibly sensitive PCR process. This can be done by amplifying the DNA molecules that contain the start node V1 and end node V5 using primers. After the PCR operation is accomplished, there should be numerous number of DNA strands representing the start node V1 and end node V5 traveling through a possible number of nodes.

Fig. 2. DNA duplex for path V1 - V3 - V4 - V5. The arrowhead indicates the 3’ end

The output solution of PCR operation is brought for gel electrophoresis operation. During this operation, the DNA molecules will be separated in term of its length and hence, the DNA molecules V1 – V2 – V5 representing the shortest path starting from V1 and end at V5 would be extracted for sequencing.

4 Lower Bound Analysis Basically, according to the DNA synthesis rules, the lower bound is achieved when:

3 2

ωα − β = 0

(4)

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At this time, the minimum weight, which can be encoded by oligos, ωmin is attained as:

ω min =

3β 2α

(5)

5 Conclusions This paper is written to analyze a lower bound of direct proportional length-based DNA computing for graph problems. Importantly, the definition of lower bound is given. From the analysis, the lower bound is basically depends on the length of node sequences, α and the direct proportional factor, β. The main conclusion of this study is that lower bound can be kept as low as possible by controlling the length of the node sequences, β and the direct proportional factor, α . It is now clear that in order to keep the lower bound effect as low as possible, one should decrease the parameter β, whereas the parameter α , should be increased at the same time. However, from the experimental view, one can not simply decrease the parameter β and increase the parameter α because such parameters will greatly affect the performance of the computation. Therefore, the best value for the length of the node sequences and the direct proportional factor will be further investigated during experimental setup for an accurate direct proportional length-based DNA computing for weighted graph problems.

References 1. Adleman, L.: Molecular Computation of Solutions to Combinatorial Problems. Science, Vol. 266 (1994) 1021-1024 2. Ibrahim, Z., Ono, O., Tsuboi, Y., Khalid, M.: Length-Based DNA Computing for 1-Pair Shortest Path Problem. Proc. of the Ninth International Symposium on Artificial Life and Robotics (2004) 299-302 3. Lee, J.Y., Shin, S.Y., Augh, S.J., Park, T.H., Zhang, B.T.: Temperature Gradient-Based DNA computing for Graph Problems with Weighted Edges. Lecture Notes in Computer Science, Vol. 2568 (2003) 73-84 4. Narayanan, A., Zorbalas, S: DNA Algorithms for Computing Shortest Paths. Proceedings of Genetic Programming (1998) 718-723 5. Udo, F., Sam, S., Wolfgang, B., Hilmar, R.: DNA Sequence Generator: A Program for the Construction of DNA Sequences. In N. Jonoska and N. C. Seeman (editors), Proceedings of the Seventh International Workshop on DNA Based Computers (2001) 23-32

Key Management for Secure Multicast Using the RingNet Hierarchy Guojun Wang1, 2, Lin Liao2, Jiannong Cao1, and Keith C. C. Chan1 1

Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 2 School of Information Science and Engineering, Central South University, Changsha, Hunan Province, P. R. China, 410083

Abstract. We propose a novel multicast communications model using a RingNet hierarchy, called the RingNet model, which is a combination of logical trees and logical rings for multicast communications. The RingNet hierarchy consists of four tiers: Border Router Tier (BRT), Access Gateway Tier (AGT), Access Proxy Tier (APT), and Mobile Host Tier (MHT). Within the hierarchy, the upper two tiers are dynamically organized into logical rings with network entities. In this paper, based on the RingNet model, local group concept is proposed. For simple illustration, we choose each AG in AGT as the controller of each local group. Each local group has its own independent local group key. The member’s join or leave in a local group only affects the local group, which makes multicast communications potentially scalable to very large groups. In this paper, we propose a novel key management scheme for secure multicast with the RingNet model.

1 Introduction Multicast is an efficient service that provides delivery of data from a source to a group of receivers. It reduces transmission overhead and network bandwidth. Recently with the convergence of Internet computing and wireless communications, research on multicast communications in mobile Internet becomes more and more active and challenging. In mobile Internet, more concerns should be considered. Firstly mobile hosts such as laptop computers, PDAs, and mobile phones have severe resource constraints in terms of energy and processing capabilities. Secondly, wireless communications involves high error rate and limited bandwidth problems. Thirdly, the number of mobile hosts may be very huge and they may move very frequently. Thus in mobile Internet the security issues of multicast are more complicated than in traditional Internet. The remainder of this paper is organized as follows. In section 2, we introduce some related works about key management for secure multicast. In section 3, we introduce our RingNet communications model, which is an efficient multicast communications model with the notion of a combination of tree and logical ring structures. In section 4, we describe the key management for secure communications using the RingNet model, and show how to implement secure multicast in RingNet and how it works when compared with others. The final section concludes this paper. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 77–84, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Related Works In a group communications system, the basic requirement is that newly-joined users are not allowed to access the former group communications and thus the group key should be rekeyed when new members join; and departed users are not allowed to access the current and future group communications after the group key is rekeyed. Conceptually, since every point-to-multipoint communications can be represented as a set of point-to-point communications, the current unicast technology can be extended in a straightforward way to do secure group communications. However, such an extension is not scalable to very large groups. As we previously mentioned, when a user joins a group, a new group session key ( KGSK ) would be generated to replace the former one, which will be distributed to all current and joining users. A simple way is to multicast new KGSK to current users encrypted by the old KGSK . Accordingly the joining user will be informed of the new KGSK by means of unicast. In case of user departure, since we should transmit the new KGSK to all remaining users, we can use respective key materials to encrypt it individually. As a result, we have to take separate users into account for each leave and join. If extended to large dynamic group, the scalability problem is a potential bottleneck. In order to resolve the scalability issue and improve efficiency in secure group communications, many solutions are proposed. The mainstream ideas are the Iolus system [1] and the Key Graph system [2]. Based on these schemes, different rekeying policies in terms of user departure, user join and traffic source rate are proposed, such as periodic rekeying [3], batch rekeying [4], and exposure-oriented rekeying [5]. Iolus is a novel framework for scalable secure multicast. A group is divided into many subgroups. Iolus uses independent keys for each subgroup and the absence of a general group key means membership change in a subgroup is treated locally. Thus scalability is achieved by having each subgroup to be relatively independent. Iolus uses entity-GSC (Group Security Controller) to manage the top-level subgroup, and entity-GSI (Group Security Intermediary) to act as proxy of GSC. However, it requires decryption and encryption of data packets while transmitted into different subgroups. Except for Iolus, the other main idea is to organize users and server into a tree structure. In such a centralized system, there is only one central controller that doesn’t rely on any auxiliary entity to perform secure access control. The typical scheme is the Key Graph system. Due to its verticality, the tree structure is easy to be destroyed in a single node especially for the group key. Furthermore, users’ join and leave will cause rekeying and affect other users. By means of the tree structure, cost will be exaggerated when the number of users becomes huge.

3 The RingNet Communications Model Researchers have proposed many mobile Internet architectures, such as Unified Wireless Networks Architecture [6], System Architecture for Mobile Communication System [7], All-IP Wireless/Mobile Network Architecture [8], and FIT-MIP Global System Architecture [9]. Based on them, we propose a multicast communications model called a RingNet hierarchy shown in Figure 1.

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Fig. 1. The RingNet Hierarchy

The four tiers of the RingNet hierarchy are Border Router Tier (BRT), Access Gateway Tier (AGT), Access Proxy Tier (APT), and Mobile Host Tier (MHT). The higher two tiers are dynamically organized into logical rings. Each logical ring has a leader node, which is also responsible for interacting with upper tiers. Access Proxies (APs) are the Network Entities (NEs) that communicate directly with the Mobile Hosts (MHs). Access Gateways (AGs) are the NEs that communicate either between different wireless networks or between one wireless network and one wired network. Border Routers (BRs) are the NEs that communicate among administrative domains. Notice that only those NEs that are configured to run the proposed protocol will be involved in the hierarchy. In order to form such a hierarchy, we require each AP, AG, and BR having some knowledge of its candidate contactors, either some candidate neighbor nodes through which it can join a logical ring, or some candidate parent nodes through which it can attach to an existing hierarchy. Multicast communications using the RingNet hierarchy is simple: Multicast Senders (MSs) send multicast messages to any of the BRs at the top logical ring. Then the multicast messages are transmitted along each logical ring, and downward to all the children nodes. Finally the MHs will receive multicast messages from their attached APs. Thus the multicast data are delivered to all users efficiently. Ideally, there is only one RingNet hierarchy containing all the operational group members. The RingNet membership management works as follows. Each MH can join or leave a group at will, or fail at any time. The membership change message is firstly captured by the MH’s attached AP node. Then it is propagated to the AP’s parent AG node. If the AG happens to be a leader node, then it propagates such message to its parent node; if not, then it propagates it to the leader node in the logical

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ring where it resides. This process continues until the leader node in the top logical ring is reached. Loosely speaking, the proposed RingNet hierarchy is a novel distribution vehicle that combines advantages of both logical tree and logical ring. Each logical ring is dynamically organized according to some criteria such as locality/proximity or Quality of Service (QoS). Due to the combination of ring and tree, fault tolerance is stronger than the tree structure that is fragile because of single node being attacked easily. What’s more, due to the setting of logical rings, it’s easy to ensure key packet transmitted along one vertical path even though some of the rings are destroyed. However, the latency incurred by logical ring is a drawback of RingNet. Therefore, in our model, we consider small logical rings. Based on these assumptions, we discuss some security issues.

4 Key Management Using the RingNet Model In [10], we introduce the RingNet hierarchy for totally ordered multicast, which are proved to be scalable, reliable, and self-organizable in large dynamic group communications. Based on these works, we will discuss key management using the RingNet hierarchy. In RingNet, the rekeying process is different from both the Iolus system and the Key Graph system. Due to the setting of logical rings, it ensures that non-leader AGnode receives key messages safely without being derived from leader AG-node through which the messages are forwarded. In order to solve the scalability problem, we borrow some idea from Iolus. We consider every AG node and its attaching AP/MH nodes as a local group. Then the multicast communications group is divided into many local groups and they are linked together by some rings. The local groups have their own local group keys ( KLG ) and each AG serves as a trusted server proxy. Here we use “local group” other than “subgroup” to emphasize that, the local groups in our RingNet hierarchy are dynamically formed, while the subgroups in Iolus are statically configured. In general, a global server in the top ring is used to control all the local groups, which are controlled by the AG nodes. Local groups obtain the rekeyed group session key KGSK created by the global server. In each local group, if the members change within a local group, the local group changes its own KLG and its members’ individual keys. On the other hand, local group feedbacks its change to the global server. Each AP member only need to know its local group key and the server node has a record for each leader local group’ KLG . In order to simplify the problem, we assume that initially the number of APs in every AG local group is L ; the number of AGs under each BR is K ; the number of nodes of each AG ring is R ; the number of nodes in each BR ring is B . Each local group has a unique number to be distinguished from each other, with the label like LGijk , where 0 ≤ i ≤ B - 1, 0 ≤ j ≤ K - 1, and 0 ≤ k ≤ R - 1. Multicast data sender firstly reaches the BRT and one of the BR nodes can be the server as shown in Figure 2. BR nodes will transmit the data packet to its next BR node and its children nodes almost at the same time, which will work in the same way as the server BR. Therefore, we put the other BR nodes aside because they are the

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same and act like duplicators of the BR server. In the following, we will describe the protocols in four situations.

Fig. 2. Local Group Core Architecture in RingNet

4.1 An AG-Local Group Joins When an AG-local group joins a multicast group, the APs and MHs involved in the AG-local group are not concerned in the rekeying directly. After the AG node and the server node have authenticated for each other, the server node creates a new KLG of the local group. The server node renews the KGSK , and multicasts it to all former AG nodes encrypted by old KGSK . During this process, the multicast rekeying messages are firstly forwarded to the leader AG-nodes and then they forward the messages to the ring members as second level servers. The process is specifically expressed as follows assuming LG0 (k-1)(r-1) wants to join.

LG0 (k-1)(r-1) requests for joining a new group associated with a server node; LG0 (k-1)(r-1) and the server node will do authentication for each other; The server node generates KLG of LG0 (k-1)(r-1) and renews KGSK to K ′GSK ; The server node sends key packet with ( K ′GSK ) KGSK to leader nodes of local groups from LG0 (k-1) 0 to LG000; 5. Key packet with K ′GSK encrypted by KLG of newly joining LG0 (k-1)(r-1) is sent to LG0 (k-1)(r-1) by the server node; 6. Key packet with ( K ′GSK ) KGSK is transmitted to the non-leader AG-nodes along the logical rings by each leader AG-node except for the newly joining node. 1. 2. 3. 4.

Notice that using K to encrypt K ′ is expressed as ( K ′) K . The key packet with ( K ′GSK ) KGSK firstly needs to be informed to the leader AG-nodes in step 4, and then the leader AG-nodes will transmit it in their AG-rings in step 6.

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4.2 A Non-leader Local Group Leaves A non-leader local group leaving means that all the attached MHs leave. After MHs leave, the link between the AG node and the adjacent nodes will detect that the AG is not active. Then the server sets the AG node as half-active. After a certain period of time, the server confirms that the AG is not connected. Then two neighbors of the unconnected AG establish a new link and the AG node disappears. After confirming the departure, the server node will re-create a new group session key K ′GSK . The following procedure will be a little different with a local group joining, for the departed AG node has known the old KGSK . The new group session key K ′GSK will be multicast to all the remaining AGs encrypted by their respective KLG grouped by the logical rings. 1. LG0 (k-1)(r-1) requests for leaving a group associated with a server node; 2. The server node confirms the departure and makes the new ring work as well; 3. The server node renews KGSK to K ′GSK ; 4. For each logical AG ring, the server node sends an individual key packet with K ′GSK encrypted by KLG ; then AG nodes in this ring can recover the K ′GSK using the key packet using its own KLG . 4.3 A Local Group with Leader Node Leaves Different from ordinary hierarchy, a local group leaving with leader node is quite different in RingNet, because leader node is the intermediary between two tiers. Once the leader node is requesting for leaving, the server node will establish a connection with an adjacent node, give it a leader certificate and update the membership information. Except for the above process, the remaining procedure is the same as a non-leader local group leaves. 4.4 Membership Changes Within a Local Group If the membership changes within a local group, to some degree the local group hierarchy will hide such kind of changes, for these changes only affect within its own local group. As to the inner local group change, it firstly should be rekeyed like an independent group. We can use any existing rekeying approach such as tree key graph to rekey the local group and a new KLG will be generated. Then the server node will receive the change message and update the membership information. Scalability is sufficed by means of local group hierarchy. The whole process can be represented as follows: 1. An MH of LG001 requests for leaving or another MH request for joining LG001; 2. LG001 is rekeyed and the leader AG-node of the group generates a new KLG , i.e., K ′LG ; 3. Key packet with ( K ′LG ) KLG is propagated upward to the server node through leader node LG000; but the leader AG–node doesn’t obtain the packet because it doesn’t know KLG of LG001; 4. The server node gets the K ′LG , and updates the key information.

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It’s concluded that the server node can’t overwrite the KLG autonomously except the server node initiates the local group and the local group itself generates a new KLG . The members of AG local group only need to know its KLG , which becomes the bridge of members and the server node.

5 Conclusion In this paper, we introduced the RingNet model and proposed a key management scheme based on the model. Complementary to the scalability, reliability and selforganizability of the RingNet model, we tackle the security issue in RingNet. Since RingNet has three kinds of network entities, theoretically we can generate at least three local group schemes. Furthermore, some combinations of these local group schemes can also be possible. However in this paper, we just consider every AG as a local group controller and the upper distribution structures rely on the RingNet inner structure. In order to take advantages of the local groups, the AG-tier local group scheme is probably the best choice for medium to large sized groups.

Acknowledgments This work was supported by the Hong Kong Polytechnic University Central Research Grant G-YY41, the University Grant Council of Hong Kong under the CERG Grant PolyU 5170/03E, and the China Postdoctoral Science Foundation (No. 2003033472).

References 1. Mittra, S., Iolus: A Framework for Scalable Secure Multicasting, Proceedings of the ACM SIGCOMM ’97 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, (1997) 227-288. 2. Wong, C.K., Gouda, M., Lam, S.S.: Secure Group Communications Using Key Graphs, Proceedings of the ACM SIGCOMM ’98 Conference on Applications, Technologies, and Protocols for Computer Communication, (1998) 68-79. 3. Setia, S.J.S., Koussih, S., Jajodia, S., Harder, E.: Kronos: A Scalable Group Re-keying Approach for Secure Multicast, Proceedings of the 2000 IEEE Symposium on Security and Privacy, Berkeley, CA, (2000) 215-228. 4. Zhang, X.B., Lam, S., Lee, D.Y., Yang, Y.R.: Protocol Design for Scalable and Reliable Group Rekeying, IEEE/ACM Transactions on Networking, Vol.11, No.6, (2003) 908-922. 5. Zhang, Q., Calvert, K.L.: On Rekey Policies for Secure Group Applications, Proceedings of the 12th International Conference on Computer Communications and Networks (ICCCN 2003), (2003) 559-564. 6. Lu, W.W.: Compact Multidimensional Broadband Wireless: The Convergence of Wireless Mobile and Access, IEEE Communications Magazine, Vol. 38, Issue 11, (2000) 119-123. 7. Otsu, T., Umeda, N., Yamao, Y.: System Architecture for Mobile Communication Systems beyond IMT-2000, Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM 2001), Vol. 1, (2001) 538-542.

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8. Zahariadis, T.B., Vaxevanakis, K.G., Tsantilas, C.P., Zervos, N.A., Nikolaou, N.A.: Global Roaming in Next-Generation Networks, IEEE Communications Magazine, Vol. 40, Issue 2, (2002) 145-151. 9. Morand L., Tessier, S.: Global Mobility Approach with Mobile IP in all IP Networks, Proceedings of the 2002 IEEE International Conference on Communication (ICC 2002), Vol. 4, (2002) 2075-2079. 10. Wang, G.J., Cao, J.N., Chan, K.C.C.: A Reliable Totally-Ordered Group Multicast Protocol for Mobile Internet, Proceedings of the 2004 International Workshop on Mobile and Wireless Networking (MWN 2004), held in conjunction with the 33rd International Conference on Parallel Processing (ICPP 2004), Montreal, Quebec, Canada, August 1518, 2004.

Open Middleware-Based Infrastructure for Context-Aware in Pervasive Computing Xianggang Zhang, Jun Liao, and Jinde Liu Micro Computer & Network Technology Research Institute, College of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, P. R. China [email protected]

Abstract. Due to the lack of open infrastructure support, the development of context aware systems in pervasive computing environment is difficult and costly. To solve this problem, we have implemented an open middleware-based contextaware infrastructure for context aware in pervasive computing, named ocaInfrastructure. In oca-Infrastructure, (1) a generic layered model is proposed to specify the functional elements of context-aware computing and provides contextaware computing systems with robust separation of concerns. (2) Wireless CORBA is used to enable distributed components to communicate each other and support for wireless access and terminal mobility. (3) Context-aware supporting platform is created to mask the dynamic environment. (4) Context query is issued based on type-subject model. The context message is delivered in XML. (5) Knowledge-based access control is used to improve security. Finally, we have presented detailed examples to evaluate the feasibility of oca-Infrastructure.

1 Introduction How to provide best-suited services to users in pervasive computing environment [1][2]? The context plays an important role. In the paper, we designed and implemented an open middleware-based context-aware infrastructure, called ocaInfrastructure, which uses CORBA to enable distributed components to find and communicate with one another and provides the functions to meet the essential requirements for context aware computing in pervasive computing, which are: (1) Supports for context-aware. This includes context acquisitions, context model and representation, context aggregation, context query, context interpretation and so on; (2) Supports for pervasive computing environment; (3) Supports for open systems, which includes portability, interoperability, scalability, security and privacy. In the rest of the paper, section 2 is related to the related works. In section 3, we propose a layer model for context aware in pervasive computing. In section 4, the architecture of oca-Infrastructure is showed. In section 5, we explain the details of oca-Infrastructure. Then we build a location-aware system with oca-Infrastructure to evaluate it in section 6. Finally, section 7 is related to the further work and we summarize the paper. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 85–92, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Related Work Dey and etc developed a set of abstractions, Context Toolkit [3], for sensors data processing in order to facilitate reuse and make context aware applications easier to build. The Stick-e notes system is a general framework for supporting a certain class of context-aware applications [6]. The Solar [4] system architecture proposed a graph-based abstraction for context aggregation and dissemination. The Gaia project [5] developed at the University of Illinois is a distributed middleware infrastructure that provides support for context aware agents in smart spaces. To make a summary, the above-mentioned context aware architectures cannot provide a complete solution for all the essential requirements for context aware computing in pervasive computing.

3 A Layered Model for Context Aware in Pervasive Computing In this section, we present a generic layered model as a design approach for contextaware computing in pervasive computing. Fig.1 shows the layer model.

Fig. 1. A layer model for context-aware

Fig. 2. The architecture of oca-Infrastructure

Context model forms the foundation for expressive context representation and high-level context interpretation [8]. Context representation is the foundation for communication and interoperation. The lowest level is context acquisition layer, in which context in raw format may be acquired from a wide variety of ubiquitous context sensors. The context aggregation layer aggregates and relates contexts from distributed context sources to form a centralized context repository. The context interpretation layer leverages reasoning/learning techniques to deduce high-level, implicit context needed by intelligent services from related low-level, explicit context. The context-binding layer maps the context queries of the applications to the context

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services in order to adapt to the dynamic environment. Finally, on the uppermost level, context aware applications utilize context to adjust their behaviors.

4 Overview of oca-Infrastructure Fig. 2 shows the architecture of oca-Infrastructure. From bottom up, the lowest layer is the hardware layer. The second layer is OS and driver layer. The third layer is Context-aware infrastructure. It is composed of, from bottom up, underlying middleware, context aware supporting platform and distributed services. The middleware layer provides the communication capability for distributed components. The middle layer is context aware supporting platform, which provides interface for context query and dynamically binds. In the upper layer, there is the service layer. The top layer is Context aware applications, which utilize both raw and abstract context to adjust their behaviors.

5 Implementation 5.1 Context Service and Taxonomy A Context Service is a software (or software and hardware) component. It encapsulates the details of process and provides context information. Through the context service, context consumer is provided separation of concerns. All context services are implemented on top of CORBA. All of context services have a similar structure showed in fig.3. They can be encapsulated into higher Context services.

Fig. 3. General architecture of context service

The Core Functional of a Context Service implements context acquisition, aggregation, or the other functions. For example, GPS context service reads signals from the serial ports and analyzes signal stream, then derives the location information in form of (x, y, z). The Uniform Interface is composed of three components: Registration and de-registration, Callback, Synchronous querying. The Registration and Callback Components are adopted for the asynchronous delivery of events. The registration and de-registration interfaces allows an application to register and de-register some context event (represent some situation of circumstance), and context service

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uses callback interface to deliver context events to applications when the context events occur. The synchronous interface is provided to acquire context information synchronously. Using this, context information are returned immediately. The part of Data Management is provided to store context events, templates and history context information and so on. Furthermore, we propose taxonomy for context services based on the functional requirements of context aware systems. The different taxonomy of the context service has a similar structure and the different core function. − Elementary Context Service: An elementary context service offers a uniform way to encapsulate a physical sensor such as a thermometer, or any computational component that can be used as a source of physical data. For example, suppose we encapsulate a GPS device within an elementary context service. Then, core function acquires the signals of GPS, process the special-device details, output uniform context information through interface. − Aggregation Service: The aggregation service aggregates and relates contexts from distributed context services to form a centralized context repository. Aggregation service helps to merges the required information which is related to a particular entity (e.g., ‘user’), or which is of relevance of a particular context aware system (e.g., the entire context needed by the smart phone service), and then provides a basis for further interpretation over the related contextual knowledge. It also simplifies the query of distributed services through a centralized manner instead of distributed approach. In some degree, context aggregation by its nature is to provide the functionalities of a context Knowledge Base. − Translation Service: A translation service performs type recasting but does not change the meaning, or the level of abstraction of the values received. For example, a translation service is used to transform input temperatures from one representation system to another (for example Celsius, Fahrenheit, Kelvin). − Interpretation Service: The interpretation service receives multiple context Data, then derives higher level of abstraction than that of the input data types. Context can be interpreted with various kinds of reasoning and/or learning mechanisms to derive additional context. − Abstract Context Services: So far, we have introduced the basic classes of context services. The Context services may be composed into abstract context services, whose internal composition is hidden to other system components. 5.2 Context Model and Representation Context model forms the foundation for expressive context representation and highlevel context interpretation [8]. A uniformed context models can facilitate context interpretation, context sharing and semantic interoperability. Authors’ assumptions are: (1) each context is anchored in an entity. (2) Contextawareness is always related to an entity. (3) Specifying context around the notion of context types provides a general mechanism for context sharing and semantic interoperability. In oca-Infrastructure, we choose to use a general entity-oriented context model called type-subject model. In such context model, context information is structured

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around a set of entities, each describing a physical or conceptual object such as a person or an activity. Furthermore, the context set about an entity is classed by context type. For example, “room” has a location context, a temperature context and a light context. In oca-Infrastructure, standard common representations for context has a form of 3-tuple as follows: (Subject,type, attribute_set)

(1)

Subject represents the entity name with which the context is anchored, for example: person1; Type describes the type of context, for example: location context, and so on; Attribute_set is a set of attributes about context, which has several elements or none. Each element of attribute_set has a form of 2-tuple as follows: (Attribute type, attribute value)

(2)

For example: ( userId-1, Location, (format, GPS; precision, 50m)) represent userId-1’s location information, which has a data format of GPS and the precision of it is 50m. Context event represent a situation of environment. Application can register ocaInfrastructure with some context events. When context event occur, oca-Infrastructure notifies application that the registered situation occur. Element context event has a form of 3-tuple: (Context, relater, referenced_value )

(3)

Context represents some context information, whose form is same as above (1). Referenced_value is a value associated with the context, Relater is something that relates the context and referenced_value. Relater can be a comparison operator (such as =, >, or 0, then (vi,vj) is called a positive arc. If fij Te ⎪⎭ 0,

(4)

' e

where t is the transient time; τ is the time lag of active stress, Te is the activation period. σ o' is the active force of a myocardial fiber and which is a function of fiber length, time t, fiber directions, etc. In the calculation, the stress and strain vector is expressed with respect to two coordinate frames of reference: global coordinate system X-Y-Z and local coordinate system ξ-η-ζ. The nodal force equivalent to the active contractile force is calculated based on equation (4) and the isoparametric transformation: Le

{F f }e = − ∑ ∫ l =1

ξl

1

1

∫ ∫

ξ l −1 −1 −1

[ B ]T T {0,0, σ e' ,0,0,0}Tl J dξdηdζ

(5)

where [B] is geometric matrix of element, l, Le stand for the number and total number of layers in an element respectively, T is the transformation matrix between the fiber coordinate and global coordinate. {0,0, σe' ,0,0,0}Tl is the active force row vector in the

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fiber-coordinate system, |J| is the determinant of the Jacobian matrix. ξ, η, ζ are the local coordinate system with the magnitudes ranging from –1 to 1; ξl and ξl-1 represents individually the coordinate values along ξ direction on the front-side and backside of layer l in an element. ξl-1=-1 when l=1 and ξl= 1when l=Le. 2.3 Deformation Calculation

Strain analysis is a method to describe the internal deformation of a continuum body. It is an appealing tool to study and quantify myocardial deformation. The Lagrangian strain E is used to describe systolic deformation in a region surrounding a point in the heart wall relative to its initial position at end-diastole. E was calculated from the relationship:

E = 1 / 2( F T F − I )

(6)

where the superscript T represents the matrix transpose, F represents deformation gradient tensor, and I, the identity matrix. The deformation gradient tensor F can be calculated for the relationship:

Fpq = ∂xp / ∂X q

(7)

where X and x represent the initial and final position of a point in the material respectively, the subscripts p and q range from 1 to 3 and denote one of the 3D Cartesian coordinates. The tensor, F, includes both the rotation and deformation around a point in the material.

3 Results Based on the model we constructed above, the motion of ventricles was analyzed. At first, on the basis of myocardial physiological property as well as some references [11, 12], the material constants are employed as follows: Young’s modulus shear modulus GLT : 10 Kpa ; Poisson’s raEL : 50 Kpa, ET :11 Kpa ; tio: µ LT = µ TT = 0.49 ; The initial value of σ 0' = 53 Kpa . In the simulation, the time incremental step of simulation is 7 ms. Activation period Te = 353 ms . The active force and material constants are adjusted slightly in order to get proper results. We did not consider the blood pressure in the simulation. Fig. 3 shows the displacements of endocardium of RV at four different times during the period of systole, the color bar denotes the length of displacements (mm). The white dots mean the position of nodes at end-diastole, the red dots mean the position of nodes at different times through the systole, and the red line between the white dots and red dots mean the direction of nodes’ displacements. We can see that there is a considerable displacement of the free wall towards the septum and a large displacement of the base towards the apex in the free wall, which contributed to a smaller RV cavity. The results are similar to those obtained from the Tagged MRI [7].

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Fig. 3. The displacements of endocardium of RV at four different instants (T0: endisovolumetric contraction T1: middle-maximum ejection T2: end-maximum ejection T3: endejection)

Fig. 4. The negative minimum principal strains and their directions of endocardium of RV at four different instants (see Fig. 2)

As the RV has complicated shape/geometry, it is difficult to find a single axis about which to calculate twisting and radial contraction like those of LV. Here we use coordinate-system-independent principal strains and their directions to describe the deformation of RV. These quantities are derived by finding the eigenvalues and

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397

eigenvectors of the Lagrangian strain tensor, respectively. The eigenvalues of E are the principal strains, where a positive value indicates extension while a negative value indicates compression. The minimum principal strain, E3, is the smallest eigenvalue of E, and along with the minimum principal strain directions, supplies potentially useful information about the magnitude and direction of contraction in the heart [8]. Fig. 4 shows the distribution of E3 at the endocardium of RV. The short red lines denote the directions of E3 of the central point of finite elements at the endocardium of RV. It can be seen that the minimum principal strain is not uniform at the endocardium. A maximum value of –0.35 is at the apex and the directions of E3 mostly towards the apex, which means that the maximum contraction occurs towards the apex and in the approximate direction of the muscle fibers. These results are also correlated well with those from the Tagged MRI [7, 9].

4 Conclusion The right ventricular wall motion and deformation caused by the cardiac electrical activation have been analyzed based on a biventricular model and some general parameters, such as displacements, minimum principal strain, which are accepted in clinic, were used to describe the motion and deformation of the heart. The simulation results are in good accordance with solutions obtained from MR tagging images that reported in the literature. The future work will investigate the inter-ventricular dependence and ventricular wall relative motion within this framework.

Acknowledgments This work is supported by the National Natural Science Foundation of China (30170243, 30370400), a Special Grant to Authors of Excellent Doctoral Dissertations by the Ministry of Education (1999941), and 973 National Key Basic Research & Development Program (2003CB716106).

References 1. Papademetris, X., Sinusas, A.J., Dione, D.P., Constable, R.T. and Duncan, J.S.: Estimation of 3-D Left Ventricular Deformation From Medical Images Using Biomedical Models. IEEE Trans. Med. Imag. 21 (2002) 786-800 2. Azhari, H., Oliker, S., Rogers, W.J., Weiss, J.L., and Shapiro, E.P.: Three-Dimensional Mapping of Acute Ischemic Regions Using Artificial Neural Networks and Tagged MRI. IEEE Trans. Biomed. Eng. 43 (1996) 619-626 3. Linares, P., Torrealba, V., Montilla, G., Bosnjak, A., Jimenez, C., and Barrios, V.: Deformable Model Application on Segmentation in 3-D Echocardiography. Computers in Cardiology 23 (1996) 413-416 4. Lu, W. and Xia, L.: Computer Simulation of Epicardial Potentials Using a Heart-Torso Model with Realistic Geometry. IEEE Trans. Biomed. Eng. 43 (1996) 211-217

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5. Scollan, D.F., Holmes, A., Winslow, R.L.: Histological Validation of Myocardial MicroStructure Obtained from Diffusion Tensor Magnetic Resonance Imaging. Am. J. Physiol. 275 (1998) H2308-H2318 6. Liu, F., Lu, W., Xia, L. and Wu, G.: The Construction of Three-Dimensional Composite Finite Element Mechanical Model of Human Left Ventricle. JSME Int. J. C44 (2001) 125-133 7. Haber, I., Metaxas, D.N., and Axel, L.: Using Tagged MRI to Reconstruct A 3D Heartbeat. IEEE Comput. Sci. Eng. 2 (2000) 22-34 8. Haber, I., Metaxas, D.N., and Axel, L.: Three-Dimensional Motion Reconstruction and Analysis of the Right Ventricle Using Tagged MRI. Med. Imag. Ana. 4 (2000) 335-255 9. Young, A.A., Fayad, Z.A., and Axel, L.: Right Ventricular Midwall Surface Motion and Deformation Using Magnetic Resonance Tagging. Am. J. PhysioL. 271 (1996) H2677H2688 10. Chang, F.K., Perez, J.L., and Chang, K.Y.: Analysis of Thick Laminated Composites. J. Compos. Mater. 24 (1990) 801-822 11. Tokuda, M., Sekioka, K., Ueno, T., Hayashi, T., Havlicek, F. and Sawaki, Y.: Numerical Simulator for Estimation of Mechanical Function of Human Left Ventricle (Study of Basic System). JSME Int. J. A37 (1994) 64-70 12. Beyar, R. and Sideman, S.: A Computer Study of the Left Ventricular Performance Based on Fiber Structure, Sarcomere Dynamics, and Transmural Electrical Propagation Velocity. Circ. Res. 55 (1984) 358-375

Growing RBF Networks for Function Approximation by a DE-Based Method Junhong Liu, Saku Kukkonen, and Jouni Lampinen Lappeenranta University of Technology, Department of Information Technology, PO Box 20, 53851 Lappeenranta, Finland {junhong.liu, Saku.Kukkonen, jlampine}@lut.fi

Abstract. The Differential Evolution (DE) algorithm is a floating-point encoded Evolutionary Algorithm for global optimization. It has been demonstrated to be an efficient, effective, and robust optimization method especially for problems containing continuous variables. The paper concerns applying a DE-based method to perform function approximation using Gaussian Radial Basis Function (RBF) networks with variable widths. This method selects centres and decides weights of the networks heuristically, then uses the Differential Evolution algorithm for local and global tuning iteratively to find the widths of RBFs. The method is demonstrated by training networks that approximate a set of functions. The Mean Square Error from the desired outputs to the actual network outputs is applied as the objective function to be minimized. A comparison of the net performances with other approaches reported in the literature has been performed. The proposed approach effectively overcomes the problem of how many radial basis functions to use. The obtained initial results suggest that the Differential Evolution based method is an efficient approach in approximating functions with growing radial basis function networks and the resulting network generally improves the approximation results reported for continuous mappings. Keywords: Radial Basis Function, Neural Network, Differential Evolution, Evolutionary Algorithm.

1

Introduction

Radial Basis Functions (RBFs) emerged as a variant of artificial neural networks in the late 80’s. RBFs are embedded in a three-layer network, i.e., the input layer, the hidden layer, and the output layer. Each unit in the hidden layer implements a radial activation function. The output units implement a weighted sum of hidden unit outputs. Approximation capabilities of RBFs have been studied in [10, 8]. Due to their nonlinear approximation properties, RBF networks are able to model complex mappings. The performance of a trained RBF network depends on variable factors, like the number of the RBFs as well as their locations, shapes, weights, and the method used for learning the input-output mapping. Different approaches J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 399–406, 2004. c Springer-Verlag Berlin Heidelberg 2004


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[1, 2, 4, 6, 9, 11, 15, 16] for training RBF networks have been developed and can be divided into three categories: (i) learning the centres and widths in the hidden layer; (ii) learning the connection weights from the hidden layer to the output layer; (iii) learning the network structure; and (iv) hybrid learning: learning the centres, widths, weights, or the network structure together. Among these approaches, evolutionary techniques become outstanding, because they do not require high order derivatives when applied to nonlinear optimization problems, especially those with stochastic, temporal, or chaotic components. One of such technique is the Differential Evolution (DE) algorithm introduced by Price and Storn [12], a floating-point encoded Evolutionary Algorithm (EA) for global optimization. This paper introduces a DE-based method for finding the set of Gaussian RBFs with variable widths to provide the best function approximation. The DE-based method, characterized as a growing method, can be classified in Category (iv), starting with a single hidden node network and iteratively growing the network. A centre plus its weight is decided heuristically based on the difference between the desired outputs and the actual outputs of the existing RBF network. The adaptation of widths is conducted using DE locally and globally. The paper is structured as follows: the formulation of an optimization problem is explained in Sect. 2; Sect. 3 describes the optimization system of RBF networks using the DE-based method—how to combine iteratively the selection and training procedures to learn the network structure and the widths in order to achieve an overall efficient method; experimental results are shown in Sect. 4; and the conclusion is given in Sect. 5.

2 2.1

Optimization Problem Formulation Gaussian Radial Basis Function Networks

RBFs have their origin in the solution of the multivariate interpolation problem [3]. An arbitrary function g(v) :
d →
can be approximate by mapping, using a RBF network with a single hidden layer of p units: g
(v, x) =

p  j=1

wj rj (v, σj , cj ) =

p 

wj φj (σj , v − cj ),

(1)

j=1

where v ∈
d ; x is the vector of all variables including w0 , wj , σj , and cj ; p denotes the number of basis functions; w = (w1 , w2 , ..., wp )T are the weight coefficients; rj (·) represents the d-dimensional activation function (also known as the radial basis function) from
d to
; cj , j = 1, 2, ..., p, are the centres of the basis functions; σj , j = 1, 2, ..., p, are the widths, which are called scaling factors for the radii v − cj , j = 1, 2, ..., p, of the basis functions, respectively; and φ(·) is a non-linear function that monotonically decreases (or increases) as v moves away from cj .

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401

In order to simplify the notation, coordinate axes-aligned Gaussian RBF functions are used. When a 1-dimensional Gaussian radial basis function is centred at the centroids cj , it follows from (1) that g
(v, x) =

p 

−

wj e

j=1


v−cj
2 2σ 2 j

=

p 

−

wj e

(v−cj )2 2σ 2 j

,

(2)

j=1

where x is the vector of all variable factors and can be written as xT = (w1 , ..., wj , ..., wp , σ1 , c1 , ..., σj , cj , ..., σp , cp )T .

(3)

The network can be trained to approximate an unknown function g(v) by finding the optimal vector x given (possibly noisy) training set V = {(vn , yn ) | n= 1, 2, ..., N, vn ∈
d , yn ∈
}. 2.2

Objective Function

The objective function is defined as to minimize the Mean Square Error (MSE): f (x) =

2.3

N  1  yn − g
(vn , x) . N n=1

(4)

Brief Description of the Differential Evolution Algorithm

The optimization target function is of the form f (x) :
D →
.

(5)

The optimization objective is to minimize the value of the target function by finding the optimal values of vector x, which is composed of D objective function parameters. The parameters of the target function are also subject to lower and (L) (U ) upper boundary constraints x(L) and x(U ) : xk ≤ xk ≤ xk , k = 1, 2, ..., D. DE is a parallel direct search method with three control parameters, which remain constant during the optimization process (mutation amplification, crossover operator, and the number of population members) that utilizes D-dimensional parameter vectors, xi,G , i = 1, 2, ..., Npop , as a population for generation G.

3 3.1

Optimization of Gaussian Radial Basis Function Networks by a Differential Evolution Based Method Control Parameters’ Setting of DE

The control parameters’ setting affects the performance of DE, its values were chosen based on discussions in [13, 5] and are given in Table 1.

402

J. Liu, S. Kukkonen, and J. Lampinen Table 1. Control parameters’ setting of DE

3.2

Variable

Value

Strategy

DE/rand/1/bin

Crossover operator: Cr

0.9

Mutation amplification: F

0.9

Number of population members: Npop

100

Differential Evolution Based Method

Training. The entire sample points in training set V are used for training. vn ∈
d , n = 1, 2, ..., N , possible centre candidates are in set Ve and each can only be chosen once. Initially the number of hidden nodes, p, is zero. 1. (i) p is increased by 1; and (ii) the sample pair (vi , yi ) from set Ve , for which the function approximation is the worst—having the highest difference between the desired output and the actual output of the existing RBF network (i.e., before adding the new node), is chosen to be taken away from Ve as a new node centre, i.e., yi − g
p−1 (vi ) = max{yn − g
p−1 (vn ), (vn , yn ) ∈ Ve , n = 1, 2, ..., N − p + 1}, where g
p−1 is the existing Gaussian RBF network. 2. Growing: (i) the chosen node vi is added to centres’ set C ={cji | j = 1, 2, ..., p, i = 1, 2, ..., d}, where p is the number of hidden nodes present in the RBF network; (ii) the weight of the node is set as wp = yi − g
p−1 (vi ), i.e., the error between the desired output and the existing RBF network output. 3. Local tuning: find the width of this newly added node after Glocal generations, using DE. Each newly generated parameter vector mentioned in Sect. 2.3 of a population is based on the boundaries of the discussed function, v

(U )

−v

(L)

(U )

(L)

g(v), i.e., xji ∈ (0, i 2 i ], where vi and vi are the upper and lower limits of the defined region of the computed function. 4. Global tuning: the widths of the entire RBF network are learned after Gglobal generations, using DE, setting dimensionality D = p. 5. Criterion: if f (x) ≥ f and Ve =∅, where f is a threshold, go to Step 1. Otherwise, stop the process. Testing. For each function, testing set Vt is different from V and contains the same number of testing samples as in the training set, but are uniformly distributed random values in the function domain.

4

Experimental Results and Analysis

The proposed approach is applied to single-input and single-output test functions in Table 2 without any disturbance.

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403

Table 2. Test functions Index

Test function

1

A Hermite polynomial: g1 (v) = 1.1 · (1 − v − 2v 2 ) · e−v

2

g2 (v) = sin(12v), v ∈ [0, 1]

3

g3 (v) = sin(20v 2 ), v ∈ [0, 1]

4

g4 (v) = 1 + (v + 2v 2 )sin(−v 2 ), v ∈ [−4, 4]

5

g5 (v) = sin(v) + sin(3v) + sin(5v), v ∈ [−0.35, 3.5]

6

g6 (v) = 0.5 · e−v ·sin(6v), v ∈ [−1, 1]

7

g7 (v) = sin(v) + sin(3v) + sin(6v), v ∈ [−0.35, 3.5]

8

g8 (v) =

9

g9 (v) = v, v ∈ [0, 1]

4

n=1



n · e−n

2

·(v−4+2n)2

2

/2

, v ∈ [−4, 4]



, v ∈ [−4, 4]

For a continuous function g(v), the input is considered as data set V , containing N data points in the function’s defined region: V = {(vn , yn ) ∈
d ×
, 1 ≤ n ≤ N, yn = g(vn )}, where d denotes the dimension of the discussed function g(v), i.e., d = 1 for a single input function, and vn , n = 1, 2, ..., N , are N uniformly spaced noiseless points in the defined region of the computed function. The functions in Table 2 were tested. The approach performed with the control parameters set in Table 1 and N = 101. Key experimental results are: 1. Fig. 1 shows the examples of the net functions in Table 2, the approximated functions as well as their individual composing RBFs, and the convergence histories: (i) g8 can be represented by a network of four hidden nodes with the objective function value 1.8868 · 10−5 ; and (ii) g9 can be represented by a network of eight hidden nodes with the objective function value 7.6906·10−6 . 2. Table 3 lists the numerical results of the experiments. 3. As can be seen from Fig. 1 and Table 3, the DE-based approach is effective with respect to the objective function in approximating the original functions with growing RBF networks and the proposed method is efficient since most of the functions in Table 2 can be represented by a certain number of RBFs with very small error, for example, for g1 , the maximum approximation error is 2.24 · 10−2 and the standard deviation is 5.4 · 10−3 and the maximum testing error is 1.64 · 10−2 with the standard deviation 5.3 · 10−3 , for g2 , the maximum approximation error is 8.24 · 10−2 and the standard deviation is 9.4 · 10−3 and the maximum testing error is 3.01 · 10−2 with the standard deviation 5.5 · 10−3 and so on. 4. Table 4 shows the comparisons between the DE-based method (short as DE) and the method (short as EA) proposed by Esposito et al. [4] for functions g5 , g6 , g8 , and g9 . Esposito et al. proposed an incremental algorithm for growing RBF networks by means of an evolutionary strategy and showed their strategy can achieve better performance than a greedy algorithm [14]

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a.

b.

c.

d.

e.

f.

Fig. 1. Examples of original functions, approximations as well as the decomposition of individual RBF networks, and convergence histories. (i) a and b: net functions g8 and g9 ; (ii) c and d: the decomposition of respective RBF networks approximating functions g8 and g9 ; (iii) e and f: respective convergence histories (Figure legends in c and d: “·” network output;“–” individual RBF)

and Wavelet Neural Network [17] both in terms of net size and in terms of computation time. Setting the sizes of training set and testing set the same as reported by the authors for each function, the DE-based method got worse results than their method for g5 but better solutions for the rest three.

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405

Table 3. Experimental results Test

p

Training

Function

Training error

(10−5 )

Testing

Maximum error

std

(10−2 ) (10−3 )

g1 (v)

16

9.4648

2.24

g2 (v)

10

18.412

g3 (v)

14

86.318

g4 (v)

22

g5 (v) g6 (v)

Testing error

Maximum

(10−5 )

error

std

(10−2 ) (10−3 )

5.4

13.142

1.64

5.3

8.24

9.4

11.533

3.01

5.5

7.07

17.9

77.32

6.97

16.8

190260

813.61

105.79

181710

708.31

990.7

10

49.735

5.13

13.2

52.135

5.16

1.31

7

11.842

4.42

6.7

7.1339

2.08

5

g7 (v)

10

190

11.74

27.5

160

11.74

25.5

g8 (v)

4

1.8868

1.88

3.7

1.4703

g9 (v)

8

0.76906 1.51 2 0.71346 Note: std stands for standard deviation.

1.88

3.2

1.02

1.8

Table 4. Comparisons Func- Algo- N

p

tion rithm

Training Maximum

−5

−2

error(10

5

Testing

Training

g5 (v) DE

40

9

420

g5 (v) EA

40

6

500

g6 (v) DE 100

9

2.1354

g6 (v) EA 100

25

0.11

g8 (v) DE 400

5

15.668

g8 (v) EA 400

6

22

g9 (v) DE 500

6

0.87505

g9 (v) EA 500

6

)

error

(10

11.89 2.16

)

Testing error

(10

−5

Maximum )

error

(10−2 )

1010

36.25

400

18

1.9292

1.53

0.42 9.190

12.326

3.85

24 1.55

0.94226

1.32

1.4

Conclusions

The DE-based method was applied to growing Gaussian RBF networks. The method starts from a single-hidden-node network and finally achieves a minimum network through an iterative procedure of local tuning and global tuning. The choice of the optimal network parameters corresponds to the minimum Mean Square Error between the desired outputs and the actual network outputs. A set of continuous functions were used to demonstrate the approach. The proposed approach effectively overcomes the problems of how many RBFs to use. The

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results obtained from this initial investigation suggest that the DE-based method is efficient and effective in approximating functions with growing RBF networks, and further studies on complicated and high dimensional data are therefore motivated and needed.

References 1. Alexandridis A., Sarimveis H., and Bafas G.: A new algorithm for online structure and parameter adaptation of RBF networks. Neural Networks 16 (2003) 1003-1017 2. Billings S. A. and Zheng G. L.: Radial basis function networks configuration using genetic algorithms. Neural Networks 8(6) (1995) 877-890 3. Broomhead D. S. and Lowe D.: Multivariable functional interpolation and adaptive networks. Complex Systems 2 (1988) 321-355 4. Esposito A., Marinaro M., Oricchio D., and Scarpetta S.: Approximation of continuous and discontinuous mappings by a growing neural RBF-based algorithm. Neural Networks 13 (2000) 651-665 5. Lampinen J. and Zelinka I., On stagnation of the differential evolution algorithm. Proc. 6th Int’l Conf. on Soft Computing (MENDEL 2000), Brno, Czech Republic, June 7-9 2000 (2000) 76–83 6. Leonardis A. and Bischof H.: An efficient MDL-based construction of RBF networks. Neural Networks 11 (1998) 963-973 7. Musavi M. T., Ahmed W., Chan K. H., Faris K. B., and Hummels D. M.: On the training of radial basis function classifiers. Neural Networks 5 (1992) 595-603 8. Park J. and Sandberg J. W.: Universal approximation using radial-basis-function networks. Neural Computation 3 (1991) 246-257 9. Plagianakos V. P. and Vrahatis M. N.: Neural network training with constrained integer weights. Proc. 1999 Congress on Evolutionary Computation, Washington, DC USA, 6-9 July 1999 3 (1999) 2007-2013 10. Poggio T. and Girosi F.: Networks for approximation and learning. Proc. IEEE, MIT, Cambridge, MA, USA September 1990 78(9) (1990) 1481-1497 11. Schmitz G. P. J. and Aldrich C.: Combinatorial evolution of regression nodes in feedforward neural networks. Neural Networks 12 (1999) 175-189 12. Storn R. and Price K.: Differential Evolution a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4) (December 1997): 341-359 13. Storn R. and Price K.: On the usage of Differential Evolution for function optimization. 1996 Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS), Berkeley, CA USA, 19-22 June (1996) 519–523 14. Vinod V. and Ghose S.: Growing nonuniform feedforward networks for continuous mapping. Neural computing 10 (1996): 55-69 15. Wang Z. and Zhu T.: An efficient learning algorithm for improving generalization performance of radial basis function neural networks. Neural Networks 13 (2000) 545-553 16. Zhu Q., Cai Y., and Liu L.: A global learning algorithm for a RBF network. Neural Networks 12 (1999) 527–540 17. Yong F. and Chow T.: Neural network adaptive wavelets for function approximation. Intern report. Department of Electrical Engineering. City University of Hong Kong (1996)

Dual-Source Backoff for Enhancing Language Models Sehyeong Cho MyongJi University, Department of Computer Science, San 38-2 Yong In, KyungGi, Korea [email protected]

Abstract. This paper proposes a method of combining two n-gram language models to construct a single language model. One of the corpora is constructed from a very small corpus of the right domain of interest, and the other is constructed from a large but less adequate corpus. This method is based on the observation that a small corpus from the right domain has high quality n-grams but suffers from sparseness problem, while a large corpus from another domain is inadequately biased, but easy to obtain bigger size. The basic idea behind dual-source backoff is basically the same with Katz’s backoff. We ran experiments with 3-gram language models constructed from newspaper corpora of several millions to tens of millions words together with models from smaller broadcast news corpora. The target domain was broadcast news. We obtained significant improvement by incorporating a small corpus around one thirtieth size of the newspaper corpus.

1 Introduction Language modeling is an attempt to capture the regularities and make predictions, and is an essential component of automatic speech recognition. Statistical language models are constructed from large text, or corpus. However, it is not easy to collect enough spoken language text. Other corpora are readily available, but the difference in spoken and written language leads to a poor quality. This granted, what we need is a way of making use of existing information to help lower the perplexity of the language model. However, simply merging two corpora will not help much, as we shall see later in the next section.

2 Related Work Linear combination is probably the simplest way of combining two language models:

Pcombined ( w | h) =

∑ λ P (w | h) . Linear interpolation has the advantage of k

k

k =1..n

extreme simplicity. It is easy to implement, easy to compute. Linear combination is consistent as far as n-gram models are concerned. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 407–412, 2004. © Springer-Verlag Berlin Heidelberg 2004

408

S. Cho

Maximum entropy method[1] can be used to incorporate two information sources. For instance, suppose we had an n-gram model probability and a trigger pair model probability: P(bank | in, the) and P (bank | loan ∈ history) . When both conditions are satisfied, then maximum entropy method can find a solution without sacrificing the consistency by imposing that the constraints are satisfied on the average. However, if we had the same event space, then Maximum entropy method will result in trouble, because

E

h ends in ' in the'

and h ends

E

in 'in the'

[ P combined

( bank

[ Pcombined

| h )] = P 2 ( bank

( bank

| h )] = P1 ( bank

| in , the )

| in , the )

should both be true.

However they contradict because P1 (bank | in, the) ≠ P2 (bank | in, the) . Akiba [2] proposed using selective backoff. Their approach is similar to ours in that they use backoff with two different models. One of the models is probabilistic model and the other is a grammar network. The aim of their combination is to delete probabilities of all unnecessary n-grams, that is, those that are not possible word sequences according to the simpler grammar-based transition network. Adaptation([3], for example) is a dynamic switching of language models based on the present situation. While adaptation focuses on dynamically detecting the shift among domains or topics, our problems deals with constructing a language model per se by using information from two models.

3 Proposed Approach Define a primary corpus as a corpus from a domain of interest. A secondary corpus is a (relatively larger) corpus, from another domain. A primary language model, then, is a language model constructed from a primary corpus. A secondary language model is a language model constructed from a secondary corpus. primary corpus, and

C1 is the

C2 is the secondary corpus. P1 denotes the probability obtained

by maximum likelihood estimation from the primary corpus. discounted primary probability.

P1 denotes a

P2 and P 2 are likewise defined.

We measured perplexity[4] of spoken language models and written language models against broadcast script. With the same 3-gram hit ratio, the perplexity of the latter is almost twice higher (e.g., 17.5% / 560 / 970). Conversely, with similar perplexity, hit ratio of the primary model is lower. In other words, a small primary

Dual-Source Backoff for Enhancing Language Models

409

model has quality 30gram statistics, while a large, secondary model has simply more 3-grams. Then it would be nice if we had a way of combining the two. Therefore given appropriate sizes, we may be able to take advantage of n-gram probabilities in both models. We assumed that the secondary corpus is at least one order of magnitude larger than the primary corpus. We also assumed primary 3-gram statistics best reflect the actual probability. Next are 3-gram(secondary), 2-gram(primary), 2gram(secondary), 1-gram(primary), and 1-gram (secondary), in order. The basic idea is this: the probability of a trigram x,y,z is calculated from primary 3-gram, if any. If it doesn’t exist, use probability of a trigram x,y, z from secondary 3grams, then primary 2-gram, and so on. In order to be consistent (i.e., sum of probabilities equal to 1), we do as follows, based on Katz’s idea[5]. We first discount[6] the MLE probabilities of the non-zerotons. Let β = 1− P1 ( z | x, y ) . Then we redistribute the mass to zeroton 3-grams (i.e., the 3-

∑

xyz∈C1

gram xyz’s, such that xyz ∉ C1 ), in proportion to either secondary 3-gram probability or primary 2-gram, as in equation 1.

⎧ P1 ( z | xy) ⎪ P ( z | xy) = ⎨ α xy P 2 ( z | xy) ⎪ α P( z | y) ⎩ xy In the above formula,

α xy

α xy =

if xyz ∈ C1 (1)

if xyz ∉ C1 , xyz ∈ C 2 otherwise

is a normalizing constant, defined by equation 2.

∑

xyz∉C1

β P 2 ( z | xy ) +

xyz∈C2

∑ P( z | y)

(2)

xyz∉C1

xyz∉C2

Unlike Katz’s coefficients, there is no simple computation procedure for

α xy , and

thus repeated summation is required, which took hours in a machine with two Xeon 2GHz processors. Fortunately, the calculation needs to be done only once and it need not be calculated in real-time. The 2-gram probability P ( z |

y ) and 1-gram probability are defined in a similar

manner, as in equation 3 and equation4, respectively.

⎧ P1 ( z | y ) ⎪⎪ P( z | y ) = ⎨α y P 2 ( z | y ) ⎪α P ( z ) ⎪⎩ y

if yz ∈ C1 if yz ∉ C1 , yz ∈ C2 otherwise

(3)

410

S. Cho

⎧ P1 ( z ) ⎪⎪ P( z ) = ⎨α 0 P 2 ( z ) ⎪α ′ ⎪⎩ 0

if z ∈ C1 if z ∉ C1 , z ∈ C2 otherwise

(4)

4 Results We used CMU-Cambridge toolkit to construct secondary models in ARPA-format from newspaper corpora (Dong-A Ilbo news) from 4 million to 8 million words. We also constructed 4 primary models from SBS broadcast news corpora (100K to 400K words). Test corpus was a separate SBS broadcast news text of 10K size. By simply mixing up primary and secondary models, we obtained 10 to 17 percent decrease in perplexity. With optimal mixing ratio by linear interpolation, additional 5 to 6% decrease was seen [7]. The result of the dual-source experiment showed around 30% decrease in perplexity. Considering that 20% decrease in perplexity shows notable increase in the accuracy of the speech recognizer, this can be regarded a meaningful result. Table 1. Resulting Perplexity of interpolated model and dual-source backoff model

Size(1-ary/2ndary) 100K/4M 200K/5M 300K/6M 400K/8M

Linear Interpolation (1:1) 377 359 333 300

dual-source backoff 242 244 230 206

5 Discussion The experiment clearly showed some improvement. However, it is not certain if this is indeed the optimal. As we discussed earlier the relative quality of the primary and the secondary n-grams depend on the corpora sizes. For instance, if the size of the primary corpus is very small compared to the secondary model, the secondary 2-gram probability may prove to be more reliable than the primary 3-gram. Lastly, the algorithm needs to be generalized to n-gram models of arbitrary n values. Theoretically, it is a straightforward generalization of equation 4 into equation 5:

⎧ P1 ( wm | w1..n−1 ) ⎪ P ( wm | w1..n−1 ) = ⎨α w1.. n−1 P 2 ( wm | w1..n−1 ) ⎪α ⎩ w1.. n −1 P ( wm | w2..n−1 )

if w1..n ∈ C1 if w1..n ∉ C1 , w1..n ∈ C 2

(5)

otherwise

However, the real problem is in determining the order of applications. This is not merely a theoretical problem, but a practical one, since it may well depend on the

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sizes of the corpora – relative or absolute – and also on the similarity among primary, secondary, and the test corpora. Unigram case is a little more complicated. Actually in the experiment, dual-source backoff is not applied to unigrams (i.e., equation 4), because we found that it has negative impact. The reason is this. Usually, when unknown words appear in a text, they are mapped to a single symbol, sometimes referred to as UNK.(stands for unknown). For practical reasons in speech recognition, this is acceptable. If the speech recognizer hears a word which it doesn’t know, it should say that it doesn’t know it. However, for the purpose of comparing the perplexity – the measure of the quality of a language model – it is not fair. Replacing all “infrequent” words by a single symbol makes the probability of the word higher, thus making the perplexity lower that it actually is.. If one model recognizes the word and the other model doesn’t, then the former should be deemed better. In order to do justice with the complexity, we compare the perplexity of a language model using “complete” vocabulary, or a sufficiently large vocabulary. Given a language model, we assume the probability of an unknown word to be the total probability of unknown word divided by the total number of unknown word types. In effect, we are assuming the language model is using a backoff, by discounting the unigram model. Now, the problem is in determining the discount ratio. The “exact” discount ratio is practically impossible to obtain, but we can obtain an approximate value by using a relatively large corpus. Since we are dealing with very small spoken language corpora, say, some tens or hundreds of thousands of words, a few million words will be enough for obtaining the probability of unknown words.

3300 3100 2900 2700

single backoff dual backoff single, merged corpora

2500 2300 2100 1900 1700 1500

1

2

3

4

5

Fig. 1. Perplexity measures in unigram language models. X-axis indicates the size of the corpora in 100,000 words. The secondary is a 10M newspaper corpus

412

S. Cho

Given that,

α'

is computed as the ratio of appearance of words in the

“purportedly infinite” corpus which were not in

C1 , nor in C2 , divided by such

word types. The result of applying this to a unigram-only dual-source backoff is shown in Figure 1 below[8]. The result in Table 1 does not count for the enhancement that can be obtained through applying 1-gram dual-source backoff. It is clear from Table 1 and Figure 1 that the combination of 1,2,3-gram dual-source backoff will bring further improvement, but the extent of the improvement needs to be seen. We are still working on continued enhancement. Among the plans are: 1) combining 1,2, and 3-gram dual-source models, and 2) dual-source backoff with 4 and higher n-gram models. Acknowledgement. This work was supported by grant R05-2003-000-11830-0 from the Basic Research Program of the Korea Science and Engineering Foundation.

References 1. Rosenfeld, R.: Adaptive Statistical Language Modeling: A Maximum Entropy Approach, Ph.D. dissertation, Carnegie-Mellon University (1994) 2. Akiba, T., Itou, K., Fujii, A., and Ishikawa, T.: Selective Backoff Smoothing for Incorporating Grammatical Constraints into the n-gram Language Model. In: Proc. International Conference on Spoken Language Processing (2002) 881-884 3. Chen, S. F., Seymore, K., and Rosenfeld, R.: Topic Adaptation for Language Modeling using Un-normalized Exponential Models. In: Proc. ICASSP'98, Vol. 2. (1998) 681-684 4. Jelinek, F., Mercer, R. L., Bahl, L. R., and J, K. B.: Perplexity – A Measure of the Difficulty of Speech Recognition Tasks. Journal of the Acoustics Society of America, 62, S63. Supplement 1, (1977) 5. Katz, S.M.: Estimation of Probabilities from Sparse Data for the Language Model Component of a Speech Recognizer. IEEE Transactions on Acoustics, Speech and signal Processing, vol. ASSP-35 (1987) 400-401 6. Good, I.J.: The Population Frequencies of Species and the Estimation of Population Parameters. Biometrica, vol.40, parts3,4 (1952) 237-264 7. Cho, S.: Experimental Results of Applying Dual-source Backoff. Technical Memo TM-CS2004-9, Department of Computer Software, MyongJi University (2004) 8. Cho, S.: A Dual-course Back-off for Exploiting Large Text of Non-spoken Language Corpora in Constructing a Language Model for Speech Recognition: the Case of 1-gram. Tech memo TM-CS-2004-3, Department of Computer Software, MyongJi University (2004)

Use of Simulation Technology for Prediction of Radiation Dose in Nuclear Power Plant Yoon Hyuk Kim and Won Man Park School of Advanced Technology, Kyung Hee University, Yongin-si, Gyeonggi-do, 449-701, Korea [email protected], [email protected] http://web.khu.ac.kr/~vbeslab

Abstract. In this study, a simulation program based on virtual environment concerning radiation work at nuclear power plants was developed. VRML and Java Applet were used to develop this simulation program. Radiation exposure levels were predicted through radiation work in a virtual reality environment, and high dose danger zones were visually represented by graphically visualizing dose rates so that it is possible to predict exposure rates of virtual workers. As a result of the simulation it turned out that the work traffic line that moved to the area where the dose rate concentric circle was light-shaded receives the lowest exposure dose radiation exposure level. According to the conventional method, the shortest work time or the shortest work path has the lowest radiation, but the result of the simulation showed that the exposure dose not depended on only work time, but also the distance between the worker and the radiation source.

1 Introduction In this study the authors developed a simulation program based on virtual environment concerning radiation work at nuclear power plants. VRML and Java Applet were used to develop this simulation program. Radiation exposure levels were predicted through radiation work in a virtual reality environment, and high dose danger zones were visually represented by graphically visualizing dose rates so that it was possible to predict exposure rates of virtual workers.

2 Materials and Methods For the 3D graphic work in this study a commercial graphic program and VRML 97 were used, which is the latest version of the VRML protocol. For modeling control of the VRML language Java Applet was used. VRML enables control through Java EAI. Both VRML and Java Applet are Web languages, and they are executed on the InterThis work was financially supported by MOCIE through IERC program. Corresponding author : Yoon Hyuk Kim, School of Advanced Technology, Kyung Hee University, Korea, (Tel) +82-31-201-2028, (e-mail) [email protected] J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 413–418, 2004. © Springer-Verlag Berlin Heidelberg 2004

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net browser. The environment of the latest Java Applet program development is JDK(Java TM Development Kit) 1.4.2, but for interoperability with VRML through the Applet, JDK 1.1.8 was used in this study. In the simulation program developed in this study, graphic simulation was performed through VRML, and the data resulting from simulations was displayed through the Java Applet instead of the VRML panel (Fig. 1).

Fig. 1. Flow chart of virtual work simulation program

For first-person work VRML's 'NavigationInfo' was used, and for computation of the distance between the worker and the radiation source VRML's 'ProximitySensor' was inserted in the virtual work space, thus enabling the computation of the coordinates of the virtual worker. Java receives the coordinates obtained in VRML and calculates the exposure level, and then displays it in the Applet window. After the work is finished, it is outputted to a data file (Fig. 1). In the simulation program the 'Choice' command was used to apply 8 radioactive materials such as 192Iridium, 51Chromium, 60 Cobalt and 226Radium, and 8 values such as 5, 10, or 40 to the radiation source and radioactivity concentration, and the program was developed in such a way that these values are applied simultaneously to two point isotropic radiation sources. In case Java applet accesses a file in the computer, e.g. executing interconnected programs inside the simulation program and saving the simulation results, 'Security exception' occurs. This is a mechanism for maintaining the stability of the computer system. In this study the authors made arbitrary certificates to take care of the 'Security exception'. If a certificate is made and inserted in the HTML file, a window for accepting the certificate is displayed when the simulation program is executed through the Web browser. Acceptance of the certificate means that Java Applet is allowed to access files in the computer, thereby making it possible to save simulation results in a file and execute interconnected programs. The work space for virtual work simulation was set up as illustrated in Fig. 2. Two identical point isotropic radiation sources (Source Point 1, Source Point 2 in Fig. 2) were assumed in a space 31m wide and 15m high. In a movement starting from the start point (Point 1 in Fig. 2), passing through the two points (Point 2 and Point 3 in

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Fig. 2) and returning to the start point, the traffic line was varied to compare radiation exposure levels. Here, the assumption is that the worker is a point with his/her volume ignored, and the worker's movement velocity is constant.

Unit [m] Fig. 2. Virtual work space with 2 sources on 3 predefined paths

In computing the radiation exposure level in motion by given path is calculated by integrating the dose rate (E) dependent on the distance between the radiation source and the worker with respect to time.

3 Results and Discussion The simulation program consists of two VRML panels and two Java Applet panels (Fig. 3). For the two VRML panels, the 'ViewPoint' of VRML is set up differently in each panel by means of one VRML file so that it is displayed in a different screen. The start and end of simulation is controlled by the 'Button Event' of the Java Applet, and results such as the work time for the performance of work simulation, the distance of movement, the current location, and the dose rate of the current location, and the exposure level are displayed in the Java Applet panel on a real-time basis, and they are saved in a data file after the completion of the simulation. To solve the 'Security Exception' that occurs at this time, the Java Singed Applet was used. Movements in the virtual work space were executed by the arrow keys on the keyboard and the mouse. The 'NavigationInfo' of the VRML used to develop the simulation program enables forward movement and backward movement by means of the ‘↑ and ↓’ buttons on the keyboard, and left and right rotation by means of the ‘← and →’ buttons, thereby making it possible for the simulation performer to move about in the virtual work space. 'NavigationInfo' also supports movement by the drag of the mouse. In addition, 'TouchSensor' was inserted in the door to the virtual work space so that the simulation performer can click on the door to open it and enter the work space. When a radiation source is selected, the radiation exposure level per unit time due to a certain gamma ray can be calculated, and accordingly the dose rate is visualized as a concentric circle shown in the Minimap (panel C) in Fig. 4 (b), (c), (d) so that the simulation performer can visually identify the location where the dose rate is low. Then, it was possible to find the path with a relatively low radiation exposure level,

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since the radiation exposure level was expressed by the integral of the dose rate with respect to time. After simulation is completed, the resulting data file is entered in such programs as Microsoft® Excel(Microsoft Corp. USA) so that the radiation exposure level per hour according to the worker's location and work traffic line can be reexamined. In calculating the radiation exposure level during simulation, the assumption was that the walls surrounding the work space and the door to the work space are completely shut off, with only the radiation exposure in the work space taken into consideration.

(a) Initial scene

(b) Simulation scene 1

(c) Simulation scene 2

(d) Simulation scene 3

Fig. 3. Developed simulation program for calculation & visualization of dose. Panel A : simulation panel. Panel B : data input/output panel. Panel C : Minimap and dose rate distribution display panel. Panel D : simulation control panel

In this simulation 20 Ci 192Ir was selected as the radiation source, and the worker entered the virtual work space through the door. Along the 4 paths such as the work path connecting the areas in low concentration on the Minimap, and the shortest work path, the worker passed the two points (Point 2 & Point 3) and exited the work space through the door. The graphs in Fig. 4 represent the worker's movement path(left) during simulations with different traffic lines and the radiation exposure level and dose rate(right) between jobs.

Use of Simulation Technology for Prediction of Radiation Dose

(a) Path 1 (The path through the areas with dose rates in low concentration on the Minimap)

(c) Path 3 (Rectangular path)

417

(b) Path 2 (The shortest path)

(d) Path 4 (Hybrid path)

Fig. 4. Simulation result about dose variation by paths Table 1. Radiation dose during movement along four different paths in simulation

Path No.

Time [sec]

Movement [m]

Velocity [ms-1]

Dose(E) [mSv]

E/Epath1

1

19.1

69.9

3.66

9.81*10-1

1.00

3.93

1.11*10

0

1.13

1.14*10

0

1.16

1.01*10

0

1.03

2 3 4

16.7 23.0 18.6

65.7 80.3 70.2

3.49 3.77

According to the previous method assuming that the dose rate of the work space is constant, the shortest work path is 13% (2.4 seconds) shorter than the work traffic line that passes the area where the concentric circle is light-shaded, so the exposure level must be lower, but the result of the simulation showed that the exposure level was 13% higher on the contrary. In the shortest movement (path 2), it was possible to reduce the distance of movement and work time, but as it approached the radiation source during movement, it recorded a relatively higher radiation exposure level than Path 1. In addition, path 3 with focus on the distance from the radiation source showed a high exposure dose due to increased work time. The exposure dose received during work is a value determined by a combination of factors such as work time, and the distance between the worker and the radiation source according to the movement path, so reduction of work time alone cannot de-

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crease the exposure dose. As the result of the simulation showed, the work path is an important factor that affects radiation exposure. It is an essential consideration when a work plan is formulated for optimal radiation protection. Therefore, the authors expect that it will be possible to secure a work traffic line capable of ensuring the best radiation protection through selection of an appropriate work path that takes the distance from the radiation source into consideration.

4 Conclusions In this study the virtual reality technology was used to develop a radiation exposure level prediction and dose rate visualization simulation program. The simulation program based on VRML and Java Applets was developed to calculate the radiation exposure level of the worker during radiation work, and the dose rate was visualized by means of a concentric circle around the radiation source. To this end, the radiation exposure level computation expression was derived through numerical analysis, and Java EAI and Java Signed Applet were used. By means of the dose rate distribution visualized by the concentric circle around the radiation source through the virtual work simulation program, high-dose danger zones were visually represented so that it was possible to predict work paths more favorable in terms of radiation protection. In addition, work simulation was performed to compute radiation exposure levels, and through graphic representation utilizing the file in which the results of simulation of work time, movement distance and radiation exposure levels are saved, work paths were visually verified, and problems of each path were identified. The results of simulation performance showed that exposure levels varied depending on work paths.

References 1. 2. 3. 4. 5.

VRML 97, International Specification ISO/IEC IS 147772-1, http://www.vrml.org (1997) Java Development Kit 1.4.2 , http://java.sun.com/j2se/1.4.2 Java Development Kit(JDKTM) 1.1.x-Signed Applet, http://java.sun.com/security/ ICRP, Recommendations of the ICRP, ICRP pub. 60, Pergamon Press (1991) Fumizawa, M., Kameda, A., Nakagawa, T., Wu, W., Yoshikawa, H.: Development of Simulation-based Evaluation System for Iterative Design of Human-machine Interface in Nuclear Power Plant-Application for Reducing Workload. Nuclear Technology 141 (2003) 78-87 6. Hornaes, A., Hulsund, J. E., Végh, J., Major, C., Horváth, C., Lipcsei, S., Kapocs, G.: The EOP Visualization Module Integrated into the Plasma On-Line Nuclear Power Plant Safety Monitoring and Assessment System. Nuclear Technology 135 (2001) 123-130

A Numerical Model for Estimating Pedestrian Delays at Signalized Intersections in Developing Cities Qingfeng Li, Zhaoan Wang, and Jianguo Yang School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China [email protected] {zawang, yjg}@xjtu.edu.cn

Abstract. Considering the traffic situations in developing cities like Xi’an, China, a numerical model is developed to estimate pedestrian delays at signalized intersections. In the model, signal cycle is divided into a series of subphases, and each subphase lasts 1 second. The model estimates the average conflicting vehicle flow rate for each subphase firstly, and next estimates the average delay of pedestrians arriving during each subphase using probability theory and gap acceptance theory, and then estimates the overall average delay by aggregating the average delay of pedestrians arriving during each subphase. Finally, field data collected from a crosswalk at a signalized intersection in Xi’an are used to validate the numerical model, and the validation results indicate that the model is able to estimate pedestrian delays accurately.

1 Introduction Pedestrian delay, which is defined as the additional travel time experienced by pedestrians, is the key performance index to evaluate intersections’ level-of-service (LOS) for pedestrians [1]. Therefore, basing on the studies conducted in developed cities, several models for estimating pedestrian delays at signalized intersections have been developed [1-6]. However, at signalized intersections in developing cities like Xi’an, China, traffic situations are significantly different. Though vehicles usually comply with traffic signals, the signal noncompliance rates of pedestrians arriving during nongreen phases are usually quite high. And since vehicles start and run slower, and drivers get used to pedestrians’ signal noncompliance, pedestrians usually can cross successfully during non-green phases. Therefore, in this paper a numerical model is proposed to estimate pedestrian delays at signalized intersections in developing cities like Xi’an. The model divides signal cycle into a series of subphases, and each subphase lasts 1 second. It estimates the average conflicting vehicle flow rate for each subphase firstly, and then estimates the average delay for pedestrians arriving during each subphase using probability theory and gap acceptance theory, and finally obtains the overall average pedestrian delay by aggregating the average delay of pedestrians arriving during each subphase. And the model is validated using the field data collected from a crosswalk at a signalized intersection in Xi’an. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 419–424, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 A Numerical Model At signalized crosswalks, usually there are 3 kinds of phases for pedestrians: green phases, clearance phases and red phases. In China, a clearance phase usually includes two parts: the signal is flashing green during the first part, and the signal is all-red during the second part, i.e., both pedestrians and pedestrians’ conflicting vehicles receive red signals. At the beginning, pedestrians are divided into two groups: complying pedestrians and opportunistic pedestrians. Complying pedestrians are not willing to enter crosswalks during non-green phases even if there are acceptable gaps. Opportunistic pedestrians are willing to enter crosswalks during non-green phases if there are acceptable gaps. The average delay of complying pedestrians can be estimated accurately using the model proposed by Braun and Roddin [2], and then it can be integrated into the overall average delay if the percentage of complying pedestrians is known. Therefore, the key problem the numerical model needs to solve is the estimation of the average delay of opportunistic pedestrians. And considering that walking directions might influence pedestrian delays at signalized intersections, the numerical model estimates respectively the delays of downward-to-upward (D2U) pedestrians, who encounter the downward vehicle flow firstly, and the delays of upward-to-downward (U2D) pedestrians, who encounter the upward vehicle flow firstly. Here the downward vehicle flow is the vehicle flow leaving an intersection, and the upward vehicle flow is the vehicle flow entering an intersection. For the purpose of simplification, it is assumed that pedestrians do not influence each other; the walking speeds and the critical acceptable gaps of pedestrians arriving during the same subphase are the same; pedestrians decide wait or walk according to the vehicle flow faced, but the other vehicle flow does not influence pedestrians’ decisions; pedestrians do not influence vehicles; the control scheme adopted by intersections is pre-timed two-phase control, which is the most popular control scheme in Xi’an; and there is no vehicle queue overflow. 2.1 Estimation of Conflicting Vehicle Flow Rates Let qU be the average upward vehicle flow rate and qD be the average downward vehicle flow rate. And the algorithm for qU and qD estimation is as follows. Firstly, the signal cycle is divided into two parts. For the upward vehicle flow, the first part includes the green phase, the flashing green phase, the all-red subphases, and the subphases when vehicles recognize signal, start and arrive at the crosswalk. And all the other subphases are included in the second part. For the downward vehicle flow, the first part includes the medium and latter subphases of the green phase, the flashing green phase, the all-red subphases, and the subphases when the vehicles from the opposite approach recognize signal, start and arrive at the crosswalk. And the second part includes the other subphases of the red phase and the former subphases of the green phase, when the remaining vehicles from the opposite approach cross the crosswalk. Secondly, qU and qD for each subphase during the first part of the cycle are estimated. For the upward vehicle flow, if right-turn-on-red (RTOR) is permitted, and

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there is an exclusive lane for right-turn, right-turn vehicles cross the crosswalk uniformly during the first part of the cycle; or else, qU is zero. For the downward vehicle flow, right-turn and left-turn vehicles from the other two approaches cross the crosswalk uniformly during the first part of the cycle. Thirdly, qU and qD for each subphase during the second part of the cycle is estimated. For the upward vehicle flow, the second part of the cycle begins with saturation flow, and then qU decreases gradually. The basic idea of the algorithm is to estimate the distribution of queue length, and then determine the probability of no queue during each subphase, and finally determine qU for each subphase. Assume vehicles arrive randomly with uniform distribution, let n be the number of vehicles arriving within a cycle, then n satisfies Poisson distribution:

P{n = k} =

λk exp(−λ ) k!

, k = 0, 1, 2, ... ,

(1)

where λ is the mean of n. Assume the newly arriving vehicle is also queued if there is a queue, then,

l = RE

snRE , n nRE n n 2 RE n + + +" = C Cs C C 2 s 2 C Cs − n

(2)

where l is the queue length, s is the saturation flow rate, RE is the effective red time for conflicting vehicles, and C is the signal cycle length. And then, according to the correspondence between l and n, the probability distribution of l can be determined. Assume the queue dissipates with saturation flow rate, the probability of no queue during each subphase can also be determined. Next, assume the flow rate equals saturation flow rate when there is queue, and the flow rate equals arrival flow rate when there is no queue (if arrival flow rate is not greater than saturation flow rate), qU for each subphase can be determined. The algorithm to estimate qD for each subphase during the second part of the cycle is a little bit different. At the beginning of the second part of the cycle, the through vehicles from the opposite approach cross the crosswalk, and the flow rate is the saturation flow rate of the opposite approach multiplied by the percentage of though vehicles at the opposite approach. And if RTOR is permitted, and there is an exclusive right-turn lane, the right-turn vehicles from another approach cross the crosswalk uniformly. 2.2 Estimation of Pedestrian Delays After the determination of qU and qD for each subphase, the probability of no vehicle during each subphase can be estimated. Since the average headway is about 2 seconds for saturation vehicle flow at a lane, and a subphase lasts only 1 second, it is reasonable to assume that at most one vehicle crosses the crosswalk during a subphase at a lane. And then, according to the classical probability model,

p = (1 − q / N ) N , q / N < 1 ,

(3)

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where p is the probability of no vehicle within the subphase, N is the number of lanes for the vehicle flow, q is the vehicle flow rate. Next, the average delay for pedestrians arriving during each subphase can be estimated. Pedestrian critical acceptable gap and walking speed are two key parameters here. During the latter part of green phases, flashing green phases, and the former part of red phases, to avoid big delays, pedestrian critical acceptable gaps are smaller, and walking speeds are higher. These subphases are named special subphases. For pedestrians arriving during the m-th subphase, according to the classical probability model, the probability distribution of delays received during the crossing of one vehicle flow is,

P{d = 0} = p (m ) p (m + 1)… p ( m + [t c ] − 1)

, (1 − (t c − [t c ]) + (t c − [t c ]) p ( m + [t c ])) P{d = 1} = (1 − P{d = 0}) p (m + 1) p (m + 2)… p ( m + [t c ])

(1 − (t c − [t c ]) + (t c − [t c ]) p (m + [t c ] + 1))

,

P{d = 2} = (1 − P{d = 0} − P{d = 1}) p (m + 2) p (m + 3)… p (m + [t c ] + 1) (1 − (t c − [t c ]) + (t c − [t c ]) p (m + [t c ] + 2)) ……

(4) ,

where tc is the critical acceptable gap, and [tc] is the integral part of tc. And similar method can also be used to determine the probability distribution of the delays received during the crossing of the other vehicle flow. And finally the average delay for the pedestrians arriving during the subphase can be determined. Finally, the overall average delay of D2U and U2D pedestrians can be estimated respectively, by averaging the average delay of pedestrians arriving during each subphase. Non-random arrivals can be considered if pedestrian arrival patterns are known. And if the percentage of complying pedestrians is known, their delays can also be considered in the overall average delay estimation.

3 Model Validations The data used in model validations were collected from the crosswalk on the eastern leg of the intersection of West Xianning Road and South Xingqing Road in Xi’an, China. The phase plan adopted by the intersection is pre-timed two-phase control, and RTOR is permitted at the intersection. The signal cycle length is 123 seconds. For the crosswalk, there are 45 seconds for the green phase, 2 seconds for the flashing green phase, and 76 seconds for the red phase. And the red phase for conflicting vehicles begins 2 seconds ahead of the green phase for pedestrians, but ends 2 seconds later. To decrease data amount requirements, the subphase in the field study is longer than the subphase in the numerical model. The pedestrian green phase is divided into 5 subphases (PG1-PG5), 10 seconds each, except that 7 seconds for PG5 (the 2second flashing green phase is included in PG5). The pedestrian red phase is divided into 8 subphases (PR1-PR8), 10 seconds each, except that 6 seconds for PR1.

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Average delay (sec)

In field data collection, firstly 5 hours were chosen to take videos in the tall buildings near the intersection. The hours were selected under the condition that the weather is sunny or cloudy, during 3:00 p.m. to 5:00 p.m., from July 7 to July 10, 2003 (all the days are ordinary workdays). And then, playing back the videos, the delay and the arriving subphase of each pedestrian were measured. Totally 1050 D2U pedestrians and 634 U2D pedestrians were recorded. The major parameters of the model are estimated as follows. For the upward vehicle flow, the first part of the cycle includes subphase 1-55, the second part includes subphase 56-123; for the downward vehicle flow, the first part includes subphase 1165, and the second part includes subphase 66-123 and subphase 1-10. The critical acceptable gap is 4.2 seconds for D2U pedestrians, 4.5 seconds for U2D pedestrians during usual subphases, and 3 seconds for both during special subphases. And the time needed to cross one vehicle flow is 6 seconds during usual subphases, and 3 seconds during special subphases. For U2D pedestrians, the special subphases are subphase 43-52; for D2U pedestrians, the special subphases are subphase 43-57. Besides, all pedestrians are assumed to be opportunistic. Model inputs are mainly average vehicle flow rates and saturation flow rates, which are set using the data collected within about 30 minutes. As the upward vehicle flow is concerned, the average vehicle flow rate is 0.32 veh/sec, and no vehicle crosses the crosswalk during green phases. And the saturation flow rate for the upward vehicle flow is 0.64 veh/sec. As the downward vehicle flow is concerned, the average through vehicle flow rate from the opposite approach is 0.19 veh/sec, the average left-turn vehicle flow rate is 0.03 veh/sec, and the average right-turn vehicle flow rate is 0.12 veh/sec. And the highest vehicle flow rate from the opposite approach is 0.44 veh/sec. And then, after implementing the numerical model using MATLAB, estimations of pedestrian delays are obtained by executing the model, and then compared with field measurements to perform validations, as show in Fig. 1 and Fig. 2. Since each subphase lasts only 1 second in the numerical model, but 6-10 seconds in the field study, the estimated average delay used in comparison is actually the mean of estimated average delays of pedestrians arriving during several subphases.

30 20

Measured Estimated

10 0 PG1 PG2 PG3 PG4 PG5 PR1 PR2 PR3 PR4 PR5 PR6 PR7 PR8

Arriving Subphase Fig. 1. Comparison of measured and estimated average delay of D2U pedestrians

Q.F. Li, Z.A. Wang, and J.G. Yang

Average delay (sec)

424

40

Measured

30

Estimated

20 10 0

PG1 PG2 PG3 PG4 PG5 PR1 PR2 PR3 PR4 PR5 PR6 PR7 PR8

Arriving Subphase Fig. 2. Comparison of measured and estimated average delay of U2D pedestrians

The comparison results indicate that the numerical model is able to estimate the average delay of pedestrians arriving during each subphase with satisfactory accuracy. Therefore, if pedestrian arrival patterns are known, the numerical model is also able to estimate overall average delay accurately.

4 Conclusions Considering the traffic situations in developing cities like Xi’an, a numerical model is proposed to estimate pedestrian delays at signalized intersections. And the model is validated using the field data collected from a crosswalk at a signalized intersection in Xi’an, and the validation results indicate that the model is able to estimate pedestrian delays accurately.

References 1. Transportation Research Board: Highway Capacity Manual. National Research Council, Washington, D.C. (2000) 2. Braun, R., Roddin, M.: Quantifying the Benefits of Separating Pedestrians and Vehicles. National Research Council, Washington, D.C. (1978) 3. Rouphail, N., Hummer, J., Milazzo II, J., Allen, P.: Capacity Analysis of Pedestrian and Bicycle Facilities: Recommended Procedures for the "Pedestrians" Chapter of the Highway Capacity Manual. U.S. Department of Transportation, Washington, D.C. (1998) 4. Virkler, M.: Pedestrian Compliance Effects on Signal Delay. Transport. Res. Rec. 1636 (1994) 88-91 5. Pretty, R.: The Delay to Pedestrians and Vehicles at Signalized intersections. ITE J. 49 (1979) 20-23 6. Hunt, J.G., Al-Neami, A.H.K.: Effectiveness of Pedestrian Facilities at Signal Controlled Junctions. P. I. Civil Eng.-Transp. 111 (1995) 268-277

Feature Selection with Particle Swarms Yu Liu1 , Zheng Qin1,2 , Zenglin Xu1 , and Xingshi He3 1

3

Department of Computer Science, Xian JiaoTong University, Xian 710049, P.R. China [email protected] http://www.psodream.net 2 School of Software, Tsinghua University, Beijing 100084, P.R. China Department of Mathematics, Xian University of Engineering Science and Technology, Xian 710048, P.R. China

Abstract. Feature selection is widely used to reduce dimension and remove irrelevant features. In this paper, particle swarm optimization is employed to select feature subset for classification task and train RBF neural network simultaneously. One advantage is that both the number of features and neural network configuration are encoded into particles, and in each iteration of PSO there is no iterative neural network training sub-algorithm. Another is that the fitness function considers three factors: mean squared error between neural network outputs and desired outputs, the complexity of network and the number of features, which guarantees strong generalization ability of RBF network. Furthermore, our approach could select as small-sized feature subset as possible to satisfy high accuracy requirement with rational training time. Experimental results on four datasets show that this method is attractive.

1

Introduction

Feature selection is widely used as the first stage of classification task to reduce the dimension of problem, decrease noise, improve speed and relieve memory constraints by the elimination of irrelevant or redundant features. Basically, there are two types of approaches for feature selection [1,2,3] : filter approach where feature selection process occurs before and is independent to learning algorithms, and wrapper approach where feature selection is seen as a subroutine and feature subsets are evaluated by the learning algorithms. The wrapper approach is generally better because the search of optimum is guided by the learning algorithm in order to get good measures of accuracy and efficiency [4]. Genetic algorithms are often used to select feature subsets. Using genetic algorithm to perform feature selection requires many iterations. If the learning algorithm is an iterative one, the computational cost of the whole process would be very expensive, since in each iteration learning algorithm is used to evaluate the fitness for every individual. Most learning algorithms for neural networks are iterative methods. Therefore, it is infeasible to directly adopt these learning algorithms in feature selection for neural networks because of too expensive J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 425–430, 2004. c Springer-Verlag Berlin Heidelberg 2004


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computational cost. The combination of feature selection and neural network classifier as wrapper approach is a challenge task. Yang et. al [5] used a fast constructive neural network learning algorithm called DistAL, which is not iterative, to build the neural network classifier for the evaluation of feature selection. But the no-iterative learning method [6] can just train multiple layer networks of threshold logic units. Brill et. al [7] employed nearest-neighbor error estimation for feature selection due to spending less time compared with the corresponding neural network estimation. Subsequently, a counterpropagation network (CPN) was constructed with only the selected features as inputs. The success of this method strongly depends on the close relationship of nearest-neighbor classifier and counterprogagation neural network. The above two methods can just work on special neural networks. This paper proposes a novel method to resolve the problem of feature selection for neural network classifier as wrapper approach. The new method is that feature selection and neural networks training are processed at the same time by Particle Swarm Optimization (PSO), which do not depends on special neural networks. This method is simple and practical because there is no iterative sub-algorithm in each iteration of PSO algorithm. The rest of this paper is organized as follows: Section 2 gives the description of PSO algorithm.Section 3 presents our PSO solution to the combination of feature selection and neural network training. Section 4 presents and analyzes the experimental results on 4 UCI data sets. Finally, Section 5 gives conclusions.

2

Particle Swarm Optimization

Particle Swarm Optimization (PSO), a new population-based evolutionary computation technique inspired by social behavior simulation, was first introduced in 1995 by Eberhart and Kennedy [8]. PSO is an efficient and effective global optimization algorithm, which has been widely applied to nonlinear function optimization, neural network training, and pattern recognition. In PSO, a swarm consists of N particles moving around in a D-dimensional search space.The po(t) sition of the ith particle at t iteration is represented by Xi = (xi1 , xi2 , . . . , xiD ) that are used to evaluate the quality of the particle. During the search process the particle successively adjusts its position toward the global optimum according to the two factors: the best position encountered by itself (pbest) denoted as Pi = (pi1 , pi2 , . . . , piD ) and the best position encountered by the whole swarm (gbest) denoted as Pg = (pg1 , pg2 , . . . , pgD ). Its velocity at t iteration is repre(t) sented by Vi = (vi1 , vi2 , . . . , viD ). The position at next iteration is calculated according to the following equations: (t)

Vi

(t−1)

= λ(ω ∗ Vi

(t−1)

+ c1 ∗ rand() ∗ (Pi − Xi (t)

Xi

(t−1)

= Xi

(t−1)

) + c2 ∗ rand() ∗ (Pg − Xi (t)

+ Vi

)) (1) (2)

where c1 and c2 are two positive constants, called cognitive learning rate and social learning rate respectively; rand() is a random function in the range [0, 1] ;

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w is inertiaf actor; and λ is constrictionf actor. In addition, the velocities of the particles are confined within [V min, V max]D . If an element of velocities exceeds the threshold V min or V max, it is set equal to the corresponding threshold.

3 3.1

Feature Selection with PSO Feature Selection for Neural Network

Neural network offers an attractive framework for the design of trainable pattern classifiers for real-world pattern classification tasks. In order to remove the redundant or irrelevant features, feature selection is often used as the first stage of classification task for neural network classifiers. In a neural network classifier, the number of features determines the number of neurons in input layer. Therefore, if different features are selected, subsequent neural network must be trained according with the corresponding training set determined by the selected features. In this paper, we propose that feature selection and neural network training are done simultaneously in each iteration. We formulated the combination of feature selection and neural network as an optimization problem and employed PSO algorithm to resolve it. RBF neural network was employed as classifier in this paper. PSO algorithm is a population based iterative global optimization algorithm. In each iteration, each particle consists of two components: feature subset and neural network configuration. The former encodes the feature subset and determines the training set and the number of neurons in input layer of RBF network, while the latter determines the number of neurons in hidden layer and corresponding parameters of RBF neural network. The resulting RBF neural network is measured on the training set formed by feature selection to evaluate the fitness of a particle. Fitness function of PSO takes into account three measures: mean squared error (MSE) between network outputs and desired outputs, the complexity of networks, and the number of features. Therefore, the swarm evolves toward the following configuration: minimal number of features and the corresponding RBF that has not only minimal MSE but also appropriate network architecture. Thus the resulting RBF network has strong generalization ability. Moreover, in each iteration of PSO algorithm, there is no iterative process to train the RBF neural network, so it saves a great deal of time. Depending on the powerful evolutionary mechanism of PSO, feature subset and RBF neural network evolve to better configuration in next iteration simultaneously. 3.2

Encoding Feature Selection and Neural Network

Traditional methods just encode features, while we encode features and subsequent neural network at the same time. Therefore, the position of a particle is represented by concatenation of feature subset and neural network as shown in Figure 1. Here SF lagi (1 ≤ i ≤ f max) indicates whether or not the i-th feature is selected. If SF lagi > 0, then the i-th feature is selected, else not selected. The encoding neural network is described in detail. RBF network is three-layer

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Feature selection array SFlag1 SFlag2

...

Center existence array CFlag1 CFlag2

...

Neural network array

SFlagfmax

Center vector array

CFlaghmax Center1 Center2

...

Centerhmax

Fig. 1. Structure of a particle

feedback network. The number of neurons in hidden layer determines the complexity of networks. Too few hidden neurons lead to low classification accuracy due to limited flexibility, while too many result in poor generalization ability since the noise in the training data is fitted. The number of input neurons is variable, which is determined by selected features, so it is impossible to specify the number of hidden neurons in advance. The hidden layer is evolved during the search. CF lagi (1 ≤ i ≤ hmax) indicates whether or not the i-th hidden neuron is involved into the network. If CF lagi > 0, the i-th hidden neuron is included in the network. Otherwise the i-th hidden neuron is removed from the network. Since the performance of RBF networks mainly depends on the centers of hidden neurons, we just encode the centers into the particle for stochastic search. Then the widths of hidden neurons and weights between hidden layer and output layer are determined by heuristic methods and analytic methods, respectively [9]. Designing Fitness Function. In the way mentioned above, in every iteration particles can be interpreted into networks with variable number of hidden neurons. According to the following formula, the resulting network is measured on the training set that is determined by feature selection. PN N SelectedF eature 1
N hidden F itness = k1 · tp − op 2 + k3 · + k2 · N maxF eature P N p=1 N maxhidden

(3) where ki ( i = 1, 2, 3) are constant and indicate the weight of each component respectively; N SelectedF eature indicates the number of features selected and N maxF eature indicates the total number of features; P N input-target patterns are given; tp and op are the desired output and network output for pattern p respectively; N hidden is the number of hidden units involved in networks; N maxhidden is predefined as the max number of hidden units.

4

Experiments

Four data sets from UCI Repository of machine learning databases [10] were used in our experiments. These data sets are image segmentation, page-blocks,

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ionosphere and wine. The properties of these four data sets were described in Table 1. Two training schemes were compared. One was PSO algorithm without feature selection [9], and the other was PSO algorithm with feature selection, which was proposed in this paper. The parameters of PSO algorithm were set as follows: weight w decreasing linearly between 0.9 and 0.4, learning rate c1 = c2 = 2, and V max = 1. Max iterations were set to 2000 iterations. All the experiments were conducted 10 runs. In each experiment, each data set was randomly divided into two parts: 2/3 as training set and 1/3 as test set. As each feature was normalized as the following formula, normalized values were in range [-1,1]. Original value Normalized value = (4) | max(orinial values of all instances) | Table 1. The information of data sets and results of two training schemes for different data sets Wine

Ionosphere

Image segmentation

Page-blocks

Data sets information Instances

178

351

300

5473

Features

13

34

30

10

Numeric

Numeric

Numeric

Numeric

3

2

7

5

15

42

40

15

TrainCorrect

0.9995

0.9605

0.9661

0.9474

TestCorrect

0.9688

0.9012

0.9086

0.9121

Feature type Classes

RBF Without feature selection Hidden neurons

RBF With feature selection Selected features

4

8

5

2

Hidden neurons

12

20

32

5

TrainCorrect

0.9815

0.9707

0.9736

0.9255

TestCorrect

0.9488

0.9209

0.9116

0.9073

The results were listed in Table 1. TrainCorrect and TestCorrect refer to mean correct classification rate averaged over 10 runs for the training and test set, respectively. The number of selected features and hidden neurons achieved for each data set were averaged over 10 runs, and then were round off to integer. As can be seen from Table 1, the percentage of the number of selected features to the total number of features in each dataset is relatively small. Although, many features are removed from the original feature set, the mean classification rate

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still remains high. Moreover, feature selection improves the correct classification rate on date sets, Ionosphere and Image segmentation.

5

Conclusions

In this paper, we have proposed a new feature selection method, in which PSO is employed. RBF neural network is used as the classifier to evaluate the accuracy of selected features. The PSO algorithm simultaneously considers three measures as the fitness function: MSE, the complexity of networks and the number of features, guaranteeing strong generalization ability of RBF network. Experimental results on the datasets from UCI repository show that this method effectively selected features with high accuracy as well as small feature subset size. Furthermore, this method is efficient because it encodes not only feature subset but also neural network configuration in each iteration of PSO algorithm, and hence avoiding time-consuming process to train neural network in each iteration.

References 1. Blum, A., Langley, P.: Selection of relevant features and examples in machine learning. Artificial Intelligence 97 (1997) 245–271 2. John, G.H., Kohavi, R., Pfleger, K.: Irrelevant features and the subset selection problem. In: International Conference on Machine Learning. (1994) 121–129 3. Kohavi, R., John, G.H.: Wrappers for feature subset selection. Artificial Intelligence 97 (1997) 273–324 4. Martin-Bautista, M.J., Villa, M.: A survey of genetic feature selection in mining issues. In Angeline, P.J., Michalewicz, Z., Schoenauer, M., Yao, X., Zalzala, A., eds.: Proceedings of the Congress on Evolutionary Computation. Volume 2., IEEE Press (1999) 1314–1321 5. Yang, J., Honavar, V.: Feature subset selection using a genetic algorithm. In Koza, J.R., Deb, K., Dorigo, M., Fogel, D.B., Garzon, M., Iba, H., Riolo, R.L., eds.: Genetic Programming 1997: Proceedings of the Second Annual Conference, Stanford University, CA, USA, Morgan Kaufmann (1997) 380 6. Yang, J., Parekh, R., Honavar, V.: Distal: An inter-pattern distance-based constructive learning algorithm. Intelligent Data Analysis 3 (1999) 55–73 7. Brill, F.Z., Brown, D.E., Martin, W.N.: Fast genetic selection of features for neural network classifiers. IEEE Transactions on Neural Networks 3 (1992) 324–328 8. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceeding of IEEE International Conference on Neural Networks (ICNN’95). Volume 4., Perth, Western Australia, IEEE (1995) 1942–1947 9. Liu, Y., Qin, Z., Shi, Z., Chen, J.: Training radial basis function networks with particle swarms. In: Proceeding of the IEEE International Symposium Neural Networks. Lecture Notes in Computer Science, Springer (2004) 10. Blake, C., Merz, C.J.: UCI repository of machine learning databases, http:// www.ics.uci.edu/~mlearn/MLRepository.html (1998)

Influence of Moment Arms on Lumbar Spine Subjected to Follower Loads Kyungsoo Kim1 and Yoon Hyuk Kim2 1

Impedance Imaging Research Center, Kyung Hee University, Yongin-si, Gyeonggi-do, 449-701, Korea [email protected] 2 School of Advanced Technology, Kyung Hee University, Yongin-si, Gyeonggi-do, 449-701, Korea [email protected]

Abstract. In this paper, an influence of moment arms on the lumbar spine subjected to the follower load was investigated. A two-dimensional finite element model of the lumbar spine including idealized trunk muscles was developed to evaluate the muscle force activation generating the follower load when the lengths of moment arms varied. The follower forces, the shear forces and the resultant joint moments were also calculated to confirm the generation of the follower load. Finally, the dependence of the lengths of moment arms on the deformed shape of the lumbar spine model concerning the spinal stability was examined.

1 Introduction It has been shown by several past literatures e.g. [1-3] that the human lumbar spine can maintain its stability when external loads are transmitted along the path that approximates the tangent to the curve of the spinal column, called the follower load path. The resultant compressive loads described above are called the follower loads. The trunk muscles were assumed to have an essential role in generating the follower loads. However, it is quite difficult to measure the magnitudes of muscle forces experimentally, so that the computational investigations are attempted [4-6]. It was verified with simplified anatomical data that there were activations of the human trunk muscles generating the follower loads and maintaining the spinal stability when physiologically meaningful external forces and moments were applied to the spine. Thus, it is necessary to study the dependence of the simplified anatomical data on the response of the lumbar spine, especially the stability. In this paper, the influence of the distance as a moment arm between the body center and the attachment point of a muscle in each vertebra on the lumbar spine subjected to the follower load was investigated. This study was partly supported by RRC program of MOST and KOSEF. Corresponding author : Yoon Hyuk Kim, School of Advanced Technology, Kyung Hee University, Korea, (Tel) +82-31-201-2028, (e-mail) [email protected] J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 431–436, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Materials and Methods A two-dimensional finite element model of a human lumbar spine in the frontal plane with a laterally flexed standing posture was developed. The response of the whole lumbar spine (L1-S1) subjected to the follower load and the activations of muscles on the lumbar spine were investigated as in [5, 6]. A global coordinate system in the frontal plane was defined, with the origin at the center of the first sacral vertebra, the x-axis pointing horizontally to the right, and the y-axis pointing upwards. Five node points of finite elements identified with the vertebral body centers of L1-L5 using geometric data in [4-6] (Fig. 1). Each finite element was assumed to have elastic stiffness properties given in [7, 8]. As shown in Fig. 1, a vertical load (P) was applied at the top body center (L1) to simulate an external load including an external force and an external moment. (F1F10) denoted by unknown muscle forces applied at five nodes along the idealized lines of action of muscles whose fascicles had a distal attachment in the sacrum/pelvis region and a proximal attachment near the vertebral body centers. Muscles were assumed to be activated statically. The distances between the vertebral body centers and the proximal attachment points of ten muscles were regarded as perpendicular moment arms. In this model, it was supposed that all the length of the moment arms were identical while L denoted the length. The length L of moment arms were assumed to vary from 0mm to 30mm in order to examine the influence of the length of moment arms on the lumbar spine model subjected to the follower load.

L1 F5 L2

P

F6

F4 F7 L3 F3 L4 F2 F1 Attachment point

F8 F9

L5 F10 Attachment point

Fig. 1. Two-dimensional finite element model of the lumbar spine

A follower load path was defined as having a direction parallel to the bisection of two adjacent segments at each node. A local coordinate system at each node in the frontal plane could then be defined with the origin at the node that is the vertebral body center. The x-axis is in the opposite direction to the follower load path, i.e., the follower direction, and the y-axis is in the perpendicular direction to the x-axis, or the shear direction. At each node, the resultant joint force could be decomposed into two

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force components, one in the follower direction and one in the shear direction. The former is called as the follower force and the latter the shear force. The lumbar spine model is in static equilibrium when all the forces and moments at each node equal zero. The forces and moments used in the analysis consist of muscle forces and moments derived by muscle forces, motion segment forces and moments by the stiffness property, as well as applied external forces and moments as in [5, 6, 8]. The total static equilibrium equations at each vertebral segment are as follows: Fm − K ⋅ d + Fext = 0

(1)

where Fm represents the muscle forces and the moments activated by muscles, Fext the external forces and moments acting on the five lumbar vertebrae, K the global stiffness matrix of motion segments in the lumbar spine, and d the translations and the rotations at each node, respectively. In this analysis two translations and a rotation at each vertebra and ten muscle forces were considered as state variables. The number of unknowns that consisted of magnitudes of muscle forces and displacements exceeded that of equations describing the equilibrium state of the lumbar spine model so that the optimization technique is necessary to solve this redundant problem. In this study, the quadratic sequential programming method was utilized to solve this optimization problem using MATLAB®(MathWorks Inc., USA). The optimization problem minimizing the sum of follower forces was formulated allowing no shear forces as follows: ne

Minimize f =

∑F

i

f

(2)

i =1

subject to Fsi = 0 , i = 1, …, ne and Fm − K ⋅ d + Fext = 0 where Ffi denoted the follower force at the i-th node, i = 1, …, ne , Fsi the shear force at the i-th node, i = 1, …, ne , ne the number of elements. Here ne = 5. In the optimization problem, the sum of follower forces was minimized in order to reduce the intervertebral disk stresses. Two loading cases were tested for various values of L, L=0, 10, 20, 30 mm: (a) Case 1: P=350N and 3.5Nm (the clockwise direction is positive), (b) Case 2: P=350N and 0.0Nm. In this paper, the muscle force activations generating the follower load were calculated for the variation of the length L of moment arms under both loading cases. The corresponding resultant joint forces (the follower forces and the shear forces) and the resultant joint moments, and the deformed shapes of the model were also derived. Finally, tilts of elements, which were angles between the vertical axis and the elements, were investigated for each L and their changes with the variation of L were examined in order to verify the influence of the length of moment arms on the deformed shapes.

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Results and Discussion

Muscle force activations satisfying constraints of the formulated optimization problem could be obtained for various L under both loading cases. Five muscle forces (F1, F2, F3, F4, F6) were zero for every L in each loading case and the others were presented in Fig. 2. It was verified that all the shear forces were eliminated at every node regardless of the length L and the load case. This indicated that the calculated muscle force activations generated the follower load. While the length L of moment arms changed, the magnitudes of activated muscle forces did not vary so much at each vertebra. The follower forces corresponding to those muscle force combinations also had little variations (Fig. 3). These observations implied that muscle force activations and the follower forces at all vertebrae were less dependent on the length of the moment arms.

300 L=30

250

L=20

L=10

L=0 Muscle force (N)

Muscle force (N)

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200 150 100 50

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L=30

L=20

L=10

F7

F8

F9

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200 150 100 50

0

0 F5

F7

F8

F9

F10

F5

(a) Case 1: P=350N & 3.5Nm

F10

(b) Case 2: P=350N & 0.0Nm

Fig. 2. Nonzero muscle force activations for various L

1000

1000 L=20

L=10

L=0

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Follower force (N)

Follower force (N)

L=30

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800

L=30

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600 400 200 0

L1

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(a) Case 1: P=350N & 3.5Nm

L1

L2

L3

L4

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(b) Case 2: P=350N & 0.0Nm

Fig. 3. Follower forces subjected to the follower load for various L

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5 4 3 2 1 0 -1 -2 -3 -4 -5 L1

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L=20

L2

L3

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L=0

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(a) Case 1: P=350N & 3.5Nm

Joint moment (Nm)

Joint moment (Nm)

However, the resultant joint moments at L1 were affected by the length of moment arms in both loading cases though joint moments at the other vertebrae changed a little (Fig. 4). There were tendencies that the amounts of joint moments decreased as the length of the moment arms reduced. These phenomena would be observed since the moment arm is directly used to calculate moments in opposite to forces. Thus, attachment points of muscles need to be investigated carefully in order to estimate the resultant joint moment precisely. 5 4 3 2 1 0 -1 -2 -3 -4 -5 L1

L=30

L=20

L2

L3

L=10

L=0

L4

L5

(b) Case 2: P=350N & 0.0Nm

Fig. 4. Resultant joint moments subjected to the follower load for various L

The deformed shapes of the finite element model were close to the initial shape regardless of the length L of moment arms and the loading case. This meant that the stability of the model could be preserved under the follower load as shown in the previous researches. However, the tilt of each element decreased as the lengths of moment arms increased for both loading cases. Figure 5 represented tilts of L1-L2 for various lengths L. From these results, it was verified that the length of moment arms was an influencing factor on the deformed shape while the follower load maintained the spinal stability.

Fig. 5. Tilts of L1-L2 subjected to the follower load for various L

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Conclusion

The influence of the moment arm on the lumbar spine subjected to the follower load was investigated by using a two-dimensional finite element model of the lumbar spine including the idealized trunk muscles in the frontal plane. The distance between the body center and an attachment point of a muscle in each vertebra was regarded as moment arm in this study. The deformed shape of the finite element model and the tilt of each element as well as the resultant joint moment at each vertebral body center were dependent on the length of the moment arm while the muscle force activations to generate the follower load, and the corresponding follower force and shear force at each vertebra were influenced little by the moment arm. In this manner, the length of the moment arm obtained by the anatomical data, such as the positions of muscle attachment points and vertebral body centers, could be an important factor in studying computational works in biomechanics fields. Therefore, proper and precise knowledge of the human anatomy can contribute to the development and improvement of computational researches on biomechanics, biomedical engineering and so on.

References 1. Patwardhan, A. G., Havey, R. M., Meade, K. P., Lee, B., Dunlap, B.: A follower load increases the load-carrying capacity of the lumbar spine in compression, Spine 24 (1999) 1003-1009 2. Patwardhan, A. G., Havey, R. M., Ghanayem, A. J., Diener, H., Meade, K. P., Dunlap, B., Hodges, S. D.: Load-carrying capacity of the human cervical spine in compression is increased under a follower load: Spine 25 (2000) 1548-1554 3. Rohlmann, A., Neller, S., Claes, L, Bergman, G., Wilke, H.-J.: Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine. Spine 26 (2001) E557-E561 4. Patwardhan, A. G., Meade, K. P., Lee, B.: A frontal plane model of the lumbar spine subjected to a follower load: Implications for the role of muscles. J. Biomech. Eng. 123 (2001) 212-217 5. Kim, Y. H., Kim, K.: Musculoskeletal modeling of lumbar spine under follower loads, Lecture Notes in Computer Science Vol. 3044. Springer-Verlag, Berlin Heidelberg New York (2004) 467-475 6. Kim, Y. H., Kim, K.: Numerical analysis on quantitative role of trunk muscles in spinal stabilization, JSME Int. (submitted) 7. Gardner-Morse, M. G., Laible, J. P., Stokes, I. A. F.: Incorporation of spinal flexibility measurements into finite element analysis. J. Biomech. Eng. 112 (1990) 481-483 8. Stokes, I. A. F., Gardner-Morse, M. G.: Lumbar spine maximum efforts and muscle recruitment patterns predicted by a model with multijoint muscles and joints with stiffness. J. Biomech. 28 (1995) 173-186

Monte Carlo Simulation of the Effects of Large Blood Vessels During Hyperthermia Zhong-Shan Deng and Jing Liu Cryogenics Laboratory, P.O. Box 2711, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100080, P.R. China {zsdeng, jliu}@cl.cryo.ac.cn

Abstract. Large blood vessels can produce localized cooling in heated tissues during tumor hyperthermia. This study has developed a Monte Carlo algorithm to simulate the cooling effect of large blood vessels during hyperthermia. Similar to previous formulations, heat transfer coefficients are used to calculate heat transfer of large blood vessels, and several typical vascular geometries are applied. The corresponding thermal model combines the Pennes bioheat transfer equation for perfused tissues and the energy equation for blood vessels with a constant Nusselt number. Using the Monte Carlo algorithm, numerical analyses are performed to test the influences of large blood vessels to the temperature distributions of tissues. The results indicate that during hyperthermia the presence of large vessels can be an important source of temperature non-uniformity and possible under-dosage. Reduction of blood flow through the large vessels is found to be an effective approach of reducing the localized cooling.

1 Introduction Hyperthermia treatment is the induction of temperatures above 42 ºC in order to treat diseases. The clinical application of hyperthermia is mainly as a combined therapy to radiotherapy and/or chemotherapy against cancer [1]. In hyperthermia, heating is usually limited to the tumor and a small margin of the surrounding healthy tissue. Because the temperatures in the rest of the body remain normal, the blood that supplies the tumor will be relatively cold. As a result, tissue in the treatment volume that is close to a large blood vessel may remain below the desired treatment temperature. In fact, both theoretical and clinical studies have demonstrated that during hyperthermia large blood vessels can produce steep temperature gradients around the vessels with associated thermal under-dosage near the vessels [2,3]. The problems in reaching therapeutic temperatures in all of the treatment volume are hindering the use of hyperthermia in the clinics. One effective strategy for preventing regions of thermal under-dosage is by compensation of power deposition. More heat must be deposited where there is localized cooling caused by the larger vessels. For this purpose, the power deposition patterns must be carefully devised to effectively heat the tumor without overheating normal tissues. Consequently, there has been an increasing amount of work dedicated to the effects of large blood vessels on temperature distributions during hyperthermia [4,5]. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 437–442, 2004. © Springer-Verlag Berlin Heidelberg 2004

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In these works, many vascular models were developed, which account for the convective effects of large blood vessels. The complexity makes the analysis of heat transfer of large vessels rather hard, and only numerical approaches work well. Considering that the conventional numerical methods such as finite difference method, finite element method, and boundary element method must solve the temperatures at all mesh points simultaneously, and that in hyperthermia only the temperatures at specific area are useful for determination of power deposition pattern, the newly developed Monte Carlo algorithm [6] was extended in this study to investigate the effects of large blood vessels on the temperature distributions during hyperthermia. The particularly attractive feature of Monte Carlo method lies in that the temperature at any desired point can be obtained independently from solutions at the other points, which is an asset when temperature are needed only at some specific area [6]. Aiming at developing a new highly flexible method for the thermal analysis of large vessels, only several typical vascular models were studied in this article.

2 Models and Algorithm Development In this study, several vascular models with typical geometrical configurations are applied to simulate the cooling effect of large blood vessels during hyperthermia. The vascular models are shown in Fig. 1 (the bioheat transfer equation model, BHTE, is not presented here for brevity). The boundary conditions are a constant temperature of 37 °C on all surfaces of the parallelepiped, and the initial condition is defined as uniform temperature of 37 °C over the whole area. Similar vascular models were firstly developed by Chen and Roemer [2]. In these models, the whole tissue domain consists of perfused tissue and large blood vessel domains. For the perfused tissue, thermal equation is described by the Pennes bioheat transfer equation

ωρc ∂T ( X, t ) Q ( X, t ) = α∇ 2 T ( X , t ) − b b b T ( X , t ) + , X ∈ Ω1 . ∂t ρc ρc

(1)

where Q ( X , t ) = Qm ( X , t ) + Qr ( X , t ) + ρb cbωbTa ; α = k ρ c is the thermal diffusivity of tissue; ρ , c , k are the density, the specific heat, and the thermal conductivity of the tissue respectively; ρ b , cb denote density and specific heat of blood; ωb the blood perfusion; Ta the arterial temperature; Qm is the metabolic heat generation, and Qr the distributed volumetric heat source due to spatial heating; X contains the Cartesian coordinates x , y and z , and Ω1 denotes the perfused tissue domain. For the large blood vessel, the thermal balance is governed by the convective heat transfer equation [7]

ρb cb

∂T hP ∂T = (Tw − T ) − ρb cbv + Qr (X, t ) , X ∈ Ω2 . ∂t S ∂z

(2)

where h = Nu·kb /D is the convective heat transfer coefficient between the blood and tissue, D is the diameter of the vessel, P is the perimeter of the vessel, S is the crosssectional area of the vessel, v the mean blood velocity along the vessel, Nu the Nusselt

Monte Carlo Simulation of the Effects of Large Blood Vessels During Hyperthermia

439

number, Tw the wall temperature of the vessel, and Ω2 denotes the large blood vessel domain. Like the study of Chato [8], conduction inside the vessel in the z direction (flow direction) is neglected for large flow rate, and a constant Nusselt number is assumed. The sign of blood velocity v is assigned as positive, i.e., the velocities for bloods in artery and vein are positive and minus respectively. y

y normal tissue

normal tissue artery

z

z x artery

tumor

x vein

tumor

(b)

(a)

Fig. 1. Illustration of the typical vascular models. The central region is tumor and the outer is normal tissue. (a) a model with a single artery transiting the tumor, SATT; (b) a model with counter-current flow vessels transiting the tumor, CVTT

The probability model for Eq. (1) had been presented in our previous work [6]. The detailed derivation is not repeated here for brevity. If the large blood vessel is present, the probability model in blood vessel domain needs special treatment. In order to avoid the convective numerical instabilities, the up-wind scheme is used to discretize the convective term in equation (2). Then the probability models for the vessels can be written as

Ti ,nj+,k1 = p1Ti ,nj ,k + p2Ti n+1, j ,k + p3Ti −n1, j ,k + p4Ti ,nj +1,k + p5Ti ,nj −1,k + p6Ti ,nj ,k −1 + Qr F1 .

(3)

where p1 = a1 F1 , p2 = a2 F1 , p3 = a3 F1 , p4 = a4 F1 , p5 = a5 F1 , p6 = a6 F1 , a1 = ρ b cb ∆t , a2 = 1 ( S ⋅ Ri +1 2 ) , a3 = 1 ( S ⋅ Ri −1 2 ) , a4 = 1 ( S ⋅ R j +1 2 ) , a5 = 1 ( S ⋅ R j −1 2 ) ,

a6 = ρb cb v ∆z , F1 = a1 + a2 + a3 + a4 + a5 + a6 . The subscripted R ’s are the thermal resistance between the center vessel node ( i, j, k ) and the four neighboring tissue nodes outside the vessel. These thermal resistances are composed of two parts, the convective and conductive resistances. The total thermal resistances between the two nodes, ( i, j, k ) and ( i − 1, j, k ), ( i, j, k ) and ( i + 1, j, k ), ( i, j, k ) and ( i, j − 1, k ), ( i, j, k ) and ( i, j + 1, k ), are respectively [2, 7]

Ri −1 2 = Ri +1 2 =

4 2 ∆x 4 2 ∆y + + , R j −1 2 = R j +1 2 = . ln ln hπ D π k D 2 hπ D π k D 2

(4)

The thermal resistance between the artery and the vein is

Ra −v =

8 4 ∆y . + ln hπ D π k D

(5)

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For the four neighboring tissue nodes outside the vessel, the probability models are different from those for the other tissue nodes, which are not listed for brevity (the finite difference formulations can be found in [7]). The probabilistic interpretations of the above equations are similar to that given in [7], and detailed description is omitted here for brevity. The computer code compiled in this article is revised from the code developed in our previous study [6], which had been validated through comparing the numerical results with the one-dimensional exact solution.

3 Results and Discussion

48

0.20

44

0.16

40

39

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z (m)

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The tissue domain is prescribed in a rectangular geometry with 10×10×20 cm in the x, y and z directions respectively, and the dimensions of the tumor (which is located at the center of the tissue region) are 3.2×3.2×3.2 cm for all configurations. The blood flow velocity is set as 10 cm/s, and the vessel diameter is set as 1 mm, based on the data compiled by Chato [8]. The constant Nusselt number is taken as Nu=4 [2, 8]. The typical tissue properties for normal and tumor tissues are applied in this study, which can be found in [9]. The power deposition pattern used in this article is: Qr = 12000W m 3 , X ∉ Ω t , Qr = 120000W m 3 , X ∈ Ωt .

40 0.20 36 0.00 0.16 0.02 0.12 0.04 0.08 0.06 0.04 0.08 z (m) 0.00 0.10 y (m)

44

0.12 0.08

43 46

47

44 46 47

43

42

0.04 0.00 37 0.00

0.02

0.04

0.06

0.08

0.10

y (m)

Fig. 2. Temperature distribution at section x=0.05m when t=2000s for SATT model

0.20 40

0.16 44 40 36 0.20 0.00 0.16 0.02 0.12 0.04 0.08 0.06 0.04 0.08 0.00 0.10 z (m) y (m)

40

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48

44

39

42 43 44 46 47

46 43 42

0.08 0.04 39

0.00 37 0.00 0.02

0.04

0.06

0.08

0.10

y (m)

Fig. 3. Temperature distribution at section x=0.05m when t=2000s for CVTT model

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Figure 2 depicts the result for SATT model, in which the central line of the single artery is at (x=0.05m, y=0.05m). Figure 3 depicts the result for CVTT model, in which the central line of the counter-current flow vessels are at (x=0.05m, y=0.048m) and (x=0.05m, y=0.05m), respectively. In order to better illustrate the effects of blood vessel on the temperature distributions of tissue during hyperthermia, similar calculation for BHTE model is also performed, and the corresponding result is depicted in Fig. 4. It can be seen from these figures that blood vessel has produced significant temperature non-uniformity around the vessel. Due to the cooling behavior of the flowing blood in large blood vessel, the temperatures of tissues near the vessel for the case of SATT and CVTT models are much lower than that for the case of BHTE model. This may result in thermal under-dosage in the tumor tissue near the large vessels during hyperthermia. For effective killing of tumor, the power deposition around large vessels must be carefully devised to compensate the cooling of vessels.

48 44 40 36 0.20 0.16 0.00 0.02 0.12 0.04 0.08 0.06 0.04 z (m) y (m) 0.080.100.00

Fig. 4. Temperature distribution at section x=0.05m when t=2000s for BHTE model

52

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Temperature (°C)

52

48

no vessel v=1cm/s v=2cm/s v=5cm/s v=10cm/s

44 40 36 0.00

0.05

0.10 z (m)

0.15

0.20

Fig. 5. Comparison of the cooling effects of different blood flows

In all the above calculations, the blood flow velocities were taken as 10 cm/s. To see the cooling effects of large vessels under different velocities, Fig. 5 depicts the blood temperatures along the single artery under different blood flow velocities for SATT model. As comparison, the tissue temperatures at the same area for BHTE model are also shown in Fig. 5 (depicted by solid curve, i.e., the case of no vessel). It is clearly seen that the larger the flow velocity, the stronger the cooling effect. Therefore, reduction of blood flow through the large vessel may possibly be served as an effective approach of reducing the localized cooling. Besides, it is also seen that the temperature at some area for SATT model is much higher than that at the same area for BHTE model. This indicates that the blood in large vessel may carry away deposition energy from the tumor to the backward normal tissue along the vessel, possibly causing undesired damage to healthy tissues. Compared with the cooling behavior of large vessel, this feature has received relative few attentions up to now, and must be carefully considered during devising power deposition pattern for hyperthermia. To prevent cold regions in tumors around large vessel and to obtain improved hyperthermia temperature fields, optimal heating protocols must be found. Since this research involves three dimensional inhomogeneous models with different types and

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configurations of blood vessels, a complete optimization study would involve many parameters and be very complicated. Therefore, an exhaustive optimization study is beyond the scope of the present work and should be done in the near future.

4 Conclusions This study has developed a Monte Carlo algorithm for solving three-dimensional heat transfer problems of biological tissues embedded with large blood vessels. In the algorithm, both the convective mechanism for the blood flow in the vessels and the thermal effects for the perfused blood are considered. Using this algorithm, the effects of large blood vessels to the tissue temperature distributions during hyperthermia are investigated. The computation results indicate that the presence of large vessels can produce large temperature non-uniformity around the vessel and thus possibly result in thermal under-dosage in the tumor during hyperthermia, and that reduction of blood flow can reduce the cooling effect of the large vessel. It concludes that to improve the tumor killing effect, the power depositions must be carefully devised to compensate the cooling of large vessels.

Acknowledgment This work was partially supported by the National Natural Science Foundation of China under Grant 50325622.

References 1. Roemer, R.B.: Engineering aspects of hyperthermia therapy. Annu. Rev. Biomed. Eng. 1 (1999) 347-376 2. Chen, Z.P., Roemer, R.B.: The effects of large blood vessels on temperature distributions during simulated hyperthermia. ASME J. Biomech. Eng. 114 (1992) 473-481 3. Levin, W., Sherar, M.D., Cooper, B., Hill, R.P., Hunt, J.W., Liu, F.F.: The effect of vascular occlusion on tumor temperatures during superficial hyperthermia, Int. J. Hyperther. 10 (1994) 495-505 4. Crezee, J., Lagendijk, J.J.W.: Temperature uniformity during hyperthermia: the impact of large vessels. Phys. Med. Biol. 37 (1992) 1321-1337 5. Koliost, M.C., Sherar, M.D., Hunt, J.W.: Large blood vessel cooling in heated tissues: a numerical study. Phys. Med. Biol. 40 (1995) 477-494 6. Deng, Z.S., Liu, J.: Monte Carlo method to solve multidimensional bioheat transfer problem. Numer. Heat Tran. B. 42 (2002) 543-567 7. Deng, Z.S., Liu, J.: Effects of large blood vessels on 3-D temperature distributions during simulated cryosurgery. submitted to ASME J. Biomech. Eng. (2004) 8. Chato, J.C.: Heat transfer to blood vessels. ASME J. Biomech. Eng. 102 (1980) 110-118 9. Chato, J.C.: Selected thermophysical properties of biological materials. In: Shitzer, A., Eberhart, E.C. (eds.): Heat Transfer in Medicine and Biology, Vol.1. Plenum Press, New York, (1985) 413-418

A Delimitative and Combinatorial Algorithm for Discrete Optimum Design with Different Discrete Sets Lianshuan Shi
and Heng Fu Computer Department, Tianjin University of Technology and Education, Tianjin 300222, P.R. China [email protected] Abstract. The sequential delimitative and combinatorial algorithm for optimum design of structure with discrete variables is popularized to the optimum design, in which, the number of elements of the allowable discrete set of design variables is the same, but the allowable discrete sets of design variables are different. Firstly, the optimal problem is converted into several sequential sub-problems with lower dimensions and similar structures by recurrent method. Secondly, the algorithm generates all combinations according to a certain order of the magnitude of objective function by using a multi-level generating method of proceeding for higher place. In the procedure of delimiting, the objective function and constraint functions are converted into new functions by the linear transforms. And, these new functions are used to delimit.

1

Introduction

Consider a linear programming problem with discrete variables, P min f (X) =

n


s.t. g i (X) =

ci xi

i=1 n


aij xj ≥ bi

j=1

i = 1, 2, ..., m x j ∈S j (p) = {sj1 , sj2 , ..., sjp } s j1 < sj2 0, j=1   n α
|bji (t)|Li , then Eq.(1) is globally asymptotically stable if k2 (t) = maxi αji j=1

1)

∞

k1 (s)ds = +∞ t − k (u)du 2) t0 k2 (s)e s 1 ds ≤ δ < 1. 0

t

(20)


n Proof. Let z(t) = i=1 αi |yi (t)|. Calculating the upper right derivative of z(t) along the solutions of Eq.(17), we have D+ z(t) ≤

n 

αi D+ |yi (t)|

i=1

⎧ ⎫ n n ⎨ ⎬   ≤ αi −ci (t)|yi (t)|+ |aij (t)|Lj |yj (t)|+ |bij (t)|Lj |yj (t−τj (t))| ⎩ ⎭ i=1 j=1 j=1 ⎫ ⎧ n n n ⎬ ⎨    αi −ci (t)|yi (t)|+ |aij (t)|Lj |yj (t)|+ |bij (t)|Lj |¯ yj (t)| ≤ ⎭ ⎩ i=1 j=1 j=1 ⎡ ⎤ n n  αj  αi ⎣ci (t) − |aji (t)|Li ⎦ |yi (t)| =− αi j=1 i=1 ⎡ ⎤ n n   αj αi ⎣ |bji (t)|Li ⎦ |¯ + yi (t)| αi j=1 i=1 n 

≤ −k1 (t)z(t) + k2 (t)¯ z (t)

(21)

Using the above Lemma,
n if the conditions 1) and 2) are satisfied, we have limt→∞ z(t) = limt→∞ i=1 αi |yi (t)| = 0, this implies that limt→∞ yi (t) = 0. The proof is completed.

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Remark 1. Note that the condition obtained here is independent of delay and the coefficients ci (t), aij (t) and bij (t) may be unbounded.

4

Conclusion

We analyze global asymptotic stability of non-autonomous delayed cellular neural networks by establishing a delay differential inequality. A new stability condition is presented. Compared with the Lyapunov functional method which is widely used in the stability analysis, our method is simpler and more straightforward. Since the condition does not impose the differentiability on delay, it is less restrictive than some previously given in the earlier publications.

References 1. Arik, S.: An Improved Global Stability Result for Delayed Cellular Neural Networks. IEEE Trans. Circuits Syst. I. 49 (2002) 1211–1214 2. Arik, S.: An Analysis of Global Asymptotic Stability of Delayed Cellular Neural Networks. IEEE Trans. Neural Networks. 13 (2002) 1239–1242 3. Cao, J., Wang, J.: Global Asymptotic Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Syst. I. 50 (2003) 34–44 4. Chua, L.O., Yang, L.: Cellular Neural Networks: Theory and Applications. IEEE Trans. Circuits Syst. I. 35 (1988) 1257–1290 5. Huang, H., Cao, J.: On Global Asymptotic Stability of Recurrent Neural Networks with Time-Varying Delays. Appl. Math. Comput. 142 (2003) 143–154 6. Roska, T., Wu, C.W., Chua, L.O.: Stability of Cellular Neural Network with Dominant Nonlinear and Delay-Type Templates. IEEE Trans. Circuits Syst. 40 (1993) 270–272 7. Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Syst. I. 50 (2003) 1353–1358 8. Zhang, J.: Globally Exponential Stability of Neural Networks with Variable Delays. IEEE Trans. Circuits Syst. I. 50 (2003) 288–290 9. Zhang, Q., Ma, R., Xu, J.: Stability of Cellular Neural Networks with Delay. Electron. Lett. 37 (2001) 575–576 10. Zhang, Q., Ma, R., Wang, C., Xu, J.: On the Global Stability of Delayed Neural Networks. IEEE Trans. Automatic Control 48 (2003) 794–797 11. Zhang, Q., Wei, X.P. Xu, J.: Global Exponential Convergence Analysis of Delayed Neural Networks with Time-Varying Delays. Phys. Lett. A 318 (2003) 537–544 12. Jiang, H., Li, Z., Teng, Z.: Boundedness and Stability for Nonautonomous Cellular Neural Networks with Delay. Phys. Lett. A 306 (2003) 313–325

Allometric Scaling Law for Static Friction of Fibrous Materials Yue Wu1, Yu-Mei Zhao1, Jian-Yong Yu1, and Ji-Huan He2,3,* 1

College of Textiles, Donghua University, Shanghai, China College of Science, Donghua University, 1882 Yan’an Xilu Road, Shanghai 200051, People’s Republic of China jhhe@ dhu.edu.cn 3 Key Lab of Textile Technology, Ministry of Education, Shanghai, China 2

Abstract. Scaling relationship between the friction and its normal force for fibrous materials is discussed, the scaling exponent is about 2/3 for fibre-fibre contact.

1 Introduction Friction is a vital important factor in the application of fibrous materials to engineering. Fibers are assembled into various textile products and structures largely to say the least through friction mechanisms. However, due to the complex nature of the inter-fiber friction, our understanding of this fundamental phenomenon is scarce and primitive. 1.1 Historical Development As it is well-known that the static friction can be written in the form [1]

F = µN

(1)

where F is the frictional force, µ friction coefficient, N normal force. The frictional behavior probably was first understood by Leonardo da Vinci, who found that the frictional force is independent of the area of contact between the two faces and is proportional to the normal force between them. The phenomena were rediscovered by Amontons in 1699, and were verified by Coulomb in 1781. He also pointed out the distinction between static friction and kinetic friction. The Amontons’ law for a yarn passing round a guide can be expressed in the form[1]

T2 / T1 = e µθ

(2)

where T1 and T2 denote incoming tension and leaving tension respectively, µ the coefficient of friction, and θ angle of contact.

*

Corresponding author. College of Science, Donghua University, Shanghai 200051, China. [email protected]

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 465–470, 2004. © Springer-Verlag Berlin Heidelberg 2004

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Many experimental data show that the ratio of frictional force F to normal load N for fibres is found to decrease as the load is increased. In other words, Coulomb’s law or Amontons’ law is not obeyed. The study of fibrous friction between soft materials or between soft material and metal has largely been the experimental observation of departures from these laws, the reasons for such departures, and their consequences. Among the various mathematical relations that have been used to fit the experimental data are the following[1]:

F = µN + αS

(3)

F / N = A − B log N

(4)

F = aN + bN c

(5)

F = aN c

(6)

where S is the area of contact, µ , α ,A,B,a,b, and c are constants determined from experiment data. In this paper, we will apply allometric approach to the discussed problem, and the technology has emerged as an interesting and fascinating mathematical tool to the search for the scaling relations of various real-life problems[2~8].

2 Allometric Scaling in Nature Scaling and dimensional analysis actually started with Newton[5], and allometry exists everywhere in our daily life and scientific activity. Generally, the form of an allometric relation can be expressed as

Y ~ Xb

(7)

where Y and X are two measures describing an organism or an event, such as the weight of the antlers X and total weight of a deer Y. When b=1 the relationship is isometric and when b ≠ 1 the relationship is allometric. The exponent is critically important, Ref.[3] points out that and the exponent is relevant to space dimension for allometry, so (7) can be re-written in the form

Y ~ X D /( D+1)

(8)

Y ~ X k /( D +1)

(9)

or

where D is dimension of the discussed problem, k is an integral. Allometry is widely applied in biology, the most fruitful achievement is the allometric scaling relationship relating metabolic rate (B) to organ mass (M)[6,7,8]

Allometric Scaling Law for Static Friction of Fibrous Materials

B ~ M D /( D +1)

467

(10)

where D is the dimension of the organism construction, for example D=2 for a leaf, and D=3 for whole body of an animal. Similar phenomenon arises from our daily life observation. The best known example is the simple pendulum, with the period:

T ~ R D /( D +1) ,D=1.

(11)

Allometry is very effective to quantitative analysis. Conductive textile is widely used as a new kind of intelligent material[3], the classic Ohm law is not valid for calculation of the resistance for intelligent textile. The Ohm’s resistance formulation for metals reads

R~

L A

(12)

where R is the resistance, L length of the metal wire, A its section area. This scaling (12) is valid only for the case of plentiful free electrons in the conductor. For non-metal material, (12) should be modified as (13) L

R~

A D /( D +1)

Here D=2 for case when moving charges are distributed on a section, and D=1 if the moving charges ( for example, in electrospinning[3]) are distributed only on its surface. For conductive textile we have (D=2)

R~

L A2 / 3

(14)

If we want to design an electrochemical cell constructed of two electrodes, which are made of knitted, woven or non-woven conductive textile material, the allometry leads to the following formulation

R=k

L cA2 / 3

(15)

where k is a constant, L the distance between the electrodes, A the surface area of the electrodes, and c the concentration of the electrolyte solution.

3 Allometric Scaling Law for Fibrous Static Friction 3.1 Solid-Solid Friction Coulomb’s law is valid for metal-metal friction, the scaling relation between frictional force F and the normal force N can be written in the form

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F ~ N1

(16)

The frictional metal-metal force is independent of the area (A) of the contact between the two surfaces:

F ~ A0

(17)

These two scaling relations (16) and (17) are invalid for non-metals. 3.2 Viscous Friction for Newtonian Flow We consider the viscous friction of Newtonian flow. The viscous friction F is proportional to its area: (18) 1

F~A

The relations (17) and (18) are valid for two extreme conditions respectively, the former for stability contact, and the later for instability contact. 3.3 Friction for Soft Materials The frictional force between soft materials, e.g. cotton flow, scales as

F ~ Aα , 0 < α < 1

(19)

where the scaling exponent α represents the mechanical character for the frictional partners. When α = 0 , the friction is of solid-solid type, and when α = 1 , it turns out to be viscous friction. Soft material behaves in neither the manner of Newtonian flow, nor solid contact, so the value of α lies between 0 and 1. According to He Chengtian’s interpolation(see Appendix), the value of α can be approximated as (20)

n m+n where m and n are integers. When n is fixed, m → ∞ corresponds to solid-solid contact; when m is fixed, n → ∞ corresponds to viscous flow. The most successful relation is α (1,1) = 1 / 2 , which can be used for cotton flow.

α (m, n) =

3.4 Fibre-Fibre Friction Now we consider fibre-fibre (e.g. nylon-nylon, nylon-acetate)friction, we have

F ~ Aβ , 0 < β < α

(21)

In case β = 0 , the frictional partners can be considered as rigid bodies, and β = α for flexible bodies. Most textile productions has a fixed surface similar to a solid surface, but the fibrous flexibility leads to a similar phenomenon as flow, especially as cotton flow, so the value of β generally lies between 0 and 1/2, i.e.,

Allometric Scaling Law for Static Friction of Fibrous Materials

0 0.05). However, significant difference was found in the median threshold selection for generation of aortic stents between VR and VE with a p value less than 0.001.

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All of the stent-covered renal arteries remained patent on axial CT images and were visualized clearly on SSD, MIP, VR and VE in 27/28, 28/28, 27/28 and 28/28, respectively. Stent position relative to the renal artery/ostium was clearly visualized in nearly all of the MIP, VR and VE images and only displayed in 12 out of 28 patients on SSD. Image quality was more affected in SSD than other 3D methods due to the interference of artifacts caused by stent wires, which limited the observation of stent position relative to the renal artery in more than half of the patients (Fig1). The number of stent wires crossing the renal ostium was best demonstrated on VE images as intraluminal views were clearly demonstrated regarding the degree of encroachment to the ostium (Fig1D).

Fig. 1. Various 3D reconstruction techniques in a patient with AAA after aortic stent grafting. Renal arteries were shown to be patent on SSD (A), however, stent wires relative to the renal arteries was difficult to visualize. High-density stent wires and their relationship with renal arteries were easily identified on MIP (arrowheads in B) and VR (red color) images. Left renal ostium was found to be covered by two stent wires peripherally as shown in VE (D). White arrows indicate the renal arteries, while black arrows point to the left renal ostium

3

Discussion

Helical CTA has been recognized as the preferred imaging modality for evaluating the abdominal vasculature as well as stent grafts [7, 8]. There is growing awareness of the necessity to interpret 3D reconstructions in conjunction with the axial source images [10]. CTA-generated 3D postprocessing methods have been reported to complement conventional axial images and enhance our understanding of the effect of aortic stent grafting [11]. Among these four 3D reconstructions presented in our study, SSD, MIP and VR are most commonly used in aortic stent grafting, while VE is a relatively new technique which allows intraluminal views of aortic lumen as well as stent wires [11]. Reliable recognition of the advantages and disadvantages of these 3D techniques will aid clinicians to make efficient use of 3D reconstructions and evaluate the treatment of aortic stent grafting, especially the effect of suprarenal stent on the renal arteries. Although SSD makes images appear very three-dimensional and intuitive, it has serious limitations. As only gray-scale information is used for surface

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estimation, a large proportion of the available data is lost and not represented. It is very sensitive to changes in threshold and it is often difficult to determine which threshold range results in the most accurate depiction of the actual anatomic structures. This was observed in our study which showed that visualization of stent relative to the renal artery was significantly affected in more than half of the cases. MIP images are most commonly used in vascular imaging as they provide excellent differentiation between vascular and nonvascular structures. They clearly demonstrate contrast-enhanced arteries as well as aortic stents as shown in our study. However, MIP images lack depth information and MIP is a time-consuming technique due to manual editing of volume data. The median time of nearly 30 min required for generation of MIP images in our study prevents it from being accepted by clinicians as a routine imaging technique in clinical practice. VR was found to be the most efficient reconstruction in aortic stent grafting, according to our study. VR is often combined with depth and surface shading and rotation to give the viewer a realistic sense of three-dimensionality. The use of varying degree of transparency combined with color coding of different structures allows simultaneous display of superficial and deep structures in an image, as shown in Fig1. 3D relationship between suprarenal stent wires and renal arteries was also clearly visualized by VR images regarding the encroachment or coverage of stent wires to the arterial branches. The final image quality depends on the segmentation of the volume data that are given to the rendering algorithm, which is the main limitation of VR. VE was found to be particularly useful in the demonstration of stent wires relative to the renal ostium due to its capability of providing intraluminal views. We consider VE as a valuable technique in the follow-up of patients with AAA after aortic stent grafting as it provides clinicians with additional information when compared to other reconstruction methods regarding the effect of suprarenal stent wires on the renal ostium. The uniphasic contrast enhancement and scanning parameters inherent in single slice CT used in our study resulted in inhomogeneous image quality with minor artifacts in 50% of cases when the contrast reached the iliac arteries. This limitation can be overcome using biphasic or multiphasic contrast enhancement, which has been reported to produce homogenous enhancement along the abdominal aorta [12, 13]. With the emergence of multislice CT in most clinical centres, we believe that image quality of CT volume data acquired on multislice CT will definitely improve with subsequent improvement of 3D reconstruction methods on account of its fast scanning, thinner collimation and high-spatial resolution [14].

4

Conclusion

We found in our study that VR is the most efficient technique in aortic stent grafting and VE is particularly useful in demonstration of the encroachment to the renal ostium by suprarenal stent wires. Further study of validation of

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diagnostic value of these 3D rendering techniques in a large cohort of patients deserves to be investigated.

References 1. Government Statistical Service: Hospital episode statistics. 1. Finished Consultant Episodes By Diagnosis, Operation and Speciality. England: Financial Year 19921993. London: HMSO (1995) 2. Lawrence, P.F., Gazak, C., Bhirangi, L, Jones, B, Bhirangi, K, Oderich, G, Treiman, G.: The Epidemiology Of Surgically Repaired Aneurysms In The United States. J. Vasc. Surg. 30 (1999) 632 -640 3. Parodi, J.C., Palmaz, J.C., Barone, H.D.: Transfemoral Intraluminal Graft Implantation For Abdominal Aortic Aneurysms. Ann. Vasc. Surg. 5 (1991) 491-499 4. Parodi, J.C., Barone, A., Piraino, R., Schonholz, C: Endovascular Treatment Of Abdominal Aortic Aneurysms: Lessons learned. J. Endovasc. Surg. 4 (1997) 102110 5. Malina, M., Lindh, M., Ivancev, K., Frennby, B., Lindblad, B., Brunkwall, J: The Effects Of Endovascular Aortic Stents Placed Across The Renal Arteries. Eur. J. Vasc. Endovasc Surg. 13 (1997) 207-213 6. Lau, L.L., Hakaim, A.G., Oldenburg, W.A.,Neuhauser, B, McKinney, J.M., PazFumagalli, R, Stockland, A.: Effect Of Suprarenal Versus Infrarenal Aortic Endograft Fixation On Renal Function And Renal Artery Patency: A Comparative Study With Intermediate Follow-up. J. Vasc. Surg. 37 (2003) 1162-1168 7. Broeders, IAMJ., Blankensteijn, J.D., Olree, M., Mali, W., Eikelboom, B.C.: Preoperative Sizing Of Grafts For Transfemoral Endovascular Aneurysm Management: A Prospective Comparative Study Of Spiral CT Angiography, Arterial Angiography And Conventional CT Imaging. J. Endovasc. Surg. 4 (1997) 252-261 8. Armerding, M.D., Rubin, G.D., Beaulieu, C.F., Slonim, S.M., Olcott, E.W., Samuels, S.L., Jorgensen, M.J, Semba, C.P, Jeffrey, R.B., Jr, Dake, M.D.: Aortic Aneurysmal Disease: Assessment Of Stent-Grafted Treatment-CT Versus Conventional Angiography. Radiology 215 (2000) 138-146 9. Sun, Z., Winder, J., Kelly, B., Ellis, P., Hirst, D.: CT Virtual Intravascular Endoscopy Of Abdominal Aortic Aneurysms Treated With Suprarenal Endovascular Stent Grafting. Abdom. Imaging. 28 (2003) 580-587 10. Zeman,R.K., Silverman , P.M., Vieco, P.T., Costello, P.: CT Angiography. A. J. Roentgenol. 165 (1995) 1079-1088 11. Sun, Z, Winder, J, Kelly, B,Ellis, P, Kennedy, P, Hirst, D.: Diagnostic Value Of CT Virtual Intravascular Endoscopy In Aortic Stent Grafting. J. Endovasc. Ther. 11 (2004) 13-25 12. Choe, Y.H., Phyun, L.H., Han, B.K.: Biphasic And Discontinuous Injection Of Contrast Material For Thin-Section Helical CT Angiography Of The Whole Aorta And Iliac Arteries. Am. J. Roentgenol. 176 (2001) 454-456 13. Bae, K.T., Tran, H.Q., Heiken, J.P.: Multiphasic Injection Method For Uniform Prolonged Vascular Enhancement At CT Angiography: Pharmacokinetic Analysis And Experimental Porcine Model. Radiology. 216 (2000) 872-880 14. Hu, H., He, H.D., Foley, W.D., Fox SH.: Four Multidetector-Row Helical CT: Image Quality And Volume Coverage Speed. Radiology 215 (2000) 55-62

A New Fuzzy Penalized Likelihood Method for PET Image Reconstruction
Jian Zhou, Huazhong Shu, Limin Luo, and Hongqing Zhu Lab of Image Science and Technology, Department of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China [email protected], {shu.list, luo.list, hqzhu}@seu.edu.cn

Abstract. In positron emission tomography (PET) image reconstruction, classical regularization methods are usually used to overcome the slow convergence of the expectation maximization (EM) methods and to reduce the noise in reconstructed images. In this paper, the fuzzy set theory was employed into the reconstruction procedure. The observations of emission counts were viewed as Poisson random variables with fuzzy mean values. And the fuzziness of these mean values was modelled through choosing an appropriate fuzzy membership function with several adjustable parameters. Coupled with this fuzzy method, the new fuzzy penalized likelihood expectation maximization (FPL–EM) method was proposed for PET image reconstruction. Simulation results showed that the proposed method might perform better in both the image quality and the convergence rate compared with the classical maximum likelihood expectation-maximization (ML–EM).

1

Introduction

Statistical iterative methods for PET reconstruction have become popular since Shepp and Vardi introduced the ML–EM method [1]. However, the ML–EM method is of slow convergence and low resolution due to the ill-conditioned problem of PET. One way to overcome these problems is to use the regularization (or penalized) method. Statistical regularization methods are thought as an appropriate way to solve the maximum of likelihood function for reconstruction with considering several additional penalty terms. In this paper, we proposed a new penalty term through investigating the fuzziness of the observations’ mean values. According to fuzzy set theory (see [2] and [3]), in PET the observations can be modelled as random variables with noncognitive uncertainty known for the Poisson distribution and cognitive uncertainty embedded in their mean values. We addressed this cognitive uncertainty with an appropriate membership function that can be in


This work was supported by National Basic Research Program of China under grant No. 2003CB716102.

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terpreted as a degree of belief for some parameters. Guided by this way, we presented our new fuzzy penalized method for PET reconstruction. The rest of paper is organized as follows: The new reconstruction method is presented in Sec. 2; The experimental results are given in Sec. 3; Finally, Sec. 4 concludes the paper.

2 2.1

Method Statistical Model and the ML Estimation

In the Poisson model for PET, the photon counts are represented as a spatial, inhomogeneous Poisson process with unknown intensity [1]. Suppose that the reconstruction regions are subdivided into Np pixels, such that the emission counts in data collection time at different locations are independent and at location j constitutes a Poisson variable with mean xj . Then the photon counts collected by Nd detector pairs, denoted yi , i = 1, ..., Nd , are also independent Poisson random variables with mean value ξi , ξi = (Ax)i =

Np


aij xj

(1)

j=1

where the element aij in the system matrix A is the probability that a photon emitted at location j is detected by the detector pair i. For the Poisson random variable Yi , we have the following probability density function ξ yi P (Yi = yi ) = exp (−ξi ) · i . (2) (yi )! Then the likelihood function can be given by the multiplication of the probability density function of each Yi , i = 1, ..., Nd . In PET reconstruction, the equivalent log-likelihood function [1]   Nd
−(Ax)i + yi · log (Ax)i (3) Φ(x) = i=1

is often used (terms independent to x are ignored). Therefore, the maximum likelihood (ML) estimation for image x can be computed by solving the following nonlinear optimization problem, ˆ M L = arg max Φ(x) subject to: x ≥ 0. x 2.2

Fuzzy Reconstruction Method

We first make the following assumption: For each i = 1, ..., Nd , the mean value ξi may take its value near around a ξi∗ , where ξi∗ is a properly selected value. In most cases, this assumption holds because the system model usually has limited

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accuracy which leads to a bounded error for any ξi given the emission image intensities. Under this assumption, for each i = 1, ..., Nd , we define a fuzzy subset Ωi ,   Ωi =

ω|ξi∗ − δ ≤ ω ≤ ωi∗ + δ, ω ∈ Z +

where Z + is the set of positive integer and Ωi ⊂ Z + . Since the emission counts must be nonnegative, each element in Ωi should be nonnegative integer. δ(δ ≤ ξi∗ , δ ∈ Z + ) is an adjustable parameter that controls the cardinality of the fuzzy set. For each i = 1, ..., Nd , we define a membership function α(ξi ), ∀i ∈ Z + . For any given ξi , ξi ∈ Ωi , we may set a relatively greater degree of belief α(ξi ) on Ωi . If simply let α(ξi ) = 1.0 on Ωi , then one can obtain a rectangle membership function shown in Fig. 1(a). Generally, for any fuzzy set Ωi , we can define a Gaussian membership function (GMF) shown in Fig. 1(b) which is given by   (ξi − ξi∗ )2 α(ξi ) = exp − . (4) 2σi2 In (4), the shape of function is adjusted through the parameter σi , The smaller the σi is, the smoother the curve will be. In this paper, our method is mainly developed by using this GMF.

Fig. 1. Fuzzy membership function. (a) Rectangle membership function. (b) GMF

The function α(ξi ) can also be viewed as the probability density function for the random variable Ξi if we normalize it by dividing its summation over the set Z + . The probability function P (Ξi = ξi ) for random variable Ξi is given by   1 α(ξi ) (ξi − ξi∗ )2 → (5) P (Ξi = ξi ) =  · exp − α(ηi ) Ci 2σi2 ηi ∈Z +

where Ci is the summation of α(ξi ) over the set Z + .

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The probability function P (Yi = yi ) in (2) can then be rewritten to be the conditional probability P (Yi = yi |Ξi = ξi ). Hence, the joint probability density function P (Yi = yi , Ξi = ξi ) is defined by the multiplication of P (Yi = yi |Ξi = ξi ) and P (Ξi = ξi ). Since the observations are assumed to be independent, the joint probability density can be represented as   1 ξiyi (ξi − ξi∗ )2 . · P (Yi = yi , Ξi = ξi ) = exp(−ξi ) · · exp − (yi )! Ci 2σ 2 i=1 i=1 Nd 

Nd 

(6)

Substituting (1) into (6) and taking logarithm, we obtain Ψ (x) =

Nd






−(Ax)i + yi · log (Ax)i

+

i=1

Nd
i=1



 [(Ax)i − ξi∗ ]2 − . 2σi2

(7)

Notice that any observed photons yi are realizations for Poisson random variables which, in a statistical sense, approximate the mean values. Hence, every observation yi should be fallen into our predefined fuzzy set Ωi . Moreover, we can set the greatest degree of belief at the point of yi , i.e., α(ξi∗ ) = α(yi ) = max α(ξi ), ∀ξi ∈ Ωi , which is equivalent to set ξi∗ to yi , (i = 1, ..., Nd ). The σi is a shape parameter controlling the degree of belief of each ξi . For the sake of simplicity, we apply the same shape parameter to each membership function, i.e., for each i = 1, ..., Nd , we let σi = σ, where σ is a constant. Thus we simplify (7) into the following function Ψ (x) =

Nd






−(Ax)i + yi · log (Ax)i

i=1

+

Nd
i=1



 [(Ax)i − yi ]2 − . 2σ 2

(8)

Since the observations are usually viewed as an incomplete data space, we can solve the maximum optimization problem of (8) by using the EM method [1], [4], and then obtain our FPL–EM method in which the update for each pixel is as follows Nd  yi xkj · aij (Ax k) i i=1 k+1 (9) xj = N d −2 k aij {1 + σ · [(Ax )i − yi ]} i=1

where k = 0, 1, 2, ..., indicates the iteration number.

3

Experimental Evaluation

In our experiments, we used the Shepp-Logan phantom shown in Fig. 2. The projection space was assumed to be 160 radial bins and 192 angles evenly spaced over 180◦ . The final reconstructed images were set to a size of 64 × 64 pixel matrices.

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Fig. 2. Phantom

The sinogram were globally scaled to a mean sum of 1, 000, 000 true events. And the pseudo-random Poisson variants were drawn through the model in subsec. 2.1. Data were also studied with 5% uniform Poisson distributed background events, representing the range of random coincidences in PET scans. The initial estimator x0 was set to a strictly positive vector. Fig. 3 shows the reconstructed images by using ML–EM and FPL–EM. Different shape parameter σ’s in FPL–EM were used to test its influence on the reconstructed image.

Fig. 3. Reconstructed images. (a) ML–EM reconstruction (20 iterations). (b), (c) and (d) FPL–EM reconstructions. (20 iterations for σ −2 = 0.002, 0.004, 0.006, respectively)

To evaluate the reconstructed images, the mean square error(MSE) between each iteration result xk and the true phantom x∗ was computed using the following definition xk − x∗  , k = 1, 2, ... (10) MSE(k) = x∗  where x is the Euclidean length of a vector x Fig. 4(a) shows the mean square error comparison between ML–EM and FPL–EM. Clearly, small mean square errors can be achieved by choosing an appropriate shape parameter σ in FPL–EM. In Fig. 4(a), we can observe that the FPL–EM method yields the best performance when σ −2 = 0.004. Fig. 4(b) shows the log-likelihood values versus iteration number. The fastest convergence rate was also yielded with σ −2 = 0.004 in FPL–EM. Fig. 4(c) shows the line plot of row 32 of reconstructed images. It can be seen that the FPL–EM method has better performance than the ML–EM method.

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Fig. 4. Evaluation results. (a) Mean square errors versus iteration. (b) The loglikelihood values versus iteration. (c) Line plot of row 32 at the twentieth iteration

4

Conclusions

We have proposed a new fuzzy penalized likelihood method for PET image reconstruction. The simulations proved its better performance than the ML–EM method in both image resolution and convergence. The future work will concentrate on finding the optimal shape parameter for GMF. In addition, further studies on the image prior information, such as the Gibbs distribution, are currently under investigation.

References 1. Shepp, L. A., Vardi, Y.: Maximum likelihood reconstruction for emission tomography, IEEE Trans. Med. Imag. MI-1(2) (1982) 113–122. 2. Zadeh, L. A.: Fuzzy Sets. Information and Control, 8 (1965) 338–353. 3. Chao, R. J., Ayyub, B. M.: Distributions with Fuzziness and Randomness, Proceedings of ISUMA - NAFIPS ’95 The Third International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society (1995) 668–673. 4. Lange, K., Carson, R.: EM reconstruction algorithm for emission and transmission tomography, J. Comput. Assist. Tomog. 8 (1984) 306–316.

Interactive GSOM-Based Approaches for Improving Biomedical Pattern Discovery and Visualization Haiying Wang, Francisco Azuaje, and Norman Black School of Computing and Mathematics, University of Ulster at Jordanstown, Newtownabbey, Co. Antrim, BT37 0QB, N. Ireland, UK {hy.wang, fj.azuaje, nd.black}@ulster.ac.uk

Abstract. Recent progress in biology and medical sciences has led to an explosive growth of biomedical data. Extracting relevant knowledge from such volumes of data represents an enormous challenge and opportunity. This paper assesses several approaches to improving neural network-based biomedical pattern discovery and visualization. It focuses on unsupervised classification problems, as well as on interactive and iterative methods to display, identify and validate potential relevant patterns. Clustering and pattern visualization models were based on the adaptation of a self-adaptive neural network known as Growing Self Organizing Maps. These models provided the basis for the implementation of hierarchical clustering, cluster validity assessment and a method for monitoring learning processes (cluster formation). This framework was tested on an electrocardiogram beat data set and data consisting of DNA splice-junction sequences. The results indicate that these techniques may facilitate knowledge discovery tasks by improving key factors such as predictive effectiveness, learning efficiency and understandability of outcomes.

1

Introduction

Advances in biological and medical sciences have been reflected in an explosive growth of diverse data sources. Due to its inherent complexity and the lack of comprehensive theories at the molecular and physiological levels, extracting relevant knowledge from such volumes of data represents an enormous challenge and opportunity. It has been demonstrated that artificial neural networks (ANNs) are well suited to such domains. Ideker et al. [1], for example, used Kohonen Feature Maps (SOMs) [2] to support the study of a cellular pathway model, in which they identified 997 messenger RNAs (mRNAs) responding to 20 systematic perturbations of the yeast galactose utilization pathway. Azuaje [3] applied a Simplified Fuzzy ARTMAP (SFAM) model to analyse gene expression data. In this study, the SFAM-based system not only distinguished normal from diffuse large B-cell lymphoma (DLBCL) patients, but also it identified the differences between paJ. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 556–561, 2004. c Springer-Verlag Berlin Heidelberg 2004


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tients with molecularly distinct forms of DLBCL without previous knowledge of those subtypes. While successfully addressing key biomedical pattern classification problems, most of the existing ANN-based solutions exhibit several limitations that limit its applicability. For example, a fundamental problem of ANNs is that the information that they encode cannot be easily understood by humans. The internal structure and the way in which an ANN derives an output value from a given feature vector have been traditionally concealed from the user. It has become apparent that, without some form of explanation and interpretation capability, the potential of ANNs-based pattern discovery may not be fully achieved [4, 5]. Based on self-adaptive neural networks (SANNs) together with graphical and statistical tools, this paper explores several approaches to support pattern discovery and visualization. The remainder of this paper is organized as follows. Section II describes the key component in this study: Growing Self Organizing Maps (GSOM), followed by a description of the data sets under study. The results are presented in Section IV. Discussion and Conclusions are included in the last section.

2

The GSOM

The GSOM [6] belongs to the family of SANNs, which follows the basic principle of the SOM but adapts its shape and size according to the structure of the input data. The GSOM learning process, which is started by generating an initial network composed of four neurons, includes three stages: Initialization, growing and smoothing phases. Like other SANNs, each input presentation involves two basic operations: (a) finding the best matching neurone for each input vector and (b) updating the winning neurone and its neighbourhood. The reader is referred to [6] and [7] for a detailed description of the learning dynamics of the GSOM. In the context of pattern discovery and visualization, the GSOM exhibits two important features: – The GSOM keeps a regular, 2D grid structure at all times. The resulting map reveals patterns hidden in the data by its shape and attracts attention to relevant areas by branching out. This provides the basis for a user-friendly and flexible pattern visualization and interpretation platform. – The user can provide a spread factor, SF, [0, 1] to specify the growth degree of the GSOM. This provides a straightforward way to measure and control the expansion of the networks. Based on the selection of different values of SF, hierarchical and multiresolution clustering may be implemented.

3

The Data Sets and Prediction Problems

Two data sets were used to test the approaches proposed. The first one is an ECG beat data set obtained from the MIT/BIH arrhythmia database [8]. Based on a

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set of descriptive measurements for each beat, the problem defined in this data set is to determine whether a beat is a ventricular ectopic beat (Class V) or a normal beat (Class N). Each beat is represented by 9 features. A detailed description of this data set can be found at http://www.cae.wisc.edu/~ece539/data/ecg/. The second data set is a DNA sequence data set. The problem posed is to decide, given a DNA sequence, whether it is an ’intron −→exon’ boundary (IE), ’exon −→ intron’ boundary (EI), or neither (N). The data set consists of 2000 sequences taken from [9], in which 23.2% belong to Class EI, 24.25% are IE samples and 52.55% are N samples. Each sequence, which originally includes 60 nucleotides, is represented by 180 binary attributes. Each nucleotide is replaced by a three-digit binary variable as follows: A−→100; C−→010; G−→001; T−→000. Each class is represented by a number: EI−→1; IE−→2; N−→3. The full data description is given in [9].

4 4.1

Results Pattern Discovery and Visualization Using GSOM

One of the key advantages of the GSOM is that it can develop into different shapes to reveal key patterns hidden in the data. Such visualization capabilities may highlight the inherent data structure in a more meaningful way. Based on the relevant resulting maps, the cluster structure of the underlying data can be easily interpreted. The GSOM maps with SF = 0.001 for the ECG data set shown in Fig. 1(a), for example, has branched out in two directions, representing the two main classes of the data set. An analysis of the sample distribution over each branch indicates that there is a dominant class represented in each branch. Based on a majority voting strategy, the label map(1−→N and 2−→V) is shown in Fig. 1(b). Similar data are successfully clustered. Ambiguous areas, such as

Fig. 1. GSOM-based data visualization for ECG data. (a) The resulting map.The numbers shown represent the order in which each neuron was created during the growth phase. (b) The label map. (c) Twenty-four Dunn’s indices for the three partitions

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the borders of the cluster regions, can be further analyzed with a higher SF value (see submap C1). This submap has clearly been dispersed in two directions (SubBranches C1 and C2). To identify the relationship between Branches A, B and Sub-Branches C1 and C2, a clustering identification and evaluation framework based on twenty-four Dunn’s indices [7, 10] were implemented. Fig. 1(c) shows twenty-four Dunn’s validity indices for the three possible partitions suggested by visualizing the resulting map illustrated in Fig. 1(a) and (b). Good partitions are associated with larger value of the Dunn’s indices. Fifteen validity indices indicate that the second 2-clusters partition is the optimum partition, which indicates that the Sub-Branch C1 is closer to Branch B and SubBranch C2 may be associated with Branch A. This coincides with the sample distribution in these areas. 4.2

Visualization of the Learning Process

The visualization of a learning process and its outcomes can help users to gain a better understanding of the predictions made by an ANN-based approach. Nevertheless, the study of advanced visualization techniques for ANNs has not received the attention it deserves [11]. The GSOM incrementally grows new neurons to achieve a better representation of the input data. Thus, graphical tools to visualize the phases of a GSOM learning process may provide a better understanding of the inter- and intra-cluster relationships of the data [12], as illustrated in Fig. 2 for the DNA data.

Fig. 2. The resulting GSOM map for DNA data at different learning stages: (a) NLE = 2, (b) NLE = 5; (c) NLE = 10. NLE stands for the number of learning epochs

At an early stage (NLE = 2, shown in Fig. 2(a)) the map branches out into two directions, indicating that the data set may be firstly clustered into two major categories: splice (Classes EI and IE) and non-splice (Class N) junctions. As the learning process progresses, the GSOM gradually produces a new branch (Branch C in Fig. 2(b)) to represent the underlying data structure, suggesting that the samples (splice junctions) assigned to Branch A (shown on Fig. 2(a))

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could be further classified into two different classes (Classes EI and IE). The GSOM map shown on Fig. 2(c) (NLE = 10) support this argument. 4.3

Hierarchical Clustering with the GSOM

Based on the selection on different SF values, the GSOM can be used to perform hierarchical clustering. The results obtained show that the GSOM may highlight significant groups in the data through its shape even for lower SF values. A higher resolution view can be obtained with a larger SF value in the areas of interest. The map shown in Fig. 3(b) was produced with SF = 0.01, indicating the two significant groups in the DNA data set (splice and non-splice junctions). A higher SF value is then applied (SF = 0.1) to the Branch A (Fig. 3(a)). The new map has been developed in two directions, suggesting that there may be two subgroups (Classes EI and IE) in this branch. This is consistent with the sample distribution over these two sub-branches (Branches A1 and A2). Based on this observation together with the results obtained in the last section, we argued that the hierarchical structure shown in Fig. 3(c) perhaps reflects the inherent data structure in a more meaningful and precise way.

Fig. 3. The hierarchical clustering of DNA data based on different SF values. (a) The higher resolution map of Branch A with SF = 0.1. (b) The resulting map with SF = 0.01. (c) A hierarchical description for DNA data inferred by GSOM-based technique

5

Discussion

This study indicates that a GSOM-based system may facilitate two important biomedical pattern discovery and visualization problems. For instance, instead of using a static grid representation or long lists of numbers to describe patterns revealed, this research developed a graphical environment to dynamically depict a networks’ evolution during learning. Such a facility may help scientists achieve a better understanding of the dynamics of the ANN-based model.The GSOM attempts to build a structure to represent the input data as accurately as possible. By monitoring its learning process, users can better understand how a model generates its decision. By introducing a SF, users have more control on the growth of the resulting map. Thus, hierarchical and multi-resolution clustering analysis may also be implemented. A robust framework for assessing the quality

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of clustering outcomes, which has been implemented based on the combination of cluster validity indices, provides statistical indicators that further enhance the understanding of the results generated by ANNs. The approaches discussed in this paper hold promise to deliver an iterative and interactive pattern visualization and interpretation platform. Due to the generation of new neurons in all free neighbouring positions, the GSOM inevitably generates irrelevant neurons, which sometimes can severely degrade the visualization ability of GSOM-based models. Incorporation of pruning algorithms into GSOM-based learning techniques deserves further investigation. Another problem that deserves further research is GSOM-based feature relevance assessment. In GSOM, a SF is independent of the dimensionality of the data. Thus, one can compare different maps by using the same SF and different combinations of features to identify their contributions to the cluster structure. Such a method can help the data miner to study the effect of each feature on the clustering and their relationships.

References 1. Ideker, T., Thorsson, V., Ranish, J. A., Christmas, R., Buhler, J., Eng, J. K., Bumgarner, R., Goodlett, D. R., Aebersol, R., Hood, L.: Integrated Genomic and Proteomic Analyses of a Systematically Perturbated Metabolic Network. Science, 292 (2001) 929-933 2. Kohonen,T.:Self-Organizing Maps. Heidelberg. Germany:Springer-Vin erlag (1995) 3. Azuaje, F.: A Computational Neural Approach to Support the Discovery of Gene Function and Classes of Cancer. IEEE Trans. on Biomedical Engineering, 48(3), (2001) 332-339 4. Baldi, P., Brunak, S.: Bioinformatics: The Machine Learning Approach. London: The MIT Press (2000) 5. Dybowski, R., Gant, V.: Clinical Applications of Artificial Neural Networks. London: Cambridge University Press (2001) 6. Alahakoon, D., Halgamuge, S. K., Srinivasan, B.: Dynamic Self-Oorganizing Maps with Controlled Growth for Knowledge Discovery. IEEE Transactions on Neural Networks 11(3), (2000) 601-614 7. Wang, H., Azuaje, F., Black, N.: Improving Biomolecular Pattern Discovery and Visualization with Hybrid Self-Adaptive Networks. IEEE Transactions on Nanobioscience 1(4), (2002) 146-166 8. Mark, R., Moody, G.: MIT-BIH Arrhythmia DataBase Directory. Cambridge: MIT (1988) 9. Brazdil, P., Gama, J.: DNA-Primate Splice-Junction Gene Sequences, with Associated Imperfect Domain Theory. Available at: http://porto.niaad.liacc.up.pt/niaad/statlog/datasets/dna/dna.doc.html (June 2002) 10. Bezdek, J. C., Pal, N. R.: Some New Indexes of Cluster Validity. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 28(3), (1998) 301-315 11. Haykin, S.: Neural Networks: A Comprehensive Foundation. New Jersey: Prentice Hall (1994) 12. Wang, H., Azuaje, F., Black, N.: An Integrative and Interactive Framework for Improving Biomedical Pattern Discovery and Visualization. IEEE Transactions on Information Technology in Biomedicine, 8(1), (2004) 16-27

Discontinuity-Preserving Moving Least Squares Method Huafeng Liu1,2 and Pengcheng Shi2 1

State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, China 2 Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong {eeliuhf, eeship}@ust.hk

Abstract. We present a discontinuity-preserving moving-least-squares (MLS) method with applications in curve and surface reconstruction, domain partitioning, and image restoration. The fundamental power of this strategy rests with the moving support domain selection for each data point from its neighbors and the associated notion of compactly supported weighting functions, and the inclusion of singular enhancement techniques aided by the data-dependent singularity detection. This general framework meshes well with the multi-scale concept, and can treat uniformly and non-uniformly distributed data in a consistent manner. In addition to the smooth approximation capability, which is essentially the basis of the emerging meshfree particle methods for numerical solutions of partial differential equations, MLS can also be used as a general numerical method for derivative evaluation on irregularly spaced points, which has a wide variety of important implications for computer vision problems.

1

Introduction

Data fitting and approximation is one of the central problems in computer vision, with wide range of applications in object reconstruction and recognition, image restoration, and domain partitioning. The fundamental needs come from the disparity between the continua of visual phenomena and the discreteness of measurement data that are usually corrupted by noises. A typical strategy to tackle this type of problems is to introduce a smoothness constraint: min

N


 (S(t) − Si ) + 2

α(S
)2 + β(S

)2 dt

(1)

i=1

where S(t) is the unknown smooth function and Si is the measurement data. This actually become the regularization paradigm in computer vision, with a wide range of variations and applications developed in the past twenty years [1, 3, 4, 9]. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 562–569, 2004. c Springer-Verlag Berlin Heidelberg 2004 

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Fig. 1. Influence domains (left), cubic spline weighting function (middle) and The addition of gradient-dependent virtual nodes (right)

It has been suggested that the least squares approximation ideas can be applied to generate discontinuity-preserving interpolants by introducing the notion of moving least squares approximation together with appropriate singularities in the weights used in such approximations [6]. However, for computer vision problems, the question of where to enforce the interpolation and where to perform the smoothing approximation remains unanswered. Of course, thresholding of data gradient may do the trick of detecting the singularities under certain situations, which can then be followed by the interpolating MLS procedure. Nevertheless, the selection of proper thresholds introduce a whole new set of questions. We present a MLS algorithm which performs smoothing approximation and discontinuity-preserving interpolation in a consistent fashion. Instead of direct manipulation of the MLS weight functions and/or the basis functions in order to create the singular effect at any particular data point [5, 6], we make changes to the data point distribution at the support domain around the point of interest, which in turn alters the weight distribution to achieve the desired interpolating or smoothing effect. We demonstrate the accuracy and robustness of the method with synthetic curve and surface data fitting, and present the experiment results with real images.

2

Moving Least Squares Approximation

¯ → R is to be approximated and that its It is assumed that a function f : D ¯ i = 1, 2, ..., N are given, where values fi = f (xi ) at sampling nodes xi ∈ D, ¯ domain D is assumed to be the closure of a simply connected subset D ∈ Rn . We aim to develop an smooth approximation Gf to f on the basis of the available information about f at those scattered nodal locations, which are often noise corrupted and not necessary uniformly distributed. 2.1

MLS Formulation ¯ a local approximant Lxˆ f of the global approximating ˆ ∈ D, At each point x function Gf is defined in terms of some basis functions {p(i) }ni=1 , n ≤ N and a local L2 -norm: n
ai (ˆ x)p(i) (ˆ x) (2) Lxˆ f := i=1

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Fig. 2. Noisy curve fitting with MLS, GTMLS, GWMLS, 1st derivative (left) and 2nd derivative (green) with segment partitioning at zero-crossings (right) for the 20dB GWMLS curve

where the set of coefficients ai (ˆ x), i = 1, 2, ..., n are determined such that Equation (2) is, in the least squares sense, the best approximation of f . The global ¯ approximant Gf is then defined on the entire domain for any x ˆ∈D x) = Gf (ˆ x) = Lxˆ f (ˆ

n


ai (ˆ x)p(i) (ˆ x)

(3)

i=1

Commonly used basis functions in two-dimensional cases include the linear one pT(n=3) = {1, x, y} and the quadratic one pT(n=6) = {1, x, y, x2 , xy, y 2 }. 2.2

Determination of MLS Coefficients

x) using Based on the least-squares criteria, we can calculate the coefficients ai (ˆ the equation, with a(ˆ x) = {a1 (ˆ x), a2 (ˆ x), ..., an (ˆ x)}T : A(ˆ x)a(ˆ x) = B(ˆ x)f

(4)

where A(ˆ x) = P(ˆ x)W(ˆ x)P(ˆ x) B(ˆ x) = P(ˆ x)W(ˆ x)

T

(5) (6)

where f = {f1 , f2 , ..., fn }T and P(ˆ x) is an n × N matrix whose j th row is (j) (j) (j) x) = diag(w1 (ˆ x) w2 (ˆ x) ... wN (ˆ x)) is an N × {p (x1 ), p (x2 ), ..., p (xN )}. W(ˆ N diagonal matrix of weight functions. Each weight functions wi (ˆ x), define for ¯ is non-negative and has the form wi (ˆ x) = w(|ˆ x − xi |) where |ˆ x − xi | each x ˆ ∈ D, is the distance between the point x ˆ and xi . In our implementation, we have chosen to use the following cubic spline function (see Fig. 1) which is dependent on the distance di = |x − xi |: ⎧2 for r ≤ 12 ⎨ 3 − 4r2 + 4r3 4 3 4 2 (7) w(r) = 3 − 4r + 4r − 3 r for 12 < r ≤ 1 ⎩ 0 for r > 1 in which r = di /dmi is a normalized radius. The support size dmi of the ith node is determined by dmi = dmax ci

(8)

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Fig. 3. Noisy surface (20dB) fitting with MLS (0.03 ± 1.60) and GWMLS (0.01 ± 0.37)

where dmax is a scaling parameter, and the distance ci is determined by searching for enough neighbor nodes for the matrix A in Equation (5) to be regular, i.e. invertible at every point in the domain. Together, dmax and ci ensure that the system has a unique solution, and they also serve similar role as the scale as in scale-space theory which allow multi-resolution MLS approximations of the function f . Since the basis functions are designed to be linearly independent, together with the positive-definiteness of W(ˆ x), it implies that A(ˆ x) is positive-definite. x) can be uniquely determined as Hence, the coefficients ai (ˆ x)B(ˆ x)f a(ˆ x) = A−1 (ˆ

3

(9)

Interpolating MLS

It should be noted that MLS approximations do not satisfy the Kronecker delta criterion and result in Gf (xi ) = fi , i.e. the nodal data value fi are not the nodal values of the MLS approximation Gf (xi ). Therefore, the approximation of the function at the ith node Gf (xi ) depends not only on the nodal data fi but also on the nodal data of all the nodes within the influence domain of node i. However, for many situations in computer vision such as image denoising and partitioning, the edges or discontinuities need to be preserved while the noisy data being smoothed. In these cases, one would prefer that the approximation actually performs exact interpolation (EIMLS) or near interpolation (NIMLS) at selected nodal points, usually the discontinuities, and performs approximation for the rest. With inspiration from Shepard [8], Lancaster and Salkauskas has proposed the basic principle of making weight function wi infinity or a suitable singular at the nodal point xi if Gf is to interpolate there [6]. This can be achieved by selecting proper weight function wi (x) = w(di ) such that wi → ∞ as di → 0. It has been suggested to use a function in the form of 2

w(di ) = e−di /(d2i )

(10)

which clearly has the correct asymptotic behavior at di = 0 and di = ∞. Exact interpolating MLS is, however, possible, and a scheme is developed originally intended for imposition of essential boundary conditions in the meshfree particle methods [5, 7]. The singularities introduced by the singular weight

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functions in Equation (10) are removed through algebraic manipulations and all the resulting terms are well defined. In order to achieve that goal, a new set of basis functions is generated. The first term of the new basis function u(1) (x) is obtained by normalizing the first term of the original basis functions p(1) (x): u(1) (x) ≡

p(1) |p(1) |

(11)

The remaining new basis functions are required to be orthogonal to the first basis function u(1) (x). Using the Gramm-Schmidt orthogonalization, the modified basis functions u(i) (x) are obtained through u(i) (x) = p(i) (x) − Sp(i) (x)

(12)

where the operator S is defined as Sp(i) (x) =

N


p(i) (xj )v (j) (x)

(13)

j=1

wj (x) v (j) (x) = N l=1 wl (x)

(14)

Now, the modified local and global approximant of Equation (2) and (3) becomes: n
ˆ (x) = L ˆ x f := Sf (x) + αi (x)u(i) (x) (15) Gf i=2

where αi (x), i = 2, 3, ..., n represent the modified unknown MLS coefficients to be determined from the nodal data. Since the first basis function u(1) (x) is orthogonal to the rest of the basis functions by definition, the equation for the coefficient α1 (x) can be solved separately, and resulting in Sf (x) in Equation (15). The other coefficients αT (x) = {α2 (x), α3 (x), ..., αn (x)} can be computed through ˆ ˆ A(x)α(x) = B(x)ϕ(x) ˆ ˆ −1 (x)B(x)ϕ(x) α(x) = A

(16) (17)

T ˆ A(x) = U(x)W(x)U(x)

(18)

where

T

ˆ − V(x)) U(x) = P(I ˆ B(x) = U(x)W(x)

(19) (20)

ˆ is (n−1)×N matrix that contains row 2 through n of U(x) is a (n−1)×N matrix, P matrix P, V(x) is a n × N matrix with each row being {v (1)(x) , v (2)(x) , ..., v (n)(x) }, and ϕT (x) = {ϕ1 (x), ϕ2 (x), ..., ϕN (x)} with ϕk (x) = fk − Sf (x), k = 1, 2, ..., N .

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Fig. 4. Denoising of the range data: original, noisy, MLS, and GWMLS

Since the weight functions wi (x) are singular at the respective sampling nodes ˆ xi by design, special cares must be taken in computing the terms in matrix A ˆ = Bϕ. ˆ After some algebraic manipulations [5], we have and vector Y ˆ ij (x) = A

N


(k)

(21)

(k)

(22)

a ˆij (x) i, j = 1, 2, ..., (n − 1)

k=1

ˆ i (x) = Y

N


yˆi (x) i = 1, 2, ..., (n − 1)

k=1 (k)

(k)

The values of a ˆij (x) and yˆi (x) depend on whether the point x coincides with a sampling node xk , k = 1, 2, ..., N or not:  (i) (j) s(x)v (k) (x)ck (x)ck (x), x = xk (k) a ˆij (x) = (23) u(i) (x)wk (x)u(j) (x), x =xk  (i) v (k) (x)ck (x)ϕk (x), x = xk (k) yˆi (x) = (24) (i) u (x)wk (x)ϕk (x), x =xk where s(x) = N (i)

ck (x) =

1

j=1
N

wj (x) wm (x)[p(i) (x) − p(i) (xm )]

(25) (26)

m=km=1

Note that there are no singularities in this set of equations if x =xk . Since they contain the weight function wk (x), on surface the singularities may occur for functions s(x) and v (j) (x). However, it can be shown that limx→xk s(x) = 0 (i) and limx→xk v (j) (x) = 0. The function ck (x) is not singular at x = xk because it does not include the weight function wk (x). Now, it clear that singularities ˆ and Y ˆ are well defined for for x = xk are removed and all terms needed for A all locations of the domain.

4

Data-Driven MLS for Interpolation and Approximation

NIMLS and EIMLS provide means to perform interpolations at selected nodal points and performs smoothing approximation for the rest. However, for practical problems, the questions of where to enforce the interpolation and where to

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Fig. 5. Denoising of the noisy brain image: original, noisy, Gaussian filtered, anisotropic diffusion, MLS, and GWMLS

perform the smoothing approximation remain unanswered. Of course, for computer vision applications, we can always perform discrete derivative operations, such as gradient, on the image or measurement data first. Nevertheless, the selection of proper thresholds introduces a whole new set of questions which are difficult to handle. We have developed a simple, yet powerful and flexible, alternative datadriven MLS process which treats the near interpolating at discontinuities and the smoothing approximation elsewhere in a coherent manner. Philosophically, this approach is very different from the NIMLS and EIMLS. Instead of direct manipulation of the weight functions wi (x) or the basis functions pi (x) in order to create the singular effect at any particular nodal point, we make changes to the nodal point distribution at the influence domain around the point of interest, which in turn alters the weight distribution to achieve the desired interpolating or smoothing effect. Assuming that Gf is to interpolate at node xi , the influence domain of xi contains K nodal data points xik , k = 1, 2, ..., K, and we have the weight function wi (r) as defined in Equation (7). As discussed in the last paragraph of Section 2.2, in practice only the nodes xik within the influence domain of xi are used for the MLS approximation Gf (x), realized through the careful design of the weight function wi (x) and through Equation (3). In order to interpolate at node xi , we add a number of virtual nodes xi ± j, j = 0, 1, 2, ..., M to the influence domain, where  is a position vector with very small magnitude (see Fig. 1 for illustration). These virtual nodes distribute closely to node xi , and have identical value as xi : (27) f (xi ± j) = f (xi ) The number 2×M of virtual nodes determines if the process is smoothing approximation (no virtual node, M = 0) or near/exact interpolation (the more the virtual nodes, the closer the process converges to exact interpolating MLS). This way, without any attempts to modify the weight function itself, we can manipulate the actual relative weight for each of the node inside the influence domain relative to node xi , and perform approximation or interpolation in exactly the same manner. The main advantage of this strategy is that it affords a purely data-driven scheme to enforce interpolation or approximation at various nodal points. In our applications of image denoising and curve/surface fitting, we have used the gradient/derivative magnitude at the point of interest to determine the number of virtual points being added for the MLS procedure.

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Applications

We denote the classic MLS approximation as MLS, the gradient thresholding detected singularities following by exact interpolating MLS as GTMLS, and the data-driven gradient-weighted MLS as GWMLS. Curve fitting is performed on a set of noisy curve data generated from clean curve with SN R = 20dB. The reconstructed curves are shown in Fig. 2. In these tests, the GWMLS does substantially better reconstruction than the other two. Further, the derivatives of GWMLS are used to partition the curve into different segments, and the results are shown in Fig. 2. Similarly, we apply the MLS and GWMLS to synthetic surface data as shown in Fig. 3. And once again, the GWMLS does much better job in re-producing the original surface. Using a well-known range data from the OSU/WSU/MSU Range Database, we test the ability of the GWMLS procedure on range data processing. Fig. 4 shows the wireframe plots of the range image. From these figures, it is obvious that the GWMLS does a wonderful job in reconstructing the original data. Finally, we add noise to the brain image (SN R = 20dB) and then perform Gaussian filtering (variance is 0.8), anisotropic diffusion [2], MLS, and GWMLS on the noisy brain image. The resulting images are shown in Fig. 5. Here, the GWMLS has slightly better performance than anisotropic diffusion, and much better than Gaussian filter and MLS. Acknowledgments. This work is supported by HKRGC-CERG HKUST6151/ 03E and National Basic Research Program of China (No: 2003CB716104).

References 1. Bertero, M., Poggio, T.A., Torre, V. : Ill-posed problems in early vision, Proceedings of IEEE 76 (1988) 869–889 2. Black, M.J., Sapiro, G., Marimont, D., Heeger, D.J.: Robust anisotropic diffusion. IEEE TIP 7 (1998) 421-432 3. Chin, R.T., Yeh, C.L.: Quantitative Evaluation of Some Edge Preserving Noise Smoothing Techniques, CVGIP 23 (1983) 167–191 4. Geman, D., Reynolds, G.: Constrained Restoration and the Recovery of Discontinuities. IEEE PAMI 14 (1992) 367–383 5. Kaljevic, I. Saigal, S.: An improved Element Free Galerkin Formulation. Internaltion Journal for Numerical Methods in Engineering 40 (1997) 2953–2974 6. Lancaster, P. Salkauskas, K.: Surface Generated by Moving Least Squares Methods. Mathematics of Computation 37 (1981) 141–158 7. Liu, H., Shi, P.: Meshfree Particle Method. IEEE International Conference on Computer Vision. (2003) 289–296 8. Shepard, D.: A two-dimensional interpolation function for irregular spaced points. ACM National Conference (1968) 517–524 9. Terzopoulos, D.: The computation of visible-surface representation. IEEE PAMI 10 (1991) 417–438

Multiscale Centerline Extraction of Angiogram Vessels Using Gabor Filters Nong Sang1, Qiling Tang1, Xiaoxiao Liu2, and Wenjie Weng2 1

Institute for Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan 430074, PR China [email protected], [email protected] 2 Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan 430074, PR China [email protected], [email protected]

Abstract. In this paper, we propose a new automated approach to extract the centerlines from 2-D angiography. The centerline extraction is the basis of 3-D reconstruction of the blood vessels, so the accurate localization of centerlines counts for much. The characteristics of multiscale Gabor even filter, flexible frequency bands and enhancement effects, are fully utilized to detect centerlines of the blood vessels in various size.

1 Introduction Most angiogram analysis techniques, interactive or not, initially extract the 2-D centerlines of tubular object, especially in quantitative coronary angiography. Vessel centerlines have been used in three-dimensional vessel tree segmentation and reconstruction [1], computing edge gradients and searching for border positions [2], for calculation of lesion symmetry. Medial representation of grayscale images has been well developed during the past several decades: multiscale approach has gained most attention [3], and others new methods include PDM technique by Jang [4], and snake-like algorithms [5]. Considering the curvilinear features and the complexity of the X-ray imaging artifacts, most of the reported image vessel features detectors are conventional ones: ridge detector based on level -set theory, morphological processing [6]. Many of them have high computational cost or poor robustness due to the complexity of the angiograph imaging. To cope with close proximity or crossing of vessels and varying vessel widths including large stenoses and sever imaging artifacts, we develop a new automated method for accurate detection of centerlines in angiogram images. A characteristic of multiscale Gabor filters is its ability to tune to specific frequency, which allows conducting noise suppression and centerline enhancement. This is very beneficial to accurately extract centerlines of blood vessels in poor contrast and noisy background. The resulting centerline structure can be used for 3-D reconstruction. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 570–575, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Computational Models 2.1 Gabor Functions Gabor functions were first defined by Gabor, and later extended to 2-D by Daugman [7]. A Gabor function is a Gaussian modulated by a complex sinusoid, as the following equation illustrates:

(

h(x, y ) = g ( x ' , y ' ) exp j 2πFx '

)

(1)

where (x ' , y ' ) = (x cos θ + y sin θ ,− x sin θ + y cosθ ) , denoting θ the orientation of the filter. Any desired orientation can be achieved via a rigid rotation in the x-y plane. F is the spatial center frequency, g ( x, y ) is the 2-D Gaussian function: g ( x, y ) =

1 2πσ x σ y

⎧ ⎡ ⎪ 1 ⎛ x exp ⎨− ⎢⎜⎜ ⎪ 2 ⎢⎣⎝ σ x ⎩

⎞ ⎛⎜ y ⎟ + ⎟ ⎜σ ⎠ ⎝ y 2

⎞ ⎟ ⎟ ⎠

2 ⎤⎫

⎥ ⎪⎬ ⎥⎪ ⎦⎭

(2)

where σ x and σ y correspond to the horizontal and vertical spatial extent of the filter. σ y σ x , called the aspect ratio, gives a measure of the filter’s asymmetry. σ x and σ y

are related to the filter’s frequency bandwidth and orientation bandwidth in the way illustrated in formula (3) and (4): σx =

σy =

ln 2 1 2 BF + 1 2 πF 2 BF − 1

(3)

ln 2 1 1 2 πF tan(Bθ 2 )

(4)

B F is the spatial frequency bandwidth and Bθ is the orientation bandwidth. In this

paper, the parameters B F and Bθ are set as 1.0 and 45 D , respectively. 2.2 Centerline Response of Gabor Even Filters

The accurate localization of centerlines requires a high resolution in the spatial domain. An important property of multiscale Gabor filters is that they have optimal joint localization or resolution, in both the spatial and the spatial-frequency domains [8]. These results are extensively used for edge detection, texture classification; optical flow estimation and image compression. In this paper, the Gabor even filter,

(

) (

h(x, y ) = g x ' , y ' cos 2πFx '

)

(5)

the real component of Gabor functions, is proposed as the centerline extraction operator of blood vessels. Here we demonstrate that a 1-D Gabor even filter with suitable center frequency can give maximal response at the center of tube-profile.

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The tube-profile centered at x = 0 with height 1 and width τ can be expressed by the step-edge function ε (x ) as follows: τ⎞ ⎛ τ⎞ ⎛ fτ ( x ) = ε ⎜ x + ⎟ − ε ⎜ x − ⎟ 2⎠ ⎝ 2⎠ ⎝

⎧1 ⎩0

ε (x ) = ⎨

x>0 else

(6)

While the impulse response of a 1-D Gabor even filter is: h( x ) =

⎛ x2 ⎞ ⎟ cos(2πFx ) exp⎜⎜ − 2 ⎟ 2π σ ⎝ 2σ ⎠ 1

(7)

Here we define w = 1 2 F as the width of the central excitatory region of the Gabor even filters, as shown in Fig. 1.

Fig. 1. 1-D Gabor even filter

The response of the filter to the tube-profile centered at x = a is given by convolution r ( x) = fτ ( x − a) ∗ h( x)

(8)

Then, the zero crossing point of the first derivative of response r (x ) corresponds to the maximum of the response map. r ' (x ) =

⎧⎪ ⎡ 1 ( x − a + τ 2)2 ⎤ ⎥ cos[2πF (x − a + τ 2)] ⎨exp⎢− σ2 2π σ ⎪⎩ ⎢⎣ 2 ⎥⎦ 1

⎡ 1 ( x − a − τ 2 )2 ⎤ ⎪⎫ − exp ⎢− ⎥ cos[2πF (x − a − τ 2)]⎬ 2 2 σ ⎥⎦ ⎣⎢ ⎭⎪

(9)

From formula (9), we get r ' (x ) = 0 at x = a , which is the center point we try to figure out. Additionally, if x = a is the maximum point, r ' (a − ) > 0 and r ' (a + ) < 0 are necessary. With 0 < τ ≤ 2 w , that is 0 < τ ≤ 1 / F , both the inequations can be met. Consequently, under 0 < F ≤ 1 / τ , the maximum of response r (x ) correspond to the center of tube-profile. And we also prove that when τ is fixed, and w ≥ τ / 2 is satisfied, the r (a) get its maximum while τ = w , that is to say, the center point got its

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maximum response when the width of the bar-profile signal is equal to the width of the central excitatory region of the Gabor even filter. If we take a single scale to detect the vessel centerlines, the quality of centerline extraction largely related to the value of w , the width of the central excitatory region of the filter. If too wide, that is, the center frequency is too small, the spatial extent of the filter will become so extensive that the centerline responses are seriously blurred. On the contrary, the centerline may be wrongly localized at the edges. While applying the filter in 2D image, therefore, we take multiscale approach to detect vessels in various widths by choosing the maximum response among the different scales, also different orientations. 2.3 Centerline Segmentation

Local maxima extraction is then carried out on the maximal response map of Gabor even filters. After that, we apply a hysteresis thresholding, which retains connected components with most points that have values above a low threshold and with at least one point with a value above a high threshold. The two thresholds are computed as constant quantile values (at 90%and 98%) of the histogram of response map. The output of segmentation is a list of tagged chains, which are the collection of vessel segments.

3 Results We use Gabor even filters of twelve different orientations, θ = (k − 1)π K , for k = 1, 2," , K , K = 12 . Furthermore, multiple scales are taken to adapt to the variety of the vessel size. In the original image of Fig.2, the width of the blood vessels varies from about 4 to 20 pixels. We choose five scales respectively corresponding to five center frequencies, F ∈ {0.125,0.100,0.075,0.050,0.025} . The maximum response from all 12 orientations and 5 scales for each position is taken as the output of the filter, as shown in Fig. 3.

……… Fig. 2. 2-D angiography image of the brain

Fig. 3. the maxima from all orientations and scales

The maximum response map (Fig. 3) shows the prominent advantage of our method is Gabor even filters’ ability to reduce noise and to enhance centerlines. Especially, some weak ends of the blood vessels are well intensified. After filtering, we adopt

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non-maximum suppression to detect local maxima and hysteresis thresholding to extract the final centerline. The result is shown in Fig. 4 and Fig. 5. In Fig. 6, the centerlines are overlaid on top of the original image. We can see that the centerlines are correctly localized. The multiscale Gabor even filters manifest their good capability for accurate localization. To have a clearer view about the scales of the filters, we give the following two experiments to illustrate how scales influence the centerline localization. If a large scale is taken while detecting comparatively thin vessels, like in Fig. 7, it will cause serious faintness to the image, which therefore result in the deflection. However, if the scale is relatively small, the maxima will occur at the edge of the blood vessel, which can be utilized to detect edges, but not the centerlines we need (Fig. 8).

Fig. 4. The result of non-maximum Fig. 5. The centerlines after suppression hysteresis thresholding

(a)

(b)

Fig. 6. The centerlines overlain on top of the Fig.2

(c)

Fig. 7. (a) original image (b) proper scale corresponding to center frequency F = 0.125 (c) too big scale corresponding to center frequency F = 0.025

(a)

(b)

(c)

Fig. 8. (a) original image (b) too small scale corresponding to center frequency F = 0.125 (c) proper scale corresponding to center frequency F = 0.025

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4 Conclusions We introduce an automated new multiscale method based on Gabor even filters to extract vessel centerlines of angiogram images, whose flexible and effective enhancement on the centerline of the tubular objects made the results satisfying and encouraging.

Acknowledgements This work was supported by the 973 Program of China (No. 2003CB716105).

References 1. Shechter, G., Devemay, F., Quyyumi, A.: Three-Dimensional Motion Tracking of Coronary Arteries in Biplane Cineangiograms. IEEE Transactions on Medical Imaging. Vol 22, No.4 (2000) 321-337. 2. Andress, K.M.: Evidential Reconstruction of Vessel Trees from Rotational Angiograms. Proc. IEEE Conf. Image Processing. Vol.3 (1998) 385-389. 3. Lindeberg, T.: Edge Detection and Ridge Detection with Automatic Scale Selection. International Journal of Computer Vision, Vol. 30, No. 2 (1998) 117-154. 4. Jang, J.H., Hong, K.S.: A Pseudo-Distance Map for the Segmentation-Free Skeletonization of Gray-Scale Images, Proc. IEEE Conf. Computer Vision. Vol. 2 (2001) 7-14. 5. Golland, P., Grimson, W.E.L.: Fixed Topology Skeletons. Proc. IEEE Conf. Computer Vision and Pattern Recognition. Vol. 1.(2000) 13-15. 6. Maglaveras, N., Haris, K.: Artery Skeleton Extraction Using Topographic and Connected Component Labeling. IEEE Computers in Cardiology. Vol.28 ( 2001) 17-20. 7. Dugman, J.G.: Uncertainty Relation for Resolution in Space, Spatial Frequency, and Orientation Optimized by Two-dimensional Visual Cortical Filters. J. Opt. Soc Am. A, Vol.2, No. 7 (1985) 1160~1169

Improved Adaptive Neighborhood Pre-processing for Medical Image Enhancement Du-Yih Tsai and Yongbum Lee Department of Radiological Technology, School of Health Sciences, Niigata University, 2-746, Asahimachi-dori, Niigata City, Niigata, 951-8518, Japan

Abstract. This paper presents an improved adaptive neighborhood contrast enhancement (ANCE) method for improvement of medical image quality. The ANCE method provides the advantages of enhancing or preserving image contrast while suppressing noise. However, it has a drawback. The performance of the ANCE method largely depends on how to determine the parameters used in the processing steps. The present study proposes a novel method for optimal and automatic determination of threshold-value and neighborhood-size parameters using entropy. To quantitatively compare the performance of the proposed method with that of the ANCE method, computer-simulated images are generated. The output-to-input SNR ratio and the mean squared error are used as comparison criteria. Results demonstrate the superiority of the proposed method. Moreover, we have applied our new algorithm to echocardiograms. Our results show that the proposed method has the potential to become useful for improvement of image quality of medical images.

1

Introduction

In recent decades a number of computer-aided diagnosis (CAD) schemes have been developed to aid in the interpretation of the increasing amounts of medical image data and clinical information [1]. In general the performance of CAD schemes largely depends on the image database employed. Therefore, in order to improve the performance of the schemes, enhancement of image quality of the image set is of importance. Image quality is usually characterized by contrast, resolution, and signal to noise ratio. Adaptive neighborhood contrast enhancement (ANCE) is a recent approach to contrast enhancement [2, 3]. An adaptive neighborhood is constructed for each pixel, this pixel being called a seed pixel of the neighborhood [4]. In the ANCE, a variable shape and size neighborhood is defined using local characteristics of the image. Recently, Guis et al. [5] reported a novel ANCE technique. This ANCE method consists of computing a local contrast around each pixel using a variable neighborhood whose size depends on the statistical properties around the given pixel. The obtained contrast image is then transformed into a new contrast image using a contrast enhancement function. Finally, a contrast-enhanced image is obtained by applying inverse contrast transform to the previous step. This technique provides the advantages of enhancing or preserving image contrast while suppressing noise. However, it has a drawback. The performance of the ANCE method largely depends on how to determine the parameters used in the processing steps. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 576–581, 2004. © Springer-Verlag Berlin Heidelberg 2004

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The present study proposes a method for optimal and automatic determination of threshold-value and neighborhood-size parameters using entropy. To quantitatively compare the performance of the proposed method with that of the ANCE method, computer-simulated images are generated. The output-to-input SNR ratio and the mean squared error are used as comparison criteria. Moreover, medical images obtained from various modalities are also used for performance comparison.

2

Methods

2.1

ANCE Method

Figure 1 shows the flowchart of the ANCE method proposed by Guis et al. [4]. Basic steps of the ANCE method are as follows: 1) Each pixel (i,j) is assigned an upper window Wmax centered on it, whose size is N×N (N is an odd number). Let I(i,j) be the gray level of pixel (i,j) in image I, and let T be a given threshold. 2) Pixel (k,l) within Wmax is assigned a binary mask value 0 if | I(k,l)-I(i,j)|>T, else it is assigned a binary mask value 1. This results in constructing a binary image. 3) The percentage P0 of zeros is computed over the region between the external (c+2)×(c+2) and the inner (c×c) areas (c is an odd number). The process stops if this percentage is greater than 60% or if the upper window Wmax is reached. Let c0 be the upper c value beyond which the percentage P0 is greater than 60%. The pixel (i,j) is assigned the window W=(c0+2) ×(c0+2). The set of pixels having the mask value 1 is defined as “center”, and the set of pixels having both the mask value o and which are eight-neighborhood connected at least to a pixel 1 is defined as “background”.

O rigin al im ag e S m o oth in g filter (3x 3) Tran sfo rm to con trast values A p plying enh ancem en t fu nction T ran sfo rm to gray-le vel valu es E nh an ced im age Fig. 1. Flowchart of the adaptive neighborhood contrast enhancement method proposed by Guis et al. [4]

4) A local contrast image is computed from C (i , j ) =

M c (i , j ) − M b (i , j )

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where, Mc(i,j) and Mb(i,j) are the mean values in image I of pixels labeled as the center and as the background regions around pixel (i,j), respectively. 5) The local contrast image C is then transformed into a new image C’ using C ' (i, j ) = F [C (i, j )]

(2)

where F is a contrast-enhancement function that depends on the features to be detected. For example, the sigmoidal function or the trigonometric function is used. 6) A new image E is obtained by the process of inverse contrast transform using E (i, j ) = M b (i, j )[1 − C ' (i, j )]

E (i , j ) =

M b (i, j ) 1 − c' (i, j )

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7) Repeat step 1 to step 6 for each pixel in the image I. 2.2

Our Proposed Method for Parameter Determination

Two of the most important parameters used in the ANCE method are the threshold value T and the percentage P0 of zeros computed over the region between the external and the inner areas. Guis et al. empirically used T=5 for thresholding and P0=60% for determining neighborhood size in their study [4]. In this current study, we use a method for optimal and automatic determination of threshold value and neighborhood size from the viewpoint of information amount. Namely, the two parameters are determined when the entropy of the image I is at its maximum. The detail of determination process is described as follows. 1) Determination of the threshold value T: Let d be the difference between the maximum and minimum pixel values in the region of interest (ROI) whose size is Wmax ×Wmax. The value of T is then in the range of 0≤T≤d. When the maximum entropy in the ROI is obtained by varying threshold value, this threshold value is regarded as T. The entropy of the ROI is given by

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Fig. 2. Computer-simulated image of breast microcalcifications: (a) microcalcification noise-free image with a 30% contrast level, (b) noisy image with a SNR=18dB, (c) horizontal profile of both images (a) and (b) passing through the two different sizes of microcalcifications

Improved Adaptive Neighborhood Pre-processing for Medical Image Enhancement

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ENT (t ) = − p0 t log 2 p0 t − p1t log 2 p1t

(0≤ t≤ d )

(5)

where ENT(t) is the entropy of the binary image obtained using a threshold value t, p0t and p1t are the probability of pixel value=0 and that of pixel value=1 in corresponding binary image, respectively. All the values of ENT(t) in the range of (0≤ t≤d ) are computed. The value of t is considered as T when ENT(t) is at its maximum. 2) Determination of the neighborhood size: The entropy in c×c area is calculated, where 0≤ c≤N. The value of c is used as the neighborhood size when entropy is at its maximum.

3

Performance Assessment

In order to demonstrate the effectiveness of the improved method, computer-simulated images of breast calcifications were used for quantitative evaluation. Five different contrast levels (from 10% to 50%; with a step size of 10%) and three noise levels (signal to noise ratios =10dB, 18dB, and 22dB) for each contrast level were generated. Therefore a total of 15 compute-simulated images were employed. The images consist of 256×256 pixels. The images were coded on 256 gray levels and the background level was set at gray level of 128. Figure 2 shows an example of computer-simulated image related to breast calcifications.

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Performance comparison was made among the proposed improved method, Guis’s ANCE method, 5×5 smoothing filter, and 5×5 median filter. Two criteria, namely, output-to-input SNR and the mean-squared-error (MSE), were used to quantitatively evaluate the four algorithms on computer simulated images. The output-to-input SNR parameter (called ρ) is defined as the ratio ρ=

SNRout , SNRin

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where SNRout and SNRin are the SNR after and before processing, respectively. The MSE is calculated between the noise-free image f and the result ĝ of the enhancement process on the input noisy image g:

∑ ∑ MSE = a

b

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where a and b are the numbers of pixels on the horizontal and vertical directions, respectively. It is noted that ρ is higher when much more noise is removed, whereas the MSE value is smaller when the image is denoised and the structure is preserved. Figure 3(a1), 3(a2), and 3(a3) shows the results of ρ versus contrast at SNR=23dB, 18dB, and 10dB, respectively. The improved method gives best results. Figure 3(b1), 3(b2), and 3(b3) shows the results of MSE versus contrast at SNR=23dB, 18dB, and 10dB, respectively. Similarly, the improved method gives best results. Figure 4 shows the images and the corresponding profiles obtained after applying the proposed method, Guis’s ANCE method, 5×5smoothing filter, and 5×5 median filter. Visual observation demonstrates the superiority of the proposed method. Figure 5 shows the results obtained after applying four different methods to an ultrasonic image. It is noted from visual evaluation that the images processed using the improved method give the best results.

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Fig. 5. Original and processed echocardiograms. (a) original end-diastole image, (b) image obtained using the proposed method, (c) image obtained using Guis’s ANCE method, (d) image obtained using 5×5 smoothing filter, and (e) image obtained using 5×5 median filter

4

Conclusion

In this paper we have described an improved ANCE method for enhancement of medical image quality. The improved method was based on the algorithm proposed by Guis et al. The feature of the improved method is to automatically determine the optimal threshold-value and neighborhood-size parameters using entropy. Computer-simulated images were generated to quantitatively evaluate the effectiveness of the proposed method in terms of output-to-input SNR and the mean-squared error. The proposed method was also applied to clinical echocardiograms and CT phantom images. Results show that our proposed method performed well and clinically useful.

References [1] Giger, M.L.: Computer-aided diagnosis in radiology. Acad. Radiol. 9 (2002) 1-3 [2] Dhawan, A.P., Buelloni, G., Gordon, R: Enhancement of mammographic features by optimal adaptive neighborhood image processing. IEEE Trans. Med. Imaging. 5 (1986) 8-15 [3] Paranjape, R.B., Rabie, T.F., Rangayyan, R.M.: Image restoration by adaptive neighborhood noise subtraction. Appl. Opt. 33 (1994) 2861-2869 [4] Jiang, M.: Digital Image Processing, lecture notes, Department of Information Science, School of Mathematics, Peking University (2002) [5] Guis, V.H., Adel, M., Rasigni, M., Rasigni, G., Seradour, B., Heid, P.:Adaptive neighborhood contrast enhancement in mammographic phantom images. Opt. Eng. 42 (2003) 357-366

On the Implementation of a Biologizing Intelligent System1 1

2

Byung-Jae Choi , Paul P. Wang , and Seog Hwan Yoo

1

1

School of Electronic Engineering, Daegu University, Naeri Jillyang Gyungsan Gyungbuk, 712-714 Korea {bjchoi, shryu}@daegu.ac.kr 2 Department of Electrical & Computer Engineering, Duke University, Durham NC, 27708 USA [email protected]

Abstract. According to the progress of an information-oriented society, more human friendly systems are required. Such systems can be implemented by a kind of much more intelligent algorithms. In this paper we propose the possibility of the implementation of an intelligent algorithm from gene behavior of human beings, which has some properties such as self organization and self regulation. The regulation of gene behavior was widely analyzed by Boolean network. Also the SORE (Self Organizable and Regulating Engine) is one of those algorithms. We here describe the concepts of the implementation of an intelligent algorithm through the analysis of both gene regulatory network.

1 Introduction Many complex processes are difficult to control using existing techniques because they are highly interconnected nonlinear systems that operate over a wide range of conditions. Some novel control techniques are required in order to cope with increasing demands on convenience, comfort, and high performance. Some pioneering researchers such as James Albus have even undertaken the task of constructing a road map for the engineering of the mind [1-2]. A biocontrol system is recently considered as one of most important issues in control fields. This can also play an important role in the design of a kind of human friendly systems. The development of control theory has a long history due to fairly intensive research efforts for at least half a century. Some issues were thoroughly investigated and have reached a very mature status, while others were left nearly untouched. In an article [3], John L. Casti coined the word “Biologizing” to reflect the recognition of so called “reliability and survivability” as topics of primary concern for engineers. A correct value judgment for a control system was thus finally determined. A blueribbon panel of 52 experts has nearly created a large set of research problems that lie ahead for control research engineers [4]. The concept of “feedback” in control theory is so far only known as a special trivial case of “homeostasis” - the function of an organism to regulate and to keep a 1

This research was partially supported by the Daegu University Research Grant, 2003.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 582–588, 2004. © Springer-Verlag Berlin Heidelberg 2004

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constant “internal environment”. These topics on biocontrol systems nevertheless bring much excitement and vision [5-6] to the research community. Some models for a gene regulatory network were reported: The Boolean network (BN) model had a considerable amount of attention, which was originally introduced by Stuart A. Kauffman [7]. This is also called by NK-network. In a genetic network, the total number of genes is represented by N and K is the largest number of genes which regulates any one of the N genes in the genetic network. SORE (Self Organizable and Regulating Engine) was first discovered as a classifier [8]. More interesting and robust properties subsequently emerged [9-12]. SORE is by far the most general mathematical structure of a family of automata theories listed as follows: SORE ⊃ Boolean Network ⊃ Cellular Automata ⊃ Linear Automata. Based upon the theory of Stuart A. Kauffman, a biological genetic network usually has a much smaller K to more realistically model a biological setting. However, it is the condition of K=N in which the network assumes its full strength for the best possible performance in a “biologizing” intelligent system. This K=N condition is what distinguishes SORE from the standard Boolean network [9]. We discuss Boolean network and SORE in gene regulatory networks and a concept of colonization in Section 2 and 3, respectively. In Section 4 we describe some properties for a biologizing intelligent system. Discussions and conclusions are presented in Section 5.

2 Gene Regulatory Networks The roots of the Boolean network lie in the automata theory which was a subject of Turing and von Neumann work. A Boolean network is a system of N interconnected binary elements (nodes). It is widely used to model gene regulatory networks and was originally introduced by Stuart A. Kauffman in 1969. It is frequently called by NKnetwork, where N and K are the number of genes and the maximum connectivity of a Boolean network, respectively. The number of inputs K may vary or be the same for all nodes in the network. A Boolean network G(V, F) is defined by a set of nodes (genes) V={x1, x2 , … , xn } and a set of Boolean functions F={f1, f2, … , fn}. xi∈{0, 1} is a Boolean variable, where i=1, 2, … , n. We write simply xi=1 to denote that the i_th node is expressed (xi=0 denotes that the i_th gene is not expressed). Each Boolean function fi(xi1, … , xik) with K specific input nodes is assigned to node xi and is used to update its value. The K values of all the nodes in V are then updated synchronously. In general, there are 2^2 possible Boolean activation functions for a node with K inputs. Regulation of nodes is defined by the set F of Boolean functions. In detail, given the value of the nodes V at time t, the Boolean functions are used to update the value of the nodes at time t+1. In the NK network model for gene regulation, a symbolic logic function is used to describe the self-organization and self-regulation of genes’ expressions. The Boolean functions are made up of the logical connectors AND, OR, and NOT, forming a complete logic set. The HIGH’s and LOW’s of gene expressions for the next state in the Boolean network are controlled by these Boolean functions. In order words, these logic functions become the rules that govern the HIGH’s or LOW’s of the genes’ expressions in the next instant of time. The synchronous update

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process is then repeated making the network dynamic. In order to capture the dynamic nature of the network, it may be useful to consider the wiring diagram which gives an explicit way of implementing the updating procedure. During the operation of the network, a sequence of states will converge to a limit cycle or an attractor (a limit cycle with a length of one). Each specific initial condition will converge to a specific attractor or limit cycle. For a genetic network of N genes, N there are exactly 2 possible initial states. For an example, consider the lambda bacteriophage. It is a virus that invades E. coli bacteria and 2 distinct modes of operation: 1) it can become integrated into the host cell DNA, and be replicated automatically each time the bacterium divides. 2) it can multiply in the cytoplasm of bacterium, eventually killing its host. There are 2 proteins: lambda repressor and cro protein. The lambda repressor blocks the expression of the gene for the cro protein, and vice versa. So, it can be modelled by a one-input Boolean network with 2 nodes (lambda repressor and cro protein) as shown in Fig. 1. It shows that both of the nodes are INVERSE properties because cro protein blocks the expression of the lambda repressor and vice versa. Two of four states are 10 and 01, and they correspond to the exclusive expression of each protein. There are another cycle of period 2 (11 00 11) which is not a behavior observed in the lambda bacteriophage. This shows that the simple model is not a complete description of the lambda bacteriophage system.

→ →

Fig. 1. The Boolean network model for the lambda bacteriophage

SORE is the most general Boolean network of which Stuart A. Kauffman’s NKnetwork is a special case [9]. The NK-network imposes the severe restriction of K and sets of contours belong to the slices be Cin and Cin+1. A contour line is composed of a set of vertices {v(x,y,n)}.

Fig. 1. Correspondence determination between two adjacent contours (left) fills up interior of Cin+1 as its ID’s (right) projects vertices of Cin onto Sn+1 and checks the ID of those points

When a projected vertex of a contour belongs to another contour on its adjacent slice, two contour lines are regarded as corresponding to each other. It allocates a 2Dbuffer that has the same size of a slice and fills up interior pixels of a Cin+1 as its identifier with boundary-fill algorithm. Then it projects vertices v(x,y,n) of Cin onto a slice Sn+1, and checks whether the buffer value is identical to the contour ID or not at the projected position v(x,y,n+1) (see figure 1). If the number of corresponding contour is more than two, the contour lines may produce branches.

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Fig. 2. An example of determining optimal shift value and the shortest edge (a) shift=0 (b) shift=2 (c) shift=4 (d) change the number of matched edge according to the shift value

After determining correspondence of adjacent contours Cin and Cin+1, it produces triangle strips connecting them. Since there is no topological information between two vertices on different contours, we have to determine the corresponding vertex on the adjacent contour for a specific vertex. Normally, topologically adjacent vertices have the smaller distance in comparison to the remaining vertices. Assume that the vertex lists of < Cin, Cin+1> are (p0,…,pl-1) and (q0,…,ql-1). When the length of a slice chord e(pi, qi) is less than pre-defined threshold ε, the slice chord is called a matched edge. It changes the index of starting vertex j from 0 to l-1 for Cin+1 while fixing the index of starting vertex as 0 for Cin. It determines the value of j that maximizes the number of matched edges among slice chords e(pk, q(j+k) mod l) defined by two vertex list (p0,…,pl-1) and (qj,…,ql-1,q0,…, qj-1). Here, j is the relative offset of two lists and called a shift. When applying the shift value that maximizes the number of matched edges, a slice chord that has the minimum length is regarded as the shortest edge. Figure 2 shows an example of determining the optimal shift value. While increasing the index j from 0 to l-1, in the case of figure 2(a) and (c), length of each edge e(pk, q(j+k) mod l) becomes longer and the number of matched edge is decreased. When the shift value is 2, the number of matched edges is maximized and e(p0, q2) is the shortest edge. A triangle strip is generated from the shortest edge. In order to produce visually pleased triangle strips, each triangle should be similar to equilateral triangle. When we assume that a contour is composed of equally distant vertices, we have only to minimize the length of slice chord while inserting a new vertex into a triangle strip. Let the most recently produced edge of the strip be e(pi, qi), a vertex to be added is one of the candidate vertex pi+1 and qj+1. When |e(pi, qi+1)| > |e(pi+1, qi)|, pi+1 becomes the next vertex, otherwise qi+1 is selected. A branch occurs when a contour Cin+1 corresponds to N contours { Cin ,…, Cin+ N −1 }. Our method partitions Cin+1 into N sub-contours { Ci n+1 ,…, Ci+n+N1−1 }, determines which of { Cin ,…, Cin+ N −1 } corresponds to each sub-contour, and tiles the contour pairs using the

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method described above. When two contours C0n and C1n on a slice Sn correspond to a contour C0n+1 on adjacent slices Sn+1, surface reconstruction process is as follows:

Fig. 3. An example of tiling a contour pair that contains branches

(1) Derives the center-of-gravity G0n, G1n, and G0n+1 from C0n, C1n, and C0n+1. (2) Computes a straight line L1 parallel to the line from G0n to , G1n, and its projected line passes by the G0n+1, and determines two vertices va and vb from the vertices of G0n+1 that are mostly close to L1 (figure 3 (a)). (3) Partitions the line segment va vb according to ratio of the area of C0n and C1n (A0, A1) and denotes the point as M. Area of contours can be computed by counting the number of pixels while calculating the center-of-gravity (figure 3 (b)). (4) Computes a straight line L2 perpendicular to the line segment va vb and passes by the point M, and determines two vertices vc and vd from the vertices of G0n+1 that are mostly close to L2 (figure 3 (c)). (5) Inserts shared vertices along with the line segment vc vd . Interval of shared vertices is identical to that of ordinal vertices of original contour lines. Let the coordinates of points vc, vd, and M be (xc, yc, n), (xd, yd, n) and (xM, yM, n). Z-values of shared vertices should be interpolated along with a curve from vc to vd via new points M* of which the coordinates is (xM, yM, n+0.5) (figure 3 (d)).

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(6) Partitions a contour line C0n+1 into two sub-contours C0n+1 and C0n+1 * by duplicating the shared vertices, and reconstructs contour pairs < C0n , C0n+1 > and < C1n , C0n+1 *> using the tiling method (figure 3 (e) (f)). In the case of N ≥ 3, it partitions entire contour into several sub-contours and tiles the contour pairs by recursively applying the above method until all of the subcontours have one-to-one correspondence with adjacent contour lines.

3 Experimental Results In order to show how efficient our method, we implement 3D anatomical model reconstruction system which segments contour lines of organs from 2D slices, and produces

Fig. 4. Examples of reconstructed models and their shaded images with our method (top) segmented images for inner organs (middle) skin model (bottom) trachea, meninges, and pelvis models from left to right Table 1. Time to be taken for reconstructing several anatomical structures using our method

Liver Heart Pelvis

# of contours 50 37 161

# of polygons 11642 6770 21294

Reconstruction time (sec) 2.21 1.82 4.52

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three dimensional models by tiling adjacent contours. It is implemented on a PC equipped with Pentium IV 2.2GHz CPU, 1GB main memory, and NVIDIA GeForce4 graphics accelerator. 613 horizontal MRIs of the entire body for young Korean male with standard body were scanned and 60 anatomical structures were segmented. Figure 4 shows images produced by rendering 3D anatomical models with our method. It can reconstruct accurate models from contour lines even when we dealing with considerably complex region. It produces geometric model fairly well not only for simple matching area but also for branches. Table 1 shows time to be taken for reconstruction of geometry according to the size of data and complexity. Experimental result shows that our method can reconstruct arbitrary shaped models using contour lines on slices within short time.

4 Conclusion Human body modeling is an important technology for medical applications. We propose fast reconstruction method of 3D anatomical model from contour lines. It generates a triangle strip with single tiling operation for simple matching region that does not contain branch structures. If there are some branches, it partitions the contour line into several sub-contours by considering the number of vertices and their spatial distribution. Each sub-contour can be processed by using the same method applied to matching region. Experimental result shows that our method can reconstruct arbitrary shaped models using contour lines on 2D slices within short time.

Acknowledgement This research was supported by University IT Research Center Project.

References 1. Bajaj, C., Coyle E. and Lin, K. : Arbitrary Topology Shape Reconstruction for Planar Cross Sections. Graphical Models and Image Processing, Vol. 58, No. 6 (1996) 524-543 2. Soroka, B. : Generalized Cones from Serial Sections. Computer Graphics and Image Processing, Vol. 15, No. 2 (1981) 154-166 3. Barequet, G. and Sharir, M. : Piecewise-Linear Interpolation between Polygonal Slices. Computer Vision and Image Understanding, Vol. 63, No. 2 (1996) 251-272 4. Barequet, G., Shapiro, D. and Tal, A. : Multilevel Sensitive Reconstruction of Polyhedral Surfaces from Parallel Slices. The Visual Computer, Vol. 16, No. 2 (2000) 116-133 5. Klincsek, G. : Minimal Triangulations of Polygonal Domains. Annals of Discrete Mathematics, Vol. 9 (1980) 121-123 6. Klein, R., Schilling, A. and Strasser, W. : Reconstruction and Simplification of Surface from Contours. IEEE Computer Graphics and Applications, (1999) 198-207 7. Meyers, D., Skinner, S. and Sloan, K. : Surfaces from Contours. ACM Transactions on Graphics, Vol. 11, No. 3 (1992) 228-258

Efficient Perspective Volume Visualization Method Using Progressive Depth Refinement Byeong-Seok Shin Inha University, Department of Computer Science and Engineering, 253 Yonghyeon-Dong, Nam-Gu, Inchon, 402-751, Korea [email protected]

Abstract. In recent volume visualization, high-speed perspective rendering method is essential. Progressive refinement is well-known solution for real-time image generation under limited computing environment. We propose an accelerated rendering method that exploits progressive depth refinement. While performing progressive refinement of volume ray casting, it computes depth values for sub-sampled pixels and determines the minimum value of four neighboring pixels. Original ray casting starts ray traversal from its corresponding pixel. However, rays in our method jump as the amount of the minimum z-value calculated in the previous stage. Experimental results show that our method reduces rendering time in comparison to conventional volume ray casting.

1 Introduction The most important issue in recent volume visualization is to produce perspectiveprojection images in real time. It is highly related to hardware-based approaches [1],[2]. Although they achieve 30 fps without preprocessing, it is too expensive and difficult to manipulate large volume data due to limitation of dedicated memory size. Volume ray casting is the most famous software rendering algorithm [3]. Although it produces high-quality images, it takes long time due to unnecessary sampling of empty regions. Several optimized methods have been proposed for speed-up [4],[5],[6]. They have mainly concentrated on skipping over transparent regions using coherent data structures [7],[8],[9],[10]. However they require long preprocessing time and extra storage. There are some extended algorithms that require less computation for preprocessing such as min-max octree [11] and min-max block [12]. They are still insufficient for real-time classification or rendering of time-varying dataset. Progressive refinement is regarded as simple but effective solution for real-time image generation under limited computing resources [13],[14]. Since image quality has trade-off for rendering time, it negotiates image quality against update speed. When an object or a camera rapidly changes its position or direction, it generates lowquality images by sub-sampling pixels with regular interval and casts rays only for those pixels. Colors for remaining pixels are computed by simple linear interpolation. On the contrary, the images are progressively refined for several stages when the object or camera stops moving for a moment. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 625–630, 2004. © Springer-Verlag Berlin Heidelberg 2004

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In this paper, we present an acceleration method that produces images faster than conventional progressive refinement of volume ray casting. While casting rays in some pixels, it calculates depth values (z-values) for those pixels without extra cost and determines the minimum depth for rectangular regions (grids) defined by four neighboring samples. The minimum values computed in current stage are used to accelerate ray casting in the next stage of refinement. Our method moves forward the starting point of ray traversal as the amount of the minimum depth value. It doesn’t need preprocessing or additional data structures. Experimental results show that our method is much faster than conventional progressive refinement of ray casting. In Section 2, we present our progressive refinement algorithm in detail. Experimental results and remarks are shown in Section 3. Lastly, we conclude our work.

2 Volume Ray Casting Using Progressive Depth Refinement Assume that a view plane P has the resolution of N × N for simplicity. While performing progressive refinement, we compute z-values dij for sub-sampled pixels qij, and estimate potentially empty space (PES) by comparing depth values of four neighboring samples. A PES is defined as the area between image plane (z=0) and a plane apart from view plane as the amount of minimum depth value (z=dmin). Fig. 1 shows our refinement procedure not only for colors but also for depth values, where Guv is a grid and d uvmin means the minimum depth value of Guv. Assume that initial sampling interval of progressive refinement is S (S=2i for simplicity). In the first stage (Fig. 1 (top)), it performs full range ray traversal to determine color values at four corner pixels of 2S×2S sized grid to derive initial value of d uvmin . Then it casts rays at the corner pixels (depicted as gray squares) of S×S sized grid from the points apart from view plane as the amount of d uvmin . Color values for remaining N2-(N/S)2 pixels are interpolated from the pre-computed pixel values. At the same time, it stores their zvalues into the depth buffer. A square stands for a pixel whose color and z-value are already calculated in the previous stage. A circle means an interpolated pixel. A small black circle is a starting point of ray traversal. In the following stages, the minimum depth values calculated in the previous stages are used for speedup. While a ray fires from its corresponding pixel in conventional ray casting, all the rays in our method fired from refined pixels in a grid Guv start to traverse at the points apart from their corresponding pixels as the value of d uvmin stored in the depth buffer (Fig. 1 (bottom)). Consequently, we can reduce the rendering time as the amount of PES (gray regions). Additional samples for k-th stage (k=0,…,i) is 3(kN/S)2. While computing color values for additional samples, depth values are also computed to refine the depth map more precisely. Let the average time to compute color and z-value for each pixel be trt, bilinear interpolation time be tint, and the cost for traversing a ray for our method be tminrt. Rendering time of original ray casting told and our method tnew for each stage can be defined as Eq. (1). Since tminrt is less than or equal to trt in any case, tnew is always smaller than told in all the stages of refinement.

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Fig. 1. A procedure of proposed refinement method

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⎧1 2 1 ⎞ 2 ⎛ ⎪ 2 N t rt + ⎜1 − 2 ⎟ N tint ⎝ S ⎠ ⎪S ⎪⎪ (2 2 k − 22 ( k −1) ) ⎛ 22k =⎨ N 2trt + ⎜⎜1 − 2 2 S S ⎝ ⎪ ⎪ (2 2 k − 22 ( k −1) ) ⎪ N 2trt ⎪⎩ S2

( k = 0) ⎞ 2 ⎟ N tint ⎟ ⎠

⎧ 1 3 1 ⎞ ⎛ N 2trt + N 2t min rt + ⎜1 − 2 ⎟ N 2tint ⎪ 2 2 ( 2 S ) ( 2 S ) S ⎝ ⎠ ⎪ 2k ⎪⎪ (22 k − 22 ( k −1) ) ⎛ 2 ⎞ =⎨ N 2tmin rt + ⎜⎜1 − 2 ⎟⎟ N 2tint 2 S S ⎠ ⎝ ⎪ ⎪ 2k 2 ( k −1) ) 2 ⎪ (2 − 2 N tmin rt S2 ⎩⎪

(1 ≤ k ≤ i − 1) (k = i) (k = 0) (1 ≤ k ≤ i − 1) (k = i)

.

(1)

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The most important factor is the sampling interval S. When the value of S is too large, image quality is degraded since spatial frequency of the volume data is much higher than the sampling rate. It might incorrectly estimate minimum depth values and a lot of visual artifacts may occur in final images (see Fig. 2). When S is too small, sufficient speed-up cannot be achieved. We have to choose optimal value of S to achieve maximum performance without deteriorating of image quality.

Fig. 2. An example of generating erroneous images when the sampling interval is too large in comparison to spatial frequency of volume data

3 Experimental Results Virtual endoscopy is a non-invasive diagnosis method based on computer processing of 3D data sets in order to visualize inner structures of the organ cavity [15]. It is good example to verify the performance enhancement since it requires real-time generation of high-quality perspective images and interactive classification. We compare the rendering time and image quality of original progressive refinement of volume ray casting and our method. In order to show that our method is still efficient even when it is combined with other optimization method, we take into account the min-max block method. Although it requires preprocessing to build up minmax block, it is inherently simple and fast since it does not require complicated operations. All of these methods are implemented on a PC equipped with Pentium IV 3.06GHz CPU, 2GB memory, and Radeon9800 GPU. Volume dataset is obtained by scanning a human abdomen with a MDCT of which resolution is 512×512×541. We measure the rendering time in colon cavity under fixed viewing conditions. Fig. 3 shows comparison of rendering time of original ray casting (RC), our method (PDR), acceleration using min-max block (MINMAX), and combination of our method and min-max block method (PDR+MINMAX) in several refinement stages. As the value of S decreases, rendering time gets longer since RC fires rays at more pixels. PDR produces the same quality images in much less time than RC. Rendering time of our method is only about 35% (S=1) ~ 55% (S=4) of that of RC. Rendering time of MINMAX is almost the same or longer than that of PDR. Rendering time of PDR+MINMAX is about 25% (S=1) ~ 36% (S=4) of that of RC. High-speed flythough can be possible since it provides 5.0 ~ 6.2 fps when the value of S is 4.

Efficient Perspective Volume Visualization Method

CASE2

4 2 1 grid size S (pixels) RC PDR MINMAX PDR+MINMA

rendering time(sec)

rendering time(sec)

CASE1 6 5 4 3 2 1 0

629

6 5 4 3 2 1 0 4 2 1 grid size S (pixels) RC PDR MINMAX PDR+MINMA

Fig. 3. Rendering time of RC, PDR, MINMAX, and PDR+MINMAX for CASE 1 (left) and CASE 2 (right) in the same condition. Image size is 512x512

Fig. 4. A comparison of image quality of virtual colonoscopy in different regions: Leftmost images are produced by RC and remaining ones are obtained by our method in CASE1 (top row) and CASE2 (bottom row) region. Intervals between two consecutive sub-sampled pixels decrease as 4 (2nd column), 2 (3rd column) and 1 (rightmost column)

In order to examine the influence of local surface geometry on rendering speed, we measure the rendering time in a place where surface’s tangent is almost parallel to viewing direction (CASE1) and another place where surface is perpendicular to viewing direction (CASE2). When we apply our method to those regions, rendering time in CASE2 is 15% ~ 20% shorter than that in CASE1. This implies that local surface geometry is related to rendering speed. Fig. 4 shows the quality of images produced by RC and PDR as an image is progressively refined under fixed viewing condition. It is very hard to recognize the difference between images from the two methods.

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4 Conclusion The most important issue in volume visualization is to produce high quality images in real time. We propose an efficient progressive refinement of ray casting that reduces the rendering time in comparison to the conventional algorithms in any situation without loss of image quality. Using depth-refinement scheme, our method moves forward the starting point of ray traversal as the amount of the minimum depth value calculated in the previous refinement stage. It can be applied to generate endoscopic image for any kind of tubular-shaped organs and flight-through image sequence of large-scale terrain. Experimental result shows that it normally produces high-quality images as in ray casting and takes less time for rendering.

References 1. Meissner, M., Hoffmann, U., Strasser, W. : Enabling Classification and Shading for 3D Texture Mapping based Volume Rendering using OpenGL and Extensions. Proceedings of IEEE Visualization '99. San Francisco, CA (1999) 207–214 2. Pfister, H., Hardenbergh, J., Knittel, J., Lauer, H., Seiler, L. : The VolumePro Real-Time Ray-Casting System. SIGGRAPH 99 Proceedings. Los Angeles, CA (1999) 251–260 3. Levoy, M. : Display of Surfaces from Volume Data. IEEE Computer Graphics and Applications, Vol. 8, No. 3 (1988) 29-37 4. Lacroute, P., Levoy, M. : Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation. SIGGRAPH 94 Proceedings. Orlando, Florida (1994) 451-458 5. Yagel, R., Shi, Z. : Accelerating Volume Animation by Space-Leaping. Proceedings of IEEE Visualization 93 (1993) 62-69 6. Udupa, J. K., Odhner, D. : Shell Rendering. IEEE Computer Graphics and Applications, Vol. 13, No. 6 (1993) 58–67 7. Levoy, M. : Efficient Ray Tracing of Volume Data. ACM Transactions on Graphics, Vol. 9 (1990) 245-261 8. Avila, R., Sobierajski, L., Kaufman, A. : Towareds a Comprehensive Volume Visualization System. Proceedings of IEEE Visualization 92 (1992) 13-20 9. Cohen, D., Sheffer, Z. : Proximity Clouds. An Acceleration Technique for 3D Grid Traversal. The Visual Computer, Vol. 11, No. 1 (1994) 27-28 10. Devillers, O. : The Macro-Regions: An Efficient Space Subdivision Structure for RayTracing, Proceedings of Eurographics 89 (1989) 27-38 11. Lacroute, P. : Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation. Doctoral Dissertation, CSL-TR-95-678. Stanford University (1995) 12. Kim, T., Shin, Y. : Fast Volume Rendering with Interactive Classification. Computers & Graphics, Vol. 25 (2001) 819-831 13. Gotsman, C., Reisman, A., Schuster, A. : Parallel Progressive Rendering of Animation Sequences at Interactive Rates on Distributed-Memory Machines. Journal of Parallel and Distributed Computing, Vol. 60 (2000) 1074-1102 14. Roerdink, J. : Multiresolution Maximum Intensity Volume Rendering by Morphological Adjunction Pyramids. IEEE Trans. on Image Processing, Vol.12, No. 6 (2003) 653-660 15. Hong, L., Muraki, S., Kaufman, A., Bartz, D., He, T. : Virtual Voyage: Interactive Navigation in the Human Colon. SIGGRAPH 97 Proceedings (1997) 27-34

Proteomic Pattern Classification Using Bio-markers for Prostate Cancer Diagnosis Jung-Ja Kim1, Young-Ho Kim2, and Yonggwan Won2 1

Research Institute of Electronics and Telecommunications Technology, Chonnam National University, 300 Yongbong-Dong Buk-Gu Kwangju, Republic of Korea [email protected] 2 Department of Computer and Information Engineering, Chonnam National University, 300 Yongbong-Dong Buk-Gu Kwangju, Republic of Korea {ykwon, melchi}@grace.chonnam.ac.kr

Abstract. Decision trees (DTs) and multi-layer perceptron (MLP) neural networks have long been successfully used to various pattern classification problems. Those two classification models have been applied to a number of diverse areas for the identification of ‘biologically relevant’ molecules. Surface enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDITOF MS) is a novel approach to biomarker discovery and has been successfully used in projects ranging from rapid identification of potential maker proteins to segregation of abnormal cases from normal cases. SELDI-TOF MS can contain thousands of data points. This high dimensional data causes a more complex neural network architecture and slow training procedure. In the approach we proposed in this paper, a decision tree is first applied to select possible biomarker candidates from the SELDI-TOF MS data. At this stage, the decision tree selects a small number of discriminatory biomarker proteins. This candidate mass data defined by the peak amplitude values is then provided as input patterns to the MLP neural network which is trained to classify the mass spectrometry patterns. The key feature of this hybrid approach is to take advantage of both models: use the neural network for classification with significantly lowdimensional mass data obtained by the decision tree. We applied this bioinformatics tool to identify proteomic patterns in serum that distinguish prostate cancer samples from normal or benign ones. The results indicate that the proposed method for mass spectrometry analysis is a promising approach to classify the proteomic patterns and is applicable for the significant clinical diagnosis and prognosis in the fields of cancer biology.

1 Introduction The study of the cell’s proteome presents a new horizon for biomarker discovery. The discovery, identification, and validation of proteins associated with a particular disease are difficult and laborious task. Presently, disease biomarker discovery is generally carried out using two dimensional polyacrylamide gel electrophoresis (2D-PAGE) to separate and detect differences in protein expression [1][2]. Advances have also been made in mass spectrometry to achieve high-throughput separation and J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 631–638, 2004. © Springer-Verlag Berlin Heidelberg 2004

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analysis of proteins [3]. One of the recent advances is surface enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS) which provides a rapid protein expression profile from a variety of biological and clinical samples [4]. SELDI-TOF MS can contain thousands of data points, which are mass/intensity spectra. Molecular weight (mass) and intensity are presented on the x-axis and y-axis, respectively. Due to the high dimension of data that is generated from a single analysis, it is essential to use algorithms that can detect expression patterns from such large volumes of data correlating to a given biological phenotype from multiple samples. The algorithm should serve to classify the samples into patient or normal case according to their molecular expression profile [5][6]. DT (decision tree) and MLP (multi-layer perceptron) have been widely used for many pattern classification problems successfully [7]. Decision trees generally run significantly faster in training and give better expressiveness, and the MLPs are often more accurate at classifying novel examples in the presence of noisy data. They were applied to classify human cancers and identify the potential biomarker proteins using SELDI-TOF mass spectrometry [5][6][8]. In this paper, we propose a DT and MLP hybrid system. In the proposed approach, a decision tree is first applied to select possible biomarker candidates from the SELDI-TOF MS data. At this stage, the decision tree selects a small number of discriminatory biomarker proteins. This candidate mass data defined by the peak amplitude values is then provided as input patterns to the MLP neural network which is trained to classify the mass spectrometry patterns. The key feature of this hybrid approach is to take advantage of both models: using the neural network for classification with significantly low-dimensional mass data obtained by the decision tree. We demonstrate proof of principle that our hybrid approach can more accurately discriminate prostate cancer from patients with benign prostate hyperplasia and healthy men. Data set of SELDI-TOF MS used for our work is available from [6], and materials and methods to obtain the spectrometry data were described in detail. Our results show that the hybrid approach outperforms the decision tree approach used in [6]. The result suggests that this hybrid approach can identify molecular ion patterns that strongly associate with certain disease and potentially be applicable for significant clinical diagnosis or prognosis for the cancer biology.

2 SELDI-TOF MS Data Mass spectrometry data we used for this study was obtained from the Virginia Prostate Cancer Center which is available at http://www.evms.edu/vpc/seldi [6]. There are two sets of mass spectrometry data: one is the training set for constructing a classification model and the other is the test set for validating the model. For our study, the training data set were only used, since the test set does not include the true class index. Details for the biological/chemical processes and the pre-processing procedure are described in [6]. SELDI-TOF MS is able to fast analyze on the basis of protein molecular weight in comparison with MALDI-TOF MS, finding biomarkers without pre-processing. SELDI-TOF MS experimentation must take protein chip array composition by bio-

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logical characteristic and chemical characteristic. Protein samples become to bind the same characteristic spot in protein chip array. Here, we separated and quantified proteins using Surface-Enhanced Laser Desorption/Ionization Time-of-Flight mass spectrometry (SELDI-TOF-MS) (Ciphergen, Fremont, CA), in which proteins were bound to active2 surfaces, ionized by a laser, moved to protein chip reader through energy law e = mv *, and recorded by MS(mass spectrum) [9]. Specimens from three groups of patients were used to obtain the SELDI mass spectrometry data: 82 healthy men, 77 patients with BPH(Benign Prostate Hyperplasia) and 167 patients with PCA(Prostate Cancer). SELDI protein profiling is the process that prepares the protein chip array with the patient’s serum samples after appropriate biological or chemical treatment, reads the array by the SELDI mass spectrometry reader, and generates the time-of-flight spectra for the samples. Chip reading and TOF spectra generation are automated by the Protein Biological System II which is the SELDI mass spectrometry reader (Ciphergen Biosystems, Inc.).

3 A Hybrid System for Proteomic Pattern Classification 3.1 Potential Biomarkers: Feature Selection by Decision Tree Decision tree classifies a pattern through a sequence of questions, in which the next question asked depends upon the answer to the current question [7]. Such a sequence of questions forms a node connected by successive links or branches downward to other nodes. The questions asked at each node concern a particular property of the spectrum patterns such as 3,017 0 (5)

When most points along the front approach to the object edge, Efront (t) becomes much smaller than 0, which leads F(x,y,z,t) close to 0 to halt the front. By changing the speed function from F(x,y,z) to F(x,y,z,t), the front can be efficiently prevented from overflow. An example of the improved fast marching is shown in Fig.1(c). 2.3 Morphological Reconstruction

The morphological reconstruction is a typical approach to extract seeded regions, which is defined as:

Si +1 = ( Si ⊕ k ) ∩ m

(i = 0,1,2 )

(6)

Where, S and k denotes the seed and a small disk shaped structuring element, respectively. ⊕ and |m| stand for a dilation operation and the mask accordingly. The mask is achieved via a threshold operation using a histogram analysis.

3 Hybrid Segmentation Strategy The morphological operation during the reconstruction is very computational expensive. To speed up the propagation, we need to define a good seed (marker), which is close enough to the object edge. In that case, the iteration of the morphological reconstruction could be possibly reduced to a reasonable small value. The Fast Marching method can help us get a good initial marker. We firstly employ the Fast Marching to quickly propagate the front from a user-defined seed. When the front stopped at a position close to the edge, we switch it from the Fast

Evaluation of Morphological Reconstruction

681

Marching procedure to the Morphological Reconstruction as the marker to refine the front fitting into the edge accurately. As the result, the proposed hybrid approach can achieve a result much quicker than the morphological reconstruction with similar accuracy. The procedure of the hybrid segmentation approach is described in Fig 2.

Fig. 2. Flow chart of the hybrid segmentation approach, where part A and B belong to the Fast Marching and the Morphological Reconstruction, respectively. In Part B, δ represent a user defined error tolerance between the marker and the mask

4 Evaluation Experiment A “TkSegmentation” software was developed to perform the evaluation, which is based on Visualization Toolkit (VTK), Insight Toolkit (ITK) and Python programming environment, and running on a P-IV 2.0 GHz Windows-XP PC. The source data employed in our experiments includes CT or MRI datasets of brain, heart and kidney studies. A standard CJH27 image volume derived from an average of 27 T1 weighted images of a normal brain was employed in the evaluation study, which is shown in Fig.3(a). CJH27 is a 181 217 181 voxel volume, with iso3 tropic 1 mm voxels. This standard brain was generated from a set of 3D “fuzzy” anatomical models. Each model represents a typical tissue class (white matter, gray

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matter, CSF, etc.). This model was then used as input for an MR simulator (MNI Brainweb1) that produces a realistic MR volume image for which “ground truth” is known with respect to its components. We evaluated the three segmentation methods in two aspects: the accuracy of the segmented result and the efficiency of the segmentation procedure. 4.1 Accuracy

We first evaluated the accuracy of the segmented results. The example results are shown in Fig.3.(b)-(d). The normal Fast Marching result shown in (b) indicates that most of the surface could not be accurately reconstructed. The Morphological Reconstruction brings us a more accurate result as shown in (c). The result of the proposed approach shown in (d) is quite similar to the one of the Morphological Reconstruction. In order to quantify the segmentation accuracy, we employed the idea of “similarity index” in our experiment, which is introduced by Zijdenbos [6]. We evaluated the three methods and concluded into the Table.1. The initial seeds were repeatedly defined at various locations three times. The result of our proposed approach is quite similar to the morphological reconstruction, and much better than the one from the Fast Matching method.

(a )

(b)

(c)

(d)

Fig. 3. Segmentation results, where the 2D results are indicated in high-lighted regions. (a) source image; (b) the Fast Matching result; (c) the Morphological Reconstruction result and (d) the proposed hybrid approach

1

http://www.bic.mni.mcgill.ca/brainweb/

Evaluation of Morphological Reconstruction

683

4.2 Efficiency

The computing times of the three segmentation algorithms were measured during the experiment. Table 2 describes the results of each method when three initial seeds were repeatedly defined. We can find that even the proposed hybrid method is still more costly than the Fast Matching method, but significantly improved from the Morphological Reconstruction method. It is considered as a near real time algorithm. The reason why the hybrid approach is much faster than the traditional morphological Reconstruction is that the numbers of the iteration during the reconstruction were significantly reduced. In the example, the total iterations of Morphological reconstruction and Hybrid Approach were 30 and 3 respectively. Table 1. Comparison of Similarity Index value of different approaches

1

2

3

average

Morph. Reconstruction

0.9737

0.9731

0.9747

0.9738

Fast Marching

0.6278

0.6298

0.6334

0.6302

Hybrid Approach

0.9737

0.9734

0.9721

0.9734

Table 2. The computing time of the three segmentation method

Morph. Reconstruction Fast Marching

1 197.5” 22.3”

2 184.4” 19.6”

3 184.1” 25.1”

average 188.6” 22.3”

Hybrid Approach

41.7”

45.8”

42.6”

43.4”

5 Conclusion In this paper, we presented an essential evaluation study using two typical segmentation methods and a novel hybrid segmentation approach based on a standard criterion. The evaluation results in both accuracy and efficiency revealed that the proposed hybrid approach takes the advantage of both accurate from region-based algorithm and rapid from the model-based approach, which achieved a near real time segmentation performance and high accurate results. As future works, we are scheduling to choose more algorithms from both model-based and region-based algorithms into our evaluation study. We are going to design more sophisticated analysis methods other than the similarity index to inspect experimental results more precious, and the evaluation results will be virtually presented.

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References 1. Kass, M., Witkin, A., and Terzopolous, D.: Snake: Active Contour Models. Int. J. Compt. Vision, Vol.1 (1988) 321-331 2. Osher, S., and Sethian, J.A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulation. J. of Comput. Phys., vol. 79 (1988) 12-49 3. Sethian, J.A.: Fast marching method. SIAM Review, 41(2) (1999) 199-235 4. Chop, D.: Computing Minimal Surfaces via Level Set Curvature Flow. Journal of Computational Physics, vol.106 (1993) 77-91 5. Gu, L., and Peters, T.: An Accurate and Efficient Hybrid Approach for Near Real Time 3D Brain Segmentation. Proc. Of 17th International Congress and Exhibition On Computer Assisted Radiology and Surgery, London UK (2003) 1309 6. Zijdenbos, A.P., Dawant, B.M., Margolin, R.A., and Palmer, A. C.: Morphometric Analysis of White Matter Lesions in MR Images: Method and Validation. IEEE Trans. Med. Imag., vol.13 (1994) 716-724

Utilizing Staging Tables in Data Integration to Load Data into Materialized Views 1

Ahmed Ejaz and Revett Kenneth

2

1

Information and Computer Science Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, 31261 [email protected] http://www.ccse.kfupm.edu.sa/~eahmed/ 2 Department of Computing and Information System, University of Luton, Park Square, LU1 3JU, England [email protected]

Abstract. This paper proposes an approach to data integration and migration from a collection of heterogeneous and independent data sources into a data warehouse schema. Current methodology assumes that the data is loaded into data warehouse using queries in order to extract data from multiple data sources. Extracting data from various data sources requires the establishment of generic data integration methodologies. Sometimes, various data anomalies arise when using complex queries across multiple data sources. A data warehouse can be abstractly seen as a set of materialized views. Selecting views for materialization in a data warehouse is one of the most important decisions making tasks in its design. However, there are few facilities in data integration systems that consider these important issues. In this paper, we propose the approach of introducing staging table’s schema that can be utilized to load required data from source tables into corresponding staging tables. Staging tables will be assumed to be temporary tables and each staging table will be empty before loading new data and using simple non-join queries to load data. We then focus on an approach to load data into data warehouse materialized views through staging tables including maintenance of materialized views. Keywords: Data Integration, Data Migration, Staging Tables, Global Schema, and Relational Schema.

1 Introduction As the size and complexity of data stored in data warehouses increases, the design and strategy used in staging tables becomes increasingly important. Many organizations are dependent on their data stores and survive on their ability to acquire, analyse and store data in an efficient manner as part of an Enterprise Resource Planning system (ERP). In addition, data integration and data migration is becoming a central issue in World Wide Web based data repositories. Until recently, most research regarding data integration has focused on managing and highlighting query general issues for migrating data in data warehouse as J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 685–691, 2004. © Springer-Verlag Berlin Heidelberg 2004

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mentioned in [VM1]. In this paper, strategies are proposed for managing data migration correctly and efficiently managing maintenance of materialized views. A database relational schema is defined for the implementation of staging tables followed by rules and strategies for migrating data into data warehouse correctly and efficiently. Also, our approach identifies data that is flagged for rejection during the migration process, i.e. before it becomes incorporated into the data warehouse.

2 Framework for Staging Table’s Schema In this section we illustrate formalization of a data integration system, which is based on the relational model. We will follow the nomenclature utilized in the work by Cali in paper [CD1] "Data integration under integrity constraint". We assume to have a fixed (infinite) alphabet Г of constants, and, if not specified otherwise, we will consider only databases over such alphabet. We adopt the so-called unique assumption, i.e., we assume that different constants denote different objects. Consider a symbol C for relational schema that consists of • •

An alphabet A of predicate (or relation) symbols, each one with the associated arity, i.e., the number of arguments of the predicate (or, attributes of the relation) A relational database denoted by DB for a schema C is a set of relations with constants as atomic values, and with one relation γDB of arity n for each predicate symbol γ of arity n in the A. γDB is the interpretation of the predicate symbol γ in database DB such that it contains 1. 2.

The set of tuples t that satisfying the predicate γ in DB The set of attributes as denoted by symbol A satisfying the predicate γ in DB

In this paper we will consider the following two constraints; later on we can validate them with the help of a proposed approach. • Key Constraints: A relation γ in a schema C, consists of set of tuples such that t belongs to γ. A represents set of attributes in relation γ. Then key constraint over γ is satisfied in a database DB if for each t1, t2 ∈ γDB such that t1 [A] ≠ t2 [A], where each ti[A] is the projection of the tuple t over A. • Foreign key constraints: Let γ1 and γ2 be two relations with primary keys K1 and K2 respectively. A subset α of γ2 is a foreign key referencing K1 in relation γ1 such that γ1 [K1] ⊆ γ2 [K2] means for every tuple t2 in γ2 there must be a tuple t1 in γ1 or t1 [K1] = t2 [α2]. Also, condition Πα (γ2) ⊆ ΠK1 (γ1) will be satisfied and either α = K1 or α and K1 must be compatible sets of attributes. Consider three types of schemas such as source schemas, staging schemas and global schemas for data warehousing. These three schema’s layouts are shown in figure 1. A Source schema consists of multiple databases, legacy or operational databases. In this paper the staging schema is introduced to manage the data migration tasks. In the staging schema, data is prepared for conversion into the global schema which is then validated and tested using above constraints. In staging schema, no

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constraints are applied but algorithm is used to validate all possible checks for constraints. For example, a record or a tuple from a certain table requires foreign key validity on some attribute (s); it will be tested before inserting into target table. Also, we consider staging schema as temporary schema, completely separate or it can be managed within global schema. So as defined in [CD1], G represents global schema, we mean it for staging schema as well. A data integration system Г is a triple Г = (G, S, MG,S), where G is the global schema, S is the source schema, and MG,S is the mapping. Example 1. Consider a simple example of data integration with single source option containing Г1 = (G1, S1, M1G, S) where G1 is constituted by the relation symbols customer (Cid, Cname, Caddress, CCity) orders (Oid, Otype, Odate, Cid) sold (Oid, Pid, Sprice, Qty) product (Pid, Pname, Pprice, TaxStatus) and the constraints are defined as key(customer) = {Cid} key(orders) = {Oid} key(sold) = {Oid,Pid} key(product) = {Pid} such that sold[Oid] ⊆ order[Oid], sold[Pid] ⊆ product[Pid], orders[Cid] ⊆ customer[Cid], sold[Sprice] may not be a subset of product[Pprice] 1

S consists of four sources. Source s1, of arity n (where n can be different), contains information about customers with their customer id, name, address and city. Source s2, of arity 4, contains order id (invoice id), type, date and customer id (which is a foreign key). Source s3, of arity 3, contains information about product’s id, name and price. Finally, Source s4, or arity 3, contains information about products that are sold. The mapping M1G, S is defined by ρ(customer) ρ(orders) ρ(product) ρ(sold)

= = = =

cus(X,Y,Z) , where x1, x2,…, xn are the values of features X1, X2,…, Xn. Since SVM performed best when using binary features [4], we used binary representation. In case of the selected features above, the feature values are defined by binary representation which indicates whether a particular word occurs in an email. In other cases, the attribute values are moderately defined by scaling original data according to their own properties. For example, if an email is arrived between 12 pm and 5 am, the feature value of receiving time is 1, otherwise 0. We will finally classify incoming emails into two categories: non-spam and spam mail. However, since each spam category has its own properties and SVM can only compute twoway categorization, we construct three SVM classifiers separately according to the kinds of spam mails. Three SVM classifiers are generated using the feature vectors, where three is the number of spam categories: porn spam, financing spam, and shopping spam. It is more effective than constructing only one SVM classifier for filtering all spam mails.

3 Applying Phase: Two-Phase Spam-Mail Filtering Incoming emails are processed by using the information and classifiers constructed in the training phase. If an email contains one of the definite information, it is regarded as a spam mail. Otherwise, it is passed to the next SVM applying phase. SVM classifier for porn spam mails is applied first. If an email is classified as a spam mail, the second applying phase is over. If not, it is passed to other SVM classifier in sequence (See Figure 1).

Two Phase Approach for Spam-Mail Filtering

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Incoming E-mails

1st phase: filtering with definite information Definite spam keyword lists Matching? Sender’s information - Email addresses - URL addresses

Yes

No

2nd phase: filtering with feature vectors SVM classifier for porn spam

Classifying

+

SVM classifier for financing spam

Classifying

+

SVM classifier for shopping spam

Classifying

+

Non-spam mail

Spam mail

Fig. 1. Applying process for filtering spam mails

4 Experiments The email corpus used in the experimental evaluation contained a total of 4,792 emails and 4 categories: 2,218 for legitimate mail, 1,100 for porn spam, 1,077 for financing spam, and 397 for shopping spam. To select important features, we used the weak.attributeSelection package provided by WEKA [8]. WEKA is a workbench designed to aid in the application of machine learning technology to real world data sets. WEKA contains a number of classification models. The SVM classifier used in this experiment was also provided by WEKA. SVM is tested with its default parameters settings within the WEKA. To evaluate the filtering performance on the email document corpus, we use the recall (R), precision (P), and F-measure (F) commonly employed in the information retrieval. In case of F-measure, we set the equal weight of recall relative to precision. In our experiments, we used ten-fold cross validation to reduce random variation. E-mail corpus was randomly partitioned into ten parts, and each experiment was repeated ten times, each time reserving a different part for testing, and using the remaining nine parts for training. Results were then averaged over the ten runs. Table 1 compared the performance of information gain and χ2-test in selecting features for filtering porn spam. When compared with the results by Yang [7], it

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gave almost same results. Table 2 showed the performance of 2nd phase for each SVM classifier. The method of fetching web pages achieved an improvement of F-measure by 9.4% over the method of using an original email header and body only. Compared the two methods, there is little change of precision, but recall was improved a lot when using hyperlinks. We can recognize from these results that fetching web pages plays an important role in collecting more features. To evaluate the performance of each phase, among 4,792 emails, the 4,335 emails are used for training SVM classifiers, and the remaining 457 emails are used for testing the proposed system’s performance. We see from Table 3 that the proposed two-phase method is more effective than the method applying each phase separately, since the 1st phase undertakes some portion of the 2nd phase’s workload with very high precision. Table 1. Experimental results according to the feature selection methods (for porn spam)

Feature selection method

No. of selected features 338 485 681 838 338 485 681 838

Information gain

χ2-test

Recall

Precision

F-measure

51.5 61.3 62.7 62.7 51.4 59.0 62.7 62.7

95.8 98.1 97.3 97.5 95.8 98.0 97.3 97.5

67.0 75.4 76.3 76.3 66.9 73.7 76.3 76.3

Table 2. Performance of SVM classifier

Object Original email only Original email + Fetched webpages

R

P

F

Porn Financing Shopping Porn Financing

No. of selected features 269 713 92 1085 1224

43.1 63.1 49.6 64.9 68.1

96.9 98.3 90.8 96.2 94.3

59.7 76.9 64.2 77.5 79.1

Shopping

1233

60.2

90.9

72.4

Category

Table 3. Performance of the proposed system (%)

Applying phase 1st phase only 2nd phase only 1st + 2nd phase

Recall 43.6 67.3 73.5

Precision 100 99.4 99.5

F-measure 60.7 80.3 84.6

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5 Conclusion In this paper, we proposed a two-phase method for filtering spam mails based on textual information and hyperlinks. Since the body of a spam mail has little text information recently, it provides insufficient hints to distinguish spam mails from legitimate mails. To resolve this problem, we utilized hyperlinks contained in the email body. After fetching contents of a remote webpage, we extracted all possible hints from original email body and the fetched webpage. These hints are used to construct SVM classifiers. We divided hints into two kinds of information: definite information and less definite textual information. In case that an email contains one of the definite information, there is no need to perform machine learning algorithms, since it has a very high probability of being spam mails. In other case that the email has no definite information, it is evaluated using the SVM classifiers. We discovered that fetching hyperlinks is very useful in filtering spam mails, and our two-phase method is more effective than the method using machine learning algorithm only, blacklists, or keyword-based filters. This research is very important in that our system can prevent minors from accessing adult material on spam mails by chance, and save valuable time by lightening the email checking work. We will do further research on how to automatically update definite information, find more features having high differential power, and improve the filtering performance. Finally, we will consider that personalized definite information, constructed for each user, is implemented in our system.

Acknowledgement This work is supported by Brain Korea 21 Information Technology Division, Daegu University.

References 1. Cranor, L. F. and LaMacchia, B. A., “Spam!,” Communications of ACM, Vol.41, No.8 (1998) 74-83 2. Sahami, M., Dumais, S., Heckerman, D., and Horvitz, E., “A bayesian approach to filtering junk e-mail,” In AAAI-98 Workshop on Learning for Text Categorization (1998) 55-62 3. Vapnik, V., The Nature of Statistical Learning Theory, Springer-Verlag, New York (1995) 4. Drucker, H., Wu, D. and Vapnik, V., “Support Vector Machines for Spam Categorization,” IEEE Trans. on Neural Networks, Vol.10(5) (1999) 1048-1054 5. Joachims, T., “Text Categorization with Support Vector Machines: Learning with Many Relevant Features,” ECML, Claire Nédellec and Céline Rouveirol (ed.) (1998) 6. Yang, J., Chalasani, V., and Park, S., “Intelligent email categorization based on textual information and metadata,” IEICE Transactions on Information and System, Vol.E86-D, No.7 (2003) 1280-1288 7. Yang, Y, and Pedersen, J. P., “A comparative study on feature selection in text categorization,” in Fourteenth International Conference on Machine Learning (1997) 412-420 8. Witten, I. H. and Frank, E., Data Mining: Practical machine learning tools and Techniques with java implementations, Morgan Kaufmann (2000)

Dynamic Mining for Web Navigation Patterns Based on Markov Model Jiu Jun Chen, Ji Gao, Jun Hu, and Bei Shui Liao College of Computer Science, Zhejiang University, Hangzhou 310027, Zhejiang, China [email protected]

Abstract. Web user patterns can be used to create a more robust web information service in personalization. But the user interests are changeable, that is, they differ from one user to another, and they are constantly changing for a specific user. This paper presents a dynamic mining approach based on Markov model to solve this problem. Markov model is introduced to keep track of the changes of user interest according to his or her navigational behaviors. Some new concepts in the model are defined. An algorithm based on the model is then designed to learn the user’s favorite navigation paths. The approach is implemented in an example website, and the experimental results proved the effective of our approach.

1 Introduction Web user patterns can help in improving the design of website, filtering the information and customizing the web service [1]. The study of user’s behavior has become an important issue in web mining technology. Some works have been done on the discovery of useful user navigational patterns. Most existing approaches focus on finding web association rules, navigational paths or sequential patterns from the log files and web links information. Zaiane et al [2] applied OLAP and data mining technology for pattern mining. Agrawal and Srikant [3] adopted sequential mining techniques to discover web access patterns and trends. In [4], Chen et al. proposed the maximal forward references to break down user sessions into transactions for mining access patterns. And other technologies, such as fuzzy theory, tree construction and support vector machines, are used to improve the performance of the system based on user patterns [5, 6]. Most solutions discover patterns simply according to user’s access frequency in web logs. It is inaccurate, (a) pages, which visited frequently, may not show that users have more interest in them, such as page that is only to be utilized the links of a page to another page; (b) web user interests are changeable [7], and it is difficult to track the exact pattern of web users. In this paper, we will study those two problems. The rest of this paper is organized as follows. In the following section, we first introduce the Markov model to study the J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 806–811, 2004. © Springer-Verlag Berlin Heidelberg 2004

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navigational characters of web users. Based on the Markov user model, an algorithm is proposed to learn the user’s favorite navigational paths, and experimental results are discussed. The conclusions are presented in the final section.

2 Dynamic Mining for Navigation Patterns 2.1 Markov Model The interest changes of web users can be represented from their navigational behavior, and a Markov model can extract the characters of user’s navigational behaviors dynamically. We model the navigational activities as a Markov process for the following reasons: Firstly, the information about the user’s navigation pattern is changeable. Secondly, the web user is largely unknown from the start, and may change during the exploration. Definition 1. State. A state is defined as a collection of one or more pages of the website with similar functions. Besides functional states, the model contains other two special states, Entry and Exit; Definition 2. Navigational Behavior. Navigational behavior can be viewed as remaining in one state. Two kinds of navigational behaviors are defined: (a) remaining in one state, which can be viewed as reading the contents of web pages; (b) making transitions among states, which represents the requests of pages; Definition 3. Navigational Paths. In a limited time, the sequence of user’s relative web requests in a website is defined as user navigation path. It can be viewed as a sequence set of states; Definition 4. Transition Probability pij . It is the probability of transition from state i to state j. A transition occurs with the request for one page that belongs to state j while the user resides in one of the pages belonging to state i. We suppose that if there are n kinds of different transitions to leave one state, the state that has higher transition probability reveals user interest; Definition 5. Mean Staying Time t ij . It is the mean time which the process remains in one state before making a transition to another state. The longer staying time, the more interested visiting. We suppose that if there are n kinds of different translations to leave one state, those states that have long staying time reveal user interest. The pages that are only for a user to pass have limited staying time. Although this page have many visited times, it can lower the interest level according to the staying time;

Definition 6. Favorite f ij . It integrates the weight of transition probability and mean staying time while evaluating the interest level of the state visited by the web user. It is defined as formula (1). It can prevent from only mining visited states with high probability and low staying time.

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In formula (1), pij and tij can be found out by the following methods. pij × tij ⎧ ⎪ fij = n +1 n +1 ⎪ p tij ) / n 2 ( )( ij ⎪ ⎪ j =2 j =2 ⎨ f = F ⎪ 1j threshold ⎪ f = ⎪ i ( n + 2) Fthreshold ⎪ f =0 ⎩

i, j ∈ (2, n + 1)

∑ ∑

(1)

j ∈ (2, n + 1) i ∈ (2, n + 2) Others

Method to calculate transition probabilities: (i) For the first request for state s in the session, add a transition from Entry state to the state s , State0 ( Entry ) → States ,and increment TranstionCount0 s in a matrix TranstionCount[i, j ] by 1, where TranstionCount[i, j ] is a matrix to store the transition counts from state i to state j; (ii) For the rest of user’ requests in the session, increment the corresponding transition count of TranstionCounti , j in the matrix, where i is the previous state and j is the

current state; (iii) For the last page request in the session, if the state is not the explicit Exit state then add a transition from the state to Exit state and increment TranstionCounts ,( n + 2) value by 1; (iv) Divide the row elements in matrix TranstionCount[i, j ] by the row total to generate transition probability matrix P, whose element is pi, j : pi , j =

TransitionCounti , j

∑TransitionCount

(2)

i,k

k

Method to calculate mean staying time: (i) To find out the time spent in state i before the transition is made to state j for any transition from state i to state j, except the transition from Entry state, and the transition to Exit state. If this time belongs to the interval k then, increment StayTimeCounti , j ,k by 1 in a three-dimensional matrix StayTimeCount[i, j , m] , where, StayTimeCounti , j ,k is the number of times the staying time is in the interval k at state i before the transition is made to state j; (ii) Find out the interval total for each transition from state i to state j in StayTimeCount[i, j , m] . Divide frequency count in each interval with the interval total to find out the probability of occurrence of the corresponding intervals. Repeat this to generate StayTime Pr obability[i, j , m] , whose element defined as follows: StayTime Pr obabilityi , j , m =

StayTimeCounti , j , m

∑ StayTimeCount

i, j,n

n

(3)

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(iii) Multiply each interval with the corresponding probability to generate mean staying times ( tij ), which is the elements of matrix T . tij =

∑ m × StayTime Pr obability

i, j ,m

(4)

m

A matrix of Markov user model, M ( n+ 2 )( n+ 2 ) , as a state to state matrix, is set up from web logs, whose elements include pij , t ij , and f ij . In this way, the matrix will capture a compact picture of users’ favorite navigational behavior dynamically. 2.2 Algorithm for User Favorite Navigation Path

Based on Markov user model, we design the algorithm, named MFNP (Markov-based favorite navigation paths), which is shown as follows. Algorithm MFNP Input: M, Fthreshold , Pthreshold ; Output: Favorite navigation paths; Variable: M: Matrix of Markov user model StateVisited[]: Array to store whether the state is visited or not; FS[]: Array stored the favorite navigation states; State[]: Array stated the states of website; Fthreshold : Threshold of the Transition Probability; Pthreshold : Threshold of the Favorite; program FavoritePath(M, Pthreshold , Fthreshold ) Initialize StateVisited[] and FS[]; for k=0 to (n+1) do if StateVisited[k]=false then FindFavoriteState(M,k); end program FindFavoriteState(M,i) FS[]=State[i]; if StateVisited[i]=false then StateVisited[i]=true & StateFound=false; for j=0 to (n+1) do if pij >= Pthreshold and fij >= Fthreshold then StateFound=true & FindFavoriteState(M,j); if StateFound=false then Output the elements in array FS[]; else Output the elements in array FS[]; end

The algorithm is implemented in a used-goods exchanged website, which includes 12 states: (1)Entry; (2)Home; (3)Login; (4)Register; (5)Goods Search; (6)Seller Data; (7)Leave word; (8)Goods List; (9)Goods Register; (10)Customer Support; (11) About Us; (12)Exit. As shown in table 1, no transition can be made to Entry state from any

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state, and two rows are associated with each state. The upper rows are the transition probability values and the lower rows correspond the mean staying times in minutes. Table 1. User navigation matrix of the example website State 1 2

2 0.30 0.01 0.52

3 4

0.06 0.5

3 0.13 0.21 0.86 0.36 0.54 0.28 0.91

4 0.01 0.02 0.80 0.02 0.52 0.48 0.50

7

0.02 3.12

0.12 2.10 0.10 2.78

8 9 10 11

0.01 5.60 0.21 2.52

0.04 2.64 0.06 0.85 0.06 7.20

0.01 0.52

6

0.10 2.36

7

0.14 2.52

8 0.35 0.23 1.20 0.04 1.23

9

10 0.10 0.01 0.61

11

12

0.06 1.50

0.43 0.12

0.22 0.55

0.18 0.42 0.53 0.14 0.50 0.45 1.25 0.12 0.87

5 6

5 0.11 0.05 2.27 0.02 0.50

0.08 1.37 0.28 1.21

0.20 0.50 0.05 2.50 0.20 0.67 0.32 0.50 0.33 0.61 0.02 0.77

0.18 2.78 0.20 0.62

0.10

0.10 0.68

0.37

0.12 1.85 0.23 1.32 0.11 3.36

0.34 0.50

0.11 0.05

0.58 0.55 0.06 1.52

0.05 2.53 0.12 2.66

0.42 1.78

0.05 1.56 0.23 1.18

0.24 0.10 1.00

12

100 + MFNP * Pap.[4]

90

Accuracy(%)

80

70 60 50

40

0

50

100 150 200 250 Size of interested navigation paths

300

Fig. 1. Accuracy comparison

Probability threshold and favorite threshold are assigned to 0.2 and 3 respectively. According to the algorithm, begin with Entry state. Then search the first Entry row, choose State 8 (Goods List) as favorite state. Because State 8 has not been visited, it

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begins to search from State 8 row. Then State 8 is chosen. Because State 8 has been visited, the elements in array FP[] ( from Entry to Goods List) can be output as the favorite navigational path. Finally, the set of favorite path are included: {(1, 8); (1, 8, 6, 12); (1, 8, 6, 7, 5); (1, 8, 6, 7, 10); (1, 8, 6, 7, 10, 12); (1, 2, 3); (1, 2, 8); (1, 2, 12); (1, 2, 6, 12); (1, 2, 6, 7, 5); (1, 2, 6, 7, 10); (1, 2, 6, 7, 10, 12); (1, 2, 3, 12)}, and the great favorite path is

the transition from Entry state to Goods List state. To evaluate the effectiveness of our method, we compare the accuracy of the algorithm proposed in paper [4] with our model. We implement the algorithms to mine the same number of interested navigation paths. According to those navigating path, we produce predictions as dynamic links. If users click these dynamic links, we think the corresponding algorithm is accurate. Otherwise, it is inaccurate. The experiment result is shown in figure 1. We can find our method is more accurate and effective.

3 Conclusions In this paper, we proposed a dynamic mining approach to learn the navigation patterns of web user. We constructed a Markov model to track and represent the user’s behaviors dynamically. Based on the model, we designed an algorithm to mine user’s favorite path. The algorithm was implemented in an example website and the experiment results show that our method is effective.

References 1. Perkowitz, M., Etzioni, O.: Towards adaptive web sites: conceptual framework and case study. Artificial Intelligence, 118(1-2) (2000) 245–275. 2. Zaiane, O., Xin, M., Han, J.: Discovering web access patterns and trends by applying OLAP and data mining technology on web logs. Proceedings on Advances in Digital Libraries Conference, Melbourne, Australia, (1998) 144-158. 3. Agrawal, R., Srikant, R.: Mining sequential patterns. Proceedings of the 11th International Conference on Data Engineering, Taipei, Taiwan, (1995) 3-14. 4. Chen, M. S., Park, J. S., Yu, P. S.: Efficient data mining for path traversal patterns. IEEE Transaction, Knowledge Data Engineering, 10(2) (1998) 209-221. 5. Nasraoui, O., Petenes, C.: An intelligent web recommendation engine based on fuzzy approximate reasoning. IEEE International Conference on Fuzzy Systems, (2003) 1116-1121. 6. Rohwer, J. A.: Least squares support vector machines for direction of arrival estimation. IEEE Antennas and Propagation Society, AP-S International Symposium (Digest), 1 (2003) 57-60. 7. Belkin, N. J., Croft, W. B.: Information filtering and information retrieval: two sides of the same coin. Communication of the ACM, 35(12) (1992) 29-38.

Component-Based Recommendation Agent System for Efficient Email Inbox Management Ok-Ran Jeong and Dong-Sub Cho Department of Computer Science and Engineering, Ewha Womans University, 11-1 Daehyun-dong, Seodaemun-ku, Seoul 120-750, Korea {orchung, dscho}@ewha.ac.kr

Abstract. This study suggests a recommendation agent system that the user can optimally sort out incoming email messages according to category. The system is an effective way to manage ever-increasing email documents. For more accurate classification, the Bayesian learning algorithm using dynamic threshold has been applied. As a solution to the problem of erroneous classification, we suggest the following two approaches: First is the algorithmic approach that improves the accuracy of the classification by using dynamic threshold of the existing Bayesian algorithm. Second is the methodological approach using recommendation agent that the user, not the auto-sort, can make the final decision. In addition, major modules are based on rule filtering components for scalability and reusability. Keywords: e-mail classification, dynamic threshold, bayesian algorithm, rule filtering component.

1

Introduction

As information technology develops, the quantity of information the user can have at his disposal has increased exponentially. With it, different recommendation systems have been suggested. These systems enable the user to wade through the information glut. But most of these systems are for personalizing user profiles or for recommending product items the user wants based on his prior search and buying patterns. As part of this type of recommendation system, collaborative filtering can have a major advantage in that it can provide a dynamic link through other users’ feedback information [1]. Although the possible applicability of the recommendation system is limitless, the attempt to apply this to email management has not been made as of yet [2, 3]. This study wants to suggest a recommendation agent system for email that can actively manage depending on situation and reflect the user’s opinion, rather than a system that can simply auto-sort the messages based on existing text classification. Although such system auto-sorts by category through personalized learning, it is better to have a semi-automatic system that doubles with a recommendation system rather than an automatic sort system to maximize email users’ satisfaction. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 812–818, 2004. c Springer-Verlag Berlin Heidelberg 2004


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As a solution to the problem of erroneous classification, we suggest the following two approaches: First is the algorithmic approach that improves the accuracy of the classification by using dynamic threshold of the existing Bayesian algorithm. Second is the methodological approach using recommendation agent that the user, not the auto-sort, can make the final decision. In addition, major modules are based on rule filtering components for scalability and reusability.

2 2.1

Related Work Learning Algorithm

In the process of classifying email documents, the rules are formed. When classifying the documents by category, learning algorithm can be used. For machine learning method in automatic document classification, there is Naive Bayesian, K-Nearest Neighbor, and TFIDF (Term Frequency Inverse Document Frequency) approach [4]. In this paper, we use the Naive Bayesian approach because it is the most widely in use and appropriate for email document classification. This learning method makes use of a probability model based on the Bayesian Theorem. It types in a vector model for the document to be classified and finds out a class that has the highest possibility for observing the document. The hypothesis here is a Naive Bayesian assumption that all the characteristics of the documents are independent of each other in a given category. The Bayesian algorithm applied in this study improves the accuracy of email documents’ classification by varying previously fixed threshold dynamically. 2.2

Feature Extraction for Learning

The Feature Extraction is a way to define again the importance of the learning resources’ characteristics by their category. For this, it is necessary to distinguish categories according to their learning resources’ characteristics and perform feature extraction based on it. Term weighting method can be done by considering category information to which a set of keywords belongs. In this case, more weight is given to a keyword representing each category [5, 6]. Such machine learning method for feature extraction is applied when there are two different categories, by giving more weight to the keyword for each category. It also makes use of a method, which registers the keyword on the title part as well as the body part. It is the method that takes into duplication account on the title part of email documents. 2.3

The Features of Components

Components are a system element that is independent and divisible into small units that provides service through interface. These components can be replaceable with other elements as required by the system and are part of pre-developed application codes[7] . Based on the definition of the components, it is possible to show their characteristics. Their characteristics include identifiability, replaceability, accessibility through interface, service’s fixability provided by inter-

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face, concealibility of physical realization, degree of independence, independent reusability of language and development tools, and dynamic reusability. In general, the components can be divided into logical and physical perspectives [4]. The concepts of logical component and physical component based on their features are as follows: The former means the business component which models after real-world business features. Meanwhile, the latter means engineering reconstruction by dividing the business components into independent software. This study thus approaches from logical perspective, improving scalability and reusability by implementing into components the major learning and filtering parts in email management.

3 3.1

Email Recommendation Agent System Email Classification Method

The reason this study opted for recommendation method as its email classification is that the existing auto-sort method may be problematic in applying the email system. Since email documents are highly personalized, it is difficult to satisfy the user even though they are auto-sorted by category through personalized learning. That is why we suggest in this study a recommendation agent system that can recommend a category according to its rank after classifying the email messages by category. Once the user is recommended a category, he can save the keyword in multiple categories, or manage his email inbox as the category changes with time lapse. That way, it is possible to avoid classifying email messages inadequately. The system is designed so that the user can opt for auto-sort when email messages are overwhelming or when he is satisfied with the reliability of the recommendation system. 3.2

Suggested System

The biggest characteristics of the suggested system are twofold. First, the system is modulized for more efficient interaction among email documents’ characteristic extraction, rule generation, and classification by category. In addition, the system is created with rule filtering components. Second, the system adds dynamic threshold function to the existing Bayesian algorithm, thus improving the accuracy of classification that can be the central part of the system function. The overall flow of the system is shown in Figure 1 below. The figure is a system flow chart reflecting all the processes of learning, filtering, rule generation, classification, and recommendation, based on user information. The recommendation agent system for email management has the following functions: First, once a new message reaches the user’s inbox, the system observes how the message is processed and learns from it. This is the process where feature extraction and rule generation are made and the user can set up categories according to his preferences. Second, the system forms rules by applying the Bayesian algorithm to the characteristics derived from the email processing observation module. Third, once an email message based on the new rules

Component-Based Recommendation Agent System

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Fig. 1. Modular Design (The Web Mail Interface Module, The Category Rule Generation Module and The Mail Classification Recommendation Module)

reaches the inbox, it is classified by category and then recommends the best category to the user. These are implemented by COM+, with consideration on scalability with other application systems and on reusability under distributed environment. Major interfaces and methods employed here are illustrated in Figure 2 below. The

Fig. 2. Rule Filtering Component (COM+)

second feature of the suggested system is that it improves the accuracy of filtering by dynamically varying previously fixed thresholds. This study classifies email documents through the Bayesian learning method, which is the best available learning algorithm for document classification. Suppose that C is all the category set as in (1) while C0 is where classification is not possible. Suppose again that D is the set of all the email documents. Then we can define (2) as follows:

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CategorySet C = {C1 , C2 , ..., Ck }, C0 = unknown category

(1)

E − M ailDocumentSet D = {d1 , d2 , ..., dn }

(2)

According to the Naive Bayesian classification method, conditional probability of each category cj of one di is given as follows:
(di ) = {P (di |C1 ), P (di |C2 ), P (di |C3 ), ..., P (di |Ck )}

(3)

In most systems, each document is classified by the highest probability value as in Equation (4). But this study converts the fixed threshold T , which has been used in the existing Bayesian algorithm, into the dynamic threshold T  through Equation (5). When the dynamic threshold T  is applied, it is shown, the accuracy of the system has been improved. Pmax (di ) = max{P (di |Ct )}, t = 1, 2, ..., k ⎧  ⎪ ⎨ {Cj |P (di |Cj )} = Pmax (di ) if Pmax (di ) ≥ T Pmax (di )  where T = 1 − k Cbest (di ) = P (di |Cj ) ⎪ j=1 ⎩ C0 otherwise

4 4.1

(4)

(5)

System Implementation and Result Analysis System Implementation

The suggested system is based on Web mail server that does not require a separate mail client program. The Implementation environment is used Windows 2000 Professional as OS, MS-SQL 2000 Server for database control. For rule generation and algorithm implementation, rule filtering components, and other functions, we used MS Visual C++ 6.0, COM+, and ASP and ASP components, respectively. Figure 3 below shows user interface utilized in the system. The user interface in Figure 3 can be used in the user observation process where the user can create and save categories. Besides, the user can create frequently used categories and delete unnecessary ones. The user extracts features, implements internally mail classification based on the established rules, and recommends selected categories with assigned probabilities. The user can save email messages under given categories after reviewing recommended categories. 4.2

Result Analysis

The appropriateness of an information classification system is measured both by recall ratio and precision ratio. The recall ratio refers to the ratio of suitable literature classified by the classification system among suitable literature in the information classification system. The precision ratio implies the ratio of suitable literature among all the classified literature [7]. The performance test for this study is ”How accurate does the system recommend categories to the user?”

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Fig. 3. Mail User Interface

Fig. 4. Category Accuracy

This is measured by the precision ratio and recall ratio, and by testing whether mail contents are classified according to correct categories. For this test, we set up 12 categories, collected sample data for rules, and another set of data for performance evaluation. Since the actual test involved a large amount of data, we attempted to test approximately 10,000 email messages per each category as a single data format. The data format for this test consisted of date, sender, title, number of document lines, empty lines, actual mail contents, and four empty lines. The accuracy test generated the following statistical results: After having the system learns 1,000 emails for each category and carrying out 221,371 incoming emails through the existing algorithm, we obtained the accuracy ratio of 88.6 percent (or 196,137 mails). Meanwhile, the accuracy ratio using the dynamic thresholds was 89.5 percent (or 204,795), which was an improvement of 0.9 percentage points.

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Conclusions

This paper tries to design and implement a recommendation agent system that may be helpful for the email user. As more and more email messages are being exchanged, the users will demand more convenient customized email interface in their email management. The system makes use of a recommendation method, instead of fully automated sorting method. It attempts to improve scalability and reusability by implementing the all-important filtering part as components. Although the current system is designed for the user to set up the categories himself, the future agent will incorporate both the automatic category setup and recommendation method at the same time.

Acknowledgement This work was supported by the Brain Korea 21 Project in 2004.

References 1. Pazzani M., Billsus D.: Learning and Revising User Profiles: The Identification of Interesting Web sites. Machin Learning 27. Kluwer Academic Puglishers (1997) 313331 2. Balabanovic, M., Shoham, Y.: Fab: Content-Based Collaborative Recommendation. CACM 40(3) (1997) 66-72 3. Hill, W., Stead, L., Rosenstein, M., Furnas, G.: Recommending and Evaluating Choices in a Virtual Community of Use. CHI’95 (1995) 194-201 4. Ian, H., Frank, E.: Data Mining. Morgan Kaufmann Publishers. Inc. (2000) 5. Baeza-Yates, R., Ribeiro-Neto, B.: Modern Information Retrieval. Addison-wesley (1999) 6. Cohen, W. W.: Learning Rules that Classify E-Mail, AAAI Spring symposium on Machine Learning in Information Access (1996) 18-25 7. Frye, c.: Understanding Components. Andersen Consulting Knowledge Xchange (1998)

Information Security Based on Fourier Plane Random Phase Coding and Optical Scanning Kyu B. Doh1 , Kyeongwha Kim1 , Jungho Ohn1 , and Ting-C Poon2 1

2

Department of Telecommunication Engineering, Hankuk Aviation University, 200-1 Hwajeon-dong, Goyang-city 412-791, Korea [email protected] Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA

Abstract. An information security method is presented by use of electrooptic cryptosystem. We investigate Fourier plane random phase encoding technique, a random phase coding, and holographic coding. The proposed cryptosystem is based on those combined coding technique. The target information is first random phase encoded and then multiplied by a Fourier plane random phase code and further processed into holographic coding. The electro-optic cryptosystem can be implemented in a manner that produced output of the encrypted information is to be directly sent through an antenna to a secure site for digital storage. In addition, the system has a capability of producing the encrypted information in real-time. In secure site, the encrypted information is, together with a decryption key, processed for decryption. If the encryption key and decryption key are matched, the decryption unit will decrypt the information. The proposed electro-optic cryptosystem enables us to store, transmit, and decrypt the encrypted data. We develop the theory of technique and substantiate it with simulation results.

1

Introduction

On the classical front, optical cryptography [1-2], which is based on photons, has a long-standing history. Due to the resent progress in the development of optical component and systems and their increased technical performance, optical cryptography suggests that it has significant potential for security application. In one approach of various kinds of optical data processing technology for information security, the coded image is a phase-amplitude function whose real and imaginary parts can be regarded as realizations of independent random processes [3]. Several studies have been published on the implementation of random phaseencoding and security techniques with optical system [4-8]. While most optical encryption techniques are optically coherent, there is an incoherent optical technique for encryption proposed in recent years [6]. Incoherent optical techniques process many advantages over their counterpart, such as better S/N ratio and insensitivity to misalignment of optical elements. One of the reasons of using holographic encryption is that holographic encryption as opposed to electronic J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 819–824, 2004. c Springer-Verlag Berlin Heidelberg 2004


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or digital encryption can provide many degrees of freedom for securing information. Another reason is that the encrypted information is difficult to reproduce with the usual reproduction device. When large volumes of information are to be encrypted, such as a 3-D object, the use of holographic encryption methods is probably the most logical choice. The proposed method is based on Fourier plane random phase coding and optical scanning. Advantages of the method include that since it is an scanning method, incoherent objects can be processed without the need of using spatial light modulators to convert incoherent image to coherent image and the system can perform real-time. Another advantage includes that the method is easily extendible to encrypt 3-D information.

2

Theory of Electro-Optic Cryptosystem and Simulation Results

Optical scanning technique, which first suggested by Poon [9], has been used extensively for various fields of optical applications such as incoherent image processing [10], holographic image processing [11,12], 3-D microscopy [13], optical recognition of 3-D object [14], and optical remote sensing [15]. We shall describe the electro-optic cryptosystem based on Fourier plane random phase coding and optical scanning in the encryption stage as well as in the decryption stage. The optical scanning system is based on the two-pupil synthesis processor. Since the mathematical description of the two-pupil optical system has been discussed in [9], we focus on describing the electro-optic cryptosystem for encryption and decryption operation with the results of the two-pupil synthesis system. The cryptosystem includes identical systems in the encryption and the decryption stages. Figure 1 shows the electro-optic cryptosystem for encryption stage. In the encryption system, the target information is scanned by a time-dependent Fresnel plate (TDFP). TDFP is created by the superposition of a plane wave and a spherical wave of different temporal frequency. The data are encrypted optically by Fourier plane random phase mask and input random phase encryption mask. Let I0 (x, y; z) denote the information to be encrypted and F (kx , ky ) denote the Fourier random phase mask. In lower path, the Fourier random phase

Fig. 1. Electro-optic cryptosystem for encryption

Information Security Based on Fourier Plane Random Phase Coding

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mask, F (kx , ky ), located in the front focal plane of the lens L2 is illuminated by laser beam of temporal frequency ω0 + Ω through lens system. In upper path, the illuminated laser beam of temporal frequency ω0 is focused by lens L3 on the scanning mirror. The two beam are then combined by the beam-splitter, BS, and used to encrypt the image/document, I0 (x, y; z) , located at a distance z away from the scanning mirror. The input random phase mask, m(x, y), is bonded with the target information. The photo-detector, PD, collects all the light information transmitted by the information to be encrypted. The PD is turned at frequency Ω to detect the encrypted information and then produce the current of encrypted information, iΩ (x, y; z) expressed as iΩ (x, y; z) = Re{iΩ p (x, y; z) exp(jΩt)}

(1)

Since the encrypted signal can be made at radio frequency, the signal can be directly sent through an antenna to a secure site for wireless application. To perform encryption on input I0 (x, y; z), we first investigate the Optical Transfer Function (OTF) of the two-pupil synthesis optical system to apply the proposed encryption technique. As we see that the choice of a Fourier plane random phase mask is a good encryption key. For this choice of the mask, we modify the OTF, which have been discussed in [9], as follow: OT FΩ (kx , ky ) = exp[j

z (k 2 + ky2 )]F (kx , ky ) 2k0 x

(2)

It can be shown that the spectrum of iΩ (x, y; z) is related to the spectrum of I0 (x, y; z) through the following expression:
{iΩ (x, y; z)} =
{I0 (x, y; z)m(x, y)}OT FΩ (kx , ky ; z) = [
{I0 (x, y; z)} ⊗
{m(x, y)}]OT FΩ (kx , ky ; z)

(3)

where ⊗ denotes 2−D convolution, and (3) then becomes iΩ (x, y; z) = Re[iΩ p (x, y; z) exp(jΩt)] = Re[
−1 {
{I0 (x, y; z)m(x, y)}OT FΩ (kx , ky ; z)} exp(jΩt)] = Re[
−1 {
{I0 (x, y; z)} ⊗
{m(x, y)} ×OT FΩ (kx , ky ; z)} exp(jΩt)] (4) iΩ (x, y; z) is the encrypted image and can be stored by the digital computer. We can interpret equation (4) as the random phase masked information is being encrypted by Fourier plane random phase mask and then the information is being recorded as a digital hologram. After the object has been encrypted, we need to decrypt it. For decryption, since the system is hybrid in nature, it is flexible and either optical decryption or digital decryption could be employed with the system. We let Fd (kx , ky ) denote as a decryption key. The information is now stored in the digital computer to be used to decrypt the information coming from the encryption site via transmission. To decrypt the information from (4), we provide the use of a electro-optic decryption unit

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that is basically reversal processing of the encryption unit shown in figure 1. We see that the output of the unit, Id (x, y), becomes output =
−1 [[
{I0 (x, y; z)} ⊗
{m(x, y)}] ×OT FΩ (kx , ky ; z)OT F ∗ (kx , ky ; z)Fd (kx , ky )}] =
−1 [
{I0 (x, y; z)m(x, y)}] = I0 (x, y; z)m(x, y)

(5)

We substantiate it with simulation results. Figure 2 shows the optical transfer function of the electro-optic cryptosystem. The original information to be encrypted is shown in Fig. 3. Figure 4 shows the real part of target information masked by a random phase mask placed immediately in front of the information. The following parameters are chosen that the wavelength of light used is 0.6 µm, the document to be encrypted, I0 (x, y), is located 20 away from the scanning mirror. Figure 5 shows the holographic pattern of the key according to Eq.(2). For decryption, we need to gather information and decryption key according to

Fig. 2. Optical transfer function of cryptosystem

Fig. 3. The original information to be encrypted

the manner as discussed. Figures 6 and 7 show the intensity of decrypted information of document with and without Fourier plane decryption key respectively. Since the decrypted information also has a holographic information as well, the depth information, z, play a role as an additional security key. It is apparent that the choice of phase keys would work.

3

Summary and Concluding Remarks

In summary, an information security method is presented by use of electro-optic cryptosystem. We investigate Fourier plane random phase encoding technique, a random phase coding, and holographic coding. In proposed method, the target information is first random phase encoded and then multiplied by a Fourier plane random phase code and further processed into holographic coding. For the

Information Security Based on Fourier Plane Random Phase Coding

Fig. 4. The real part of target information multiplied by random phase mask

Fig. 6. Decrypted information of document

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Fig. 5. Holographic pattern of encryption key

Fig. 7. Decrypted information of document without decryption key

purpose of holographic coding, the information to be encrypted is coded by a time-dependent Fresnel plate (TDFP). TDFP is created by the superposition of a plane wave and spherical wave of different temporal frequency. The reason of using electro- holographic encryption is that holographic encryption as opposed to electronic or digital encryption can provide many degrees of freedom for securing information. Another reason is that the encrypted information is difficult to reproduce with the usual reproduction device. While most optical encryption techniques are optically coherent, incoherent optical techniques process many advantages over their counterpart, such as better S/N ratio and insensitivity to misalignment of optical elements. Advantages of the method include that since it is an scanning method, incoherent objects can be processed without the need of using spatial light modulators to convert incoherent image to coherent image. In addition, the system have a capability of producing the encrypted information in real-time. Another advantage include that the method is easily extendible to encrypt 3-D information. Since the output of encrypted signal can be made at radio frequency, the signal can be directly sent through an antenna to a secure site for wireless application. It is important to point out that the encryption key

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and the decryption key are of the same functional form and they are actually the same key. The proposed system enables us to store, transmit, and decrypt the encrypted data digitally. This work supported in part by Regional Research Center of Korea Science and Engineering Foundation (R12−2001−051−00007−0).

References 1. Diffe, W., Hellman, M.: New directions in cryptography, IEEE Tran. Information Theory, Vol. IT-22., 644-654 (1976) 2. Singh, S.: The code book, Anchor Books, Random House, Inc. New York(1999) 3. Javidi, B., Zhang, G., Li, J.: Experimental demonstration of the random phase encoding technique for image encryption and security verification, Opt. Eng. 35, 2506-2512 (1996) 4. Wang, B., Sun, C.C., Su, W.C., Chiou, A.: Shift-tolerance property of an optical double-random phase-encoding encryption system, Appl. Opt. 39, 4788-4793 (2000) 5. Magensen, P.C., Gluckstad, J.: Phase-only optical decryption of a fixed mask, Appl. Opt. 8, 1226-1235 (2001) 6. Tajahuerce, E., Lancis, J., Javidi, B., Andres, P.: Optical security and encryption with totally incoherent light, Opt. Lett. 26, 678-680 (2001) 7. Tajahuerce, E., Javidi, B.: Encrypting three-dimensional information with digital holography, Appl. Opt. 39, 6595-6601 (2000) 8. Javidi, B., Nomura, T.: Securing information by means of digital holography, Opt. Lett. 25, 28-30 (2000). 9. Poon, T.C.: Scanning holography and two-dimensional image processing by acoutooptic two-pupil synthesis, J. Opt. Soc. Am. A 2, 521-527 (1985) 10. Indeberouw, G., Poon, T.C.: Novel Approaches of Incoherent Image Processing with Emphasis on Scanning Methods, Optical Engineering, 31, 2159-2167 (1992) 11. Doh, K., Poon, T.C., Indebetouw, G.: Twin-image noise in optical scanning holography, Opt. Eng. Vol. 35, no. 6, 1550-1555 (1996) 12. Poon, T.C., Qi, Ying.: Novel real-time joint-transform correlation by use of acoustooptic heterodyning, App. Opt. 42, 4663-4669 (2003) 13. Poon, T.C., Doh, K., Schilling, B., Wu, M., Shinoda, K., Suzuki, Y.: Threedimensional microscopy by optical scanning holography, Opt. Eng. Vol. 34, No. 5, 1338-1344 (1995) 14. Kim, T., Poon, T.C., Indebetouw, G.: Depth detection and image recovery in remote sensing by optical scanning holography, Opt. Eng. 41(6), 1331-1338 (2002) 15. Schilling, B.W., Templeton, G.C.: Three-dimensional remote sensing by optical scanning holography, App. Opt. 40, 5474-5481 (2001)

Simulation on the Interruptible Load Contract 1

1

Jianxue Wang , Xifan Wang , and Tao Du 1

2

School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, 710049, P.R. China [email protected] 2 School of Electronics and Electric Engineering, Shanghai Jiaotong University, Shanghai, 200030, P.R. China

Abstract. Interruptible load management (ILM) is an important part of Demand Side Management (DSM), especially in power market. It has deep influences on reliability and economical operation of power system. How to use a rational model to simulate the ILM becomes a hot topic in China. This paper gives the optimal purchase model of interruptible contract and sets a reasonable selected rule, i.e. the interruptible load should be priorly scheduled in the period with maximal shortage capacity. Based on the rule, the heuristic method is employed to solve the problem. Simulation results of real power system demonstrate the usefulness of the proposed model.

1 Introduction Demand Side Management (DSM) has been promoted worldwide. Considering the customer benefit, DSM provides a pathway for system operation and customer participation. Peak clipping reduces electricity demand during on-peak periods of the day, and it is the most important part of DSM [1]. In many power markets, the peak clipping is implemented through an interruptible load program (ILP) or interruptible load management (ILM). Customer enters into contract with the ISO or the power utility to reduce its demand as and when requested. The ISO/utility benefits by way of reducing its peak load and thereby saving costly reserve, restoring quality of service and ensuring reliability. The customer benefits from reduction in its energy costs and incentives provided by the contract [2]. But how to use a rational model to simulate the ILM is always a difficult problem. The prerequisite in ILM is to determine the contract contents. These have been discussed in papers [3, 4]. According to interruption duration, effective period and minimum curtailment, the interruptible load contract in China could be classified into two main types as shown in Table 1. Table 1. The types of interruptible load contracts in China Type

Effective period

Minimum curtailment

Duration

Type A

6 months

500kW

=4hours

Type B

6 months

500kW

=8hours

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2 The Optimal Purchase Model of Interruptible Load 2.1 Calculation of Shortage Capacity Because of deviation in load forecasting and generator outage, the capacities purchased in advance sometimes are not enough. The technology of Capacity Outage Probability Table (COPT) could be used to evaluate the shortage distribution [5]. In traditional method, the probability distribution of load is gotten from the sequential load curve. But in the improved method, the load probability distribution is formed on the basis of load fluctuation. Statistical material shows that the probability distribution of load fluctuation is normal distribution near the predictive load. The standard deviation δ keeps inverse proportion with square root of the load capacity. For example, δ is 3% when the load capacity is 2000MW, and δ is 1% when the load capacity is 20000MW. Using the technology of COPT, we can get the vector of shortage capacity ( g1 , g 2 ,..., g i ,..., g M ) and the vector of corresponding probability

[ p( g1 ), p( g 2 ),..., p( g i ),..., p( g M ) ]. Here g i is the shortage capacity of state i, p( g i ) is the probability of

g i , and M is total number of the states. So the shortage capacity

expectation ∆C (t ) of the period t could be expressed as: M

∆C (t ) =

∑ g × p( g ) i

(1)

i

i =1

2.2 The Optimal Purchase Model

Based on the above discussion, the large user could first select the contract type, and then give the bidding information of the interruptible load, including the interruptible capacity, price, and total interruption time. After the system load and the spot price in balance market are forecasted through some method, the electrical utilities could use the optimal model to buy the interruptible load. The objective function of optimal purchase model is described as below: tn

min f =

n

∑∑ s (t, i)P (t, i)C n

B

B

(t , i )

t =1 i =1

Where

t Index of study intervals tn Number of study intervals i Index of large users n Number of large users sn (t , i ) Selected state of the large user i at interval t . 0-1 Variable. PB (t , i ) Bidding price of the large user i at interval t C B (t , i ) Bidding capacity of the large user i at interval t

(2)

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827

It must be pointed out that the balance market also could reduce the shortage capacity, so the market is regarded as the large-capacity user to participate in the bidding process. Total Interruptible Capacity Limit. The total capacity of interruptible load is constrained by the total system shortage capacity ∆C (t ) : n

∑ s (t , i )C n

B

(t , i ) ≤ ∆C (t ) t = 1,..., t n

(3)

i =1

Notes that the ∆C (t ) could be calculated by Eq.1 in the section 2.1. Duration Limit. The duration time is specified in the contract as:

sn (t + m, i ) = 1 ( m = 1,..., nd (i ) − 1 ) if s n (t − 1, i ) = 0 and s n (t , i ) = 1

(4)

Where nd (i ) is the required duration of every interruption for user i . As shown in Table 1, the value in this model is 4 hours and 8 hours. Total Interruption Time Limit. The large user always requires the total interruption time is no more than some hours, and this requirement could be expressed as: tn

∑ s (t , i ) ≤ n (i ) n

s

i = 1,...n

(5)

t =1

Where ns (i ) is total required interruption time of user i . Time Interval Limit. The large user usually hopes that the curtailment time has an enough interval between two interruptions, and this limit can be expressed as:

r − t ≥ ni (i ) if s n (t − 1, i ) = 0 , s n (t , i ) = 1 and s n (r − 1, i ) = 0 , s n (r , i ) = 1

(6)

Where ni (i ) is the required time interval of user i between two interruptions.

3 Solution of the Model Referring to the scheduled method of unit maintenance, the model could be solved. The unit maintenance is to solve how to arrange the units with known repair time to rational period. Some rules such as equivalent reserve or equivalent risk are used to schedule the unit [5]. The optimal schedule of interruptible load is to solve how to arrange the interruptible load with required duration time to rational period. The key point of the solution is to determine the selected strategy. A reasonable selected strategy is presented in the paper that the interruptible load should be priorly scheduled in the period with maximum shortage capacity. After the interruptible load queue is formed according to the bidding price, the interruptible load could be scheduled through merit order

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method on the basis of this selected strategy. The solution flowchart is given in Fig.1a. And the key process A of arranging the ith interruptible load in Fig.1a is specially described in Fig.1b.

Arrange the ith interruptible load

Large users select the type of interruptible load contract and give the bidding information

Select the period tMax with maximum capacity scarcity in the residual period

Form merit order based on bidding price of interruptible load

Next

Form the initial capacity scarcity curve Arrange the ith interruptible load

i=i+1

Purchase the interruptible load in Selected period

N

Y

A N

All the interruptible load is calculated or the capacity scarcity is satisfied?

The purchase cost in balance market from tMax is larger than the compensation cost of interruptbile load Y Purchase the interruptible load and form the new capacity scarcity curve

Form the new capacity scarcity curve

N

Eq.4 and Eq.6 are satified?

N

Eq.3 or Eq 5 is satified?

Y

Print out the result

Y End

Fig. 1a. The solution flowchart of interruptible Fig. 1b. The arrange flowchart of the interload model by merit order method ruptible load i

4 Case Studies A real system in China and the related customer surveys in this system are employed to demonstrate the proposed model. The system has 43 large users with more than 500 kW capacity, but only a few users prefer to take part in the ILM if the compensation is no more than 2$/kWh. Table 2 gives the weekly bidding information of large users.

Simulation on the Interruptible Load Contract

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Table 2. The weekly bidding information of large users

User No.

Total interruption time

Duration (hour)

Capacity (kW)

Compensation ($/kWh)

1

2

8

3300

0.66

2

3

4

2200

0.94

3

4

4

4600

0.58

4

2

4

2300

0.75

5

2

4

1800

0.6

6

4

8

800

1.4

7

2

4

2200

1.6 0.88

8

2

4

3100

9

2

4

600

1.2

10

2

8

1600

0.95

Table 3. The utility cost reduction of one week ($) Mon. 9972

Tues. 7590

Wed. 7590

Thurs. 6458

Fri. 6513

Sat. 630

Sun. 0

SUM 38753

After the implementation of ILM, the utility could reduce the purchase cost as shown in Table 3. Based on the solution in Fig.1a and Fig.1b, the optimal schedule of interruptible load can be gotten. Users 1,3,4,5,8 have been selected. The first selected large user 3 and the last selected large user 8 are chosen to act as examples in Fig.2a and Fig.2b to illustrate the shortage capacity clipping before and after buying interruptible load.

Fig. 2a. The comparison of shortage curve before and after buying user3’s capacity

Fig. 2b. The comparison of shortage curve before and after buying user8’s capacity

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In Fig. 2a and Fig. 2b, the scheduled periods of interruptible load are selected in peak load period and this will effectively reduce the system shortage capacity in load period. Furthermore, the compensation cost is rather high. For the customer with low reliability required, this rational compensation could greatly enhance their enthusiasm to participate in ILM. At the same time, table 3 shows that after the implementation of the ILM, the utility also reduces the purchase cost in high-risk balance market. The cost reduction of utility is $38753 for one week and it reaches $2.01 millions for one year. In summarization, the simulation results show that both participants of the interruptible load management have obvious economic benefits. These will deeply reduce the resistance of the ILM promotion.

5 Conclusions This paper discusses the content of the interruptible load contract. The contract should be signed per half a year and the duration contains two types: four hours and eight hours. Considering the load stochastic fluctuation, an improved technique of capacity outage probability table is presented to calculate the system shortage capacity. Then the optimal purchase model of interruptible load is given and heuristic method is employed to solve the model. Case study shows that the customers and the utilities both have obvious economic benefits from the ILM implementation. These will deep reduce the resistance of the ILM promotion.

References 1. Malik, A.S.: Simulation of DSM Resources as Generating Units in Probabilistic Production Costing Framework. IEEE Trans. on Power System Vol. 13(4). IEEE(1998) 460-465. 2. Tuan, L.A., Bhattacharya, K.: Interruptible Load Management within Secondary Reserve Ancillary Service Market. IEEE Porto Power Tech Conference. Porto (2001)1-6. 3. Wang, J., Wang, X., Zhang, X.: The Interruptible Load Operation in Power Market and Interim System. Electric Power Automation Equipment, Vol. 24(6). Nanjin(2004) 1-5. 4. Doudna, J.H.: Overview of California ISO Summer 2000 Demand Response Programs. Proceedings of Power Engineering Society Winter Meeting. IEEE(2001) 228-233. 5. Wang, X.: Power System Planning Fundamentals. China Electric Power Press, Beijing (1994) 54-62.

Consistency Conditions of the Expert Rule Set in the Probabilistic Pattern Recognition Marek W. Kurzynski Wroclaw University of Technology, Faculty of Electronics, Chair of Systems and Computer Networks, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland [email protected]

Abstract. The present paper is devoted to the pattern recognition procedure based on the set of expert rules with unprecisely formulated weights understood as appropriate probabilities. Adopting the probabilistic model the different interpretations of rule weight are discussed and the consistency conditions of set of rules are given.

1 Introduction In statistical pattern recognition, the knowledge about probabilistic characteristics of features and classes must be known so as optimal (Bayes) decision rule could be implemented. If such knowledge is unknown or incompletely defined, a possible approach is to design a system, which will acquire the pertinent information from the actually available data for constructing a decision rule. This process of knowledge acquisition, called learning, in statistical pattern recognition may be viewed as the problem of estimation (parametric and/or nonparametric) of unknown probability distribution of features and classes. Usually it is assumed that learning data are of numerical nature, ie. they form observations or measurements of features of learning patterns. In this paper we shall focus our attention on another approach, interesting from both theoretical and practical point of view, which supposes that appropriate information is contained in expert knowledge. A typical knowledge representation consists of rules of the form IF A THEN B with the weight (uncertainty measure) α. These rules are obtained from the expert as his/her conditional beliefs: if A is known with certainty then the expert's belief into B is α [1], [2], [3]. Furthermore we suppose, that expert rules are not provided with exact value of α, but only an interval is specified (by its upper and lower bounds), into which this value belongs. Adopting statistical model we discuss different probabilistic interpretations of weight coefficient for which the conditions of consistency of the set of expert rules are given. This paper is a sequel to the author’s earlier publications [4], [5], [6], [7], [8] and it yields an essential extension of the results included therein. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 831–836, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Preliminaries Let us consider the pattern recognition problem with probabilistic model. This means that vector of features describing recognized pattern x ∈ X ⊆ R d and its class number j∈M = {1, 2, ..., M} are observed values of a couple of random variables X and J, respectively. Its probability distribution is given by a priori probabilities of classes pj = P(J = j),

j∈M,

(1)

and class-conditional probability density functions (CPDFs) of X fj (x) = f(x/j),

x∈X,

j∈M.

(2)

Let us now consider the interesting from practical point of view concept of recognition. We assume that a priori probabilities (1) and CPDFs (2) are not known, whereas the only information on the probability distribution of J and X is contained in the set of expert rules

R = {R1 , R2 ,..., RM } ,

(3)

where ( Ki )

Ri = {ri(1) , ri( 2 ) ,..., ri

}, i ∈ M ,

∑ Ki = K

(4)

denotes the set of rules connected with the i-th class. The rule ri(k ) has the following general form: (k )

IF wi( k ) ( x ) THEN J = i WITH probability greater than p (k ) and less than p i i

.

wi( k ) ( x ) denotes a predicate depending on the values of the features x, which determines in the feature space so-called rule-defined region:

Di( k ) = {x ∈ X : wi( k ) ( x ) = true} .

(5)

Let X R ⊆ X denote feature subspace covered by the set of rules R. It is clear, that

X R = ∪D ,

(6)

, i ∈ M , k = 1,2,...K i } .

(7)

where (k )

D = {Di

The rule ri(k ) denotes some restrictions imposed on probability distribution of X and J, which can be equivalently expressed in the following inequalities: (k )

p ( k ) ≤ pi( k ) ≤ p i i

.

(8)

Consistency Conditions of the Expert Rule Set in the PPR

833

Analysis of different relations between decisions and features has led to the (k )

threefold interpretation of probability pi(k ) and meaning of bounds p (k ) and p i i and in consequence, to the following kinds of rules:

1. The 1st-type rule – now pi(k ) denotes the set of values of a posteriori probability of ith class for x belonging to the Di(k ) :

pi′( k ) = { pi ( x ) for

(9)

x ∈ Di( k ) }

and inequalities (8) refer to all a posteriori probability values from the set (9). 2. The 2nd-type rule – pi(k ) is a posteriori probability of ith class on condition that

x belongs to the Di(k ) , viz.

∫

pi′′( k ) = P( J = i / x ∈ Di( k ) ) =

pi ( x ) f ( x ) dx /

Di( k )

∫

f ( x ) dx .

(10)

Di( k )

3. The 3rd-type rule – pi(k ) denotes mean a posteriori probability of ith class in the set Di(k ) :

pi′′′( k ) =

∫

pi ( x ) dx /

Di( k )

∫

dx

Di( k )

(11)

The sense of weights in expert rules plays the key role in deriving procedures of recognition algorithms and also in formulating of consistency conditions of set of expert rules. This problem will be discussed in the next section.

3 Consistency of the Expert Rule Set In order to determine consistency conditions let introduce first family of sets

B = {B (1) , B (2) ,..., B ( N )} where B (n) denote not empty constituents of family D. It is clear, that sets B (n) are disjoint and furthermore X R = ∪ B , i.e. family B forms partition of feature subspace X R [9]. (n )

Let next I i

be the set of indices of rules from Ri fulfilling the conditions

wi( k ) ( x ) for x ∈ B (n) or equivalently: ( n)

Ii

(k )

= {k : B ( n) ⊆ Di

∈ D}

(12)

The consistency conditions and the appropriate procedures of consistency checking are different for the rules of the 1st -, 2nd - and 3rd -type.

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3.1 Consistency of the 1st-Type Rules

The problem of consistency of the 1st-type rules is quite simple. According to its definition, the 1st-type rule ri(k ) determines the interval to which belongs the a posteriori probability pi ( x) at each point of Di(k ) . Inconsistency may occur between

rules indicating the same class or between rules for different classes. Inconsistency between rules for the same class occurs in the set B (n) if: (n)

pi

(n)

< p ( n) , where p i i

(k )

= min p i , p (n ) = max p (k ) . (n) i (n) i k ∈I i k ∈I i

(13)

It means that among the rules active for x ∈ B (n ) and indicating the ith class there is such a rule for which the upper bound of the probability pi ( x) is less than the lower bound of this probability given in another rule. Inconsistency between rules for various classes occurs in B (n) if one of the following conditions is satisfied: ƒ the sum of the lower bounds maxima of the a posteriori probabilities for all

classes for which there exist active rules in B (n) is greater than 1, i.e.

∑ i∈M

p(n) > 1 ,

(14)

i

(n)

where M ( n ) = {i : I i( n ) ≠ ∅} , ƒ the set of rules active for x ∈ B (n ) is locally complete ( M (n ) = M ) and the sum of the minima of the upper bounds of a posteriori probabilities is less than 1, i.e.

M (n ) = M ∧

∑

i∈M ( n )

(n)

pi

(15)

]+ In task-oriented system[9,10], a task usually divided into sub tasks, and the task is achieved by completing all sub tasks. Similarly, a task-level behavior is separated into sequence of motions[11]. To generate the motion sequences from task-level behavior, we suggested the formal task translation model. Each domain has certain kinds of behaviors and they can be converted to the high-level motion sequences regardless of domain environments. Various task-level behavior scripting languages are translated into a standardized high-level motion scripting language. Formal Task Translation Model ▪ ▪

▪ ▪ ▪

Identification of target - find location of target object and location of task-level behavior (Lt) Locomotive motion (Lm) - identification of present avatar location (La) - spatial distance between La and Lt and generate Lm, if La ≠ Lt Manipulative motion (Mm) - generate Mm for Lt Verbal information (Vi) - generate verbal speech for avatar behavior if available Speed and intensity parameters (Sp and Ip) - parameterize Lm and Mm for speed, intensity and duration

In terms of suggested formal task translation model, a task is divided into locomotive and manipulative motions with verbal information and parameters. Finally, the motions are represented in high-level motion script format. 2.2 High-Level Motion The high-level motion represents and controls the avatar motion by using parameters such as speed, intensity, direction, and so on. We analyzed the parameters which are used in the existing high-level motion scripts, and defined high-level motion script. Also, as stated above, the motion script should be applied to the formal task interpreter. By considering existing scripts and the formal interpreter, we defined the high-level motion scripting language. First, high-level motion is comprised of two parts: basic avatar characteristic such as name, role, gender, and list of avatar motions. The list is comprised of motion name, and its parameters. Major four elements of the parameters are about spatial, temporal, intensive, and aural information. These four elements contain detailed control information as shown in Figure 2.

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Spatial Spatial Parameter Parameter ••Target Target ••Direction Direction ••Destination Destination

Temporal Temporal Parameter Parameter

Char Info

Aural Aural Parameter Parameter

••Speed ••TTS Speed TTS ••Duration Duration ••Voice Voice ••Iteration Iteration ••Sequential Sequential ••Parallel Parallel

Intensive Intensive Parameter Parameter ••Intensity Intensity

Fig. 2. High-level Motion Parameters

These attributes represent avatar motion independent from both domain and implementation. Also, its parameters are abstracted from physical world such as degree of joint angle or explicit integer values. The script takes a role which is similar to mediator between task-level behavior and primitive motion shown in Figure 1. The high-level scripting language is based on XML DTD for standardized motion representation. 2.3 Primitive Motion A primitive motion is avatar motions which are supported by avatar engines or motion libraries. Primitive motion is subject to avatar control engines, and it contains physical information for specific implementation tool. For example, a high-level motion script, “” should be expressed like “<walk_to x="100" y="12" z="-2">” at the primitive motion script. The major difference between high-level and primitive motion scripting language is that high-level motion is independent from both domain and implementation while primitive motion is belonged to implementation environment. Although primitive motion controls avatar motion by parameters like high-level motion, the parameters are designed to describe physical values for avatar engine and structure of virtual world.

3 Implementation Results In real world, the usual settings of school classroom are a lecture, a blackboard, a computer, a table, a door, walls and several lecture-related objects. In task-level scripting language, author command the lecturer by combination of these components and behavior. After the example script is translated to a high-level script language by the suggested formal translator, the high-level script will be loaded to the system and converted to primitive motions and the avatar performs its tasks in Figure 3(a). The primitive motion contains the physical information of the system, so the same tasklevel script can be properly applied even though physical structure of the virtual world is reorganized as shown in Figure 3(b).

Avatar Behavior Representation and Control Technique

(a) Lecturing in 3D space

877

(b) 2D space and repositioned objects

Fig. 3. The avatar is teaching an algorithm in cyber classroom

The scripting language can be applied to completely different implementation tool or environments. For instance, the same task-level script is loaded to two applications as shown in Figure 3. Because our architecture takes layered approach, application tools and script languages are explicitly decoupled. This makes easier for user to apply script language to various implementations.

4 Evaluation and Discussion In order to measure the advantages of these scripting languages on creating scenario script and comparability, we applied our system to other implementations. First, users were asked to write down scripts for achieving 10 simple tasks by using each scripting language: AML, CPSL, and proposed script. Second, the scripts user made are applied to avatar implementation. MS Agent engine with basic motion library was selected for the implementation. Then, check the successful task achieved by the each script. 10 ta R no tic af ist a S ev tic ej bu S

10

9

9

8

8

7 6

Mean Rate

5 4 3

Mean Rate

2

2 1

et a R7 edv 6 ei hc A5 ev it 4 ecj bu 3 S 1

Proposed System

CPSL

AML

(a) User Satisfaction

0 Proposed System

AML

CPSL

(b) Achieved tasks

Fig. 4. Subjective evaluation of user satisfaction and achieved tasks

First test uses scales from 1 (the least satisfaction) to 10 (the most satisfaction) to compare the difficulty of creating scenario script and spent time. Second test also uses the same scale to compare the number of correctly accomplished tasks. A group of 20 subjects including 14 male and 6 female graduate students participated in the experiment.

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An ANOVA with repeated measures was used to analyze the result. As shown in Figure 4, the users rated that the results of the proposed system were easier and required less time to create the script. Significant effects were found between the time spent for the proposed script and the other script F(2,57) = 8.98, P < 0.05). Also, the proposed system got more number of achieved tasks. Note that CPSL has the low scores because of its implementation dependency.

5 Conclusion and Future Works We proposed three-layered architecture including task-level behavior, high-level motion and primitive motion to provide simple interface for avatar control at various application domains to users. Also each layer interacts independently. Task-level behavior is explicitly separated from implementations so that it could be reusable at different tools. Using this approach, avatar behavior can be controlled more easily in task-level and in high level and primitive motion, it is possible to control and express avatar motion with great reusability and extensibility which does not depend on implementation environment through abstract and physical expression. In future works, an intuitive graphical user interface for the input of avatar tasks, and avatar motion controls based on avatar-object interaction technique are required for providing more efficient interface to users.

References 1. Prendinger, H.: Life-like Characters. Life-like characters book, Springer-Verlag (2003) 317 2. Woo, S.: Virtual Human Trends. Journal of Korea Multimedia Society, Vol. 6. No. 4 (2000) 3. Kshirsagar, S., Thalmann, D., Kamyab, K.: Avatar Markup Language. Proceeding of the workshop on Virtual environments (2002) 169-177 4. Arafa, Y., Mamdani, E.: Scripting embodied agents behaviour with CML. Proceeding of Intelligent User Interfaces (2003) 313-315 5. Marriott, A., Stallo, J.: VHML- Uncertainties and Problems A discussion. Proceeding of Embodied conversational agents for AAMAS2002, Bologna, Italy (2002) 6. Yoshiaki, S., Matsuda, H.: Design and Implementation of Scenario Language for Cyber Teaching Assistant. International conference on Computers in Education (2001) 7. Hayashi, M.: TVML. ACM SIGGRAPH 98 Conference on applications (1998) 292-297 8. Huang, Z., Eliens, A., Visser, C.: Implementation of a scripting language for VRML/X3Dbased embodied agents. Proceeding of web technology (2003) 91-100 9. Lester, C., Zettlemoyer, S., Gregoire, P., Bares, H.: Explanatory Lifelike Avatars. Autonomous Agents (1999) 30-45 10. Ricket, J., Johnson, W.: Task-Oriented Collaboration with Embodied Agents in Virtual Worlds. Embodied Conversational Agents, MIT Press (2000) 95-122 11. Thalmann, D.: Autonomy and Task-Level Control for Virtual Actors. Programming and Computer Software, No. 4 (1995)

Avatar Behavior Representation and Control Technique: A Hierarchical Scripts Approach1 Jae-Kyung Kim1, Won-Sung Sohn2, Soon-Bum Lim3, and Yoon-Chul Choy1 1

Department of Computer Science, Yonsei University, Shinchon-dong, Seodaemun-gu, 120-749, Seoul, Korea {ki187cm, ycchoy}@rainbow.yonsei.ac.kr 2 Computational Design Group, Carnegie Mellon University, Pittsburgh, PA15213, USA [email protected] 3 Department of Multimedia Science, Sookmyung Women’s University, Chungpa-dong, Yongsan-gu, 140-742, Seoul, Korea [email protected]

Abstract. Avatar techniques have rapidly progressed in recent years, and will be widely adopted to various applications. The paper proposes hierarchical approach for representation and control techniques for avatar behavior for simpler avatar control in various domains. We proposed three-layered architecture: task-level behavior, high-level motion, and primitive motion. Thus, the user controls avatar at task-level layer and does not have to concern about low-level animation data. Our goal is to support flexible and extensible representation and control of avatar behavior by hierarchical approach separating application domains and implementation tools.

1 Introduction As importance of computer usage in our dairy living grows, many of our activities are made in virtual environment. Now, computers are considered to be the crucial intermediary of societal activities of human, not a machinery [1]. Thus, interactive user interface techniques between human and computer, which can induce interests, are becoming more and more significant. The avatar is the most common example of the interface techniques. Avatar application was selected as one of the most important communication to the 21st century by Gartner group[2]. With these avatar applications, research on avatar behavior representation and control is actively going on. As XML being web standard language, avatar behavior script can be based on XML and it is possible to standardize avatar behavior. Many XML-based multi purpose script languages are being developed including AML[3], CML[4], VHML[5], CPSL[6], TVML[7] and STEP[8]. Although, the delicate nature of high-level motion scripts is advantageous, controlling avatar motion is relatively complicated for users. 1

This work was supported by Ministry of Commerce, Industry and Energy.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 873–878, 2004. © Springer-Verlag Berlin Heidelberg 2004

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In this paper, we define the script languages for avatar behavior control by layered approach architecture to provide easy interface to users at various application domain and implementation environments. The proposed script language consists of threelayered architecture: task-level behavior, high-level motion, and primitive motion. We discuss them in the next section in detail.

2 Hierarchical Representation and Control for Avatar Behavior Our main goal is to gain high extensibility, comparability and reusability for the control of avatar behavior by defining script language for hierarchical representation and control of avatar behavior. The script languages are consisted of task-level behavior which is set of domain-dependent tasks, primitive motion which is supported by character motion engine or motion library, and high-level motion which has independent representation from these domain and motion engine or library. The characteristics of three script languages are shown in Figure 1. Cyberclass

Shopping Mall

Game

Task Domains

…

Dependent Task-level Task-level … Domain Task-level Task-level Task-level Task-level Behavior Behavior Implementation Indepen Behavior Behavior Behavior Behavior Context-based Context-based Interpreter Interpreter

Domain Independent Implementation Independent

High-level High-level Motion Motion

Primitive Primitive Motion Motion

Primitive Primitive Motion Motion

Primitive Primitive Motion Motion

Avatar Application

Avatar Application

Avatar Application

Low-level Animation

Low-level Animation

Low-level Animation

…

Domain Independent Implementation Depend

…

Avatar Application

…

Motion Library

Fig. 1. Overall Procedure of the Proposed System

Overall procedure of the proposed system is shown in Figure 1. Function and attribute of each script languages are discussed in following section. 2.1 Task-Level Behavior Script Language The definition of avatar task-level behavior in this paper is the necessary behaviors to achieve certain tasks in a specific domain environment. Each domain has different tasks, and the kind of behaviors for performing tasks would be changed. Since tasks are usually given by human scripter, the behavior should be simple and humanreadable. This will lead that the design of the scripting language for task-level behavior would be motivated by following requirements: simplicity, abstraction, readability, extensibility, parameterization, and synchronization.

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With respect to the design concept, we defined XML DTD for task-level scripting language. Since XML is machine independent and highly extensible, task-level script format is suitable. Task-level behavior DTD can be applied to various domain environments and easily extended when task domain needs additional behaviors. Our language supports required elements for scripting tasks: Task-level behavior = [|] [] []* [<synchronization>]+ In task-oriented system[9,10], a task usually divided into sub tasks, and the task is achieved by completing all sub tasks. Similarly, a task-level behavior is separated into sequence of motions[11]. To generate the motion sequences from task-level behavior, we suggested the formal task translation model. Each domain has certain kinds of behaviors and they can be converted to the high-level motion sequences regardless of domain environments. Various task-level behavior scripting languages are translated into a standardized high-level motion scripting language. Formal Task Translation Model ▪ ▪

▪ ▪ ▪

Identification of target - find location of target object and location of task-level behavior (Lt) Locomotive motion (Lm) - identification of present avatar location (La) - spatial distance between La and Lt and generate Lm, if La ≠ Lt Manipulative motion (Mm) - generate Mm for Lt Verbal information (Vi) - generate verbal speech for avatar behavior if available Speed and intensity parameters (Sp and Ip) - parameterize Lm and Mm for speed, intensity and duration

In terms of suggested formal task translation model, a task is divided into locomotive and manipulative motions with verbal information and parameters. Finally, the motions are represented in high-level motion script format. 2.2 High-Level Motion The high-level motion represents and controls the avatar motion by using parameters such as speed, intensity, direction, and so on. We analyzed the parameters which are used in the existing high-level motion scripts, and defined high-level motion script. Also, as stated above, the motion script should be applied to the formal task interpreter. By considering existing scripts and the formal interpreter, we defined the high-level motion scripting language. First, high-level motion is comprised of two parts: basic avatar characteristic such as name, role, gender, and list of avatar motions. The list is comprised of motion name, and its parameters. Major four elements of the parameters are about spatial, temporal, intensive, and aural information. These four elements contain detailed control information as shown in Figure 2.

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Spatial Spatial Parameter Parameter ••Target Target ••Direction Direction ••Destination Destination

Temporal Temporal Parameter Parameter

Char Info

Aural Aural Parameter Parameter

••Speed ••TTS Speed TTS ••Duration Duration ••Voice Voice ••Iteration Iteration ••Sequential Sequential ••Parallel Parallel

Intensive Intensive Parameter Parameter ••Intensity Intensity

Fig. 2. High-level Motion Parameters

These attributes represent avatar motion independent from both domain and implementation. Also, its parameters are abstracted from physical world such as degree of joint angle or explicit integer values. The script takes a role which is similar to mediator between task-level behavior and primitive motion shown in Figure 1. The high-level scripting language is based on XML DTD for standardized motion representation. 2.3 Primitive Motion A primitive motion is avatar motions which are supported by avatar engines or motion libraries. Primitive motion is subject to avatar control engines, and it contains physical information for specific implementation tool. For example, a high-level motion script, “” should be expressed like “<walk_to x="100" y="12" z="-2">” at the primitive motion script. The major difference between high-level and primitive motion scripting language is that high-level motion is independent from both domain and implementation while primitive motion is belonged to implementation environment. Although primitive motion controls avatar motion by parameters like high-level motion, the parameters are designed to describe physical values for avatar engine and structure of virtual world.

3 Implementation Results In real world, the usual settings of school classroom are a lecture, a blackboard, a computer, a table, a door, walls and several lecture-related objects. In task-level scripting language, author command the lecturer by combination of these components and behavior. After the example script is translated to a high-level script language by the suggested formal translator, the high-level script will be loaded to the system and converted to primitive motions and the avatar performs its tasks in Figure 3(a). The primitive motion contains the physical information of the system, so the same tasklevel script can be properly applied even though physical structure of the virtual world is reorganized as shown in Figure 3(b).

Avatar Behavior Representation and Control Technique

(a) Lecturing in 3D space

877

(b) 2D space and repositioned objects

Fig. 3. The avatar is teaching an algorithm in cyber classroom

The scripting language can be applied to completely different implementation tool or environments. For instance, the same task-level script is loaded to two applications as shown in Figure 3. Because our architecture takes layered approach, application tools and script languages are explicitly decoupled. This makes easier for user to apply script language to various implementations.

4 Evaluation and Discussion In order to measure the advantages of these scripting languages on creating scenario script and comparability, we applied our system to other implementations. First, users were asked to write down scripts for achieving 10 simple tasks by using each scripting language: AML, CPSL, and proposed script. Second, the scripts user made are applied to avatar implementation. MS Agent engine with basic motion library was selected for the implementation. Then, check the successful task achieved by the each script. 10 ta R no tic af ist a S ev tic ej bu S

10

9

9

8

8

7 6

Mean Rate

5 4 3

Mean Rate

2

2 1

et a R7 edv 6 ei hc A5 ev it 4 ecj bu 3 S 1

Proposed System

CPSL

AML

(a) User Satisfaction

0 Proposed System

AML

CPSL

(b) Achieved tasks

Fig. 4. Subjective evaluation of user satisfaction and achieved tasks

First test uses scales from 1 (the least satisfaction) to 10 (the most satisfaction) to compare the difficulty of creating scenario script and spent time. Second test also uses the same scale to compare the number of correctly accomplished tasks. A group of 20 subjects including 14 male and 6 female graduate students participated in the experiment.

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An ANOVA with repeated measures was used to analyze the result. As shown in Figure 4, the users rated that the results of the proposed system were easier and required less time to create the script. Significant effects were found between the time spent for the proposed script and the other script F(2,57) = 8.98, P < 0.05). Also, the proposed system got more number of achieved tasks. Note that CPSL has the low scores because of its implementation dependency.

5 Conclusion and Future Works We proposed three-layered architecture including task-level behavior, high-level motion and primitive motion to provide simple interface for avatar control at various application domains to users. Also each layer interacts independently. Task-level behavior is explicitly separated from implementations so that it could be reusable at different tools. Using this approach, avatar behavior can be controlled more easily in task-level and in high level and primitive motion, it is possible to control and express avatar motion with great reusability and extensibility which does not depend on implementation environment through abstract and physical expression. In future works, an intuitive graphical user interface for the input of avatar tasks, and avatar motion controls based on avatar-object interaction technique are required for providing more efficient interface to users.

References 1. Prendinger, H.: Life-like Characters. Life-like characters book, Springer-Verlag (2003) 317 2. Woo, S.: Virtual Human Trends. Journal of Korea Multimedia Society, Vol. 6. No. 4 (2000) 3. Kshirsagar, S., Thalmann, D., Kamyab, K.: Avatar Markup Language. Proceeding of the workshop on Virtual environments (2002) 169-177 4. Arafa, Y., Mamdani, E.: Scripting embodied agents behaviour with CML. Proceeding of Intelligent User Interfaces (2003) 313-315 5. Marriott, A., Stallo, J.: VHML- Uncertainties and Problems A discussion. Proceeding of Embodied conversational agents for AAMAS2002, Bologna, Italy (2002) 6. Yoshiaki, S., Matsuda, H.: Design and Implementation of Scenario Language for Cyber Teaching Assistant. International conference on Computers in Education (2001) 7. Hayashi, M.: TVML. ACM SIGGRAPH 98 Conference on applications (1998) 292-297 8. Huang, Z., Eliens, A., Visser, C.: Implementation of a scripting language for VRML/X3Dbased embodied agents. Proceeding of web technology (2003) 91-100 9. Lester, C., Zettlemoyer, S., Gregoire, P., Bares, H.: Explanatory Lifelike Avatars. Autonomous Agents (1999) 30-45 10. Ricket, J., Johnson, W.: Task-Oriented Collaboration with Embodied Agents in Virtual Worlds. Embodied Conversational Agents, MIT Press (2000) 95-122 11. Thalmann, D.: Autonomy and Task-Level Control for Virtual Actors. Programming and Computer Software, No. 4 (1995)

Analyzing iKP Security in Applied Pi Calculus
Yonggen Gu, Guoqiang Li, and Yuxi Fu BASICS

, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, China {gyg68, liguoqiang, yxfu}@sjtu.edu.cn

Abstract. The security for electronic payments is very important in electronic commerce. Many electronic payment protocols have been proposed recently to meet the security requirements. Since the design of a protocol is a difficult and error-prone task, the use of formal methods that allow for the verification of such protocols has received increasing attention. In this paper we take a look at the iKP from the point of view of the applied pi calculus. The iKP is described in the calculus and some security properties, mainly the authentication and anonymity properties, are verified.

1

Introduction

The security for electronic payments is very important in electronic commerce. Many electronic payment protocols have been proposed recently to meet the security requirements. Such protocols pay considerable attention to the requirements on the security issues like whether customers, sellers or banks can prove their authorizations to each other or whether customers can hold any anonymity etc. IBM Research Lab has developed a family of secure electronic payment protocols [5, 6], called iKP (i-Key-Protocol, where i=1,2,3), that are compatible with the existing card-based business models and payment system infrastructures. The design of an electronic payment protocol is however a difficult and errorprone task. Many popular and widely used electronic payment protocols have been shown to have flaws. For this reason, the use of formal methods for the verification of such protocols has received increasing attention. There are many ways to describe and verify security protocols, such as logic theory, proof theory etc. Using pi calculus [7] and its extensions to describe protocols is attractive because they are simple yet powerful. Recently, Abadi and Fournet have proposed the applied pi calculus for the analysis of security protocols [3]. The applied pi calculus is one of the extensions of the pi calculus with values passing, primitive functions, and equations among terms. Based on the applied pi calculus, Abadi and his collaborators have




The work is supported by The National Distinguished Young Scientist Fund of NNSFC (60225012) and The National 973 Project (2003CB316905). Laboratory for Basic Studies in Computing Science.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 879–887, 2004. c Springer-Verlag Berlin Heidelberg 2004


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analyzed several authentication protocols, mainly treating authenticity and secrecy properties [1, 2, 4]. However they have not considered complex protocols and their properties such as electronic commerce protocols. In this paper, we use the calculus to describe iKP and verify its authentication and anonymity properties. Our contribution is twofold: – We analyze the security of the iKP in a precise formal framework. We model the authentication and anonymity properties by extending the equational theory of the applied pi calculus. In particular we consider the time stamp, which can extend the analysis of the security protocols. – We use the applied pi calculus to analyze electronic payment protocols. What we have achieved is to point out a possibility to analyze and verify multiparty protocols. Furthermore iKP protocols are classical electronic payment protocols which have common properties. So our work is beneficial to the formal analysis of future electronic commerce protocols. In this short paper we assume the reader is familiar with the pi calculus and has some knowledge of the security protocols.

2

Applied Pi Calculus

In this section, we introduce the applied pi calculus briefly for the convenience of the reader. A detailed account can be found in [3]. The grammar for processes is similar to the one in the pi calculus. There is only one difference: Here messages can contain terms (not only names) and names need not be just channel names: P, Q, R ::= 0 | P |Q | !P | νn.P | if U = V then P else Q | u(x).P | u
M .P Process 0 does nothing. P |Q is the parallel composition of P and Q. !P behaves as an infinite number of copies of P running in parallel. The process νn.P makes a new name n and then behaves as P . The conditional construct “if U = V then P else Q” is standard, where U = V is an equality test. The input process u(x).P is ready to input from channel u and then evolves as P with the actual message substituting for the formal parameter x. Finally the output process u
M .P is ready to output message M on channel u and then evolves as P . The plain processes are extended with active substitutions: A, B, C ::= P | A|B | (νn).A | (νx).A | {x = V } The substitution {x = V } replaces the variable x with the term V . {x = V } can represent the situation in which a term V has been sent to the environment, but the environment may not have the atomic names that appear in V . A frame is an extended process built up from active substitutions by parallel composition and restriction. Informally frames represent the static knowledge gathered by the environment after communications with an extended process. Evaluation contexts, denoted by C[ ], are extended processes with a hole in the place of an extended process.

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Structural equivalences, written A ≡ B, relate extended processes that are equal by any capture-avoiding rearrangements of parallel compositions, restrictions and active substitutions, and by equational rewriting of any terms in processes. Reductions, written A −→ B, represent silent steps of computation (in particular, internal message transmissions and branching on conditionals). Laα belled transitions, written A −→ B, represent interactions with the environment. They consist of message inputs and message outputs, respectively written a(U )

νaU 

A −→ B and A −→ B. Reductions and labelled transitions are closed by structural equivalence, and consequently by equational rewriting on terms. We write A ⇓ a when A can send a message on a, that is, when A →∗ C[a
M .P ] for some evaluation context C[ ] that does not bind a. Definition 1. Observational equivalence (≈) is the largest symmetric relation R on the closed extended processes such that A R B implies the following: 1. If A ⇓ a then B ⇓ a; 2. If A →∗ A then B →∗ B  R A for some B  ; 3. C[A] R C[B] for all closing evaluation contexts C[ ]. Definition 2. Two terms M and N are equal in the frame ϕ, written (M = N )ϕ, if and only if ϕ ≡ νn.σ, M σ = N σ and {n} ∩ (fn (M ) ∪ fn (N )) = ∅ for some name n and substitution σ. Definition 3. Two closed frames ϕ and ψ are statically equivalent, written ϕ ≈s ψ, if dom(ϕ) = dom(ψ) and, for all terms M and N , it holds that (M = N )ϕ if and only if (M = N )ψ. We say that two closed extended processes are statically equivalent, written A ≈s B, if their frames are statically equivalent.

3

iKP

IBM Research Lab developed a family of secure electronic payment protocols, iKP (i-Key-Protocol, i=1,2,3), which are compatible with the existing card-based business models and payment system infrastructures. iKP involves three parties: the buyer (who makes the actual payment), the seller (who receives the payment) and the acquirer (who acts as an intermediary between the electronic payment world and the existing payment infrastructure). 1KP requires only the acquirer to possess a public key-pair. Buyers and sellers only need to have authentic copies of the acquirer’s public keys. 2KP demands that sellers, in addition to the acquirers, hold public key-pairs and public key certificates. 3KP further assumes that buyers have their own public key-pairs and public key certificates. In this paper, we focus on the security properties of 1KP. We firstly describe the cryptographic primitives as well as the general protocol structure. SKX stands for the secret key of Party X (X= Buyer B, Seller S, Acquirer A). We represent P K(SKX ) as its public key. H(.) is a strong collisionresistant one-way hash function which returns strong pseudo-random values; {.}y

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stands for public-key encryption with y = P k(SKX ) or stands for signature computed with y = SKX . To describe 1KP protocol we enumerate a list of quantities used in describing the protocols. The signals and their meanings are defined below: Desc SaltB

Description of purchase and delivery address. Random number generated by Buyer, used to salt Desc and consequently to ensure the privacy of the order information on the Seller to Acquirer link. Authprice Amount and currency. Date Seller’s date/time stamp, used for “coarse-rained” payment replay protection. Seller’s nonce used for more “fine-grained” payment replay N onceS protection. Seller’s id. This identifies seller to acquirer. IDS T IDS Transaction ID, an identifier chosen by the seller that uniquely identifies the context. Buyer’s Account Number. BanB Expiration Expiration date associated with Buyer’s Account Number. Random number chosen by buyer to form IDB . RB A buyer pseudo-ID which computed as IDB = IDB H(RB , BanB ). Respcode Response from the clearing network: YES/NO or authorization code. To describe the protocol flow sententiously, we use signals to represent some composite fields. These are defined below: Common Clear Slip EncSlip SigA

Authprice, IDS , T IDS , Date, N onceS , IDB , H(SaltB , Desc) IDS , T IDS , Date, N onceS , H(Common) Authprice, H(Common), BanB , RB , Expiration EA (Slip) SA (Respcode, H(Common))

There are six interaction flows in 1KP protocol. Based on the above signals, we can explain the flow-by-flow interactions as follows: – Initiate B −→ S: SaltB , IDB . Buyer forms IDB by generating a random number RB and computing IDB = H(RB , BanB ). Then it generates another random number SaltB . Finally it sends Initiate flow. – Invoice S −→ B: Clear. Seller retrieves SaltB and IDB from Initiate, obtains Date, and generates random quantity N onceS . The combination of Date and N onceS is used later by A to uniquely identify this payment. Seller then chooses T IDS and computes H(SaltB , Desc). Then it forms Common as defined above and computes H(Common). Finally Seller sends Invoice. – Payment B −→ S: EncSlip. Buyer retrieves Clear from Invoice and validates Date within a pre-defined time skew. Buyer computes H(SaltB , Desc) and H(Common) and checks whether it matches the value in Clear. Next

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Buyer forms Slip and encrypt it under the acquirer’s public key. Finally Buyer sends it to the seller in the Payment flow. – Auth-Request S −→ A: Clear, H(SaltB , Desc), EncSlip. The seller now requests the acquirer to authorize the payment. It then forwards EncSlip along with Clear and H(SaltB , Desc). – Auth-Response A −→ S: Respcode, SigA . The acquirer retrieves Clear, EncSlip and also H(SaltB , Desc) from Auth-Request. It then extracts IDS , T IDS , Date, N onceS from Clear and decrypts EncSlip. It obtains Slip, from which it extracts Authprice, BanB , Expiration, RB . Acquirer then re-constructs H(Common) and checks whether it matches H(common) it received. Next acquirer uses the credit card organization’s existing clearing and authorization system to obtain on-line authorization of this payment. This entails forwarding: BanB , Expiration, etc. Finally acquirer sends AuthResponse to Seller. – Confirm S −→ B: Respcode, SigA . The seller extracts Respcode and the acquirer’s Signature from Auth-Response. It then verifies the acquirer’s signature and forwards both Respcode and Signature to the buyer.

4

The Protocol in the Applied Pi Calculus

In this section we express 1KP in the applied pi calculus. We first propose an adequate equational theory, and then define the process that expresses the protocol. 4.1

An Equational Theory

Terms of the applied pi calculus uses not only names, but also variables and function primitives. To define reductions we introduce a named equational theory that consists of algebraic equations on terms. The following grammar of terms indicates the function symbols and the notation conventions we use: T, U, V, V0 , · · · ::= A, B, S, x1 , x2 , · · · CBS , CSB , CSA , CAS , · · · N onceA , KA , Date, · · · f (T1 , · · · , Tn )

terms variable name (for channel) name (for nonces, keys and time) function application (f ∈ Σ)

Here Σ is a set of functions which includes three kinds of functions. Firstly it includes cryptographic and checker functions, in which H(u1 , ...) represents Cryptographic hash, P k(u) represents Public key derivation, {T }V represents Public key encryption or private key signature, decrypt(w, u) represents private key decryption, checksig(w, u) represents public key check signature and checktime(T ime, Expiration) represents check time expiration. Secondly it includes constructing for protocol messages functions, which in turn includes the followings:

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Initiate(u1 , u2 ), Clear(u1 , u2 , u3 , u4 , u5 ), Common(u1 , u2 , . . . , u7 ), Slip(u1 , u2 , u3 , u4 , u5 ), ARequest(u1 , u2 , u3 ), AResponse(u1 , u2 ), and Conf irm(u1 , u2 ).

Lastly the set also includes projection functions, which means to select the j-th parameter of the construct for protocol message functions. For example, Initiate.j(Initiate(u1 , u2 )) means to select the j-th parameter from Initiate(). This kind of functions also includes the followings: – – – – – –

Clear.j(Clear(u1 , u2 , u3 , u4 , u5 )), Common.j(Common(u1 , u2 , . . . , u7 )), Slip.j(Slip(u1 , u2 , u3 , u4 , u5 )), ARequest.j(ARequest(u1 , u2 , u3 )), AResponse.j(AResponse(u1 , u2 )), and Conf irm.j(Conf irm(u1 , u2 )).

Equational theory is a special feature of the applied pi calculus. An equation represents semantic equality rather than syntactic identity. The equations in the model of this paper are the followings: Decrypt({x}P k(z) , z) = x checksig({x}z , P k(z)) = true
true if time ∈ Expiration checktime(time, Expiration) = f alse otherwise T uple.j(T uple(x1 , · · · xl )) = xj for j < i, T uple ∈ {Initiate, Clear, Common, Slip, ARequest, AReponse, Conf irm} 4.2

The Protocol

Based on the terms and equational theory defined above, we give a formal counterpart to the description of the message flows of 1KP protocol in this subsection. Messages: We rely on substitutions in order to define the protocol messages. With the construction of the protocol message functions we defined in Section 4.1, the protocol messages can be defined as follows: def

σ1 = {x1 = Initiate(SaltB , IDB )} def

σ2 = {x2 = Clear(IDS , T IDS , Date, N onceS , H(Authprice, IDS , T IDS , Date, N onceS , Initiate.2(x1 ), H(Initiate.1(x1 ), Desc)))} def

σ3 = {x3 = {Slip}P k(SKA ) } def

σ4 = {x4 = ARequest(x2 , H(Initiate.1(x1 ), Desc), x3 )}

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def

σ5 = {x5 = AResponse(Respcode, {Respcode, H(Common)}SKA )} def

σ6 = {x6 = Conf irm(AResponse.1(x5 ), AResponse.2(x5 ))} Processes: The following is the encoding of the protocol. It includes definitions of the processes for the Buyer, the Seller, and the Acquirer. Moreover all the processes work asynchronously and concurrently. def

P = ((νAuthprice, Desc)PB | PS ) | PA def

PB = (νSaltB , RB )(CBS
x1 σ1  |!(CSB (x2 ).if Clear.5(x2 ) = H(Authprice, Invoice.1(x2 ), Clear.2(x2 ), Clear.3(x2 ), H(RB , BanB ), H(SaltB , Desc)) then (CBS
x3 σ3  |!(CSB (x6 ). if checksig(conf irm.2(x6 ), P k(SKA )) then FB (x6 ))))) def

PS = (νIDS , T IDS , Date, N onceS )(CBS (x1 ).(CSB
x2 σ2 |CBS (x3 ) .(CSA
x4 σ4  | CAS (x5 ).CSB
x6 σ6 .FS (x5 )))) def

PA = (νSKA )!(CSA (x4 ).if Slip.2(Decrypt(ARequest.3(x4 ), SKA )) = H(Slip.1(Decrypt(ARequest.3(x4 ), SKA )), Clear.1(ARequest.1(x4 )), Clear.2(ARequest.1(x4 )), Clear.3(ARequest.1(x4 )), Clear.4(ARequest.1(x4 )), H(Slip.3(Decrypt(ARequest.3(x4 ), SKA )), Slip.4(Decrypt(ARequest.3(x4 ), SKA ))), ARequest.1(X4 )) ∧ checktime(datetime, Slip(Decrypt(ARequest.3(x4 )))) then ((νARespcode)(CAS
x5 σ5 .FA (x4 )))) PB , PS and PA represent respectively protocol principals, and P represents the protocol. In addition, functions FB (x), FS (x), FA (x) represent respectively the actions the buyer, the seller, the acquirer is required to perform after finishing the protocol flows.

5

Authentication Properties

In this section we begin our analysis of the protocol with authentication property. η We study the executions of the protocol by examining transitions P −→ P  , where η is an arbitrary sequence of labels. When the acquirer debits a certain credit card account by a certain amount, the acquirer must be in possession of an unforgeable proof that the owner of the credit card has authorize this payment. By this security requirement, we should obtain an authentication property stated below. η

Theorem 1 (Acquirer Authentication). Suppose that P −→ P  . If the action CAS
AResponse(Respcode, {Respcode, H(Common)}P k(SKA ) ) (1) occurs in η, then the following actions

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CBS
{Slip}P k(SKA )  and CSA
ARequest(Clear, H(SaltB , Desc), {Slip}P k(SKA ) ) must occur before (1). Proof. We can interpret the theorem as a correspondence assertion [8]: Whenever Acquirer debits, we have that the owner of the credit card has authorized the payment, and the seller has asked the payment. We know that if CAS
AResponse(Respcode, {Respcode, H(Common)}P k(SKA ) ) occurs in η, which means that the acquirer has succeeded in checking identities of the buyer and the seller. The acquirer validates the buyer’s identity by BanB and also validates the seller’s by matching of H(Common). Therefore we certainly have CBS
{Slip}P k(SKA )  and CSA
ARequest(Clear,

H(SaltB , Desc), {Slip}P k(SKA ) ). The proofs of the seller authentication and buyer authentication are similar.

6

Anonymity Property

In this section, we analyze the anonymity property. In iKP buyers may also want anonymity from eavesdroppers and from sellers. Furthermore buyers may even want anonymity with respect to the payment system provider. iKP does not focus on anonymity and, in particular, offers no anonymity from the payment system provider. This might be desirable for systems that aim to imitate cash, but is not essential for the protocols, like iKP, that follow the credit card-based payment model. However, iKP does try to minimize exposure of buyers’ identities with respect to sellers and eavesdroppers. The following theorem states that buyers do not reveal their Ban to sellers and eavesdroppers. Theorem 2 (Buyers’ Anonymity Property). The buyer has BanB anonymity property: For all sellers and eavesdroppers it holds that PB (BanB ) ≈s PB (BanB ). Proof. We firstly define the frames. Let ϕ1 (PB (BanB )) be {x1 = (SaltB , H(RB , BanB )) | x3 = {Authprice, H(Common), BanB , RB , Expiration}P k(SKA ) } and ϕ2 (PB (BanB )) be {x1 = (SaltB , H(RB , BanB )) | x3 = {Authprice, H(Common), BanB , RB , Expiration}P k(SKA ) } It is obviously that no sellers and eavesdroppers can know KA . So it holds that ϕ1 (PB (BanB )) ≈s ϕ2 (PB (BanB )). Thus PB (BanB ) ≈s PB (BanB ), meaning that the buyers’ BanB is not exposed to sellers and eavesdroppers.

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For the acquirer, Slip.3(Decrypt(x3 , KA )) = BanB is valid in ϕ1 (PB (BanB )) but is not valid in ϕ2 (PB (BanB )). So we have PB (BanB ) ≈s PB (BanB ), which means that buyers do not have anonymity property to acquirer.



7

Conclusion

In this paper we use the applied pi calculus of Abadi and Fournet to describe the iKP and verify its authentication and anonymity properties. We believe that the use of the applied pi calculus is particulary appropriate for the analysis of the security protocols. We take the iKP as case study, because they are classical electronic payment protocols compatible with the existing card-based business models and payment system infrastructures. Furthermore, as noted in the introduction, this case study contributes to the development of the ideas and results for the specification and verification of the electronic payment protocols that should be useful beyond the analysis of iKP. As for future work, we plan to analyze the non-repudiation of iKP using the applied pi calculus and construct an automatic tool to help analyzing the security protocol using the framework advocated in this paper.

References 1. Abadi, M., and Blanchet, B.: Computer-assisted verification of a protocol for certified email. In: Static Anlaysis, 10th International Symposium(SAS’03). Volume 2694 of LNCS., Springer-Verlag (2003) 316–335 2. Abadi, M., Blanchet, B., and Fournet, C.: Just Fast Keying in the Pi Calculus. In: 13th European Symposium on Programming. Volume 2986 of LNCS., SpringerVerlag (2004) 3. Abadi, M., and Fournet, C.: Mobile Values, New Names and Secure Communication. In: 28th ACM Symposium on Principles of Programming Languages(POPL’01). (2001) 104–115 4. Abadi, M., and Fournet, C.: Hiding Names: Private Authentication in the Applied Pi Calculus. In: Proceedings of the International Symposium on Software Security (ISSS’02). Volume 2609 of LNCS., Springer-Verlag (2003) 317–338 5. Bellare, M., Garay, J., Hauser, R., Herzberg, A., Krawczyk, H., Steiner, M., Tsudik, G., and Waidner, M.: iKP - A Family of Secure Electronic Payment Protocols. In: Proceedings First USENIX Workshop on Electronic Commerce, USENIX. (1995) 6. Bellare, M., Garay, J., Hauser, R., Herzberg, A., Krawczyk, H., Steiner, M., Tsudik, G., Herreveghen, E.V., and Waidner, M.: Design, implementation, and deployment of the iKP secure electronic payment system. IEEE Journal of Selected Areas in Communications 18 (2000) 611–627 7. Milner, R., Parrow, J., and Walker, D.: A Calculus of Mobile Processes, parts I and II. In: Information and Computation. (1992) 1–77 8. Woo, T.Y.C., and Lam, S.S.: A semantic model for authentication protocols. In: 14th IEEE Symposium on Research in Security and Privacy, IEEE Computer Society Press (1993) 178–194

General Public Key m-Out-of-n Oblivious Transfer
Zhide Chen1 and Hong Zhu2 1

Department of Computer Science, Fudan University, Shanghai 200433, P. R. China 2 Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, P. R. China {02021091, hzhu}@fudan.edu.cn

Abstract. In the m-out-of-n oblivious transfer model, Alice has n messages, Bob has m choices. After the interaction between the two parties, Bob can get m but only m messages from the n messages, Alice cannot know which m messages Bob gets. In this paper, for the first time, we construct a m-out-of-n OT protocol based on the general secure public key system. Keywords: oblivious transfer, secure protocol, public key system.

1

Introduction

Oblivious transfer (OT) is an important primitive in modern cryptography. It has become the basis for realizing a broad class of cryptographic protocols, such as bit commitment, zero-knowledge proof, and secure multiparty computation [5, 6, 2]. It has also found its applications for e-commerce [1, 8]. OT was first introduced to cryptography by Rabin [10] in 1981. In the protocol, there are two party, one is named Alice, the other one is named Bob. Informally speaking, in an OT, Alice sends a bit to Bob that he receives half the time, Alice does not find out what happened, Bob knows if he gets the bit or nothing. In 1985, Even, Goldreich and Lempel provided another similar cryptographic tool named 1-out-of-2 oblivious transfer (OT12 ) [4]. In an OT12 , Alice has two messages m0 , m1 that she sends to Bob in such a way that he can decide to get either of them at his choice but not both. Alice cannot find out which message Bob gets. m-out-of-n OT (OTm n ) was introduced by Naor [9] and also by Yu [7] based on the discrete logarithm. However, no one has ever discussed the possibility of OTm n based on the general secure public key system (PKS). In this paper, we provide an OTm n protocol based on the PKS.


This work is partially supported by a grant from the Ministry of Science and Technology (#2001CCA03000), National Natural Science Fund (#60273045) and Shanghai Science and Technology Development Fund (#03JC14014).

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 888–894, 2004. c Springer-Verlag Berlin Heidelberg 2004


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Definition

Definition 21. 1-out-of-2 Oblivious Transfer (OT12 ) In an OT12 , Alice has input m0 , m1 ∈ {0, 1}k ; Bob has input c ∈ {0, 1}, after the interaction between Alice and Bob, the following requirements should be satisfied: Correctness: Bob can get mc if both Alice and Bob follow the protocol; Privacy for Bob: Alice cannot find out the choice of Bob if Bob follows the protocol; Privacy for Alice: Bob cannot get both m0 and m1 if Alice follows the protocol. Definition 22. m-out-of-n Oblivious Transfer (OTm n) k In an OTm n , Alice has input m1 , · · · , mn ∈ {0, 1} , Bob has m choices c1 , · · · , cm ∈ {1, · · · , n}, after the interaction between Alice and Bob, the following requirements should be satisfied: Correctness: Bob can get m messages from m1 , · · · , mn if both Alice and Bob follow the protocol; Privacy for Bob: Alice cannot find out the choices of Bob if Bob follows the protocol; Privacy for Alice: Bob cannot get more than m messages from m1, · · · ,mn if Alice follows the protocol.

3 3.1

OT12 Based on PKS PKS

In the public key system (PKS), there are an encrypted algorithm E, a decrypted algorithm D, a public key Keyp and a secret key Keys . For a secret key Keys , it is easy to compute the corresponding public key Keyp ; However, for a public key Keyp , it is hard to compute the corresponding secret key Keys , i.e. the probability to get Keys is very small. 3.2

Intuition of OT12

In an OT12 , Alice has input m0 , m1 ∈ {0, 1}k , Bob has input c ∈ {0, 1}. Firstly, Alice selects a random string C ∈ {0, 1}k and announces it to Bob. Bob constructs a secret key Keysc ∈ {0, 1}k and two public keys Keypc , Keypc ∈ {0, 1}k (c = 1 − c), where Keypc , Keysc are a pair of public key and secret key in the PKS, Keyp0 , Keyp1 and C satisfy the following condition:  
 Keyp0 11 =C (1) Keyp1 Bob announces Keyp0 , Keyp1 to Alice. Alice checks whether the public keys satisfied Equation (1), if not, reject; else encrypts her two messages m0 and m1

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with the two public keys, sends E(m0 , Keyp0 ), E(m1 , Keyp1 ) to Bob. Bob gets mc with the secret key Keysc mc = D(E(mc , Keypc ), Keysc ) 3.3

OT12

Protocol 31. OT12 (m0 , m1 )(c) 1. Alice selects a random string C ∈ {0, 1}k , announces it to Bob; 2. Bob constructs a secret key Keysc ∈ {0, 1}k and two public keys Keyp0 , Keyp1 ∈ {0, 1}k , satisfying Keyp0 + Keyp1 = C, sends Keyp0 , Keyp1 to Alice; 3. Alice checks whether Keyp0 + Keyp1 = C, if not, reject; else, sends E(m0 , Keyp0 ), E(m1 , Keyp1 ) to Bob; 4. Bob gets mc with secret key Keysc . 3.4

Analysis

Correctness: If both Alice and Bob follow the protocol, Bob can always get mc . Privacy for Bob: For Alice, the two public keys she receives are just two random strings, so Alice cannot get any information about Bob’s choice c. Privacy for Alice: By the property of PKS, Bob can only construct Keypc , Keypc , Keysc in the following way. × Keysc Keysc −→ Keypc −→ Keypc −→ It is hard for him to get Keysc , i.e. the probability that he gets mc is very small.

4 4.1

OTm n Intuition of OTm n

In this section, we provide an OTm n (m < n) in a more general way. In the protocol, Alice has input n messages m1 , m2 , · · · , mn ∈ {0, 1}k , Bob has m choices c1 , c2 , · · · , cm ∈ {1, · · · , n}. In OT12 , there is a constrain on the public keys, i.e. one of the public key is decided by the other public key. So, in OTm n, n-m of the public keys Keyp1 , Keyp2 , · · · , Keypn should be decided by the rest m public keys. The task for us is to find a suitable (n − m) × n matrix M satisfied. ⎛ ⎞ ⎛ ⎞ Keyp1 C1 ⎜ ⎟ ⎜ ⎟ M ⎝ ... ⎠ = ⎝ ... ⎠ (2) Keypn

Cn−m

All computation is in the field Zq (q > n). The following example will show us the right way to construct a suitable matrix M .

General Public Key m-Out-of-n Oblivious Transfer

 Example 41. In OT24 , Let M =

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⎛

⎞ Keyp1   ⎟ 1110 1110 ⎜ ⎜Keyp2 ⎟ = C1 . , then 0111 0 1 1 1 ⎝Keyp3 ⎠ C2 Keyp4 





We get Keyp1 − Keyp4 = C1 − C2 and Keyp2 + Keyp3 = C2 − Keyp4 . By the property of OT12 , Bob can get only one secret key from Keys0 and Keys3 and only one secret key from Keys1 and Keys2 . This is not allowed by the OT24 . From the above example we can find that, to construct an OTm n , we should construct a (n − m) × n matrix, if remove any m columns from the matrix and we should get a non-singular (n − m) × (n − m) matrix. While from the above example, we find if we remove the first and the forth column from the 2 × 4 matrix, we get a singular matrix. The matrix for the OTm n is as follows: ⎞ ⎛ 1 1 ... 1 ⎜1 2 ... n ⎟ ⎟ ⎜ M = ⎜. ⎟ .. . . .. .. ⎠ ⎝ .. . 1 2n−m−1 . . . nn−m−1

(n−m)×n

M has the following proposition: Proposition 41. Remove any m columns from the matrix M , the remanent matrix M  is non-singular. Proof. Remove any m columns from the matrix M, we get a Vandermonde matrix M  , M  is non-singular.
The Vandermonde matrix have the following proposition. Proposition 42. If M  is a Vandermonde matrix, then it has a inverse M  in the field Zq . ⎛ ⎞ 1 1 1 ... 1 ⎜ x1 x2 x3 . . . xn ⎟ ⎜ 2 ⎟ 2 2 2 ⎟ ⎜  Proof. Let M = ⎜ x1 x2 x3 . . . xn ⎟. ⎜ .. . ⎟ .. . . .. ⎝ . . .. ⎠ . . xn−1 xn−1 . . . xn−1 xn−1 n 1 2 3 Using only elementary row operations, we get: ⎛ 1 1 1 ... 1 ⎜0 − x x − x . . . x − x1 x 2 1 3 1 n ⎜ ⎜0 x2 (x2 − x1 ) x3 (x3 − x1 ) . . . xn (xn − x1 ) −→ ⎜ ⎜ .. .. .. .. .. ⎝. . . . .

⎞

⎟ ⎟ ⎟ ⎟ ⎟ ⎠ n−2 n−2 0 xn−2 (x − x ) x (x − x ) . . . x (x − x ) 2 1 3 1 n 1 n 2 3

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⎛

1 1 ⎜0 x2 − x1 ⎜ ⎜0 0 ⎜ ⎜ .. .. ⎝. .

−→

0

0

1 x3 − x1 (x3 − x2 )(x3 − x1 ) .. .

... ... ... .. .

1 1 1 ... ⎜0 x2 − x1 x3 − x1 ... ⎜ ⎜ 0 (x3 − x2 )(x3 − x1 ) . . . −→ ⎜0 ⎜ .. .. .. .. ⎝. . . . 0

0

1 xn − x1 (xn − x2 )(xn − x1 ) .. .

0

0

⎞

⎟ ⎟ ⎟ ⎟ ⎟ ⎠ . . . (xn − xn−1 )(xn − xn−2 ) · · · (xn − x1 )

⎛ 1 0 0 ... ⎜0 x2 − x1 0 . .. ⎜ ⎜0 0 (x − x )(x − x ) . .. 3 2 3 1 −→ ⎜ ⎜ .. .. .. . .. ⎝. . . 0

⎞

⎟ ⎟ ⎟ ⎟ ⎟ ⎠ n−3 n−3 x3 (x3 − x2 )(x3 − x1 ) . . . xn (xn − x2 )(xn − x1 )

⎛

0

1 xn − x1 (xn − x2 )(xn − x1 ) .. .

0 0 0 .. .

⎞

⎟ ⎟ ⎟ ⎟ ⎟ ⎠ · · · (xn − xn−1 )(xn − xn−2 ) · · · (xn − x1 )

As q is a prime and q > n, there exist a matrix M  in Zq , M  M  = In×n So, we have the conclusion of this proposition. 4.2




OTm n

The OTm n protocol is described as following: Protocol 41. OT12 (m1 , · · · , mn )(c1 , · · · , cm ) 1. Alice selects n-m random strings C1 , · · · , Cn−m ∈ {0, 1}k , sends to Bob; 2. Bob constructs Keysc1 , · · · , Keyscm , Keyp1 , · · · , Keypn ∈ {0, 1}k satisfying Equation (2), sends Keyp1 , · · · , Keypn to Alice; 3. Alice checks whether the public keys satisfy Equation(2), if not, reject; else, sends E(m1 , Keyp1 ), · · · , E(mn , Keypn ) to Bob; 4. Bob gets mc1 , · · · , mcm with secret keys Keysc1 , · · · , Keyscm . 4.3

Analysis

Theorem 41. Protocol 41 is an OTm n. Proof. Correctness: Keyp1 , . . . , Keypn can be looked as the solution of Equation (2). M is an (n − m) × n matrix so that there are at least m free variables in this equation, then in the protocol, Bob can get at least m secret keys corresponding

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to the m public keys, so he can get at least m encrypted messages sent from Alice, i.e. Bob can always get m messages mc1 , · · · , mcm . Privacy for Bob: For Alice, the n public keys she receives are just n random strings, so Alice cannot get any information about Bob’s choice c1 , · · · , cm . Privacy for Alice: Let Keysc1 , . . . , Keyscm be the m secret keys that Bob has already known. He can get the corresponding public keys Keypc1 , · · · , Keypcm . Let Keypc1 , . . ., Keypcn−m be the rest public keys, Keysc1 , . . ., Keyscn−m be the corresponding secret keys. We will show that Bob can get only m messages from the n messages. We get this by proving that Keypc1 , . . ., Keypcn−m are decided by Keypc1 , · · · , Keypcm . For ⎞ ⎛ ⎞ C1 Keyp1 ⎟ ⎜ ⎟ ⎜ M ⎝ ... ⎠ = ⎝ ... ⎠ Keypn Cn−m ⎛

By the Proposition 41 and Proposition 42, there exists n-m linear functions f1 , . . . , fn−m and matrix M  , M  such that ⎞ ⎞ ⎛ Keypc1 C1 − f1 (Keypc1 , Keypc2 , . . . , Keypcm ) ⎟ ⎜ ⎟ ⎜ .. .. M ⎝ ⎠ ⎠=⎝ . . Keypcn−m Cn−m − fn−m (Keypc1 , Keypc2 , . . . , Keypcm ) ⎛

⎛

⎞ ⎞ ⎛ Keypc1 C1 − f1 (Keypc1 , Keypc2 , . . . , Keypcm ) ⎜ ⎟ ⎟ .. ..  ⎜ ⎝ ⎠ ⎠=M ⎝ . . Keypcn−m Cn−m − fn−m (Keypc1 , Keypc2 , . . . , Keypcm ) So, each of Keypc1 , . . ., Keypcn−m are decided by Keypc1 , . . . , Keypcm , Bob can get only m messages from the n encrypted messages.
The efficiency is based on the efficiency of the public key system and the integer power in the field Zq . From [3], using repeating squaring, it only requires O(ln q) to compute the (ab mod q).

5

Conclusion

In this paper, for the first time, we construct a OTm n protocol based on the public key system, which satisfying the 3 requirements of OTm n.

References 1. Aiello, B., Ishai, Y., and Reingold, O.: Priced Oblivious Transfer: How to Sell Digital Goods. Eurocrypt’01, Lecture Notes in Computer Science, Vol. 2045 (2001) 119-135

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2. Cr´epeau, C., Van de Graaf, J., and Tapp, A.: Committed Oblivious Transfer and Private Multi-party Computations. Adva. in Crypt.: Proc. of Crypto’95 963 (1995) 110-123 3. Cormen, H., Leiserson, E., Rivest, L., Stein, C.: Introduction to Algorithms. Second Edition. MIT Press (2001) 4. Even, S., Goldreich, O., and Lempel, A.: A Randomized Protocol for Signing Contracts. Commu. of the ACM 28 (1995) 637-647 5. Goldreich, O., Micali, S., and Wigderson, A.: How to Play any Mental Game or a Completeness Theorem for Protocols with Honest Majority. Proc. 19th Annu. ACM Symp. on Theo. of Compu. (1987) 218-229 6. Kilian, J.: Founding Cryptography on Oblivious Transfer. Proc. 20th Annu. ACM Symp. on Theo. of Compu. (1988) 20-31 7. Mu, Y., Zhang, J., Varadharajan V.: m out of n Oblivious Transfer. ACISP’02, Lecture Notes in Computer Science, Vol. 2384, (2002) 395-405 8. Naor,M., Pinkas, B.: Oblivious Transfer with Adaptive Queries. Proc. of Crypto’99, Lecture Notes in Computer Science, Vol. 1666 (1999) 573-590 9. Naor, M., Pinkas, B.: Efficient Oblivious Transfer Protocols. 12th Annu. Symp. on Disc. Algo. (2001) 448-457 10. Rabin, M.: How to Exchange Secrets by Oblivious Transfer. Tech. Repo. TR81, Aiken Comp. Lab, Harvard University (1981)

Determining Optimal Decision Model for Support Vector Machine by Genetic Algorithm Syng-Yup Ohn, Ha-Nam Nguyen, Dong Seong Kim, and Jong Sou Park




Department of Computer Engineering, Hankuk Aviation University, Seoul, Korea {nghanam, dskim, syohn, jspark}@hau.ac.kr

Abstract. The problem of determining optimal decision model is a difficult combinatorial task in the fields of pattern classification and machine learning. In this paper, we propose a new method to find the optimal decision model for SVM, which consists of the minimal set of highly discriminative features and the set of parameters for the kernel. To cope with this problem, we adopted genetic algorithm (GA) which provides efficient optimization tool simulating the natural evolution procedures in iterative fashion to select the optimal set of features and set of kernel parameters. In the method, the decision models generated by GA are evaluated by SVM, and GA selects the only good models and gives the selected models the chance to survive and improve by crossover and mutation operation. Combining GA and SVM, we can obtain the optimal decision model which reduces the execution time as well as improves the classification rate of SVM. We also demonstrated the feasibility of our proposed method by several experiments on the sets of clinical data such as KDD Cup 1999 intrusion detection pattern samples and stomach cancer proteome pattern samples.

1 Introduction Recent pattern classification applications in the areas such as networks, biology, and image recognitions often have high dimensional feature space, and the performance of classification is degraded severely in terms of execution time and classification rate in such cases. Typically, the combinations of a small number of features play an important role in discriminating samples into classes. GA offers a natural way to solve this problem. Much research efforts are concentrated on combining GA and classifiers to improve the performance of classification [1-3]. GA is often applied to select the optimal set of features for the classifiers such as k-nearest neighbors (KNN), probabilistic neural network (PNN), SVM. Support vector machine (SVM) is a learning method that uses a hypothesis space of linear functions in a high dimensional feature space [4-7]. This learning strategy, introduced by Vapnik [5], is a principled and powerful method and outperformed most of the classification algorithms in many applications. However, the computational power of linear learning machines is limited in the cases of the feature space with nonlinear characteristics. It can be easily recognized that real-world applications require more extensive and flexible hypothesis space than linear functions. By using a proper kernel function, we can overcome the nonlinearity of feature space [4, 7]. Also J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 895–902, 2004. © Springer-Verlag Berlin Heidelberg 2004

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recent improvements in the area of SVM make it easy to implement and overcome the computation time problem due to a large training set [7]. Genetic algorithm is an optimization algorithm simulating the mechanism of natural evolution procedure [9-11]. Most of genetic algorithms share a common conceptual base of producing improved individual structures through the processes of selection, mutation, and reproduction. GA is generally applied to the problems with a large search space. They are different from random algorithms since they combine the elements of directed and stochastic search. Furthermore, GA is also known to be more robust than directed search methods. In this paper, we propose a new learning method using GA and SVM. In the new learning method, GA is exploited to derive the optimal decision model for the classification of patterns, which consists of the optimal set of features and parameters of a kernel function. SVM is used to evaluate the fitness of the newly generated decision models by measuring the hit ratio of the classification based on the models. Our method is different from the feature selection methods based on GA and SVM recently reported [2, 3] in that they used GA only for feature selection and then manually chose the parameters for a kernel function. We applied GA to obtain the optimal set of features and set of kernel parameters at the same time. In the comparison with other learning methods by extensive experiments on the datasets such as network intrusion pattern samples and proteome pattern samples for cancer identification, proposed learning method achieved faster convergence while searching a decision model and better classification performance for some cases. This paper is organized as follows. In section 2, our learning method is presented in detail. In section 3, we compare the proposed and other methods by the experiments with the classification of the datasets of network intrusion pattern samples and proteome pattern samples for cancer identification. Finally, section 4 is our conclusion.

2 Learning Method for Optimal Decision Model The challenging issue of GA is how to map a real problem into a chromosome. In our method, the sets of features and parameters for a kernel function should be encoded into a chromosome (Fig. 1). The chromosome consists of binary gene string and multivalued gene string representing the sets of features and kernel parameters. The binary string is composed of n-bit string and each bit represents an active or inactive state of a feature. The multi-valued gene string represents the index of a kernel function such that 1, 2, and 3 for Inverse Multi-Quadric, Radial, and Neural kernel) and kernel parameters of each kernel (See Fig. 1 and Table 1). The combination of the two gene strings forms a chromosome in GA procedure which in turn serves as a decision model (see Fig. 1).

Fig. 1. Structure of a chromosome used in GA

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Table 1. The kernel functions are used to experiments

Kernel function Inverse Multi-Quadric Radial Neural

Formula 1

x − y

e

(− γ

2

x− y

+ c 2

2

)

tanh( s ⋅ x , y − c )

In our method, GA generates a set of chromosomes, each of which represents a decision model, by evolutionary procedures. The fitness value of each chromosome is evaluated by measuring the hit ratio from the classification of samples with SVM classifier containing the decision model associated with the chromosome. m-fold validation method is used to evaluate the fitness of a chromosome to reduce overfitting [6]. Then only the chromosomes with a good fitness are selected and given the chance to survive and improve into further generations. Roulette wheel rule is used for the selection of chromosome [9]. Some of the selected chromosomes are given the chance to undergo alterations by means of crossover and mutation to form new individuals. One-point crossover is used, and the probabilities for crossover and mutation are 0.8 and 0.015 respectively. This process is repeated for a predefined number of times. At the end of GA procedure, the decision model with the highest hit ratios is chosen as the optimal decision model. The optimal decision model is used to build a SVM for the classification of novel samples and the performance of the model can be evaluated.

3 Experiments The proposed method is experimented with KDD Cup 1999 and stomach cancer datasets for the evaluation of performance. The experiments are conducted on a Pentium 1.8 GHz personal computer. We used SVM module developed by Stefan Rüping [13] for the implementation of the proposed method. The results from the experiments are presented in the following sections.

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3.1 KDD Cup 1999 Data We used the dataset for KDD Cup 1999 contest, in which the competition task was to build a network intrusion detector containing a predictive model capable of distinguishing between “bad” connections, called intrusions or attacks, and “good” normal connections (Available at: http://kdd.ics.uci.edu/databases/kddcup99/kddcup99.html ). This database consists of a standard set of data to be audited, which includes a wide variety of intrusions simulated in a military network environment. The set of the features consists of 3 symbolic features and 39 numeral features. Our training set used in H

H

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GA procedure consists of 2500 samples randomly selected from the training dataset (kddcup.data.gz). The test dataset (corrected.gz) was applied to the decision model resulted from GA. 100.00% 99.95% 99.90%

Detection Rates

99.85% 99.80%

Neural kernel

99.75%

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99.70%

Inverse multiquadric kernel

99.65% 99.60% 99.55% 99.50% 1

2

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10 11 12 13 14 15 16 17 18 19 20 21

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Fig. 2. Detection rates of validation test

We used a simple generalization method: 10-fold cross validation with 2500 samples [6]. In the experiment result, the detection rate designates the accuracy of classification. Three types of kernel functions are used for SVM in the experiment, and the classification rates from during GA procedures are depicted in Fig. 2. After GA was executed for 20 generations, the training with neural kernel achieved the highest detection rate among the kernel functions compared. At this point, the best detection rates obtained are 99.94% in case of neural kernel function, 99.92% in case of radial kernel function, and 99.93% in case of inverse multi-quadric kernel function. Table 2 shows the indexes of the features in the optimal features set obtained after 20 generations in GA procedures. The sets of selected features are different for each kernel functions used in SVM. In real network environment, GA and SVM together are used to obtain the optimal set of features suitable for the environment, and the SVM with the decision model consisting of the optimal feature set serves as an intrusion detection system. Table 2. Number of Selected Feature Kernel function

Inverse multi-quadric

Radial

Neural

Selected Feature Number 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 27, 29, 30, 32, 34, 37, 39, 41 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 32, 33, 34, 37, 38, 39 1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 34, 36, 38, 41

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The result from the classification of test dataset is depicted in Fig. 3. In case of “GA+SVM”, we used the optimal set of features obtained from GA in SVM to classify the test dataset. In case of “SVM only”, we used all the features of the dataset for the decision model in the SVM. The result shows the highest detection rates when the system uses GA and SVM with neural kernel function. Furthermore, the detection rate of the proposed system achieved 99.94%, which is higher than the results reported by KDD 1999 contest winner [12]. 100% 99% GA +SV M w ith Neural Kernel

98% 97% 96% 95%

SV M-only w ith Neural Kernel

94% 93% 92% 91%

GA +SV M w ith Radial Kernel

Detection Rates

90% 89% 88%

SV M-only w ith Radial Kernel

87% 86% 85% 84%

GA +SV M w ith Inverse Multi-Quadric Kernel

83% 82% 81% 80%

SV M-only w ith Inverse Multi-Quadric Kernel

79% 78% 77% 76% 75% 1

3

5

7

9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Testset indexs

Fig. 3. Summary of the classification of test dataset

In the experiments, proposed method shows the best result when the optimal feature set for neural kernel obtained from GA is used in the decision model. And it also shows that the system can cope with novel attacks very well since it shows detection rates more than 99%. The number of features that SVM should process can be minimized by obtaining the optimal set of features, and the speed and the detection rate of SVM based IDS can be improved. Our experiment results demonstrate the feasibility of exploiting GA and SVM together for IDS in high speed network environment. 3.2 Stomach Cancer Data The proteome pattern samples used in this case study were provided by Cancer Research Center at Seoul National University in Seoul, Korea. The proteome pattern

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samples are extracted from the sera from a group of normal persons and a group of the affected persons with stomach cancer. The stomach cancer dataset consists of 67 normal and 70 cancer samples and each sample contains 119 features. The purpose of this experiment is to classify the proteome pattern samples into the normal and the cancer pattern classes. 100% 98% 96% 94% 92% 90%

Hit Ratios

88%

Inverse multiquadric kernel

86% 84%

Radial kernel

82%

Neural kernel

80% 78% 76% 74% 72% 70% 1

7

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19 25

31

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55 61

67

73

79

85

91 97

Generations

Fig. 4. Hit ratio rates of validation test

We used simple generalization method: 4-fold cross validation with 80 samples [6]. The data was split into a training set of 80 and a test set of 57 samples. The classification rates of validation tests during GA are depicted in Fig. 4. While GA was executed for 100 generations, the learning process using SVM with radial kernel function achieved the highest hit rates among the three kernel functions compared. After 100 generations in GA, the best hit rates are 95% in case of radial kernel function, 92.5% in case of inverse multi-quadric kernel function, and 81.25% in case of neural kernel function. Table 3. Number of Selected Feature Kernel function

Inverse multiquadric

Radial

Neural

Selected Feature Indexes

1413, 1423, 1523, 2302, 2313, 2317, 3118, 3131, 3306, 4314, 4315, 4608, 5103, 5107, 5325, 5336, 5337, 5407, 6107, 6303, 6308, 6309, 6415, 7317, 7408 1413, 1418, 2301, 2419, 2818, 3115, 3412, 3611, 3613, 4111, 4213, 4314, 4315, 4319, 4322, 4409, 5308, 5313, 6308, 6409, 6420, 6504, 6519, 7313, 7322, 7326 206, 207, 413, 515, 2301, 2419, 3118, 3309, 3417, 3611, 4321, 4429, 4608, 5407, 5409, 5513, 5712, 6115, 6316, 6504, 7306, 7309, 7313, 7408, 8301, 8309

3412, 4213, 5513, 5712,

3618, 4105, 5407, 5712,

4213, 4316, 6411, 6415,

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The indexes of the features selected by GA for each kernel function are shown in Table 3. The selected features are different for each kernel function used in SVM classifier.

Fig 5. Testing rates are computed by using the optimal decision models obtained in learning phase

The ratios of correct classification are summarized in Fig. 5. The radial kernel function showed the highest hit ratio in case of SVM with GA. In contrast, the test result is not good in case of neural and inverse multi-quadric kernel. According to the result illustrated in Fig. 5, the test results of them even were lower than cases of SVM-only. In this case study, “SVM+GA” with radial kernel showed better classification rate than other cases. The computation time of SVM can be reduced and the classification rates can be improved by using optimal feature set.

4 Conclusion In this paper, we proposed a novel learning method based on GA to determine the optimal decision model for SVM. In case that the sample spaces of applications are high-dimensional and have complex characteristics, the performance of SVM is often degraded severally. To cope with this problem and improve the performance of classification, we adopted GA technique to select the optimal set of features and the set of kernel parameters at the same time. The proposed learning method showed faster convergence and better classification performance for some datasets than other methods. The experiments indicate that our method is capable of finding the optimal set of features and set of kernel parameters that improve the performance of SVM.

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Acknowledgement This research was supported by IRC (Internet Information Retrieval Research Center) in Hankuk Aviation University. IRC is a Kyounggi-Province Regional Research Center designated by Korea Science and Engineering Foundation and Ministry of Science & Technology. This research also was supported by University IT Research Center (ITRC) project.

References 1. Martin-Bautista, M.J., Vila, M.-A.: A survey of genetic feature selection in mining issues. Evolutionary Computation. Proceedings of the 1999, Vol. 2 (1999) 1321 2. Frohlich, H., Chapelle, O., Scholkopf, B.: Feature selection for support vector machines by means of genetic algorithm. Tools with Artificial Intelligence, Proceedings 15th, IEEE International Conference (2003) 142 – 148 3. Xue-wen Chen: Gene selection for cancer classification using bootstrapped genetic algorithms and support vector machines. The Computational Systems Bioinformatics Conference, Proceedings IEEE International Conference (2003) 504 – 505 4. Cristianini, N. and Shawe-Taylor, J.: An introduction to Support Vector Machines and other kernel-based learning methods. Cambridge (2000) 5. Vapnik, V.N., et. al.: Theory of Support Vector Machines. Technical Report CSD TR-9617. Univ. of London (1996) 6. HDuda, R. O.H, Hart, HHP. E., Stork, HD. G.: HPattern Classification (2nd Edition). John Wiley & Sons Inc. (2001) 7. Joachims, Thorsten: Making large-Scale SVM Learning Practical. In Advances in Kernel Methods - Support Vector Learning, chapter 11. MIT Press (1999) 8. Minsky M.L. and Papert S.A.: Perceptrons. MIT Press (1969) 9. Michalewicz, Z.: Genetic Algorithms + Data structures = Evolution Programs. 3rd rev. and extended edn, Springer-Verlag (1996) 10. Goldberg, D. E.: Genetic Algorithms in Search, Optimization & Machine Learning. Adison Wesley (1989) 11. Mitchell, M.: Introduction to genetic Algorithms, fifth printing. MIT press (1999) 12. Bernhard P.: Winning the KDD99 Classification Cup. (1999) http://www.ai.univie.ac.at/~ bernhard/kddcup99.html 13. Rüping, S.: mySVM-Manual. University of Dortmund, Lehrstuhl Informatik (2000) URL: Hhttp://www-ai.cs.uni-dortmund.de/SOFTWARE/MYSVM/H

A Mobile Application of Client-Side Personalization Based on WIPI Platform SangJun Lee Department of Computer Information Communication, Seonam University, 720 GwangchiDong, NamWon, JeonlabukDo, Korea [email protected]

Abstract. The Internet site is encouraged to take a little time to get the preferred information and bring it to the customer through personalization of customers’ information. The mobile shopping users have a strong desire to reduce the shopping hours due to the expensive telecommunication service fees. It requires much time and perseverance to input the personalization information into the server and even to input it repeatedly into a bunch of shopping malls while maintaining contact. In this paper, we develop an application to protect the general personalized information in the mobile client-side based on XML. The mobile shopping using the client-side personalization reduces the connection time and improves the personalization information management through the enhanced data transmission and data input.

1 Introduction Mobile commerce (M-commerce) implies a purchasing transaction with some monetary value between a wireless network and a mobile device[1]. A full-blown M-commerce future is expected in terms of three reasons. Compared with the personal computer (PC), first, the number of mobile device available today is not only higher but is developed more rapidly than that of the PC. Second, users are much more familiarized with the mobile device than the PC, even with constant connectivity. Third, the spot services with the mobile device can be provided much easier than the PC or TV anytime anywhere. If the users of the Internet share the preference, interesting goods and purchasing experiences on the website, the website can provide the organized pertinent information by bypassing the need to the corporations. On the one hand, for corporations, with this personalization they can obtain these following four merits. First, it brings the enhancement of customer’s loyalty. Second, it significantly lowers the cost of marketing. Third, it helps to find good consumers. Fourth, it can be possible to offer constantly enhanced and valuable services. On the other hand, users can acquire three advantages. First, they can save their time to find the wanted information. Second, it is possible for them to make a selection by their preferences. Third, they can enjoy a personalized service. To be in a win-win situation for the users and the corporations through personalization, the users make their personal information open voluntarily. Since J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 903–909, 2004. © Springer-Verlag Berlin Heidelberg 2004

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many users are unwilling to reveal their information, a guarantee of protection for their information is a good and necessary consideration [2]. Up to now, as to personalization, even if the research into both the server-centered personalization mobile service[3] and the web host access tool in the digital library[4] have been done, there is no research into mobile client-side personalization before. Considering the comparatively expensive usage cost of communications and limitations of mobile devices, the research for the personalization is momentous. In this paper, unlike the way to input the personal information into a specific website, keeping the personal information in the mobile client-side through the mobile application is introduced. The download of the application is necessary because of no function of save for personal information in mobile client in the incumbent mobile device. This paper is organized as follows. In Section 2, we examine the personalization plan and design its information. In Section 3, we implement the client-side personalization on WIPI mobile platform. In Section 4, we evaluate our research. Finally, in Section 5, we make a conclusion.

2 Personalization for Mobile Shopping 2.1 Design of Personalization Information for Mobile Shopping Like Table 1, referring to Personalization & Privacy Survey[5], we categorize the personalization information items for mobile shopping by its security level. Table 1. Personalization information for mobile shopping Category A Preference Body Information Contact Information Doing Secret

Items Goods (Clothing,Shoes,Accessories,IT Product), Color, Brand, Specification, Shopping Mall Physical Size(Height,Weight,Waist,Foot) Name, E-mail, Address, Phone Number, Age, Sex, Job, Income ID, Password, Credit Card, Account

2.2 Personalization Strategy For personalization in mobile shopping, we make a plan in a following way [6]. • Setting the goal: Make the personal information of mobile shopping user easy to save in the client. • Defining the rule: Only for the websites registered to client-side personalization information, make the basic information uploaded automatically; for the correct password of client-side personalization, input the user automatically; input the ID and Credit card number in case of correct WPKI(Wireless PKI) • Collecting data: design and input personalization information • Step-by-step personalization: step-by-step personalization of the information by the user’s shopping lists from the mobile commerce site

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For privacy protection, • Apply P3P(Platform for Privacy Preferences Project): Provide the personal information only to the sites registered to client-side personalization. (A Preference) • Apply Anonymous Personalization: Provide the site with the preference or interest without profile or additional information. (Body Information, Contact Information) • Apply Stepwise Personalization: Ask the information for each step of personalization. (Doing Secret) Since the user is unwilling to reveal the personal information, the personal information is protected in the client using the downloaded mobile application, rather than protected in the server.

3 Application for Client-Side Personalization 3.1 Environment

Basic API (and Extended API) WIPI Run-time Engine HAL (Handset Adaptation Layer) Handset Hardware & Native System Software

Fig. 1. WIPI Platform Architecture

yyy

Group Chatting

MMS

IM

Video Streaming

yyy

CSP-WIPI

Character/Bell

Games

Email

Application Manager

Location Based

Mobile platform implies a software system which has a right API(Application Programming Interface) applicable to mobile applications, or other developing environments. The mobile platform consists of two platforms at large: for downloading the application and for developing the device. The former is called wireless Internet platform and its popularized kinds are Sun Java, Qualcomm BREW and WIPI. The latter platform is known as Microsoft Windows Mobile for Smartphone, Symbian OS, PalmOS, Ericsson Mobile Platform, etc. WIPI(Wireless Internet Platform for Interoperability) is made by KWISF(Korea Wireless Internet Standardization Forum). WIPI is a mobile standard platform specification providing the environment for application program loaded on the wireless devices[7]. WIPI platform has the conceptual structure like Fig.1.

Dynamic Component

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In this paper, Client-Side Personalization based on WIPI platform(CSP-WIPI) is implemented on specification of WIPI version 2.0 which is published in April 4, 2004. As mobile phone supporting this specification will be appeared in the second half of 2004, we develop mobile application for client-side personalization information on KTF WIPI Emulator[8]. CSP-WIPI is simulated as a mobile application using WIPI Basic API. Since CSP-WIPI is abiding by the standard, the customers can use it regardless of telecommunication companies in Korea. 3.2 Implementation CSP-WIPI is developed on the WIPI Content Server using the WIPI API. Like Fig.2, the users execute the CSP-WIPI application on the content server after downloading it. Then, the client-side personalization information is created from the user’s personal information by its execution. Server Side Personalization

Client Side Personalization

Personal Information Provides (XML)

DB DB

WIPI Platform Services (Push, …)

CSP-WIPI

Mobile Shopping Mall

XML

DB DB

Services

WIPI Content Server

XML Data

XML

CSP-WIPI Environment

Mobile Shopping Mall

Services

DB DB

Fig. 2. Architecture of CSP-WIPI System

③

⑥

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Fig. 3. CPS-WIPI Application Workflow

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In mobile shopping, the mobile application for inputting the personalization information is executed in a following way. In Fig. 3, Initial Display of CSP-WIPI. After selecting CSP-WIPI among icons in command bar, push Ok. Initial menu of CSP-WIPI: Personalization Information, Password Setting, Personalization Information Modify, Data Save/ Selecting Application. Personalization submenu: Setting the value of detailed items ~ . Confirm the Total Personalization Information. Modifying the existing value: Select Information Modify; , ~ . Save the client-side personalization information as a XML file into DB.

4 Evaluation To evaluate the results of research, we make a comparison between a mobile shopping which uses client-side personalization information and the other which does not. In addition, we also compare the protection of personalization information between saved in the client and saved in the server. 4.1 Client-Side Personalization Versus Non-personalization The time used in communications between shopping mall server and mobile device up to the end of service is compared in case of applying personalization and nonpersonalization. The Data Transmission Time means the time taking from the start to the end of service and the Data Input Time means the time for the user to enter the information to get the service from DB. Table 2. Client personalization versus non personalization

Data Transmission Time Data Input Time

Personalization scheme NC * (PTT * 2) Number of Category

NC : Number of Category NTII : Number of Total Input Item

Non personalization scheme NTII * (PTT *2) Number of Total Character

PTT : Packet Transmission Time

In this paper, personalization-applied scheme saves the data transmission time by (NTTI-NC) * (PTT * 2) compared with non-personalization scheme. For example, if we use the personalization information consisting of 4 categories and 16 items, and assuming PTT is 1, we can reduce the data transmission time up to 24 seconds. In case of non personalization, the data input time depends on the number of characters to enter; whereas, in case of personalization scheme, it hardly requires time of data input.

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4.2 Client-Side Personalization Versus Server-Side Personalization There are several ways to keep the personal information safely in the mobile client in communicating with the server. For example, we can protect the data from Online dictionary attack and shoulder surfing attack by installing a safe password system[9]. The protocol using the inputted password is used to prevent the server from server compromising attack[10]. The Off-line dictionary attack and server compromise attack can be blocked by the password and authenticated key exchange protocol [11]. Table 3. Client-side personalization versus server-side personalization Classification Convenience to manage

Client-side personalization Keeping the data in mobile device

Data Input Times

One-time input

Security-related things

Protecting against loss

Server-side personalization Connecting to the server and manage the data Multiple-time input to servers Same as that of general servers

5 Conclusion We have grasped the data for personalization of mobile shopping and established the scheme of personalization. In addition, we have developed the mobile application to manage and protect the personalization information. The customers of all communication companies which select WIPI as mobile standard platform are able to download and execute the application; therefore, they can save the personalization information into their mobile devices. Without their personalization information on the server, they can get the right service when connecting with the mobile shopping server with ease.

References 1. May, P.: Mobile commerce, Cambridge University Press. (2001) 2. Personalization Survey, http:://www.zdneton.org 3. Cassel, L., Wolz, U.: Client Side Personalization, Delos Workshop:Personalization and Recommender Systems in Digital Libraries (2001) 4. Wagner, M., Balke, W., Hirschfeld, R., Kellerer, W.:A Roadmap to Advanced Personalization of Mobile Services, Industrial Program of the 10th International Conference on Cooperative Information Systems(CoopIS) (2002) 5. Personalization & Privacy Survey, http://www.personalization.org 6. Personalization Plan, http://www.personalization.co.kr 7. WIPI Specification, http://www.kwisforum.org 8. Ktf WIPI Emulator, http://wipidev.magicn.com/

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9. SeungBae, P., MoonSeol K., SangJun L.: New Authentication System, Lecture Notes in Computer Science, Vol. 3032. Springer-Verlag, Berlin Heidelberg New York (2004) 10951098 10. SeungBae, P., MoonSeol K., SangJun L.: User Authentication Protocol Based on Human Memorable Password and Using ECC, Lecture Notes in Computer Science, Vol. 3032. Springer-Verlag, Berlin Heidelberg New York (2004) 1091-1094 11. SeungBae, P., MoonSeol K., SangJun L.: Authenticated Key Exchange Protocol Secure against Off-Line Dictionary Attack and Server Compromise, Lecture Notes in Computer Science, Vol. 3032. Springer-Verlag, Berlin Heidelberg New York (2004) 924-931

An Agent Based Privacy Preserving Mining for Distributed Databases Sung Wook Baik1, Jerzy Bala2, and Daewoong Rhee3 1

Sejong University, Seoul 143-747, Korea [email protected] 2 Datamat Systems Research, Inc., 1600 International Drive, McLean, VA 22102, USA [email protected] 3 Sangmyung University, Seoul 110-743, Korea [email protected]

Abstract. This paper introduces a novel paradigm of privacy preserving mining for distributed databases. The paradigm includes an agent-based approach for distributed learning of a decision tree to fully analyze data located at several distributed sites without revealing any information at each site. The distributed decision tree approach has been developed from the well-known decision tree algorithm, for the distributed and privacy preserving data mining process. It is performed on the agent based architecture dealing with distributed databases in a collaborative fashion. This approach is very useful to be applied to a variety of domains which require information security and privacy during data mining process.

1 Introduction Privacy preserving issues [1-6] became major concerns in inter-enterprise data mining to deal with private databases located at different sites. There have been two broad approaches in the data mining considering privacy preserving issues; 1) the randomization approach to randomize the values in individual records and to reveal only the randomized values for the protection of individual privacy and 2) the secure multi-party computation approach to fully analyze data located at different sites to build a data mining model across multiple databases without revealing the individual records in each database to the other databases. The privacy preserving issues directed towards Distributed Data Mining (DDM) have been applied to process medical, insurance, credit card transaction data and so on. However, the problem with most of these efforts is that although they allow the databases to be distributed over a network, they assume that the data in all of the databases is defined over the same set of features. In other words, they assume that the data is partitioned horizontally. In order to fully take advantage of all the available data, the data mining tools must have a mechanism for integrating data from a wide variety of data sources and should be able to handle data characterized by the following: J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 910–915, 2004. © Springer-Verlag Berlin Heidelberg 2004

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1. Geographic (or logical) distribution. 2. Complexity and multi feature representations. 3. Vertical partitioning/distribution of feature sets. This paper presents a novel data mining approach for tree induction from vertically partitioned data sets. The approach integrates inductive generalization of a decision tree and agent-based computing, so that decision rules are learned via tree induction from vertically partitioned and distributed data without transferring necessary data to the others for complete analysis. Agents, in a collaborative fashion, generate partial trees and communicate the index information of the data records regardless of privacy among them for synchronization of decision trees being constructed by each agent.

2 Distributed Data Mining Approach for Agents’ Collaboration Agent-based architectures [7-11], have been developed to achieve several distributed data mining techniques. However, they focus on the distributed data mining for analyzing data from homogeneous data sites where the distributed databases are horizontally partitioned and the database schema in every site are same. In this paper, we present a decision tree algorithm in a distributed database environment and a distributed data mining system, which has an inter-agent communication mechanism on the agent based framework. The decision tree algorithm for the distributed data mining has been extended from a traditional decision tree algorithm [12], so that it is possible to build a decision tree from the distributed databases without transferring any data (or even encrypted data) related to privacy among them. The extended algorithm can naturally resolve the privacy preserving problems. Figure 1 depicts the four layered system architecture for distributed data mining. The distributed learning algorithm of a decision tree in an Agent-Mediator communication mechanism (See Figure 2) is as follows: 1. The Mediator let the distributed and privacy preserving data mining process start by invoking all the Agents. 2. Then, each Agent independently starts the process of mining its own local data. It finds the feature (or attribute) and its value that can best split the data into the various training classes (i.e. the attribute with the highest information gain). 3. The Agent sends the selected attribute, as a candidate attribute, and its associated split value to the Mediator for overall evaluation. 4. Once the Mediator has collected the candidate attributes of all the Agents, it then selects the attribute with the highest information gain as an ultimate attribute to split at the given level of the decision tree. The Agent, whose database includes the attribute with the highest information gain, is called a winner. The other Agents are losers. 5. The Mediator notifies each Agent its status (winner or loser). 6. The winner Agent then continues the mining process by splitting the data using the winning attribute and its associated split value. This split results in the formation of two separate clusters of data (i.e. a group of data satisfying the split criteria and the other group of data not satisfying it).

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Decision/Collaboration Decision/Collaboration Layer Layer

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Fig. 1. Four layered system architecture for distributed data mining

7. The Agent passes the associated indices of the data records in each cluster and the winning attribute including its associated split value to the other Agents through the Mediator. Before passing it, the index information, normally represented as a set of integers (i.e. record numbers), is converted to a bit-vector representation. In a bit-vector representation, each individual bit corresponds to the index of a single data record. To further reduce the size of the data being transferred, a bit-vector representation can be compressed. 8. The other (i.e. losers) Agents receive the index information passed to the Mediator by the winner Agent and construct the partial decision trees by splitting their data accordingly. 9. If the decision tree is completely constructed, each Agent generates the classification rules by tracking the attribute/split information coming from the various Agents and terminates the distributed data mining process. Otherwise, the mining process then continues by repeating the process of candidate feature selection by each of the Agents (go to step 2).

3 Experimentation We have used four kinds of the data sets requiring the protection of individuals' personal privacy for the evaluation of the privacy preserving data mining system dealing with the vertically partitioned and distributed databases. The data sets [13] have been widely used in knowledge discovery and data mining (KDD) fields by many research groups and their descriptions are as follows: • Health Care Database: The database contains information on medical transactions performed during a three-year period by a US Government health care provider. A

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medical transaction in the database is represented as a single billable event, e.g., a drug administration. Each record in the database is represented by a field list describing such information as the patient’s age, transaction type, provider’s location, cost, etc. • Congressional Voting Records Database: The database includes votes for each of the U.S. House of Representatives Congressmen on the 16 key votes identified by the congressional quarterly almanac. It lists nine different types of votes; 1) voted for, 2) paired for, 3) announced for, 4) voted against, 5) paired against, 6) announced against, 7) voted present, 8) voted present to avoid conflict of interest, and 9) did not vote or otherwise make a position known. • Adult Database: The database contains information collected by the US Census Bureau for predicting whether income exceeds $50K/yr based on census data. Each record in the database is represented by a field list describing such information as the adult’s age, education, work class, marital status, occupation, race, sex, capital gain, native country, and so on.

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• Insurance Database: The database contains information was prepared by the Swiss Life Information Systems Research group. Each record in the database is represented by a field list describing such information as sex, year of birth, marital status, personal state, i.e. nothing special, dead, missed or under revision as disabled person, and disabled person. Three experiments have been conducted to generate classification rules for two classes (i.e., the above $50K/yr (class A) and the below $50K/yr (class B) for the salary field in the adult database). Experiment 1: Each database described above was placed on the different site, where each agent resided to access/analyzes the database and to communicate with the others. The distributed data mining process was performed by the collaboration of four agents and a mediator. Experiment 2: The first two databases and the last two databases were manually combined into two double-sized databases, respectively. Those databases were placed into two different sites. The distributed data mining process was performed by the collaboration of two agents and a mediator. Experiment 3: All of four databases were manually combined into a database, which has sixty fields. The combined database was processed by non-distributed data mining version. The results of three experiments have been compared with each other. The comparison has revealed exactly the same rule sets for different versions of the (distributed) data mining.

4 Conclusion and Future Work This paper focused on the privacy preserving issues and provided a significant approach for the privacy preserving mining for distributed databases through the collaboration of agents and a mediator. The approach is to integrate inductive generalization and agent-based computing so that classification rules can be learned via tree induction from distributed data to be used for prediction. According to experimental results, the classification rules are exactly same for different versions of the (distributed) data mining even though necessary data are not transferred to the others for complete analysis. As a future work, we need to evaluate the performance [4] of the presented agentbased decision tree algorithm with the comparison of a centralized decision tree algorithm such as C5.0.

References 1. Agrawal, S., Krishnan, V., Haritsa, R. J.: On Addressing Efficiency Concerns in Privacy Preserving Mining. LNCS 2973 (2004) 113-124

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2. Malvestuto, M. F., Mezzini, M.: Privacy Preserving and Data Mining in an On-Line Statistical Database of Additive Type. LNCS 3050 (2004) 353-365 3. Lindell, Y., Pinkas, B.: Privacy Preserving Data Mining. LNCS 1880 (2000) 36 4. Krishnaswamy, S., Zaslavsky, A., Loke, S. W.: Techniques for Estimating the Computation and Communication Costs of Distributed Data Mining. LNCS 2329 (2002) 603-612 5. Aggarwal, C. C., Yu, P. S.: A Condensation Approach to Privacy Preserving Data Mining. LNCS 2992 (2004) 183-199 6. Kargupta, H., Datta, S., Wang, Q., Sivakumar, K.: On the privacy preserving properties of random data perturbation techniques. Proceedings of the Third IEEE International Conference on Data Mining (2003) 99-106 7. Kargupta, H., Park, B., Hershberger, D., Johnson, E.: Collective Data Mining: A New Perspective Toward Distributed Data Analysis. Advances in Distributed and Parallel Knowledge Engineering 5 (2000) 131-178 8. Kargupta, H., Hamzaoglu, I., Stafford, B.: Scalable, Distributed Data Mining-An Agent Architecture. Proceedings of the International Conference on Knowledge Discovery and Data Mining. (1997) 211-214 9. Stolfo, S., Prodromidis, A. L., Tselepis, S., Lee, W.: JAM: Java Agents for Meta-Learning over Distributed Databases. Proceedings of the International Conference on Knowledge Discovery and Data Mining. (1997) 74-81 10. Bailey, S., Grossman, R., Sivakumar, H., Turinsky, A.: Papyrus: a system for data mining over local and wide area clusters and super-clusters. Proceedings of the International Conference on Supercomputing. (1999) 11. Klusch, M., Lodi, S., Moro, G.: Agent-Based Distributed Data Mining: The KDEC Scheme. LNAI 2586 (2003) 104–122 12. Quinlan, J. R., Rivest, R. L.: Inferring Decision Trees Using the Minimum Description Length Principle. Information and Computation. 80 (1989) 13. See Web site at http://www.kdnuggets.com

Geometrical Analysis for Assistive Medical Device Design Taeseung D. Yoo1 , Eunyoung Kim2 , Daniel K. Bogen3 , and JungHyun Han1,
1

Department of Computer Science and Engineering, Korea University, Korea 2 School of Information and Communications Engineering, Sung Kyun Kwan University, Korea 3 Department of Bioengineering, University of Pennsylvania, USA

Abstract. In the computer graphics field, mesh simplification, multiresolution analysis and surface parameterization techniques have been widely investigated. This paper presents innovative applications of those techniques to the biomechanical analysis of thin elastic braces. The braces are represented in polygonal meshes, and mesh simplification and multiresolution analysis enable fast geometric computation and processing. The multi-resolution brace mesh is parameterized for strain energy calculation. The experiment results prove that 3D geometrical analysis works quite well for assistive medical device design.

1

Introduction

An elastic brace is a medical device commonly used to restrict the motion of the joints (such as wrist and knee) that suffer from musculoskeletal disorders. While the elastic brace is widely used, its mechanics has been rarely studied. The ultimate goal of the brace research is to design and fabricate custom-made braces with the desired stiffness such that they limit the joint motions. Stiffness is affected mainly by the brace geometry. Once the relationship between the brace geometry and its stiffness is obtained, it enables us to design a brace of the appropriate geometry that guarantees the stiffness prescribed by a physician. The relationship is found through sophisticated steps. The joint is scanned to generate a 3D model. When the joint is bent, brace stuck onto it is deformed following the changing surface of the joint. For each bending angle, strain energy (SE) is calculated. SE is defined as the mechanical energy stored in the elastic body due to its deformation, and its unit is N · m [1]. From the relationship of SE and deflection, stiffness of the brace is obtained: (1) the derivative of SE with respect to deflection angle is joint moment. (2) the derivative of the joint moment with respect to deflection angle is stiffness. The major contribution of our research is to find the relationship between brace geometry and its stiffness. This paper presents how the mesh simplification [2] and surface parameterization [3] techniques, which have been intensively


Corresponding Author.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 916–921, 2004. c Springer-Verlag Berlin Heidelberg 2004


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investigated in the computer graphics field, can be innovatively applied to SE analysis for efficiency purpose.

2

3D Model and Deformation

The point cloud data of a joint surface is generated using Cyberware’s 3D scanner. Then, the point cloud is converted into a triangular mesh using Paraform’s mesh generation packages. Fig. 1-(a) shows the knee mesh model with 25,600 vertices. We have too many vertices to process. As a preliminary step, the simplification algorithms discussed in the next section reduces the vertex number into 5,000 with geometric fidelity to the original mesh.

Fig. 1. Knee’s mesh model

It is very hard to devise a realistic bending transformation that can be applied to the joints. Therefore, we use simple beam bending: the original brace mesh is conceptually embedded into a solid cylindrical beam that undergoes constant curvature bending. The bending beam displaces the vertices of the brace mesh. The formulae in Eq. (1) relate the initial location of an unbent beam’s vertex to its transformed location in the bent beam. x = (ρ + x) · cos φ − ρ, y  = (ρ + x) · sin φ

(1)

where (x, y) is the initial location of a vertex, (x , y  ) is its transformed location, ρ is the radius of curvature, and φ is the angular position of the point with respect to the center of curvature of the beam. Note that φ = y/ρ. We use 15 bent models generated with 4◦ interval out of the range of 0◦ through 60◦ . After the bending transformation, the bent mesh is simplified. The simplified mesh needs to get ‘unbent.’ For such inverse bending, inverses of Eq. (1) are used.

3

Selective Simplification of 3D Mesh

When the joint deforms, some brace regions experience contraction while the other regions are expanded. Contraction refers to reduction in size. In Fig. 1-(b), the back part of the knee is contracted while the front part is expanded. In

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the contracted regions, buckling usually occurs. Buckling site must be excluded from SE calculation since it stores no energy. The preliminarily reduced number of points is still too huge and significantly degrades the performance in SE calculation. A selective simplification strategy is adopted: The higher resolution is retained in the contracted region to detect buckling effectively, and the simplification is focused on the expanded region. The most popular mesh simplification technique is edge collapse or simply ecol. See Fig. 2-(a). Garland and Heckbert [4] proposed a simplification algorithm based on quadric error metrics (QEM), where the simplified mesh maintains visual fidelity to the original mesh. We adopted an ecol version of the QEM-based simplification, and modified it: the expanded region must be simplified for fast computation, but the contracted region must maintain the original resolution. A triangle’s area can become increased or decreased after the deformation. If two triangles sharing an edge have increased areas, the shared edge is determined to lie in an expanded region. Therefore, the edge is taken as collapsible. The ecol operations are performed only with the collapsible edge set. Fig. 2-(b) shows the input mesh (5,000 vertices) and the selectively simplified mesh (3,250 vertices). Most elastic brace design systems are in a stable state if the strain energy error (SEE) is kept below 1% [5]. SEE is defined to be (Es -Eo )/Eo where Eo is SE calculated with the original mesh and Es is that with the simplified mesh. Joints have the generalized cylinder geometry. Hence, a cylinder model is a good choice for determining how much can be simplified within 1% SEE. A cylinder mesh with 1,050 vertices is bent by the largest bending angle, 60◦ . Then, ecol is repeatedly applied. SEE is calculated for each simplified mesh, and tested if it exceeds 1%. With 1% error limit, we obtain the simplified mesh of 616 vertices, i.e. 41.3% reduction. Since wrist and knee are more complex geometries than cylinder, SEE might be bigger with the same reduction rate. Hence, for general joints, the maximum reduction rate is set to 35%. As the largest bending angle (60◦ ) is used, the reduction rate 35% satisfies 1% error bound for most cases.

4 4.1

Strain Energy Calculation Surface Parameterization and Strain Energy Calculation

Elastic braces are fabricated using a sheet of elastic membrane, and the traditional choice of the 2D brace shape has been a rectangle because every human-

Fig. 2. The ecol operation, and knee meshes with different resolutions

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body joint has the generalized cylinder geometry and its flattened version roughly coincides with a 2D rectangle. We propose to use surface parameterization techniques [3], which map a 3D mesh to a 2D plane.

Fig. 3. Brace mesh parameterization

We have adapted Floater’s parameterization algorithm [6] to our context. For parameterization, the joint geometry is cut along a vertical path. See Fig. 3-(a). All the boundary vertices of the cut surface are radially projected to construct the 2D rectangle’s boundary such that the inter-vertex distances are preserved (with scaling). Then, the interior vertices are mapped using the Floater’s algorithm. Fig. 3-(b) shows the parameterization result.

Fig. 4. SE calculation. (a) parameterized plane (b) Unbent joint (c) Bent joint

The parameterization-based SE calculation is illustrated in Fig. 4. Strain energy SE1 is calculated, which is stored in the 3D brace when the brace is worn in the un-deformed joint geometry. Similarly, SE2 is for the deformed joint geometry. The net strain energy ∆SE is the difference between SE1 and SE2 . SE1 and SE2 are calculated as follows: (1) SE density is calculated at each triangle of the joint mesh. (See Section 4.2.) (2) The area of the corresponding triangle on the 2D brace is computed, then the area and the brace thickness are multiplied to produce the triangle volume. (3) The computed volume and density are multiplied to produce SE. (4) The process is repeated for every triangle, and the result is accumulated to obtain the total SE.

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4.2

Strain Energy Density Calculation

Our brace is hyperelastic, transversely isotropic, and incompressible. Strain energy density is calculated by strain energy density function (SEDF ) Wiso [7, 8] given below:
 1 Wiso = Giso Ic + IIc−1 − 3 (2) 2 In Eq. (2), Giso is the rigidity of modulus, Ic = C11 + C22 and IIc = C11 C22 , where Cii s are the components of the right Cauchy-Green deformation gradient tensor C. Given the deformation gradient tensor F = ∂x /∂X [1] where x and X are the coordinates of the 3D mesh and of the 2D parameterized plane, respectively, the tensor C is defined by FT · F [1]. The contracted regions may or may not have the buckling. Whether buckling occurs is determined by the principal stresses [9]. Therefore, we need to compute the signs and magnitudes of the principal stresses throughout the mesh. Then, we can partition the contracted regions into buckling and non-buckling sites. The variation of the joint surface geometry is random, and buckling and non-buckling sites may be intermingled. Hence, when such intermingled sites are simplified, we often end up with incorrect partitioning, which eventually leads to incorrect calculation of SE. Thus, we need a high resolution for the contracted regions. Eq. (2) is good for the expanded regions only. Therefore, we need SEDF for the contracted regions of no buckling. For this purpose, Eq. (2) is extended to Eq. (3) to calculate SE, which is caused only by tensile load [9].  
 2 2 1 2 −3 Wiso = 2 Giso C11 n1 + 2C12 n1 n2 + C22 n2 +  (C11 n21 +2C12 n1 n2 +C22 n22 )

(3)

where n1 and n2 are the two components of the principal direction vector [5].

5

Results

We have implemented the proposed algorithms in C++ on a PC with an Intel 2.6GHz Pentium 4 CPU. We have tested two 3D-scanned models: wrist (1,041 vertices) and knee (5,000 vertices). We have three major tasks: (1) mesh simplification, (2) parameterization, and (3) SE calculation. For the wrist model, the three tasks are done in real-time. For the knee model, SE is calculated in real-time but simplification and parameterization take 3 seconds and 12 minutes, respectively. However, the parameterization process with the un-simplified knee takes 31 minutes, i.e. we can save 19 minutes at the cost of 3 seconds. Since we use 15 bent models, total 285 minutes are saved at the cost of 45 seconds. Fig. 5 shows the normalized SE curves of the original mesh and the simplified mesh for wrist and knee, respectively. The curves (for original and simplified meshes) in the figure are almost identical. The largest error in SE between the original and the simplified is about 0.6% for wrist, and 0.3% for knee.

Geometrical Analysis for Assistive Medical Device Design Strain Energy Curves : Knee Model 0.025 Simplified Unsimplified

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Conclusion

This paper presented innovative and successful applications of the mesh simplification and surface parameterization techniques to the analysis of the relationship between the brace geometry and its stiffness. The relationship will enable effective design of braces. Further works may include analysis of anisotropic braces with multiple layers of single-direction fibers.

Acknowledgements This work is supported by the MOST 21st Century Frontier Program: Intelligent Robot Project.

References 1. Mal, A., Singh, S.: Deformation of Elastic Solids. Prentice-Hall (1991) 2. Luebke, D.: A developer’s survey of polygonal siplification algorithms. In: IEEE Computer Graphics and Applications. Volume 21(3). (2001) 24–35 3. Floater, M., Hormann, K.: Surface parameterization: a tutorial and survey. In: Advances in multiresolution for geometric modelling. (2004) 4. Garland, M., Heckbert, P.: Surface simplification using quadric error metrics. In: Proc SIGGRAPH ’97. (1997) 209–216 5. Yoo, T.: Analytic Mechanics of Hyper-Elastic Wrist Braces. PhD thesis, The University of Pennsylvania, Philadelphia, PA, USA (1999) 6. Floater, M.: Parameterization and smooth approximation of surface triangulations. In: Computer Aided Geometric Design. Volume 14. (1997) 231–250 7. Treloar, L.: The Physics of Rubber Elasticity. The Clarendon Press (1975) 8. Rivlin, R., Topakoglu, C.: A theorem in the theory of finite elastic deformations. In: Journal of Rational Mechanical Analysis. Volume 3. (1954) 581–589 9. Timoshenko, S., Young, D.: Elements of Strength of Materials. Prentice-Hall (1968)

Hybrid Genetic Algorithms and Case-Based Reasoning Systems Hyunchul Ahn1, Kyoung-jae Kim2, and Ingoo Han1 1

Graduate School of Management, Korea Advanced Institute of Science and Technology, 207-43 Cheongrangri-Dong, Dongdaemun-Gu, Seoul 130-722, Korea {goodguy, ighan}@kgsm.kaist.ac.kr 2 Department of Information Systems, Dongguk University, 3-26, Pil-Dong, Chung-Gu, Seoul 100-715, Korea [email protected]

Abstract. Case-based reasoning (CBR) has been applied to various problemsolving areas for a long time because it is suitable to complex and unstructured problems. However, the design of appropriate case retrieval mechanisms to improve the performance of CBR is still a challenging issue. In this paper, we encode the feature weighting and instance selection within the same genetic algorithm (GA) and suggest simultaneous optimization model of feature weighting and instance selection. This study applies the novel model to corporate bankruptcy prediction. Experimental results show that the proposed model outperforms other CBR models.

1 Introduction Case-based reasoning (CBR) often shows significant promise for improving the effectiveness of complex and unstructured decision making. Regardless of its many advantages, there are some problems that must be solved in order to design an effective CBR system. Some examples of those problems involve the fact that there are no mechanisms to determine appropriate methods of case retrieval in typical CBR systems. In this aspect, the selection of the appropriate similarity measures, feature subsets and their weights in the case retrieval step has been the most popular research issue. Recently, simultaneous optimization of several variables in CBR attracts researchers’ interest due to its better performance. As a pioneering work, there exists the approach to combine feature selection and instance selection simultaneously [5,7]. Theoretically, feature weighting may improve the effectiveness of CBR systems better than feature selection. Nonetheless, there exist few attempts which try to optimize feature weighting and instance selection simultaneously. This paper proposes genetic algorithms (GA) to optimize the feature weights and instance selection simultaneously. This study applies the proposed model to the realworld case and presents experimental results from the application. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 922–927, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Research Background 2.1 Genetic Algorithms as an Optimization Tool for CBR CBR is composed of five-step processes; presentation, retrieval, adaptation, validation and update [2]. Among these five steps, step two, case retrieval, is most critical for determining the effectiveness of CBR system. During the retrieval step, similar cases that are potentially useful for solving the current problem are retrieved from the case base. So, how to measure the similarity of the cases and how to combine the similar cases are challenging issues in this step [3]. Especially, feature weighting and instance selection for measuring similarity have been controversial issues in designing CBR system. To determine these uncertain factors of CBR system, there have been many studies that attempt to resolve these problems. Among many methods of instance selection and feature weighting, GA is increasingly being used in the CBR system. Genetic algorithms are stochastic search techniques that can search large and complicated spaces. It is based on biological backgrounds including natural genetics and evolutionary principle. In particular, GAs are suitable for parameter optimization problems with an objective function subject to various hard and soft constraints [8]. 2.2 Feature Weighting Feature weighting is assigning a weight to each feature according to the relative importance of each one. It is an important factor that determines the performance of artificial intelligence (AI) systems, so it has been the most popular research issue in designing most AI systems including CBR systems. Regarding feature weighting, Wettschereck et al. presented various feature weighting methods based on distance metrics in the machine learning literature [9]. Kelly and Davis proposed a GA-based feature weighting method for k-nearest neighbor [4]. Similar methods are applied to the prediction of corporate bond rating [8]. 2.3 Instance Selection Instance selection is the technique that selects an appropriate reduced subset of casebase and applying the nearest-neighbor rule to the selected subset. It may increase the performance of CBR systems dramatically if the systems contain many noises. So, it has been another popular research issue in CBR systems for long time. There exist many different approaches to select appropriate instances. For example, Lipowezky suggested linear programming methods for instance selection [6]. Yan suggested ANN-based instance selection method [10] and GA approach was also proposed by Babu and Murty [1]. 2.4 Simultaneous Optimization of Feature Weighting and Instance Selection In general, feature weighting includes feature selection since selection is a special case of weighting with binary weights. Consequently, simultaneous optimization model of feature weighting and instance selection model may improve the performance of the

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model of feature selection and instance selection. In this manner, Yu et al. proposed simultaneous optimization model of feature weighting and instance selection for collaborative filtering, an algorithm that is very similar to CBR [11]. However, they applied not AI techniques, but an information-theoretic approach to the optimization model. So, in the strict sense of the word, their model is not simultaneous optimization model but sequential combining model of two approaches.

3 GA for Simultaneous Feature Weighting and Instance Selection To mitigate the limitations of prior studies, this paper proposes GA as a simultaneous optimization tool of feature weighting and instance selection. To test the effectiveness of the proposed model, we compare the results of four different models. The first model, labeled COCBR (COnventional CBR), uses a conventional approach for reasoning process of CBR. This model considers all initially available instances as an instance subset. Thus, there is no special process of instance subset selection. In addition, relative importance of each feature is also not considered because many conventional CBR models do not have general feature selection or weighting algorithm. The second model assigns relevant feature weights via genetic search. This study names this model FWCBR (CBR with Feature Weighting). Similar models to it were previously suggested by Kelly and Davis [4] and Shin and Han [8]. The third model uses the GA to select a relevant instance subset. This study names this model ISCBR (CBR with Instance Selection). Babu and Murty proposed similar model to it [1]. The fourth model, the proposed model in this study, employs the GA to select a relevant instance subset and to optimize the weights of each feature simultaneously. This model is named as SOCBR (Simultaneous Optimization of CBR) in this study. The model consists of the following three stages: Stage 1. For the first stage, we search the search space to find optimal or near-optimal parameters (feature weights and selection variables for each instance). The population (seed points for finding optimal parameters) is initiated into random values before the search process. The parameter to be found must be encoded on a chromosome. The encoded chromosome is searched to maximize the specific fitness function. The objective function of the model is to classify bankrupt or non-bankrupt corporations accurately, and it can be represented by the average prediction accuracy of the test data. Thus, this study applies it to the fitness function for GA. In this stage, the GA operates the process of crossover and mutation on the initial chromosome and iterates it until the stopping conditions are satisfied. Stage 2. The second stage is the process of case retrieval and matching for a new problem in the CBR system using the parameters that are set in Stage 1. In this stage, 1-NN(one-nearest neighbor) matching is used as a method of case retrieval. And, we use the weighted average of Euclidean distance for the each feature as a similarity measure. This stage is repeated after the process of evolution (crossover, mutation) and the value of the fitness function is updated.

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Stage 3. The third stage applies the finally selected parameters - the optimal weights of features and selection of instances - to the hold-out data. This stage is required because GA optimizes the parameters to maximize the average predictive accuracy of the test data, but sometimes the optimized parameters are not generalized to deal with the unknown data.

4 The Research Design and Experiments 4.1 Application Data The application data used in this study consists of financial ratios and the status of bankrupt or non-bankrupt for corresponding corporation. The data was collected from one of largest commercial banks in Korea. The sample of bankrupt companies was 1335 companies in heavy industry which filed for bankruptcy between 1996 and 2000. The non-bankrupt companies were 1335 ones in heavy industry which filed between 1999 and 2000. Thus, the total number of samples is 2670 companies. The financial status for each company is categorized as “0” or “1” and it is used as a dependent variable. “0” means that the corporate is bankrupt, and “1” means that the corporate is solvent. For independent variables, we first generate 164 financial ratios from the financial statement from each company. Finally, we get 15 financial ratios as independent variables through the two independent sample t-test and the forward selection procedure based on logistic regression. 4.2 Research Design and System Development For the controlling parameters of GA search for SOCBR, the population size was set at 100 organisms and the crossover and mutation rate were set at 0.7 and 0.1. And, as the stopping condition, only 1500 trials (15 generations) are permitted. To compare the result of SOCBR, we also applied other models to the same data set. The compared models include COCBR(Conventional CBR), FWCBR(CBR with feature weighting), and ISCBR(CBR with instance selection). COCBR is 1-NN algorithm whose feature weights are set to 1. FWCBR is 1-NN algorithm whose feature weights are optimized by GA. In the case of COCBR and FWCBR, all the instances are used for reference case-base. However, ISCBR uses only subset of total reference case-base which is selected by GA. As the controlling parameters of GA search for FWCBR and ISCBR, the population size was set at 50 organisms and the crossover and mutation rate were set at 0.7 and 0.1. And, as the stopping condition, about 500 trials (10 generations) are permitted.

5 Experimental Results In this section, the prediction performances of SOCBR and other alternative models are compared. Table 1 describes the average prediction accuracy of each model.

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In Table 1, SOCBR achieves higher prediction accuracy than COCBR, FWCBR, and ISCBR by 5.42%, 2.99%, and 3.55% for the hold-out data. Table 1. Average prediction accuracy of the models

Model Test data set Hold-out data set

COCBR 80.75%

FWCBR 84.83% 83.18%

ISCBR 83.71% 82.62%

SOCBR 85.96% 86.17%

The McNemar tests are used to examine whether the predictive performance of the SOCBR is significantly higher than that of other models. This test is used with nominal data and is particularly useful with before-after measurement of the same subjects. Table 2 shows the results of the McNemar test to compare the performances of four models for the hold-out data. Table 2. McNemar values for the hold-out data

FWCBR ISCBR SOCBR COCBR 2.361 3.115** 10.453*** FWCBR 0.062 3.309* ISCBR 4.208** * ** *** significant at the 10% level, significant at the 5% level, significant at the 1% level. As shown in Table 2, SOCBR is better than COCBR at the 1% and better than ISCBR at the 5% statistical significance level. But, SOCBR outperforms FWCBR at only 10% statistical significance level.

6 Conclusions We have suggested a new kind of hybrid system of GA and CBR to improve the performance of the typical CBR system. This paper used GA as a tool to optimize the feature weights and instance selection simultaneously. From the results of the experiment, we show that SOCBR, our proposed model, outperforms other comparative models such as COCBR and FWCBR as well as ISCBR. However, this study has some limitations. First of all, the number of generations (trial events) in our GA experiments is too small. In fact, the search space for simultaneous optimization of feature weights and feature selection is very large, so we need to increase the number of populations and generations. Secondly, it takes too much computational time for SOCBR. As mentioned, SOCBR iterates case retrieval process whenever genetic evolution occurs. And, in general, case retrieval process in CBR takes much computational time because it should search whole case-base to make just

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one solution. Consequently, the efforts to make SOCBR more efficient should be followed in future. Moreover, the generalizability of SOCBR should be tested further by applying it to other problem domains.

References 1. Babu, T. R., Murty, M. N.: Comparison of genetic algorithm based prototype selection schemes, Pattern Recognition 34 (2001) 523-525 2. Bradley, P.: Case-based reasoning: Business applications. Communication of the ACM 37 (1994) 40-43 3. Chiu, C.: A case-based customer classification approach for direct marketing. Expert Systems with Applications 22 (2002) 163-168 4. Kelly, J. D. J., Davis, L.: Hybridizing the genetic algorithm and the k nearest neighbors classification algorithm, Proceedings of the Fourth International Conference on Genetic Algorithms (1991) 377-383 5. Kuncheva, L. I., Jain, L. C.: Nearest neighbor classifier: Simultaneous editing and feature selection. Pattern Recognition Letters 20 (1999) 1149-1156 6. Lipowezky, U.: Selection of the optimal prototype subset for 1-NN classification, Pattern Recognition Letters 19 (1998) 907-918 7. Rozsypal, A., Kubat, M.: Selecting representative examples and attributes by a genetic algorithm. Intelligent Data Analysis 7 (2003) 291-304 8. Shin, K. S., Han, I.: Case-based reasoning supported by genetic algorithms for corporate bond rating. Expert Systems with Applications 16 (1999) 85-95 9. Wettschereck, D., Aha, D. W., Mohri, T.: A review and empirical evaluation of feature weighting methods for a class of lazy learning algorithms, Artificial Intelligence Review 11 (1997) 273-314 10. Yan, H.: Prototype optimization for nearest neighbor classifier using a two-layer perceptron, Pattern Recognition 26 (1993) 317-324 11. Yu, K., Xu, X., Ester, M., Kriegel, H-P.: Feature weighting and instance selection for collaborative filtering: an information-theoretic approach, Knowledge and Information Systems 5 (2003) 201-224

Pap´ılio Cryptography Algorithm Frederiko Stenio de Ara´ ujo, Karla Darlene Nempomuceno Ramos, Benjam´ın Ren´e Callejas Bedregal, and Ivan Saraiva Silva Universidade Federal do Rio Grande do Norte, Departamento de Inform´ atica e Matem´ atica Aplicada, 59072-970, Natal-RN, Brazil [email protected], [email protected], {bedregal, ivan}@dimap.ufrn.br

Abstract. Pap´ılio is a Feistel cipher encryption algorithm where the coder process (function F ) is based in the Viterbi algorithm. The Viterbi algorithm was proposed as a solution to decode convolutional codes. There are several parameters that define the convolution code and Viterbi algorithm; one of them is the generator polynomial. To use Viterbi algorithm in cryptography, it is necessary to make some modifications. The proposed one does not depend on the parameters of Viterbi nor on the parameters of convolution. In this work we will analyze the cryptographic indices (avalanche, diffusion and confusion) of Pap´ılio considering all possible different polynomials and fix the other parameters.

1

Introduction

A.J. Viterbi in [11] developed the Viterbi Algorithm (VA) in 1967 as a solution for decoding convolutional codes. Convolutional encoder (CE) with Viterbi decoder is a FEC (Forward Error Correction) technique that is particularly suitable to channels where the transmitted signal is corrupted mainly by additive white Gaussian noise [2]. Since then, other researchers have applied VA and CE for other areas of applications such as recognition of handwritten word [8], target tracking [1], image edge detection [7]. Since the CE, increases the length of the input bitstream (it is an injective and not surjective one) and the VA only decode the bitstream generated by CE and some others few which can be recovered (is a partial not injective and not surjective function), this process can not be considered as cryptographic method. This work apply a modification in the VA, considering specific parameters for the VA and CE, in order to get a bijective function. This bijective function was inserted as the function F in a Feistel cipher with 16 rounds, blocks of 64 bits and keys of 128 bits [9, 10]. To generate the 16 sub-keys, it was used the modified Viterbi (MV). This feistel cipher will be called of Pap´ılio1 . We will show an study that chooses eight polynomials which provide to Pap´ılio better indices of cryptography and also will provide some evidences that Pap´ılio can be improved in the aspect of the complexity of cryptanalysis and the execution time. 1

The name Pap´ılio was given because the trellis of VA form a butterfly, and Pap´ılio Thoas Brasiliensis is the name of a very common sort of butterflies in Brazil.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 928–933, 2004. c Springer-Verlag Berlin Heidelberg 2004


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Modified Viterbi

VA attempts to find the closest ”valid” sequence to the received bitstream, that is, a sequence which when applied to the CE results in the received bitstream. Notice that two different sequences used as inputs for the convolution encoder result, necessarily, in two different sequences, that compute an injective function. So, the VA can be seen as a decoder. But, VA only decode bitstream generated by CE. Therefore, for VA to be used in the cryptography it is necessary that it processes any input sequence in a bijective way. The VA will be modified to deal with all possible bitstreams, in such a way that can be seen as a bijective function and therefore appropriated for cryptography. The MV algorithm proposed increases the code space matching VA with CE. For MV deal with any input sequence, independently of the current state, it was created besides output sequence S0 , an output sequence S1 . S0 presents the result of VA. S1 exhibits if each output symbol of S0 was obtained in agreement with the VA, or if it was obtained in an special shape (MV). When an output symbol of S0 is obtained in agreement with the VA, S1 generates the bit 0, otherwise S1 generates the bit 1. The MV algorithm is initialized to zero state and works as VA until an input symbol of bitstream is not appropriate in the current state, i.e. is ”invalid”. When this occurs, the symbols of not appropriated label are treated separately for the CE with initial state being the current state of MV. It is observed that CE will generate
ns  additional labels, being ns the rate of CE. With this procedure the generated labels can be treated by the VA. The application of the VA would generate a size label n for each one of the generated additional labels. However what interests in the code is the generation of an only size label n. The adopted solution consists of considering, to compose the flow S0 , just the first of the
ns  size labels n (the bitstream S1 receives the value 1). The continuation of the code process using the VA is adopted as current state the last state of the process of convolution, until a new ”invalid” label is found or the code is finished. The bitstreams S0 and S1 are independent. At the end of the code the bitstream are concatenated, in way to generate a bitstream of same length of the original. Through MV it’s possible create tables that help the code process. For example, the table 1 exhibits the MV taking into account the CE and VA where n = 1, s = 2, Q = 3, m = 2 and generator polynomial G = 111101.

3

The Encryption Algorithm Pap´ılio

Pap´ılio is a Feistel cipher encryption algorithm where the function F is the function computed by the MV algorithm whose parameters (codification rate n s , Q, m and the polynomial generator) are opens in a first moment. The main characteristics: Block Length: Actually are considered block of 64 bits. Nevertheless, because the MV does not depends on length of block, its size can be changed in a further implementation turning fix as 128 bit or variable in function of the key;

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Table 1. MV of CE with n = 1, s = 2, Q = 3, m = 2 and generator polynomial G = 111101 Current State Input 00 0 01 10 11 00 1 01 10 11

S0 0 0 1 1 1 0 1 0

S1 Next State Current State Input S0 S1 Next State 0 0 00 0 1 0 1 2 2 01 1 0 3 1 1 10 0 0 1 0 2 11 1 1 3 0 2 00 0 1 0 1 2 3 01 0 0 1 1 1 10 1 0 3 0 0 11 1 1 3

Size of the Key: 128 bits. But, its size could be variable or greater; Number of Rounds: 16. But, this quantity can be reduced to 6 or turned into variable (between 6 to 16) without losing the good cryptographic indices; Sub-key Generations: Pap´ılio uses 16 sub-keys that are generated from the 128-bit encryption key. The sub-keys are stored temporarily in an array. The scheme for generation is as follows. The first four sub-keys, labelled SC1 , SC2 , SC3 and SC4 , are generated by applying the MV in the 128-bit initial key, which generates two 64-bit bitstream. Applying MV to the two 64-bit bitstreams it generates four bitstreams of 32-bits that corresponds to the first four sub-keys. To generate the four following sub-keys, the four bitstream are concatenated generating an alone of 128-bits and the procedure to generate first four sub-keys is repeated until all 16 sub-keys are generated. Decryption: as with most block ciphers, the process of Pap´ılio decryption is essentially the same as the encryption process, except the sub-keys that are employed in reverse order. So, use SC16 in the first round, SC15 in the second round, and so on until SC1 is used in the last round. This feature avoids implementing two different algorithms, one for encryption and one for decryption; Operation Modes: Pap´ılio was implemented in the four usual modes (ECB, CBC, CFB and OFB). Programming Language: Pap´ılio was implemented in C.

4

The Choice of Better Polynomials

By simplicity and implementation’s performance, was considered for MV a CE and VA with the following parameters: codification rate ns = 12 , Q = 3 and m = 2. With this values we have 64 (2sQ ) possible polynomials. The idea is to analyze considering the behavior of each polynomials regarding to the avalanche effect (in the key and in the block), the diffusion and the confusion properties and to select the eight polynomials with better results.

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First Tests and Measure Used: First was made to each polynomials and operation mode a test for confusion and diffusion based on a book of project Gutemberg [4]. We extract from the book the first 3536 characters (including the spaces), despising the 400 first characters to erase the heading. The keys used in this test was (pseudo)randomly generated (all polynomials used the same keys). The test of avalanche effect (in the block and key) was realized on 50 blocks of plaintext and 50 keys randomly generated. To measure the avalanche effect in the block was used the arithmetic average of Hamming distances between the encryption of a plaintext block and the encryption (with the same key) of the same plaintext block changing a bit in all possible ways. Analogously, to measure the avalanche effect in the key was used the arithmetic average of Hamming distances between the encryption of a text block and the encryption of the same text block changing a bit on the key in all possible ways. The measure of diffusion was calculated using the standard deviation of frequencies of characters in the cyphertext. The confusion was measured using the average of Euclidean distances between the encryptions of plaintext with the original key and the plaintext with the original key changing only an unique bit. This result is divided by the greatest Euclidean distance possible, which allows us to normalize this value obtained a value between 0 and 1. The avalanche effect in the block for the modes ECB and CBC is, for the most of polynomials, between 0.45 (45% of bits, or more, are changed) and 0.51 which is a very good index, considering that the ideal value is 0.5. For the modes OFB and CFB, the avalanche effect is constant (0.0156), nevertheless it is not a problem of Pap´ılio, but of the modes, because we are measuring only the avalanche in an unique block, and therefore a change of a bit only affect an unique bit. The avalanche effect in the key still is better, because in the modes ECB and CBC 92% of polynomials matched between 0.48 and 0.51 and in the modes CFB and OFB 79% of polynomials matched between 0.48 and 0.51. The confusion in the modes ECB and CBC, the half of polynomials (50%) are between 0.38 (38%) and 0.41 which is not ideal (the ideal is similar to avalanche, i.e. 0.5 or 50%) but it is reasonable, more over if we consider that the Rijndael algorithm, using the implementation of Rijndael founded in [6] and in the same conditions of test, obtained confusion index of 40.5%. In the modes CFB and OFB, 47% of polynomials are between 0.38 and 0.41. In all operator modes we have more of 8 polynomials with confusion index greater than 40. The greatest diffusion index for the mode ECB was 0.0285 and 56% of polynomials have lesser than 0.02. In the mode CBC, the greatest diffusion index was 0.0255 and 81% of polynomials have an index lesser than 0.02. In the mode CFB, the greatest diffusion index was 0.0252 and 80% of polynomials have an index lesser than 0.02. Finally, in the mode OFB, the greatest diffusion index was 0.0257 and 80% of polynomials have an index lesser than 0.02. Thus, in any operator mode the symbols in the ciphertext have, practically, the same distribution which allows us to conclude that the statistical frequencies of symbols in the plaintext were destroyed. Therefore, there is not a statistical relation between the frequencies of symbols in the plaintext and the ciphertext.

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Similarity of Indices: In order to check if the indices obtained don’t depend strongly on texts and key, but only depend on polynomials used, we will make new tests for avalanche effect on the block and diffusion and then we will measure the degree of similarity between the results using the standard deviation of results. For the tests of avalanche was generated 100 series of 50 plaintext blocks and for the diffusion were made 100 series using only 3536 characters despising the 400 firsts of a book of Gutemberg project [4]. For each 10 series was used a different book. The avalanche affect on the block 98% of the polynomials have an standard deviation lesser than 0.06%, and the diffusion of all polynomials is lesser than 0.35%. Both results are very good, because indicate that Pap´ılio independently of the polynomials is very stable. Since the confusion and avalanche effect on key are, in some sense, subordinated to the avalanche effect on the block, we can conclude that both effects neither depend on the plaintext nor the key used. This also is true for the other modes. The Winner Polynomials: With the conviction that the Pap´ılio behavior depends quasi exclusively of polynomials, we will make a championship to determine the polynomial which provides to Pap´ılio the best cryptographic indices. Because the confusion strongly relates to avalanche in the block and the avalanche in the key as well as the diffusion obtained in all tests and in all polynomials well indices, beyond diffusion need more computational effort, we opted to only consider the avalanche effect on the block. The championship consisted in performing 50 news tests for avalanche effect in the block using keys and block generated randomly, at each test the polynomials that achieve the index more proximate of 50% gain a point. To avoid arrive in local optimum when a polynomial had 20 points this would classify for the next stage and the championship continued without it. In the next stage of championship was performed 100 test considering again random keys and blocks. The selected polynomials was those which obtained 50 points. For simplicity we only make the championship for the ECB mode.

5

Final Remarks

The empirical analysis showed that the proposal cipher has very good performance w.r.t. of avalanche, diffusion and confusion properties. However in spite that these properties are interesting and important, just having these properties does not mean that a cipher is secure. In order to conclude that Pap´ılio is reliable, yet is necessary a treatment of the security of Pap´ılio cipher considering modern cryptanalysis methods, such as linear cryptanalysis and differential cryptanalysis. This study will be made in further works. Considering that by the similarity degree only a few tests will be necessary to analyze the cryptographic indices of Pap´ılio for each polynomial. But even so, we perform a great number of reliable tests, resulting in the choice of eight polynomials. If we analyze the individual avalanche index round to round of each one of these polynomials we will see than we can already obtain very good

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indices from the round 6. This allows the thoght to reduce the rounds number, decreasing the execution time of Pap´ılio or yet turning it variable, which would difficult the cryptanalysis and would improve the execution time. Since MV can be applied to any length of block, we also can increase the size of the block which also would improve the execution time or variable in term of the key. Since we have eight good polynomials, we also could apply different polynomials to each round (the choice would be in function of the sub-key and current block) which would not increase considerably the computational effort but would increase considerably the cryptanalysis difficulty, once that for each block in the plaintext (fixing the key) we have 248 possible ways to encoder it (considering 16 rounds). But, considering that each polynomials if we changed the start state we will have four different results, then quantity of possible combinations of functions can arrive to 280 for each block!! which will turn eventually impossible the cryptanalysis without knowing the key, more over considering that the combination of polynomials and start states will change to each block, thus the knowledge of a combination for a block not will help to know the ciphertext. So, Pap´ılio is a very flexible cryptographic algorithm and with very good cryptographic indices.

References 1. Demirbas, K.: Target Tracking in the Presence of Interference, Ph.D. Thesis, University of California, Los Angeles, 1981. 2. Fleming, C.: A Tutorial on Convolutional Coding with Viterbi Decoding. Spectrum Applications, july, 1999. 3. Forney, G.D. Jr.: Convolutional codes II: Maximum-Likehood Decoding. Information and Control, 25(3)177-179, 1974. 4. Project Gutemberg. http://www.veritel.com/gutenberg/index.html. Access in march 2003. 5. Hopcroft, J.E. and Ullman, I.: Introduction to automata theory, languages and computation. Addison-Wesley, 1979. 6. OpenSSL project. http://www.openssl.org/ last modification in april, 17 of 2002. Access in april, 10 of 2003. 7. Pitas, I.: A Viterbi algorithm for region segmentation and edge detection. Proc. CAIP89, Leipzig, pp. 129-133, 1989. 8. Ryan, M.S. and Nudd, G.R.: The Viterbi Algorithm. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, England, February, 1993. 9. Schneier, B.: Applied Cryptography. 2nd Edition, New York, John Wiley & Sons, inc., 1996. 10. Stalling, W.: Cryptography and Network Security: Principles and Practice. 2nd edition. Prentice Hall, 1998. 11. Viterbi, A.J.: Error Bounds for Convolutional Codes and na Asymptotically Optimum Decoding Algorithm. IEEE Transactions on Information Theory, April 1967

A Parallel Optical Computer Architecture for Large Database and Knowledge Based Systems Jong Whoa Na Computer Engineering Dept., Hansei University, Kun Po Si, Kyung Gi Do, Korea [email protected]

Abstract. We propose a parallel electro-optical computer architecture that uses optical devices to exploit the data-level parallelism available in the database and knowledge base systems. The massive amount of data of the large database and knowledge base are represented in twodimensional space. The proposed system performs concurrent pattern matching operations using three-dimensional space. The execution speed is theoretically estimated and is shown to be potentially orders of magnitude faster than current electronic systems.

1

Introduction

The ever-increasing data of the multinational companies such as Citibank and GE now require the performance of the supercomputer[1]. Their business processes typically make use of very large database. What are emerging now are the facilities to make an intelligent decision by using the enormous amount of data. Rule-based Database System (RBMS) is an implementation for the intelligent database[2]. The engine of the rule-based system (RBS) is a resolution engine that requires the pattern matching operations. Since the size of the data is enormous, the pattern matching operation is the bottleneck of Rule-based Systems[3]. Also, CYC project implements the common sense reasoning system by incorporating enormous size of knowledge base[4]. Currently, the computers using the Neumann Architecture are used to solve the most of the symbolic applications as well as the numeric applications. These computers use the silicon hardware that has been the source of the remarkable developments in the computer hardware following the Moore’s law. However, these trends may end in the near future as the silicon technology approaches the physical limits. In order to overcome this problem, the researchers around the world have investigated novel computing methodologies such as molecular computing, quantum computing, and optical computing. Among these novel technologies, optical computing is more promising candidate since the optical technologies have been around us as the high performance data communication and networking fields such as optical fiber, WDM optical networking system as well as the imaging applications such as CMOS imaging sensors, projection display devices. In addition, due to its inherent parallelism, large spatial and J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 934–939, 2004. c Springer-Verlag Berlin Heidelberg 2004


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temporal bandwidth, and low crosstalk, optics can be a potential solution for the communication overhead and synchronization problem exposed by electronic parallel RBS. It has been known that optical interconnection networks offer many advantages over electrical counterparts[5]. In this paper, we propose a high performance Optoelectronic Integrated Circuit (OEIC)-based Expert System (OES) tailored for the high performance RBS implementations. Specifically, the architecture is designed for the hardware for CYC that uses the resolution principle. In addition, we tried to exploit the data-level parallelism available in the resolution operations by using the optical components[6]. The OES uses OEIC for parallel inference engine while electronics for the rest of the system. To take advantage of the OEIC properties, we represent facts and rules in two-dimensional space so that the proposed inference engine performs he three-dimensional processing. The inference engine is logically transformed into an optical interconnection network that can carry out inference optically and hence in a highly parallel passion.

2

Organization of the OEIC Expert System(OES)

The major objective of the OEIC-based Expert System (OES) is the exploitation of maximum parallelism in expert systems. Among many operations in RBS, performing the match operation is the most time-consuming operation. The reason is that the size of interconnection network between every fact and every condition elements grows rapidly as the size of the knowledge base increases. Although the processor technology now reaches 4 GHz clock speed, the speed of the internal bus or interconnection network is relatively slower due to the crosstalk, EMI interference, and power dissipation problems. Optical interconnect can be an alternative to this problem owing to the advantage of optical interconnects such as high speed, EMI immunity, and massively parallel structure. By using optical interconnect instead of electrical interconnect, OES can send as many input facts as possible to the condition elements of the rule. For OES, we have developed a translation algorithm that translates the knowledge base into the data format suitable for the execution in the OES. OES uses a 2-D array called Condition Table (CT) and an 1-D array called Fact Vector (FV) and one 1-D array called conflict set vector (CSV), as shown in Fig. 1. A rule consists of a condition part and an action part. In Fig. 1, each row of the condition table (CT) represents a rule and each pixel of the row represents a condition element of a rule. The condition part of a rule consists of conjunction of the condition element. In OES, the Object-Attribute-Value tuple of a predicate is evaluated as follows: Each entry of the input fact vector (FV) represents the Value of a fact that is to be compared with the Object of the condition variable. The Value, which was an optical signal, is converted into electrical signal using photodiodes. Then the Value and the Object are processed according to the Attribute in of the tuple is specified by the predicate. In this way, we can exploit the data-level parallelism.

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Fig. 1. Knowledge representation and operation principles in OES: FV, CT, and CSV represents fact vector, condition table, and conflict set vector respectively

The evaluation result of each row is converted back into an optical signal via a LASER or LED. These signals form the conflict set vector (CSV) representing the result of the evaluation of the condition elements of a rule in a given microtheory. In Fig. 1, the beam expansion implies sending the source of light representing a fact to multiple destinations representing the condition part of the rule. The light representing the value of a fact is spread (in parallel) into the four condition slots of a rule. Thus, parallel evaluation of the predicate is implemented. Likewise, beam collimation implies collecting the results of the evaluation of the condition elements of a rule. By using a collimating optics, the outputs of a rule from the CT are collimated into the CSV.

3 3.1

Architecture of OES OEIC-Based Match(OM) Module

The FT can be implemented using a two-dimensional VCSEL (Vertical Cavity Surface Emitting Laser) or a LED array. Each pixel of the source array consists of 8-VCSEL or 8-LEDs to represent the 8-bit data representation. The OM module consists of a CT, a beam splitter and two cylindrical lenses. The CT is an OEIC-based smart pixel array where each pixel consists of an 8-photodiodes, an 8-bit register, a comparison logic circuit, and an optical source such as VCSEL or LED. The 8-photodiodes are used to receive the optical input data from the FV. The 8-bit register is used to store the constant part of the condition element of a rule. The contests of the register are compared with the data from the FV at the comparison logic circuit. The comparison logic is designed to perform the magnitude comparison operations such as =,
=, >, ≥, ts(RCTL(x)) and whether PTi is arrived or not, it decides to wait for or to commit Tj. For example, for the read operations of Tj, rj(x), rj(y), and rj(z), suppose that ts(rj(x)) > ts(RCTL(x)), ts(rj(y)) > ts(RCTL(y)), and ts(rj(z)) > ts(RCTL(z)). If the timestamp of a transaction Tj is larger than the timestamp of propagation transaction PTi and PTi arrived, Tj can commit without delay. If PTi was not arrived, Tj waits for PTi until PTi arrives(arbitrary interval: maximum propagation time from a root to its terminal node in RT), and when PTi arrives, if ts(Tj(x)) > ts(RCTL(x)), PTi executes and Tj commits. If ts(Tj(x)) < ts(RCTL(x)), Tj aborts regardless of the arrival of PTi according toTSO rule.

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2.2.2 Propagation of Updates When an update transaction commits, the coordinator of the transaction submits its update operations to the corresponding primary sites. The coordinator decides the commit of a transaction using 2PC protocol after the transaction executed its all operations. After completing update operations of the committed transaction at all its primary sites, its propagation transaction is created for each update and is propagated along the its RT. If the coordinator site does not correspond to primary site, it should inform the primary site of the result of decision. The primary site received the commit decision updates its own RCTL information and propagates its update results to its children in the tree after it executes update operations. The timestamp of the committed transaction is assigned to the update operation to be propagated. When the read-only transaction commits, for all data x not in the primary site, it informs the primary site of x of the fact that it has committed. CAM-RT algorithm is described by pseudo code briefly as follows.

begin When a transaction T is submitted to a site Si; if (T is a propagation transaction PT) perform PT-propagation; /* propagate the updates*/ if (T is a Transaction) TM assigns unique timestamp to T; perform OP-distribution;/*distribute operations to execute*/ perform OP-schedule; /*schedule operations from scheduling queue according to TSO rule*/

if (the execution of last operation in T finished) /*start 2PC after a coordinator executed the last operation of T */ perform 2PC-1phase; /*execute 1st-phase of 2PC protocol*/ perform 2PC-2phase; /*execute 2nd-phase of 2PC protocol*/

end. /* 2PC-1phase */ begin if (operations executed in other sites exist) a coordinator sends a vote request to all participants;

if (operation executed in the participants == w(x)) vote YES/NO to coordinator whether executed or not; if (operation executed in the participants == r(x)) /*check up of existence of transaction committed while executing*/

poll RCTL information to the primary site of x ; if (ts(T) < ts (RCTL(x)) vote NO to coordinator; else if ( w_ts(x) == ts(RCTL(x)) vote YES to coordinator; /*PT arrives */ else { wait until PT arrives; execute PT as soon as PT arrives; vote YES to coordinator; } end;

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3 Performance Evaluation To evaluate the performance of the proposed algorithm, we performed simulation experiment using CSIM(C SIMulator) simulator. We use transaction abort ratio and response time as performance measures. The proposed algorithm(CAM-RT) has been compared with existing methods(LHD) while varying three parameters: the number of nodes(sites), the replicas ratio, and the read operation ratio. The unit of response time is milliseconds. The result of simulation is as follows. First, the performance comparison has been done while varying the rate of read operations: 10, 30, 50, 70, and 90%. Read ratio means the rate of read operations to write operations. The result of simulation is shown as in Fig.2. Next, we simulated two algorithms while varying replicas rate; 20%, 40%, 70%, and 100%. The replicas ratio means the number of replicas nodes for the number of total nodes. The result of simulation is shown as in Fig.3. Third, we experimented LHD and CAM-RT while varying the number of nodes;7, 10, and 15. The node means a server or a site. The result of simulation is shown as in Fig.4. The simulation result shows that CAM-RT has better performance than LHD since the transaction abort ratio and the response time are reduced.

0.7 0.6 tio0.5 ar 0.4 rt o0.3 b a 0.2 0.1 0

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10 #nodes

20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

) s m ( e im t e s n o p s e r

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Fig. 2. Abort Ratio and Response Time for the Read Operation Ratio

0.8 0.7 0.6 tio0.5 a r rto0.4 b a0.3 0.2 0.1 0

LHD CAM- RT

10%

30% 50% 70% R/ W ratio

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10000 9000 8000 7000 m 6000 ti e 5000 s n o 4000 p s 3000 e r 2000 1000 0 ) s m ( e

LHD CAM- RT

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Fig. 3. Abort Ratio and Response Time for the Replicas Ratio(Write-Operation Ratio 0.1)

Transaction Processing in Partially Replicated Databases

0.7 0.6 0.5 io t ra0.4 tr o0.3 b a 0.2

LHD CAM- RT

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Fig. 4. Abort Ratio and Response Time for the Number of Nodes

4 Conclusion Recently, there is a tendency that databases are to be scalable and to be partially replicated according to the degree of importance and necessity of data. For preserving consistency in the partially replicated databases, the replication management needs an efficient update propagation method that guarantees serializable execution. This paper proposed the updates propagation method CAM-RT based on the replicas tree of each data. It can be applied to the ubiquitous environment that needs partially replicated databases. The proposed method guarantees the serializable execution of transactions by using timestamp and SDB. It reduces the updates propagation delay since it uses a tree of replicas that needs only to be updated. SDB of each site holds PSL and RCTL. It is necessary for propagating update operations as fast as possible and for avoiding the conflicts between transactions and lazy propagation transaction. Through the simulation experiment, we compared CAM-RT with a representative method LHD while varying the number of sites, replicas ratio, schedule time, and read operation ratio. We found out performance improvement of our method compared to LHD since our method can reduce the transaction abort ratio and response time.

Acknowledgement This work was supported by Korea Science and Engineering Foundation (KOSEF #R05-2003-000-10532-0).

References [1] Jim, G., Pat, H., Patrick, O., Dennis, S.: The Danger of Replication and a Solution. In Procs. of ACM SIGMOD International Conf. on Management of Data, Montreal Canada (1996) 173-182 [2] Todd, A., Yuri, B., Henry, F.K. , Avishai, W.: Replication, consistency and practicality: Are these mutually exclusive?. In Procs. of the ACM SIGMOD International Conf. on Management of Data, Seattle WA (1998) 484-495

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[3] Xiangning, L., Abdelsalam, H. and Weimin, D.: Multiview Access Protocols for Large Scale Replication. ACM Transaction on Database Systems Vol.23 No.2. (1998) 158-198 [4] Yuri, B., Henry, F..K.: Replication and Consistency: Being lazy helps sometimes. In Procs. of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Tucson Arizona (1997) 173-184 [5] Esther, P., Eric, S.: Update Propagation Strategies to Improve Freshness in Lazy Master Replicated Databases. VLDB Journal ( 2000 ) 305-318 [6] Marta, P.M., Ricardo, J.P, B.Kemme, G.Alonso: Scalable Replication in Database Clusters. In Proc. of Distributed Computing Conf. DISC'00 volume LNCS1914, Toledo Spain (2000) 315-329 [7] Theodore, J., Karpjoo, J.: Hierarchical Matrix Timestamps for Scalable Update Propagation. http://w4.lns.cornell.edu/~jeong/index-directory/hmt-paper.ps (1996)

Giving Temporal Order to News Corpus Hiroshi Uejima1 , Takao Miura1 , and Isamu Shioya2 1

2

Dept. of Elect. & Elect. Engr., HOSEI University, 3-7-2 KajinoCho, Koganei, Tokyo, 184–8584 Japan Dept. of Management and Informatics, SANNO University, 1573 Kamikasuya, Isehara, Kanagawa, 259–1197 Japan

Abstract. In this investigation, we propose a new mechanism to give temporal order to a news article in a form of timestamps. Here we learn temporal data in advance to extract ordering by means of incremental clustering and then we estimate most likely order to news text. In this work, we examine TDT2 corpus and we show how well our approach works by some experiments. Keywords: TDT, Stream data, Incremental Clustering, Timestamp Estimation.

1

Motivation and Big Pictures

Recently we have seen many news texts supplied constantly through internet from multiple sources. About some of them we know explicitly when and what kinds of affairs happen, but not about others. This environment drives many researchers to put much attention on grasping their contents easily and quickly. One of the typical approaches is Topic Detection and Tracking (TDT)[1, 4]. In TDT tasks, data are processed in temporal order and all the data are assumed to carry temporal information explicitly or implicitly. Without any temporal aspects, we can’t harmonize any data into consistent states through the tasks. If we can give timestamp to news text with strong confidence, we could capture topics or trends of articles more easily and smoothly so that we could extract closer and deeper relationship among articles. In this investigation, we discuss how to estimate timestamp to a news article n using a collection M of articles where each article of M carries temporal aspects. Intuitively it seems better to look for m1 ∈ M which is the most similar to n and then to put the timestamp of m1 to n. But it is not really nice because the similarity among articles doesn’t always mean the similarity among topics. Here we take event detection and tracking approach, and estimate timestamp to n based on the event which n belong to. Therefore, our timestamp estimation process is according to following outline. (1)Clustering from (temporal) news texts M into events, (2)Assignment the most suitable cluster C(that was created in (1)) to the news n. (3)Looking at C we extract timestamp value and put it to n. From the view point of machine learning, the process above corresponds to J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 947–953, 2004. c Springer-Verlag Berlin Heidelberg 2004


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supervised learning where training data means clusters C and the classification problem means timestamp estimation. In first step of our timestamp estimation, we make clustering M (that are collection of stream data with timestamp) as the materials to predict the timestamp and event(cluster) of n. In TDT activity, it is well-known [8] that temporal clustering works very well with event detection, that is, very often an event corresponds to a temporal cluster1 . Here we introduce a Forgetting function[3] to reflect temporal distance among documents in stream for clustering of M . Moreover, M grows continuously since M is text stream, and we have to think about incremental clustering. In this investigation, we discuss a general batch clustering algorithm to compare incremental ones. Here we take Single Pass Clustering[5, 8] as a incremental method and k-means as a batch method. Second step of our timestamp estimation is assignment of news n to the most suitable cluster created in former step. To estimate timestamp of n based on the event which n mentions, we have to predict the event of n by the cluster assignment. Here we propose two cluster assignment methods, the top 10 method (TOP10) and the Nearest Neighbor method (NN). Finally, we estimate a timestamp of a news article n by result of clustering of collection M and event(cluster) assignment of n, which is the main topic of this paper. Here we give the estimation of the timestamp based on “Similarity of n and some articles m (m ∈ M ) that are top 10 articles similar to n and belong to the cluster C that is assigned to n” and “Timestamp distribution of the cluster C”. We should examine the timestamp distribution of a cluster because a collection of news articles arise in a short period [1]. This timestamp estimation is called TOP10 method. To evaluate the timestamp estimation based on event, we propose the nearest neighbor method (NN). In our experiments, we have to evaluate not only timestamp estimation but also clustering of M and event assignment of n since we estimate timestamp to n based on the event which n belong to.

2

Incremental Clustering

In this investigation, we represent a document X as follows: (1)Vector of term weight X = (t1 , ..., tn ), (2)j-th value tj in a documentX means term frequency T F (j) of the j-th word, (3)Utilizing only noun and proper noun words for the document expression by BrillTagger. Similarity of a document X and a cluster C (sim(X, C) where the center is VC is defined by cosine similarity of X and VC . Forgetting function wλ (t) is defined as wλ (t) = λt where λ means forgetting speed (0 ≤ λ ≤ 1.0). We define a timestamp timeC of a cluster C as the last timestamp of a document in the cluster C. We denote current by timenow . Then we extend a notion of similarity sim involving the function λ as follows. 1

Thus, we can say that event detection is deeply related with clustering while topic tracking corresponds to dynamic classification of the clusters.

Giving Temporal Order to News Corpus

sim (X, C) = wλ (|timenow − timeC |) × sim(X, C)

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(1)



In the following, we apply a single pass clustering with sim to text stream.

3

Assigning Clusters

In this section, we discuss how to assign a cluster (event) to a news text n by clustering result of M as the second step of our timestamp estimation. – TOP10 method: We select the cluster of n by means of voting by top 10 articles similar to n. i.e., we obtain the top 10 articles similar to a n from a collection M and select a cluster C that accounts for the most articles. For example, in a figure 1,the readers see a news document n belongs to C1 by TOP10 method. – NN method: We take the most similar document m to a n and select the cluster which m belongs to. For example, in a figure 1, a new document n belongs to C3 by NN method.

Fig. 1. Selecting a cluster for an article n

4

Fig. 2. Timestamp Estimation of 5 articles

Estimating Timestamp

In this section, we discuss how to estimate a timestamp of a news article n. By NN method, we put the timestamp of the most similar article to n. For example, in a figure 1, the most similar article m is in C3 , and we estimate the timestamp of n as the one of m. By Top10 method, we look for the top 10 articles similar to n and extract the articles TC from the 10 articles which belong to the cluster C that is assigned to n. Then we estimate timestamp of n from TC and n. In a figure 1, among the top 10 articles similar to n, we take 5 articles in a cluster C1 and estimate the timestamp. Let tC be an article in TC . Then we give the estimation of the timestamp by the following rule: T Sn,tC ,λ (date) = sim(tC , n) × distr(C, timetC ) × wλ (|timetC − date|)

(2)

This equation is illustrated as a curve of timestamp estimation where a function distr(C, timetC ) means the number of articles at time timetC according to

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a distribution in a cluster C . Here we introduce all the sum to tCi ∈ TC of the timestamp estimation T S obtained by equation 2:
T Sn,tCi ,λ (date) (3) T Sn,TC ,λ (date) = tci ∈TC

For example, in a figure 1, we have 5 articles in TC1 and a figure 2 shows our curve of timestamp estimation. Here to evaluate the timestamp estimation, we introduce allowable error of timestamp which is the maximum difference between true timestamp and estimated. Based on allowable error, we maximize all the sum of difference within the error constraint, and the timestamp value daten is given by:  date+m T Sn,TC ,λ (date) daten = MaxArgdate date−m

For example, in figure 2, given an allowable error m days, we give timestamp (daten ) by which we get the maximized sum of timestamp estimation before and after m days.

5

Experimental Results

5.1

Datasets and Protocol

In this experiments, we examine TDT2 corpus. Settings of our experiments are shown below: “ Examine news stories in English”, “ Utilizing transcribed broadcast news stories as training data like M , and newswired stories as test data like n”, “Examining only 4 topics that have are more than 200 articles in both Broadcast and Newswire with confirmation tag YES”, “Assuming these news make quick reports and generally we can expect transaction time means valid time”. We process TDT2 data in transaction time order. Here we assume that k-means results represent situation in reality since we don’t have the correct answer of event. Let C1 , ...., Cx be the results by single pass clustering, K1 , ..., Ky 2 be the results by k-means clustering. We want to examine which cluster in C1 , ..., Cx is the most similar to a cluster Ki . To do that, we count the number of articles in both Ki and Cj for j = 1, .., x, and select Cj of the maximum. Then we say Ki corresponds to Cj . In the same way, given a cluster C, we select a cluster event as the most dominant topic in the articles of C. 5.2

Evaluation Criteria

We compare TOP10 method based on incremental and batch clustering techniques, and NN method with each other (thus 3 cases in total) from the 3 points of views as follows. 2

In our experiment, we give k as the double number of the number of clusters C1 , ..., Cx , i.e., k = 2x.

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– clustering(clustering accuracy = β/α): whether incremental approach is really comparable to batch approach and topics or not. where α is the number of the total input articles, and β is the number of articles which are assigned to both Ki and Cj (i,j=1,...) with respect to batch clustering, and it is the number of articles of which topic is same as the one of the cluster assigned from the view point of topics. – event assignment(event accuracy = γ/α): whether clustering results correctly describe events obtained by the refinement of topics of TDT2 or not. where γ is the number of articles of which topic is same as the dominant one of a cluster C assigned with respect to topics, and it is the number of articles of which topic is correctly estimated with respect to batch clustering. When n is assigned to C in incremental clustering and K in batch clustering, we say “ topic is correctly estimated”. – timestamp estimation(timestamp accuracy = δ/α): whether estimated timestamp falls in the correct date with allowable error or not. where δ is the number of articles of which timestamp is correctly estimated. In this experiments, we give two cases of allowable error (1 week and 1month). Whenever we apply a single pass clustering algorithm to a collection of broadcasted news articles at a date tm, we give timestamp to all of the newswired articles that have appeared before tm. We examine 3 accuracy in every month. 5.3

Results

First of all let us show clustering accuracy by means of incremental and batch clustering. As the readers see, we have extremely good results here. Note that we say a cluster is meaningful if the cluster contains more than 5 articles and we got 21 clusters eventually after the above processes (in 6 months). Thus we give k = 42 to k − means clustering. A table 2 contains the results of event accuracy in incremental and batch approaches. In any aspects, we have excellent results here. Finally let us show timestamp accuracy in two cases of 1 week allowance and of 1 month allowance (a table 3,4, a figure 3). Table 1. Clustering Accuracy of TDT2 Jan. Feb. Mar. Apr. May June k-means 86.16 79.81 77.72 81.98 79.26 88.68 topic 96.89 96.11 96.38 96.55 96.7 97.04

5.4

Table 2. Event Accuracy in TDT2 k-means k-means topic topic

TOP10 NN TOP10 NN

Jan. 83.72 80.23 93.80 95.16

Feb. 85.78 83.74 96.62 96.31

Mar. 75.95 71.57 96.53 95.90

Apr. 81.29 75.83 96.67 96.40

May 81.93 74.62 97.07 96.25

June 86.03 74.59 96.81 96.69

Discussion

As shown in a table 1, we got high quality (more than 80%) of clustering accuracy to the comparison with batch approaches. With respect to topics, every test shows more than 96% thus we can say every cluster corresponds to an event.

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Table 3. Timestamp accuracy in Allowable Error of 1 Week Jan. Feb. Mar. NN 70.93 57.11 51.91 k-means TOP10 69.19 59.15 53.96 incremental TOP10 73.06 60.88 55.30

Apr. 48.27 50.93 53.00

May 44.91 49.55 49.81

June 43.59 46.6 47.38

Table 4. Timestamp accuracy in Allowable Error of 1 Month Jan. Feb. Mar. NN 100 93.72 87.27 k-means TOP10 100 96.78 90.95 incremental TOP10 100 98.59 91.09

Apr. 80.83 83.69 85.62

May 75.13 81.36 82.12

June 72.55 77.24 78.33

Fig. 3. Timestamp Accuracy

Looking at a table 2, we got good event accuracy, say about 80% by TOP10 and NN methods on incremental clustering compared to the cases of batch clustering. Event accuracy wrt topics also shows almost 95%. As for timestamp accuracy, we got almost same results by either batch or incremental approach as in figures 3: we got 50% with allowable error 7 days, and more than 70% with allowable error 1 month. Compared to NN method, TOP10 method is generally superior and suitable for timestamp estimation. In TDT2 corpus, each event depends heavily on temporal aspects, thus the results by TOP10 are not really affected by long allowable error. In fact, in figures 3, the longer error becomes, the bigger difference arises between TOP10 and NN. Let us discuss the correlation of event accuracy and timestamp accuracy. Tables 5 contain the correlation to all the 6 months articles by incremental TOP10 approach. In a case of allowable error of 7 days, we see Table 5. Incorrect Timestamp correct topic incorrect topic

correct TS incorrect TS 778 830 9 44

(a) Error 7 days

correct topic incorrect topic

correct TS incorrect TS 1262 346 39 14

(b) Error 30 days

topics are correctly assigned to 1608 (=778+830) articles but timestamps are incorrectly estimated to the half of them. On the other hand, we see topics are incorrectly assigned to 53 (=9+44) articles and timestamps are incorrectly estimated to more than 80% of them. In a case of 30 days we have the similar story, which means timestamp estimation based on event detection works well. In a single pass clustering, we got the best result with a threshold h = 0.24 and a forgetfulness function of λ = 0.97. We have examined several cases and obtained empirically optimal values though we couldn’t get any useful characteristics to clustering. This is because TDT2 contains only articles in 6 months and are not enough to analyze them.

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Conclusion

In this investigation, we have discussed how to estimate timestamp aspects of news articles by clustering news stream in an incremental mode. Our experiments show that we expect about 50% accuracy against 1 week error allowance of TDT2 news corpus.

Acknowledgements We are very grateful to Prof. Wai Lam in Chinese University of Hong Kong for his sincere help.

References 1. Allan, J., Carbonell, J., Doddington, G., Yamron, J. and Yang, Y.: Topic Detection and Tracking Pilot Study: Final Report, proc. DARPA Broadcast News Transcription and Understanding Workshop (1998) 2. Fukumoto, F. Suzuki, Y. et al.: Detecting Shifts in News Stories for Event Tracking, IPSJ Journal 44-7, pp.1766-1777, 2003 (in Japanese) 3. Ishikawa, Y. ,Chen,Y. and Kitagawa, H.: An On-line Document Clustering Method Based on Forgetting Factors, in Proc. 5th European Conference on Research and Advanced Technology for Digital Libraries (ECDL’01),2001 4. National Institute of Standards and Technology (NIST): http://www.nist.gov/speech/tests/tdt/ 5. Papka, R. and Allan, J.: On-line new event detection using single-pass clustering, Technical Report UMASS Computer Science Technical Report 98 - 21, Department of Computer Science, University of Massachusetts, 1998 6. Uejima, H., Miura, T. and Shioya, I.: Improving Text Categorization by Synonym and Polysemy, IEICE Trans.on Info.& Systems J87-D-I-2, pp.137-144, 2004 (in Japanese) 7. Wayne, C., Doddington,G. et al.: TDT2 Multilanguage Text Version 4.0 LDC2001T57, Philadelphia: Linguistic Data Consortium (LDC), 2001 8. Yang, Y., Pierce, T. and Carbonell,J.: A Study on Retrospective and On-Line Event Detection, Proc. SIGIR-98, ACM Intn’l Conf. on Research and Development in Information Retrieval, 1998

Semantic Role Labeling Using Maximum Entropy


Kwok Cheung Lan, Kei Shiu Ho, Robert Wing Pong Luk, and Hong Va Leong Department of Computing, The Hong Kong Polytechnic University, Hong Kong {cskclan, csksho, csrluk, cshleong}@comp.polyu.edu.hk

Abstract. In this paper, semantic role labeling is addressed. We formulate the problem as a classification task, in which the words of a sentence are assigned to semantic role classes using a classifier. The maximum entropy approach is applied to train the classifier, by using a large real corpus annotated with argument structures.

1

Introduction

The problem of semantic role labeling was first formally studied by Gildea and Jurafsky [1]. They divided the task into two sub-problems: argument identification and role classification. The semantic role classifier was built based on likelihood probabilities, which were maximized by linear interpolation. The inputs to the classifier included syntactic features generated by full parsing. Their work has been extended along various directions. For example, Gildea and Palmer [2] used shallow parsing instead of full parsing for generating the syntactic features. Works have also been done that used other grammar formalisms instead of the traditional phrase-structure grammar, like combinatory categorial grammar [3] and tree adjoining grammar [4], to evaluate how syntactic representation affected classification accuracy. On the other hand, various learning algorithms were applied for training the classifier, such as conditional learning [1], generative learning [5], and discriminative learning [6]. Considerable success has been achieved. Researchers have also attempted to use different types of features, particularly semantic features, to improve the performance of semantic role classification [7]. Existing approaches also differed in the granularity of the elements labeled. In the word-by-word approach [2, 6], each individual word is separately classified into one of the semantic role classes. In the constituent-by-constituent approach [1], the words of the input sentence are first grouped into syntactic constituents of varying sizes as identified by full parsing, and a semantic role label is then assigned to each constituent. In the chunk-by-chunk approach [8], syntactic phrases, as generated by shallow parsing, are separately labeled.


The work described in this article was fully supported by a grant from The Hong Kong Polytechnic University (4Z03D).

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 954–961, 2004. c Springer-Verlag Berlin Heidelberg 2004


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Previously, Ratnaparkhi [9, 10] proposed the Maximum Entropy (ME) approach to natural language processing, viewing the task as a classification problem to assign a class label a ∈ A to a linguistic context b ∈ B. To tackle the problem, a large data set is employed from which co-occurrences of different combinations of a’s and b’s are recorded. They are called observed events. The classifier is then defined by estimating the probability distribution p(a, b) that is consistent with the observed events. In this way, given a linguistic context b ∈ B, the probability p(a|b ) is estimated for each possible a ∈ A, and b is assigned to the class a where a = arg maxa∈A p(a|b ). In general, more than one probability distribution may be found. Yet, some combinations of a’s and b’s may appear only a few times in the data set, such that the frequency of occurrence is not statistically significant. In that case, out of the possible p’s, the one that maximizes the entropy of p should be selected, based on the Principle of Maximum Entropy [11]. The ME approach has previously been applied to various natural language problems, like part-of-speech tagging [12] and parsing [13]. In this paper, the maximum entropy approach is applied to tackle the semantic role labeling problem, following Ratnaparkhi’s formalism closely [9, 12, 10, 13]. A large data set called PropBank [14] is assumed, which contains real sentences annotated with predicate-argument structure. A set of feature functions are designed and co-occurrence statistics are collected from the data set, which are used to approximate a probability distribution for labeling the semantic roles of the words of unseen sentences, based on the word-by-word approach.

2 2.1

Modeling Semantic Role Labeling Using ME Data Set

Two data sets are commonly employed in semantic role labeling research, namely, FrameNet [15] and PropBank (Proposition Bank) [14]. The strength of FrameNet is that target words are annotated with word senses. Moreover, besides verbs, adjectives and nominal phrases are annotated. The sentences are also shorter, thus avoiding ambiguities. Despite these advantages, we have adopted PropBank in our study for several reasons. First, the sentences in PropBank are longer and more complex. They are thus more suitable for real-world applications. Since PropBank is created from TreeBank [16], it contains richer syntactic information than FrameNet. Moreover, the sentences have a more even coverage of the predicates. So the data is less sparse, which helps classification performance. However, the formal release of PropBank is not publicly available until recently. As a result, we replicate a subset of PropBank using TreeBank. Since the sentences in TreeBank are represented as phrase structure trees originally, they need to be “flattened” first. Phrase position is then assigned to each word, using a perl script contributed by Tjong and Buchholz [17]. Each word is annotated by two more features: part-of-speech and semantic role. While the part-of-speech label can be directly adopted from TreeBank, the semantic role information has to be derived from the predicate-argument structure of the sentence. The semantic role classes are encoded using the IOB2 format [18]. The total number of

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semantic role classes is 438. Table 1 shows the top few classes in terms of their occurrence frequencies in the data set. Among the 438 classes, 75 of them (i.e., 17.1%) occur only once in the data set. This causes a sparse data problem to the classifier. Fig. 1 shows an example of an annotated sentence. We name the resulting data set Replicated PropBank, which contains 53,022 annotated sentences. Totally, there are 1,440,594 tokens. So, each sentence consists of about 27 tokens. There are 1,564 unique predicates, with most of them (about 42.8%) occurring fewer than 10 times in the data set. These predicates appear in about 5.03% of the total sentences only. This creates another sparse data problem, making it difficult to generalize on their argument structures. Table 1. Distribution of the semantic roles in the data set O

Semantic role

I-ARG1 I-ARG0 B-ARG1 I-ARG1 I-ARGM-ADV Others

Occurrence frequency 743,732 255,041 77,886 44,821 35,516 Occurrence percentage 51.63% 17.70% 5.41% 3.11% 2.47%

Word

An

IBM spokeswoman said

the

POS

DT

NNP

NN

VBD

DT

B-NP I-NP

I-NP

B-VP B-NP

Phrase position Semantic role

O

O

O

company told customers Monday about NN

VBD

NNS

NNP

I-NP

B-VP

B-NP

B-NP

O

O

O

O B-ARG0 I-ARG0

IN

the

bugs and

DT

NNS CC

B-PP B-NP I-NP O

O

O

O

29,903 2.08%

temporarily stopped

253,695 17.61%

shipping

the

product

RB

VBD

VBG

DT

NN

.

B-VP

I-VP

I-VP

B-NP

I-NP

O

O B-ARGM-TMP

rel

.

B-ARG1-PRD I-ARG1-PRD I-ARG1-PRD O

Fig. 1. Example showing how a sentence is annotated

2.2

Encoding Feature Functions

Each sentence in the Replicated PropBank is encoded using the set of features shown below, based on a 5-word sliding window approach [6]: – – – – – – – –

Predicate (pred) Word (w) Part-of-speech (pos) Phrase position (p pos) Previous role (r) Word position (w pos) Voice (v) Path (p)

Consider the sentence shown in Fig. 1. When the sliding window is centered at “customers”, the encoded feature vector is as shown in Table 2. The correct semantic role prediction is “O”. With reference to the maximum entropy approach, the set of all feature vectors constitute the set of linguistic contexts B while the set of all possible semantic roles form the set of class labels A. The feature vector, together with the semantic role prediction, form an event. Duplicate events are filtered. The events are then used for generating the binary feature functions fj ’s for maximum entropy modeling. In general, for each event, a feature function fj is defined by pairing one of its 21 features with the semantic

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Table 2. Example of encoded feature vector (sliding window centered at “customer”) pred

pred = stopped

w pos p pos r w pos v p

w0 = customers w-1 = told w-2 = company w+1 = Monday w+2 = about pos0 = NNS pos-1 = VBD pos-2 = NN pos+1 = NNP pos+2 = IN p pos0 = B-NP p pos-1 = B-VP p pos-2 = I-NP p pos+1 = B-NP p pos+2 = B-PP r-1 = O r-2 = I-ARG0 w pos = before v = active p = NNS → NP → NP → PP → NP → O → VP → VBD

role label (with duplicate feature functions being filtered). For example, given the feature vector in Table 2 and the semantic role label “O”, the following feature function is defined:
fj (a, b) =

1 0

: :

if a = O & pos0 (b) = NNS otherwise

The expectation of fj is equal to Ep˜[fj ] =

N  i=1

(1)

p˜(ai , bi )fj (ai , bi ) =

1 N

N  i=1

fj (ai , bi ),

p(ai , bi ) being its observed probability where (ai , bi ) is the i-th observed event (˜ of occurrence) and N is the total number of unique events. 2.3

Training the Classifier

Given a set of sentences, feature functions are defined for finding a probability distribution p that satisfies the constraints: Ep [fj ] = Ep˜[fj ] for j = 1, 2, . . . , k (k being the number of feature functions). In general, more than one p may be found. Based on the Principle of Maximum Entropy [9, 11], the most appropriate probability distribution, denoted by p∗ , should be the one that maximizes the entropy H(p):  H(p) = −

p(a, b) log p(a, b)

(2)

a∈A, b∈B

p∗ = arg maxp∈P H(p)

(3)

Ratnaparkhi [9] showed that p∗ should have the following form: p∗ (a, b) =

k 1  fj (a,b) αj Z(b)

where 0 < αj < ∞

(4)

j=1

Here, Z(b) =

k   a∈A j=1

αj fj (a,b) is a constant to ensure that

 a∈A, b∈B

p∗ (a, b) = 1.

The αj ’s are called model parameters, with αj corresponding to the weight for the j-th feature function. They can be found by an iterative algorithm called Generalized Iterative Scaling (GIS) [9]. 2.4

Labeling Sentences

After finding p∗ , the classifier can be used to assign semantic roles to an unseen sentence. During operation, the words in the sentence are labeled one by one in

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Let the input sentence be w1 , w2 , . . . , wn , where wi are the words; U ← ∅; for i = 1 to n do if (U = ∅) then Encode w1 to give feature vector b1 ; U
← {(a, p∗ (a|b1 )) | a ∈ A}; else repeat Remove an element (S, p∗ (S)) from U ; Let ai−2 and ai−1 be the last two semantic roles of S; Encode wi to give feature vector bi (wi−2 and wi−1 being labeled by ai−2 and ai−1 ); X ← {(a, p∗ (a|bi )) | a ∈ A}; U
← ∅; for j = 1 to N do Remove (a
, p∗ (a
|bi )) from X where ∀(a, p∗ (a|bi )) ∈ X, p∗ (a
|bi ) ≥ p∗ (a|bi ); Append a
to S to give S
; Compute p∗ (S
) ← p∗ (S) × p∗ (a
|bi ); Add (S
, p∗ (S
)) to U
; until (U = ∅); for j = 1 to N do Remove (S
, p∗ (S
)) from U
where ∀(S, p∗ (S)) ∈ U
, p∗ (S
) ≥ p∗ (S); U ← U ∪ {(S
, p∗ (S
))}; Remove (S
, p∗ (S ∗ )) from U where ∀(S, p∗ (S)) ∈ U , p∗ (S ∗ ) ≥ p∗ (S); Output S ∗ as the sequence of semantic roles labeling the words of the sentence;

Fig. 2. Beam search algorithm. For a sequence S = a1 , a2 , . . . , ak , p∗ (S) denotes the joint probability that the word wi is labeled by ai , where i = 1, 2, . . . , k

a left-to-right manner. Given a word w, a feature vector bw is generated, The most appropriate semantic role aw of w can thus be found: aw = arg maxa∈A p∗ (a|bw )

(5)

However, the feature vector of a word depends on the semantic roles assigned to its preceding words in the sentence. As a result, one is faced with a sequence labeling problem. Beam search is thus employed, following [12], for finding an appropriate sequence of semantic roles for a sentence. The algorithm is shown in Fig. 2, which is characterized by a parameter called beam size, denoted by N . In the experiments (see Section 3), a beam size of 3 was used. Other values were tried also, but no significant impact on performance was noted.

3

Experimental Evaluation

Out of the 53,022 sentences in the replicated PropBank, 50,000 sentences were randomly selected. The data set was shuffled and divided into two sets equally: 25,000 sentences for training and 25,000 sentences for testing. The 25,000 training sentences were first used for finding the target probability distribution p∗ , using the GIS algorithm. The number of iterations was set to 100. The resulting classifier was then evaluated, by measuring its performance in assigning semantic roles to unseen sentences in the testing set. With 10-fold cross validation, our system achieved 63.3% precision, 51.4% recall and 56.37% F1-measure, as shown in Table 3. The classification performances for different semantic roles varied. Table 4 shows the top 10 classes in terms of classification accuracy.

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Table 3. Evaluation results of our approach 1

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Average

Precision 65.42% 49.74% 64.78% 64.90% 64.75% 64.50% 64.86% 64.61% 64.38% 64.78% 63.27% Recall 50.54% 64.80% 50.05% 50.00% 49.80% 49.67% 49.84% 49.73% 49.68% 49.91% 51.40% F1-measure 57.03% 56.28% 56.47% 56.48% 56.30% 56.12% 56.37% 56.20% 56.08% 56.38% 56.37%

Table 4. Classification performances for some of the semantic role classes Semantic role Precision Recall F1-measure

ARGM-MOD ARG2-EXT ARGM-NEG

ARG0

ARG4-to

ARG3-from ARGM-EXT

ARG3-on

ARG1

ARG0-by

87.98% 83.65% 80.28% 75.16% 77.80% 81.85% 82.03% 100.00% 60.32% 59.82% 73.21% 70.62% 68.81% 64.88% 60.61% 55.92% 49.76% 42.86% 56.15% 54.36% 79.92% 76.58% 74.10% 69.64% 68.14% 66.45% 61.95% 60.00% 58.16% 56.96%

In general, classification performance varies for different number of training sentences used. Thus, several sets of experiments were performed, each using a different number of training sentences. As depicted in Fig. 3, classification performance steadily improves as the number of training sentences is increased. The effect of the beam size has been studied. A set of 10,000 sentences were randomly selected for training the classifier. Another set of 10,000 sentences were randomly selected from the remaining 40,000 sentences for testing. Classification performance was evaluated using both training and testing sentences. The results in Fig. 4 indicate that the beam size has no significant performance implication. To further evaluate our system, we compare its performance with other approaches. The results are shown in Table 5. Note that the works by Baldewein et al. [19] and Lim et al. [20], which also applied the maximum entropy approach to the semantic role labeling problem, were only published recently in the CoNLL2004 shared task (i.e., May 2004). As such, we believe that their works and ours are concurrent works. 70%

65%

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Fig. 4. Effect of the beam size on the performance of the semantic role classifier Table 5. Performance comparison with other approaches

As depicted, the other two works applying the maximum entropy approach outperform ours marginally. We argue that it is mainly due to the larger number of classes involved. In our work, the total number of classes is 438, with a significant proportion of them occurring only once in the data set, causing serious data sparseness problem. In contrast, in the CoNLL-2004 shared task, there were 75 classes only. Hence, the classification task was inherently easier. In addition, their data sets contained richer features, such as clauses and named entities, which are absent from our replicated PropBank. These extra input features can definitely help classification performance. Moreover, they adopted the chunk-bychunk approach whereby phrases instead of individual words were labeled. But in our approach, each word is separately labeled and a phrase is correctly labeled only if all the words it contains are assigned to the correct semantic role classes. Definitely, this makes our task more difficult.

4

Conclusion

In this paper, we have successfully applied the maximum entropy model to build a classifier for semantic role labeling. Preliminary evaluation reveals that it has

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satisfactory performance. For future work, we will study various ways to improve the system performance, such as incorporating other sources of information to the classifier (e.g., co-reference). Other types of feature functions will be explored as well, to see whether they can boost classification accuracy. We are also working on the application of the semantic role classifier in information extraction.

References 1. Gildea, D., Jurafsky, D.: Automatic labeling of semantic roles. Computat. Linguistics 28 (2002) 245–288 2. Gildea, D., Palmer, M.: The necessity of parsing for predicate argument recognition. In: Proc. ACL-2002, Philadelphia, USA (2002) 3. Gildea, D., Hockenmaier, J.: Identifying semantic roles using combinatory categorial grammar. In: Proc. EMNLP-2003, Sapporo, Japan (2003) 4. Chen, J., Rambow, O.: Use of deep linguistic features for the recognition and labeling of semantic arguments. In: Proc. EMNLP-2003, Sapporo, Japan (2003) 5. Cynthia, A., Levy, R., Christopher, D.: A generative model for semantic role labeling. In: Proc. ECML-2003, Dubrovnik, Croatia (2003) 6. Pradhan, S., Hacioglu, K., Krugler, V., Ward, W., Martin, J., Jurafsky, D.: Support vector learning for semantic argument classification. Technical Report TR-CSLR2003-03, Center for Spoken Language Research, University of Colorado (2003) 7. Surdeanu, M., Harabagiu, S., Williams, J., Aarseth, P.: Using predicate-argument structures for information extraction. In: Proc. ACL-2003, Sapporo, Japan (2003) 8. Carreras, X., Marquez, L.: Introduction to the CoNLL-2004 shared task: Semantic role labeling. In: Proc. CoNLL-2004, Boston, USA (2004) 9. Ratnaparkhi, A.: Maximum Entropy Models for Natural Language Ambiguity Resolution. PhD thesis, University of Pennsylvania (1996) 10. Ratnaparkhi, A.: A simple introduction to maximum entropy models for natural language processing. Technical Report 97-08, Institute for Research in Cognitive Science, University of Pennsylvania (1997) 11. Jaynes, E.: Information theory and statistical mechanics. Physical Review 106 (1957) 620–630 12. Ratnaparkhi, A.: A maximum entropy model for part-of-speech tagging. In: Proc. EMNLP-1996, Philadelphia, USA (1996) 13. Ratnaparkhi, A.: Learning to parse natural language with maximum entropy models. Mach. Learn. 34 (1999) 157–175 14. Kingsbury, P., Palmer, M.: From TreeBank to PropBank. In: Proc. LREC-2002, Las Palmas, Spain (2002) 15. Baker, C., Fillmore, C., Lowe, J.: The Berkeley FrameNet project. In: Proc. COLING-ACL-1998, Montreal, Canada (1998) 16. Marcus, M., Santorini, B., Marcinkiewicz, M.: Building a large annotated corpus of English: the Penn TreeBank. Computat. Linguistics 19 (1993) 313–330 17. Tjong, K.S.E., Buchholz, S.: Introduction to the CoNLL-2000 shared task: Chunking. In: Proc. CoNLL-2000 and LLL-2000, Lisbon, Portugal (2000) 18. Tjong, K.S.E., Veenstra, J.: Representing text chunks. In: Proc. EACL-1999. (1999) 19. Baldewein, U., Erk, K., Pado, S., Prescher, D.: Semantic role labeling with chunk sequences. In: Proc. CoNLL-2004. (2004) 20. Lim, J.H., Hwang, Y.S., Park, S.Y., Rim, H.C.: Semantic role labeling using maximum entropy model. In: Proc. CoNLL-2004. (2004)

An Instance Learning Approach for Automatic Semantic Annotation Wang Shu and Chen Enhong Department of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, 230027, P.R.China [email protected], [email protected]

Abstract. Currently there appear only few practical semantic web applications. The reason is mainly in that a large number of existed web documents contain only machine-unreadable information on which software agent can do nothing. There have been some works devoting to web document annotation manually or semi-automatically to solve this problem. This paper presents an automatic approach for web document annotation based on specific domain ontology. Because complete semantic annotation of web document is still a tough task, we simplify the problem by annotating ontology concept instances on web documents and propose an Ontology Instance Learning (OIL) method to extract instances from structure and free text of web documents. These instances of the ontology concept will be used to annotate web pages in the related domain. Our OIL method exhibits quite good performance in real life web documents as shown in our experiment.

1 Introduction Semantic Web has shown its usefulness in intelligent information integration by providing a technical means to share and exchange knowledge and information between humans and machines [1]. But the prospect of semantic web applications is still unclear for now. The bottleneck lies in that there exist a large number of web pages containing only machine-unreadable information on which software agents can do nothing. The acquisition of semantic knowledge from web documents is a crucial task. One approach is adding semantic annotation on existed web document. Some works have been done in [2, 3]. S-CREAM is a semi-automatic annotation framework based on knowledge extraction rules, and these rules are learned from a set of manually annotated web documents as training set. This paper will focus on the automatic annotation. Our approach is maintaining an ontology instance base through ontology instance learning (OIL) and adding semantic annotations to web page by matching the concept instances occurred in the pages with those in the instance base. We will focus on the learning method -- OIL (ontology instance learning) considering both the non-grammatical tabular HTML/XML structure and the data-rich free text in web document. In the following sections we will illustrate our OIL method in detail. Section 2 and 3 will focus on the problem of instance learning from structure and free text. In secJ. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 962–968, 2004. © Springer-Verlag Berlin Heidelberg 2004

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tion 4 we will present experiments to show the instance extraction capability of OIL. Section 5 contains the concluding remarks.

2 Instance Learning from Structure In our case study, we find that web documents use relational structure patterns to enumerate information related to some specific domain knowledge concepts (see Figure 1). In these structures, we can find instances of related concepts. For example, in the table structure on Figure 2, the concept {TA} has instances as “Jon Bodner” We presuppose that some terms in such list are known as concept instances of our domain specific ontology, we can enrich the instance base of this concept by adding other terms in this list to the instance base. In the following part of this section we will use a frequent tree pattern (FREQT) [6] extraction method to discover instances under such context.

Fig. 1. A segment of a HTML page

We use the Hepple tagger [7] to transform the name entities to their linguistic taggers, the meanings of these taggers are illustrated in [7]. For example in Figure 2, {Jon Bodner, 358, 6:10, MW} is changed into linguistic tags as {NP, CD, CD, NP} for the frequent tree pattern discovery algorithm. We have introduced a tree comparing technique based on Hash in [4]. Here it is adopted to simplify the tree comparing process in FREQT, and add linguistic information for every node into the Tree Pattern Finding process.

TR Jon Bodner 358 6:10 MW

TD Jon Bodner

TD 358

TD

TD

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MW

Fig. 2. Finding Frequent Tree Pattern in web document

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For every maximum pattern (patterns that do not contain any other patterns), we can find an instance list by which we can enrich our instance base for the corresponding concept.

3 Instance Learning from Free Text In this section, we will consider how to extract instances from free text in web document. Our approach is based on lexicon-syntactic patterns in form of regular expressions. Generally pattern based approaches are heuristic methods using regular expressions that originally have been successfully applied in the area of information extraction [5]. We observe that the instances are mainly organized in three kinds of patterns; we will design different instance learning methods for each scenario respectively. 3.1 Three Scenarios for Instance Learning in Free Text Scenario 1: Concept Instance Pattern One or more instances and their related concept are connected by some specific words. These specific words include “or other, such as, especially, for example…” Under such context, if we have known the word representing some certain concept, we can easily find the instances of that concept using predefined lexicon-pattern mapping function. For example: Fiddle, cello, viola or other stringed instruments … Stock market especially NASDAQ, NYSE … We can learn that {fiddle, cello, viola} are instances of the concept {stringed instrument}, {NASDAQ, NYSE} are instances of the concept {stock market}. Table 1 defines Concept Instance Pattern to learn instances in such scenario. Table 1. Concept Instance Pattern Pattern Name Noun Pattern (NP) Proper_Noun Pattern1 (PNP1) Proper_Noun Pattern2 (PNP2) Proper_Noun Pattern3 (PNP3) Proper_Noun Pattern4 Concept_Instance1 (CI1) Concept_Instance2 (CI2) Concept_Instance3 (CI3) Concept_Instance4 (CI4) Concept_Instance5 (CI5)

Lexicon_pattern {((DT)?(JJ)?(NN(S)?))} {((DT)? (JJ)? (NP(S)?))} { PNP1 (and|or) PNP1 } {PNP1(,PNP1)? (and|or) PNP1} {PNP1(,PNP1)} {NP such as (PNP1 | PNP2 | PNP3)} {PNP4 (or | and) other NP1} {NP (especially | including) (PNP1 | PNP2 | PNP3)} {such NP as (PNP1 | PNP2 | PNP3)} {PNP1 (VB|VBD|VBP) NP}

Scenario 2: Juxtaposition Instance Pattern Some instances are arranged side by side separated by “,”, “or” or “and”. Based on the syntax assumption, these words are instances of the same concept. If one of these

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words is known as an instance of a concept C, all the other words in the Juxtaposition Instance Pattern might also be instances of concept C. For example: 1. …Jim, Michael, Susan and Jane … 2. …French, English, Germany, Chinese… If we have known {Susan} is an instance of concept {Student}, then, we got three more instances of concept {student} as {Jim, Michael, Jane}. If we have known {Chinese} is an instance of concept {Language}, then, we learn three more instances of this concept as {French, English, Germany}. We define the following lexicon-syntactic patterns as Juxtaposition Instance Pattern to learn instances in such scenario in Table 2. Table 2. Juxtaposition Instance Pattern Pattern Name Juxtaposition Instance 1 (JI1) Juxtaposition Instance 2 (JI2)

Lexicon_pattern {NP((,| and) NP)+}} {PNP1((,| and) PNP1)+}}

Scenario 3: Relation-word pattern Definition: relation-word is a verb or verb_proposition phrase which has the most important relation to the instance noun according to its syntax role in a sentence. For example, if the instance is the subject or object of a sentence, the relation-word would be the predication verb; if the instance is the object of verb_proposition phrase, the relation-word would be the verb_proposition phrase before the instance noun. According to the different syntax roles of instance noun, we can divide the relation-word patterns into following patterns. Subject_Predication Pattern: instance noun is the subject of a sentence and the relation-word is the predication verb in such sentence. Its lexicons-syntactic pattern is {PNP1 VB (D|G)} Predication_Object Pattern: instance noun is the object of a sentence and the relation-word is the predication verb in such sentence. Its lexicons-syntactic pattern is {VB (D|G) PNP1} Preposition_Object Pattern: instance noun is the object of verb_proposition phrase in a sentence and the relation-word is the verb_proposition phrase in such sentence. Its lexicons-syntactic pattern is {VB (D|G)? IN PNP1} In our approach, first, we will extract the relation-word for each existed concept instance; second, according to the relation-word pattern, the algorithm use respective pattern matching strategy to learn more instance nouns. A similar method is adopted using ASIUM [5]. In the further step of our approach we will use the verb clustering method to extract instances occurred with the same cluster of verbs, the verb cluster we use is given by ASIUM. In the following example, we will use Subject_Predication pattern to extract the subjects as concept instances:

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1. Jim travels by car 2. Michel travels by train 3. Tina drives a saloon car. Using this pattern, we can extract the subject {Jim, Michel, Tina} and the verb {travel, drive}. Supposed that we have known {Jim} is an instance of concept {Student}, our algorithm will find all the representative predication verbs in all sentences whose subject is {Jim}. In this example the predication verb set is {travel}. After that, we will find all the subjects in all sentences whose predication verb is {travel} and the subject set {Michel, Jim}. Now we can extend the instance set of concept {student} by adding an instance {Michel}. Furthermore, after using verb cluster method in ASIUM, we know that {travel} and {drive} belong to the same verb cluster set, and get all the subjects in all sentences whose predication verb is {drive}. In this example, the subject obtained is {Tina}. Thus {Tina} can be added as an instance into the instance base of concept {student}.

4 Experiments To evaluate the effectiveness of our algorithm OIL, we designed two experiments on real-life datasets. The datasets for the first experiment are a collection of HTML pages from the training data in Web_KB project in CMU. We chose the page set which is classified into concept {course} (686 pages totally) to learn the instances on concepts {faculty, person} which include four sub-concepts {Instructor (faculty), Associate Instructor (faculty), Professor (faculty), TA (person)}. We define a simple ontology to describe the structure of faculty in university, some related concept instances are given. In Table 3, we show the results of OIL with given instances, the enriched instances and accuracy. Clearly we can see that considerable instances are learned by HTML/XML structure analysis and free text analysis. Table 3. Instances of concepts {Instructor, Associate Instructor, TA, Professor} Instructor given instances learned from structure learned from free text accuracy

20 60 84 75.7%

Associate Instructor 5 25 8 78.8%

TA 10 0 60 61.7%

Professor 10 30 65 100%

The datasets chosen for the first experiment are really domain specific. In our second experiment, we will use documents from diverse domains. We adopt Reuters21578 as our datasets. Reuters-21578 consists of 12344 news articles from all possible domains. The ontology used in this experiment is built from SUMO [9]. But SUMO is really huge so we extract a mini-ontology containing 70 concepts as the ontology used in our experiment. Because documents in Reuters-21578 are data rich free texts without any structure patterns, we only use our Ontology Instance Learning methods from free text.

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Among 70 concepts in this ontology, 8 concepts in Table 4 are most frequently occurred. Through this experiment we find that the reasons for the low accuracy of the Relation-word pattern methods are mainly due to the following two factors: Much complicated grammar structures in real dataset. The inability to deal with multiword expressions. For instance, “Gulf War” can not be interpreted separately as “Gulf” and “War”. The first problem can be handled by adopting complicated customized lexicon patterns, while the second can be solved by using WordNet [8] which offers synonymous lexicon set and the power to interpret these multiword expressions. Table 4. Instances of concepts {8 concepts} with accuracy given instances Scenario1 Scenario2 Scenario3

Country 3

3

Region

Benefit 3

Institution 3

3

Crop

Product 3

Person 3

Infrastructure 3

4(100%) 0 5(45.5%)

4 (100%) 2 (100%) 4 (30.2%)

6 (100%) 1 (100%) 9 (55.0%)

4 (100%) 2 (100%) 4 (83.2%)

10(100%) 0 6(51.4%)

16(100%) 3 (100%) 3(53.7%)

13 (100%) 4(100%) 10 (100%) 0 17 (33.3%) 3 (84.5%)

5 Conclusion Our paper presents an automatic annotation approach for adding semantic annotation on web documents. We describe a method called OIL to extract concept instances from both the non-grammatical tabular HTML/XML structure and the data-rich free text in web document to maintain an instance base for all the concepts in the domain specific ontology. In our experiment, we find that the instance extraction process on the nongrammatical tabular HTML/XML structure shows quite high performance, because web documents contain a lot of tabular HTML/XML structures to present information. Though the result of instance extraction from data-rich free text is satisfactory, there still exist low accuracy problems in the instances extracting process, partially due to our assumption on the organization of instances in free text and partially due to the obstacle for parsing complicated grammar structures and multiword expressions. We would solve these problems using more powerful NLP techniques with WorldNet in the future.

Acknowledgements This work was supported by National Natural Science Foundation of China (No.60005004) and the Natural Science Foundation of Anhui Province (No.01042302).

References 1. Tim, B L. James, H. and Ora, L.: The Semantic Web-A new form of Web content that is meaningful to computers will unleash a revolution of new possibilities. Scientific American May 17, 2001.

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2. Siegfried, H. Steffen, S. and Alexander, M.: CREAM - creating relationalmetadata with a component-based, ontology-driven annotation framework. In First International Conference on Knowledge Capture 3. Siegfried, H. Steffen, S. and Fabio, C.: S-CREAM Semi-automatic CREAtion of Metadata (2002) 13th International Conference on Knowledge Engineering and Knowledge Management (EKAW02) 4. Wang, Q. Chen, E H. and Wang, S.: Efficient incremental pattern mining from semistructured dataset. Lecture Notes in Computer Science 3007, Springer 2004. 5. Maedche, A. and Staab, S.: Learning ontologies for the semantic web. In Semantic Web Worshop 2001. 6. Asai, T. Abe, K. Kawasoe, S. and Arimura, H.: Efficient substructure discovery from large semistructured data. In SIAM SDM'02, April 2002. 7. Diana M.: Using a text engineering framework to build an extendable and portable IE-based summarisation system. In Proc. of the A CL Workshop on Text Summarisation, 2002. 8. Miller, G.: WordNet: A lexical database for English. CACM, 38(11):39–41, 1995. 9. Farrar, S. Lewis, W.: A Common Ontology for Linguistic Concepts. In Proceedings of the Knowledge Technologies Conference, 2002.

Interpretable Query Projection Learning
Yiqiu Han and Wai Lam Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

Abstract. We propose a novel lazy learning method, called QPL, which attempts to discover useful patterns from training data. The discovered patterns (Query Projections) are customized to the query instance and easily interpretable. As a pattern discovering method, QPL does not require a batch training process and still achieves excellent classification quality. We use some benchmark data sets to evaluate QPL and demonstrate that QPL has a prominent performance and high reliability.

1

Introduction

Suppose we need to predict the class label of an unseen instance, called the query. A straightforward learning method is to collect a number of similar known instances to predict the query. This kind of method is described as “instancebased” or “memory-based”. For example, the family of k-nearest neighbor (kNN) learning algorithms [5, 2, 3, 6] is one of the most classical and widely adopted learning methods. In this paper, we propose a novel learning method which can infer useful patterns called query projections (QPs) for classification. This learning method is called Query Projection Learning (QPL). A query projection is represented by a set of attribute values, which are shared by the query and some training instances. Given a query and a set of labeled training data, QPL first calculates the maximal QPs shared by the query and different training instances. Then QPL analyzes those QPs and attempts to obtain an appropriate set of QPs as premises for the final prediction, which is made by combining some statistics of the selected QPs. QPL has several distinct characteristics. First, different from common instance-based learning, QPL has a good interpretability for the class label learning. It can output discovered QPs as the explanation for prediction. Second, unlike many instance-based learning methods such as kNN, QPL does not employ ordinary Euclidean distance metric. The analysis of QPs helps achieve a balance between precision and robustness with a richer hypothesis space. Third,


The work described in this paper was substantially supported by grants from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project Nos: CUHK 4187/01E and CUHK 4179/03E) and CUHK Strategic Grant (No: 4410001).

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unlike eager learning algorithms such as decision trees [9] or association rule discovery [7, 8], our method focuses on the local QPs rather than learning a set of rules which form a general classifier. The inferring process is tailored to the query rather than partitioning the whole attribute hyperspace to obtain a global classifier such as a decision tree. Particularly, for real-world problems where the training data need to be frequently updated such as spam email filtering problem, QPL has an advantage of reducing the cost of maintenance and operation. In Section 2, we introduce the concept of interpretable QPs and how to obtain useful QPs from the query and the training data. We also show how to infer more useful QPs from existing QPs. The detailed algorithm is presented in Section 2.3. The experimental results and discussions on some benchmark data sets are given in Section 3.

2 2.1

QPL Framework Extracting QPs from Training Data

The learning problem is defined on a class variable C and a finite set F = (F1 , . . . , Fn ) of discrete random variables, i.e., attributes. Each attribute Fi can take on values from respective domains, denoted by V (Fi ). A query instance t whose class label is to be predicted is represented by the full set of attributes as t = (t1 , . . . , tn ) where ti ∈ V (Fi ). We mainly address discrete-valued attributes in our discussion. To handle continuous-valued attributes, discretization methods [4] can be employed as a preprocessing step. To simplify the discussion without loss of generality, we assume that class variable C is a Boolean variable since a multi-class variable can be broken into a set of binary variables. Each training instance is transformed into a binary string where each bit is associated with an attribute value. If a training instance shares the same value as the query on a particular attribute, then the corresponding bit is set to “1”, otherwise it is set to “0”. Thus the query can be represented by a binary string of all “1”. Given the query t, a training instance d = (d1 , . . . , dn ) becomes a bit string b1 b2 . . . bn where each bit is defined as an indicator of di = ti . After such a transformation, all training instances are mapped into binary strings. Since two or more training instances may have the same binary string, such a binary string can be regarded as a projection of the query. Hence the task of discovering QPs can be accomplished by a series of Boolean operations which can be computed efficiently. We count the frequency for each binary string and investigate the class distribution among associated training instances. Generally, we prefer the QPs that have a uniform class label and sufficient associated training instances as support. Moreover, useful QPs should have sufficient “1” in its string which means that its associated training instances are very close to the query. Such kind of QPs have a higher utility to help predict the query. The purpose of our learning method is to discover a set of such useful QPs to conduct the prediction reliably.

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Consider two QPs represented by two binary strings, denote by A = A1 A2 . . . Am and B = B1 B2 . . . Bm . We define B is “more-general-than” A as: ∀ i,

Ai ∧ Bi = Bi

Reversely, we can also say A “includes” B. In QPL, two QPs can be compared only when they have this relationship. Given the “more-general-than” or inclusion relationship, QPL attempts to discover an appropriate u containing set of QPs for learning. We develop the following rules to facilitate the discovery of QPs. – Rule of Exclusiveness: Any two discovered QPs in u should not have the “more-general-than” relationship. It is obvious that if one QP includes another, then its associated training instances share more characteristics with the query and are more useful in learning. Thus once a particular QP is selected, all QPs included by this QP need not to be considered. – Rule of Completeness: The final set u of QPs should cover every ti ∈ t to utilize the full attribute information of the query: ∀ti ∈ t, (∃ui ∈ u such that ti ∈ ui )

(1)

In other words, the discovered QPs should offer a complete view for t. Note that in general, the discovered QPs can be overlapping or non-overlapping. This also differentiates QPL from many existing learning methods that are restricted to non-overlapping partitioning over all attributes. – Rule of Pruning: Since any two discovered QPs will be mutually exclusive, whether to select or discard a particular QP triggers a family of QPs to be pruned. Once a QP is discovered, all its children QPs in terms of the subset relationship will be pruned from further search. On the other hand, when a QP is discarded after consideration, all its children QPs will also be pruned from further consideration. When the QP being processed has a large cardinality, the remaining QPs can be reduced significantly, hence the exploration is accelerated. If a QP is selected according to the above rules, its binary string can be regarded as a premise for an interpretable pattern. Given such a binary string denoted by b1 b2 . . . bn , the corresponding QP can be interpreted as: IF ∧bi =1 (Fi = ti ) THEN C = c where the predictor c is the class label of the training instances satisfying the Boolean expression. Those training instances are supposed to have a uniform class label otherwise their associated QP will not be selected. After a set of such interpretable QPs are discovered for the query, they can be output together with the prediction. These discovered QPs are more interpretable than a list of training instances nearest to the query. They can also be saved as discovered knowledge for future query. When users get the output of prediction from QPL, they can also obtain detailed explanation of the prediction.

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2.3

Discovering QPs for Prediction

After the training instances are used to produce a set of QPs denoted by P . QPL attempts to produce a compact set, denoted by M , of useful QPs from the original set P . For small data sets with small attribute dimensions, this process can be done by exhaustive searching. If the data size is large, QPL can discover useful QPs in an efficient way as discussed below. Since any two discovered QPs cannot include each other, QPL attempts to obtain a compact set of maximal QPs among which no inclusion relationship exists. We denote this intermediate set Q. The processing starts from the QPs in P with the largest cardinalities and moves them into Q. Once a QP with the maximal cardinality is selected into Q, all QPs included by it are also removed from P . This operation continues until no elements were left in P . Then QPL considers the QPs in Q one by one. If any of those QPs have sufficient training instances which have a uniform class label, it will be selected for the final prediction. On the contrary, if a QP with sufficient supporting instances is not capable of producing a reliable prediction, then we remove this QP from Q. Thus we can also ignore all QPs included by it in the next step. However, in practice, the QPs with the largest cardinality generally have few associated training instances. Thus we may not utilize them directly as useful QPs. If Q has no elements that have both a uniform label and sufficient support, QPL employs an inferring process to discover useful patterns from Q. The elements of Q are then treated as the seeds for inference and are divided into groups according to the class label. QPL will process these seeds iteratively. At each step, the common subsets of the original seeds are calculated and investigated. If they are not selected into M for final prediction, they will serve as the seeds for the next step. After every group is processed, if M is still empty, then the set Q is directly utilized for final prediction. This may occur when the training data is relatively sparse considering the attribute dimensions. Finally, we combine the training instances associated with those QPs in M to generate the final prediction for the query. Majority voting is applied among the frequencies summed up from each selected QP. Note that a training instance may contribute to the final prediction for more than once via different QPs. Generally, the more similar a training instance is to the query, the more contribution the training instance can do for the final prediction. The details of QPL is depicted in Figure 1. As shown in this algorithm, the learning process is customized to local QPs for the query. Most steps only involve bitwise Boolean operations on binary strings. Moreover, this algorithm can even infer some new QPs that do not appear in the initial set.

3

Experiments

To evaluate the learning performance of QPL algorithm, we have conducted experiments on 12 benchmark data sets from the UCI repository of machine

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——————————————————————————————— 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Generate the initial set P of QPs, as discussed in Section 2.1. Initialize three empty QP sets Q, Q
, and M . LOOP Move the elements with the maximal cardinality in P to a set Q
. Remove QPs in P that are included by any element of Q
. UNTIL |P | = 0 LOOP Q = Q
FOR each element Qi in Q IF Qi meets the properties as an interpretable QP, Move Qi from Q to M . IF |M | = 0 FOR every pair (Qi , Qj ) in Q with the same associated class label IF their common subset Cij has a uniform class label, Insert Cij into Q
and remove Qi and Qj from Q
if exist. UNTIL (|M | > 0 or |Q
| = 0) IF |M | = 0 Move the elements with the maximal cardinality in Q to M . FOR every class ci , Fi = 0 FOR every elements Mj of M , Fi + = fij where fij is the associated frequency of Mj with class ci . Predict the query t with the class with the maximum Fi .

———————————————————————————————Fig. 1. Pseudo-code of QPL algorithm

learning database [1]. These data sets are collected from different real-world problems in various domains. We partitioned each data set into 10 even portions and then conducted 10-fold cross-validation. In these experiments, we have also investigated the performance of Naive Bayesian, kNN, and Decision Tree (J48) provided by Weka-3-2-6 machine learning software package. All these models used default settings during the entire evaluation process. For kNN, we set k = 10. The results of experiments are depicted in Table 1, showing both the average and the standard deviation of classification accuracy (in percentage) on different data sets. Compared with existing approaches, in most of the data sets, QPL achieves prominent performance. For some data sets such as Labor, Sonar, and Zoo, QPL significantly outperforms all other classical classifiers. The results on the Labor data set also show that QPL excels at handling data sets with poor data quality or incomplete data values. On average, the classification accuracy of QPL on these 12 benchmark data sets is 91.2%, which explicitly shows improvement over other existing models.

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Table 1. Classification performance of QPL and other classifiers, measured by classification accuracy (in percentage) and standard deviation of 10-fold cross-validation Data Set Annealing Breast(W) Credit(A) Glass Heart(C) Iris Labor Letter Mushroom Sonar Vowel Zoo Average

QPL 97.1±2.53 96.9±2.57 84.9±3.09 72.0±13.43 82.6±5.40 95.3±4.12 96.1±11.67 95.5±0.94 99.8±0.33 86.3±5.01 91.5±2.86 96.0±6.09 91.2

kNN 96.1±1.50 96.4±3.10 85.8±3.26 63.5±7.88 82.2±8.75 96.0±5.62 89.3±12.15 94.8±0.36 99.9±0.09 73.0±10.19 57.2±6.06 88.2±6.10 85.2

Naive Bayesian 86.5±3.45 96.0±2.31 77.7±5.43 48.5±6.34 84.5±6.69 96.0±4.66 90.0±11.67 64.2±11.05 95.8±0.79 65.9±12.55 61.4±4.32 95.2±6.65 80.1

J48 98.4±0.78 95.3±3.69 86.0±3.81 67.2±10.08 79.2±6.75 95.3±4.50 78.7±11.46 87.8±0.75 100±0.00 74.1±5.43 78.3±4.98 92.1±4.18 86

References 1. Blake, C., Keogh, E., and Merz, C.: UCI repository of machine learning databases. http://www.ics.uci.edu/~mlearn/MLRepository.html. 2. Dasarathy, B.: Nearest neighbor (NN) norms: NN pattern classification techniques. IEEE Computer Society Press, 1991. 3. Dasarathy, B.: Minimal consistent set (MCS) identification for optimal nearest neighbor decision systems design. IEEE Transactions on Systems, Man, and Cybernetics, 24(3):511–517, March 1994. 4. Fayyad, U., and Irani, K.: Multi-interval discretization of continuous-valued attributes as preprocessing for machine learning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pages 1022–1027, 1993. 5. Friedman, J.: Flexible metric nearest neighbor classification. Technical report, Stanford University, November 1994. 6. Lam, W., and Han, Y.: Automatice textual document categorization based on generalized instance sets and a metamodel. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(5):628–633, 2003. 7. Li, W., Han, J., and Pei, J.: CMAR: Accurate and efficient classification based on multiple class-association rules. In Proceedings of the IEEE International Conference on Data Mining (ICDM), pages 369–376, 2001. 8. Liu, B., Hsu, W., and Ma, Y.: Integrating classification and association rule mining. In Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining (KDD), pages 80–86, 1998. 9. Mehta, M., Rissanen, J., and Agrawal, R.: MDL-based decision tree pruning. In Proceedings of the First International Conference on Knowledge Discovery and Data Mining (KDD’95), pages 216–221, 1995.

Improvements to Collaborative Filtering Systems Fu Lee Wang Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong SAR, China [email protected]

Abstract. Recommender systems make suggestions to users. Collaborative filtering techniques make the predictions by using the ratings on items of other users. In this paper, we have studied item-based and user-based collaborative filtering techniques. We identify the shortcomings of current filtering techniques. The performance of recommender systems was deeply affected by user’s rating behavior. We propose some improvements to overcome this limitation. User evaluation has been conducted. Experiment results show that the new algorithms improve the performance of recommender systems significantly.

1 Introduction As the rapid development of internet, the information-overloading problem has become significant. We are overwhelmed by information. As a result, we need some technologies to help us to explore what information is valuable to us. Collaborative filtering is a promising technique to make the recommendations to users [2, 3, 5, 8]. Recommendations are part of our daily life. We usually make decisions based on other users’ ratings on the items. Collaborative filtering stores the users’ ratings on items in a database. When a user asks the system for recommendation, the system will match the user against the database to discover user’s neighbors, which are the people who have similar taste as the user. As the user will probably like the items that his neighbors like, the system ranks the items based on his neighbors’ ratings and make recommendations accordingly. One well-known problem of collaborative filtering is the scalability problem [5, 7]. There may exist a large number of users or a large number of items. As a result, two collaborative filtering techniques have been proposed, namely, user-based collaborative filtering and item-based collaborative filtering. The first filtering technique searches for neighbors among a user population, and then make recommendation based on neighbors’ ratings. User-based filtering can avoid the problem of huge number of items. The second filtering technique searches for relationships between items first, and then the system recommends items which are similar to items with a high rating given by the user [7]. Item-based filtering can solve the problem of huge number of users. Both filtering techniques are proved to be useful and practical; therefore, they are widely adopted by recommender systems. In this paper, we applied two filtering techniques in restaurant recommender system. Hong Kong is known as “Gourmet Paradise”, because there are a large number J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 975–981, 2004. © Springer-Verlag Berlin Heidelberg 2004

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of restaurants offering a wide variety of culinary delights. Some of them retain their exotic flavors, some of them are localized, and some of them even mix different flavors together. It is quite difficult to classify the restaurants into different groups. On the other hand, Hone Kong people go out for dinning frequently. Therefore, restaurant recommender systems are very useful in Hong Kong. After experiments of the restaurant recommender system have been conducted, we identify the main shortcomings of these techniques. The performance of collaborative filter was deeply affected by the users rating behavior. Some users give their ratings within a narrow range and some users’ ratings shift to one side of the scale. We propose new techniques together with standard score that do not suffer from the limitations. Evaluation of the system has been conducted. The experimental results show that new algorithms significantly outperform previously proposed algorithms.

2 User-Based Collaborative Filtering Technique Collaborative filters help people make choice based on preference of other people. The user-based collaborative filtering technique is based on a simple assumption: predictions for a user should be based the ratings of other users and the similarity between their user profiles [6]. In user-based collaborative filtering technique, a user is matched against the database to find their neighbors by comparing their ratings of items. The correlation r between two users u and v are measured by Pearson correlation coefficient [3], i.e., ru ,v =

(

∑ Ru ,i i∈item (u , v )

( (

∑ Ru ,i − Ru

i∈item u , v )

)(

− Ru Rv,i − Rv

)

2

)

( (

∑ Rv,i − Rv

i∈item u , v )

)

2

(1)

Where, Ru,i is the user u’s rating on item i; Rv,i is the user v’s rating on item i; Ru is the mean of ratings on all items given by user u; Rv is the mean of ratings on all items given by user v; and item(u,v)is the set of items which are rated by both users u and v. After the similarities between the users’ profiles are obtained, they can be used to compute the prediction on items for user u. A threshold value is chosen filter out dissimilar users, only the users with correction coefficient to user u higher than threshold t are choose as user u’s neighbors. The prediction p of user u’s rating on item i can be found by the following weighted average of the ratings of those neighbors on the item i [6]. pu , i = Ru +

(

∑ ru , v Rv, i − Rv v∈rater (i )∩ neighbor (u ) ∑

v∈rater (i ) ∩ neighbor (u )

)

(2)

ru , v

Where, the rater(i) is the set of users who have given their rating on item i and neighbor(u) is the set of neighbor of user u. In the user-based collaborative filtering, the default value of rating on item i is given as the mean of all ratings given by user u. This value is adjusted by the ratings

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of raters of item i among all the neighbors of user u. However, experimental results show that the user’s rating behavior can highly affect the performance of a recommender system. For example, some users give their ratings within a very narrow range, and some users shift their ratings to one side of the scale. The previous filtering technique has addressed the latter problem, because it uses the deviation from the mean instead of the actual value of the ratings to adjust the prediction, and this can solve the problem of dispersion of data. In the experiment, we found that the predictions of items are close to the mean. In order to solve the problem of dispersion of ratings, we propose to use standard score to replace the deviation in the formula, because standard score is a promising technique in statistics to solve the problem of dispersion of data. The standard score z of data x is measured as the deviation from the mean µ in standard deviations σ: x−µ

zx =

(3)

σ

The standard score is used to measure how x is compared against the mean of all data, after taking into consideration of the dispersion of data. The standard score allows a comparison of scores drawn from different distributions, and it can eliminate the problem of dispersion of ratings. The improved user-based collaborative filtering together with standard score is given as below: ∑

p'u, i = Ru +

v∈rater (i )∩ neighbor (u )

ru, v

(R

v,i

∑

v∈rater (i ) ∩ neighbor (u )

− Rv

σv

) σu

ru , v

(4)

The σu and σv are the standard deviation of ratings given by users u and v respectively. If no ratings for item i are given by neighbors of user u, the prediction is equivalent to the mean of all the ratings given by user u. Otherwise, this prediction is adjusted by the weighted standard score of all the raters among user u’s neighbors.

3 Item-Based Collaborative Filtering The bottleneck in user-based collaborative filtering is the search for neighbors among a large user population of potential neighbors. Item-based collaborative filtering is proposed to eliminate this problem [7]. In item-based collaborative filtering, the system will first compute the similarity between two items i and j by Pearson correlation coefficient [3], i.e., ∑

ri , j =

u∈rater (i , j )

((

(R

∑ Ru ,i − Ri

u∈rater i , j )

u ,i

)

2

)(

− Ri Ru, j − R j

∑

u∈rater (i , j

(R )

u, j

) − Rj

)

(5)

2

Where the rater(i, j) is the set of users who have rated both items i and j. The similarities between items are static; therefore it can be preprocessed to save comput-

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ing time. Similar to filtering of dissimilar users in the user-based collaborative filtering, a threshold value is chosen to filter out dissimilar item pairs. After the similar items are obtained, the system computes the prediction on item i for a user u by computing the weighted sum of ratings given by user u on the items which are similar to item i [7]. ∑

pu ,i =

j∈all similar items

ri , j × Ru , j

∑

j∈all similar items

(6)

ri , j

After detail analysis of the item-based collaborative filtering, it is found that the previous formula (Equation 6) is actually equivalent to the following expression. ∑

p'u,i = Ru +

j∈all similar items

(

ri , j Ru , j − Ru

∑

j∈all similar items

)

(7)

ri , j

However, the above filtering technique will be deeply affected by problem of sparse rating [5]. If there are only a small number of similar items, the prediction of item i will be very close to the mean of ratings given by user u. As a result of sparse rating, the system cannot make recommendations very well because all the items are indifferent, because all of them have a prediction close to the user’s mean of ratings. Our improvement was motivated by the idea that if there are only a few similar items, the prediction of item i should be approximated as the mean of ratings on the item i by different users. Therefore, we formulate the item-based collaborative filtering in symmetrical way as the user-based collaborative filtering, i.e., ∑

p'u, i = Ri +

j∈all similar items

(

ri , j Ru , j − R j

∑

j∈all similar items

)

(8)

ri , j

As it might be expected, the item-based collaborative filtering will be affected dispersion of ratings given on items. Taking in to consideration of the dispersion of data, we use the standard score of ratings instead of deviation from the mean to adjust the prediction. The following improved item-based collaborative filter together with standard score is proposed: ∑

p'u , i = Ri +

j∈all similar items

∑

ri , j

(R

j∈all similar items

u, j

− Rj

σj

ri , j

) σi

(9)

Where the σi and σj are the standard deviation of ratings of all the raters on items i and j respectively. If no similar items are available, the prediction is equivalent to the mean of all the ratings from all raters on item i. Otherwise, this prediction is adjusted by the weighted standard score of all the ratings on similar items by the user u.

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4 Experimental Result The performance of a recommender system can be measured by Mean Absolute Error [1] and the Pearson correlation coefficient [3] between the actual value and the predicted value of item ratings. Both measurements in the experiment have shown that the improved algorithms outperform the pervious algorithms. In the experiment, 50 subjects are asked to rate 100 selected restaurants with different flavors. If the subject has visited the restaurant before, he need to rate the restaurant on a 1 to 10 scale. For each subject, one quarter of his ratings will be randomly selected and made invisible to the system. The system is then asked to make predictions on those restaurants with invisible rating. The performance of the system can be measured by comparing the pairs of actual value and the predicted value of the ratings for the restaurants with invisible rating. The Mean Absolute Error (MAE) measures the prediction accuracy of a recommender system [1]. The MAE calculates the mean deviation of the predictions from the actual values by the following formula. ∑ actual − predicted MAE =

(10)

all predictions

number of predictions

The MAE measurements of four algorithms are shown as Figure 1. The MAE of improved user-based algorithm is less than the previous user-based algorithm by 0.144, which corresponds to 15.1% improvement. The MAE of improved item-based algorithm is less than the previous item-based algorithm by 0.160, which corresponds to 13.5% improvement. To further analyze the results, we have performed the one-tailed paired t-test of the absolute error in improved algorithm against the previous algorithm. The improved user-based algorithm outperforms the previous algorithm at 90% confidence level and the improved item-based algorithm outperforms the previous algorithm at 95% confidence level.

1.4 1.2 1 0.8 0.6 0.4 0.2 0 MAE

User-based

Improved user-based

Item-based

Improved item-based

0.956

0.812

1.184

1.024

Fig. 1. The MAE between Actual Value and Predicted Value

The performance of a recommender system can be also measured by the Pearson correlation coefficient between the actual value and the predicted value [1]. Table 1 shows the results.

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Table 1. The Pearson Correlation Coeffcient between Actual Value and Predicted Value User-based 0.8372

Improved user-based 0.8564

Item-based 0.7279

Improved item-based 0.7597

In the analysis of Pearson correlation coefficient, it is found that the predicted value is more positively correlated with the actual value in the improved user-based algorithm than the previous user-based algorithm. The similar observation is also made in the item-based algorithm. Combining the result of MAE analysis and the correlation analysis, it is concluded that the improved algorithms outperform the pervious algorithms. However, if we compare the user-based and item-based algorithm, it is found that previous user-based algorithm outperforms the previous item-based algorithm and the improved user-based algorithm outperforms the improved item-based algorithm. Therefore, the user-based algorithms are more promising techniques in collaborative filtering. Therefore, most efforts are currently devoted into researches of user-based collaborative filtering techniques. As the item-based algorithms can also produce very good results, it is also important to do more researches in this area.

5 Conclusion As the amount of information available increases exponentially, techniques are required to assist users in finding relevant information. We have reviewed the userbased and item-based collaborative filtering techniques, some improvements have been proposed. We introduce collaborative filtering techniques together with standard score to eliminate the impact of different user’s rating behavior. User evaluation has been conducted. The experimental results show that the new filtering techniques outperform the pervious techniques significantly.

References 1. Cayzer S., and Aickelin U. A Recommender System based on the Immune Network, Proc. of the 2002 Congress on Evolutionary Computation, 2002. 2. Hill W., Stead L., Rosenstein M., and Furnas G. Recommending and evaluating choices in a virtual community of use. Proc. on Human Factors in Computing Systems, pp. 194-201, 1995. 3. Kendall M., and Gibbons J., Rank Correlation Methods, fifth ed. New York: Edward Arnold, 1990. 4. Konstan J., Miller B, Maltz D., Herlocker J., Gordon L., and Riedl J. GroupLens: Applying Collaborative Filtering to Usenet News. Communication of ACM 40(3) pp. 77-87, 1997. 5. Lee W. S. Collaborative learning for recommender systems. Proc. Of 18th International Conf. on Machine Learning, pp 314-321. Morgan Kaufmann, San Francisco, CA, 2001. 6. Resnick P., Iacovou N., Suchak M., Bergstorm P., and Riedl J. GroupLens: An Open Architecture for Collaborative Filtering of Netnews. Proc. of ACM 1994.

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7. Sarwar B., Karypis G., Konstan J., and Riedl J. Item-based Collaborative Filtering Recommendation Algorithms. Proc. of the 10 International World Wide Web Conference. Hong Kong, 2001. 8. Shardanand U., and Maes P. Social information filtering: algorithms for automating word of mouth. Proc. on Human factors in computing systems, pp. 210-217, 1995.

Looking Up Files in Peer-to-Peer Using Hierarchical Bloom Filters Kohei Mitsuhashi1 , Takao Miura1 , and Isamu Shioya2 1

2

Dept. of Elect. & Elect. Engr., HOSEI University, 3-7-2 KajinoCho, Koganei, Tokyo, 184–8584, Japan Dept. of Management and Informatics, SANNO University, 1573 Kamikasuya, Isehara, Kanagawa 259–1197, Japan

Abstract. In this investigation, we propose a new mechanism for looking up files in Peer-to-Peer over internet environment so that we can look up files in a location-transparent manner. To do that, we introduce hierarchical Bloom filters to local file structures which allow us to query full/part of the structures. We show some experimental system with major features of JXTA where we put attentions on serverless and multi-casting communication, and we examine empirical results on the system. Keywords: File Look-up, P2P Distributed System, JXTA, Bloom Filter.

1

Managing Data Under P2P Environment

The P2P environment has been targeted for three major application domains, i.e., data sharing, distributed computing, and autonomous systems. By data sharing we mean database aspects such as query evaluation techniques, scalability issues and efficient data structuring. For distributed computing, we are interested in parallel processing for load-balancing to many computer resources. Non-centralized, non-hierarchical and not pre-determined connections are of our attention. Autonomous systems mean that we can join and leave the network any time without any notice of other sites. Here main concern is durability of the system. For data inquery under P2P, we should put our attention on granularity for the purpose of data management. For instance, when we keep record as a unit, we have to map every key in a record to one location. Typical approach is found in Distributed Hash Table (DHT) technique [1] where each key item is hashed into IP-based location-space and the record be found there. This is not suitable for our autonomous requirement because we want to keep our own records and migrate them according to our own reasons. The deficiency comes from the granularity and we’d better manage file as a unit. Since file is managed by its name, we should discuss file look-up mechanisms under new environments. Traditionally several types of file look-up mechanism have been proposed in several P2P systems. The most naive one is the server approach where central J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 982–988, 2004. c Springer-Verlag Berlin Heidelberg 2004


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computers play dominant roles on the jobs and the users come to the servers via
F ileN ame, Server parameters. The second approach is server hierarchy. The inqueries are automatically routed to appropriate servers and the users don’t care which server they visit. The third approach is found in peer-to-peer servers where every server is connected without any governing sites. Here we take P2P approach paying our attention on efficiency of directory/file look-up and reduction of communication amount. Virtually each query is broadcasted to all the servers thus we might get huge amounts of communication which reduce total throughput of the mechanism. Also we introduce super peer sites for controlling purpose, which contradict a notion of pure P2P. In an approach based on DHT to file names, every file is connected to some site statically. This seems unsuitable for migration purpose where we want to move in and out any files from/to any sites, although many inqueries assume reading files. We assume each peer (local site) works with file look-up using identical principle. That is, every peer may ask other peers of any file look-up requests and should work with the requests for other peers. In this experimental implementation we discuss two basic ideas, Bloom filters for file look-up that is the main issue of this paper, and packet management based on JXTA for P2P communication. Here we assume communication activities over wide-spread network but not so heavy such as sensor-net thus JXTA is powerful enough to satisfy the activities.

2

Looking Up Files by Bloom Filters

To look up files in P2P environment, we propose Bloom filter which has been devised for distributed database processing[3]. Several investigation with some empirical studies has been made for looking up files so far[4]. In naive queries, all the files are examined thoroughly so that we get mountains of non-relevant information. Usually we assume some techniques to filter out desired files. But naive bitmap filters (called Bloom filter as described later) are too simple to capture directory structures, although general query processing is quite efficient. Compressed filters are any filters compressed for the purpose of distributed queries among sites, but not useful directly within local sites. Aggregated filters are targeted for summarizing all the files in each local sites but not for (partial) structures. In this investigation we assume there exists a file management mechanism where all the files are managed hierarchically and we can get to every file by specifying path from the top. Generally we see hierarchical structures to manage files in each site in Windows, Unix, MacOS, IBM Mainframe OS and so on. As described below, we examine several files in our company case. The reader might imagine similar notation as XML/XPath. (1) MaterialDept/PartTimeEmp/Address describes all the addresses of part time employees in material department.

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(2) /Tokyo//Address/ means all the addresses of employees in Tokyo Office. The top /Tokyo describes ”Tokyo” appears as the top entry. (3) /Tokyo/*/Address means all the addresses in one level lower from the top entry ”Tokyo”. The character * means a wild card to any file name in one level while // means a wild card to any levels of the structure. To tackle hierarchical directory structures, basically we take Bloom filter approach with both one level and aggregate level filters. Bloom filter is bit vector (a sequence of bits), which is obtained by signature coding. That is, given a directory and collection of file names in the directory, we calculate each name into a sequence of bits by means of hash functions, and we take logical-or operation to them. The signature value is called Local Bloom Filter (LBF) at the site. Note every subdirectory file has its name and is coded as a part of signature. On the other hand, given a directory, Global Bloom Filter (GBF) is generated by taking logical-or to all the descendant LBFs. GBF is recursively defined where a leaf file contains an empty GBF. Each peer node keeps a pair of LBF and GBF and each peer (site) manages very top level of LBF and GBF. To evaluate any query at a site, the pair is examined efficiently to decide whether the site contains the desired file or not. The mechanism is called hierarchical Bloom Filter that we have implement. Let us exemplify a query C//xyz against hierarchical structure in a figure 1. Let us denote LBF values of C and xyz by BF(C) and BF(xyz) respectively. Also we denote a GBF value and an LBF value of A by GBF(A) and LBF(A) respectively. If GBF(A) contains BF(C) and BF(xyz), this site may contain the partial structure. We ask whether LBF(A) contains BF(C) or not. Since this is the case, we proceed to the next step. GBF(C) contains BF(xyz) but LBF(C) doesn’t contain BF(xyz). Thus we examine whether GBF(D) contains BF(xyz) and whether GBF(E) contains BF(xyz). In the former case we have the answer NO, but YES in the latter case. Note there can be no xyz file even if GBF(E) contains BF(xyz), which is called false positive. But we can’t have the answer YES when a Bloom filter dosn’t contain a signature.

Fig. 1. Hierarchical Bloom Filter

Fig. 2. System Architecture

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System Architecture

To obtain fully P2P system, i.e., serverless, loop-free and multicast communication with low overhead, we utilize the JXTA mechanism[2, 5] as our basic host communication mechanism and discuss how to implement our experimental system. JXTA technology provides a fundamental mechanism called pipe by which services and applications are built in a uniform manner. This approach helps us to maintain interoperability among various P2P systems. In a figure 2, we illustrate architectural framework of communication mechanism in JXTA and the control flows. Rectangles mean Peers, they belong to a PeerGroup that says five peers share one service. A circle means a propagation pipe for host communication. Messages come in from peer0 and they are propagated to all the peers in the same peer-group. On the way back to peer0, peer4 assumes a pointo-to-point pipe to peer0. Thus peer has two ways to hear messages from other sites. Our basic architecture consists of a P2P communication mechanism using JXTA, GUI-based user interface and distributed file management using hierarchical Bloom filters. As said above, JXTA provides us with multicast communication mechanism (called propagation pipe) in P2P mode independent of platforms (operating systems). We design and implement our file management mechanism from scratch on the JXTA communication mechanism.

Fig. 3. Whole Flow

In a figure 3, we illustrate architectural framework and the control flows. First one peer called peer0 sends a request message to a common pipe by (1), e.g.,peer0 requests a file which is form of ”dir1//dir2/hosei.dat”. then the request is propagated as (2). The whole process is managed by means of JXTA

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multicast communication. Once each peer receives the request message, it works by using hierarchical Bloom filtering technique. When some peer, say, peer4, finds any files to be desired, the peer sends the reply directly to the peer0 as in (3), e.g.,peer4 sends the reply which includes the size of file(10kB), the host name(peer4) and the path from a published top directory (xx/dir1/xx/xx/dir2/ hosei.dat). Finally the originating peer peer0 asks peer4 of file transfer. In our experimental system we utilize FTP mechanism by clicking the lines desired. As said previously, we introduce LBF/GBF mechanism to obtain efficient file look-up. In our implementation, each LBF has 1024 bits length represented as an array of integer. We examine each directory, and we decompose each file name within the directory into four parts, one of which is hashed and logical-ored into 128 bits signature. We decide which part should be used by means of a hash function to the file name. We repeat this operation 8 times (128 × 8 = 1024) and eventually we obtain an LBF. Note that very often we see similar names such as XXXX_name.dat and the algorithm can prevent from biased signature values. When there are subdirectories, we generate GBF from their (sub) GBF.

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Experiments

We have designed and implemented experimental system on three equivalent computers under the environment of Pentium IV 1.8GHz, 256MB memory, 100MB FastEther LAN with FreeBSD 4.6.2 in JAVA SDK 1.3.1. We have examined 77845 files in 800 MB in total without any replica. Here is the summary information (Files contain directory).

CPU1.Files (directory) CPU2.Files (directory) CPU3.Files (directory) Total Files (total dir)

Level 1Level 2Level 3Level 4Level 5Level 6Level 7Level 8 Total 31 385 4257 6050 1505 8 0 012236 24 211 496 147 1 0 0 0 879 6 136 1755 14568 17356 5538 148 039507 6 98 630 1404 432 7 0 0 2577 8 130 1063 2276 9559 9953 2750 36326102 8 66 219 722 801 207 14 0 2037 45 651 7075 22894 28420 15499 2898 36377845 38 375 1345 2273 1234 214 14 0 5493

In our system we have randomly selected five files in level 2 and 5 respectively and we give query them as test cases. The files in level 2 and 5 are examined five times in a form of /top/file and dir1/file, /dir2//file denoted by ”Level 5 (1)” and ”Level 5 (2)” respectively. A table 1 contains all the average results of our queries where BF means Elapsed Time in second for Bloom Filter process, JXT A means Elapsed Time for JXTA Communication, BF (stdev), JXT A(stdev) mean the standard deviation of BF and JXT A respectively. Graphs 4,5 and 6 illustrate the situation. Looking at the tables and the graphs, we can say that BF values vary but JXTA values stay unchanged for file look-up while the standard deviation on

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Table 1. Files in Level 5 and Level 2

Fig. 4. Files in Level 5(1)

Fig. 5. Files in Level 5(2)

Fig. 6. Files in Level 2

JXTA varies. BF should vary since we examine several files and the results depend on file location, cache buffering or any other situation but the standard deviation values are very small. On the other hand, JXTA may take small amount of time but it varies heavily compared to BF. This may come from some delay of discovery service of pipes. Finally, to see the feasibility of our system, we have examined whether any peer can join and leave our network or not in our laboratory, and we didn’t find any problem.

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Conclusion

In this investigation, we have proposed P2P file look-up mechanism and implemented experimental system based on JXTA communication package. We have examined file inquery and evaluated the feasibility of P2P availability as well as performance efficiency. By this experiment, we have shown hierarchical Bloom filters play important roles on P2P file look-up. Unfortunately, with current JXTA implementation, very often it takes time for discovery service of pipes thus is not suitable for real-time processing.

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References 1. Balakrishnan,H. et al.: Looking Up Data in P2P System, C.ACM 46-2, pp.43-48, 2003 2. Gong, Li: Industry Report – JXTA: A Network Programming Environment, IEEE INTERNET COMPUTING, 2001 June 3. Kossman, D.: The State of the art in Distributed Query Processing, ACM Comp.Survey 32-4, pp.422-469, 2000 4. Ledlie, J., Serban, L. and Toncheva, D.: Scaling Filename Queries in a Large-Scale Distributed File System, Harvard Univ. TR03-02, 2002 5. Wilson, B.J. et al: JXTA (Voices(New Riders)), Macmillan Computer Pub., 2002

Application of Web Service in Web Mining Beibei Li and Jiajin Le

，

Computer Science Department, Donghua University 200051 Shanghai, China [email protected] [email protected]

Abstract. To solve the problems we now encounter in web mining, We first propose a new distributed computing strategy—web service. It suggests building a web mining system based on web service, which can share and manage semi-structured data from heterogeneous platforms. Moreover, the system can integrate the mining services and algorithms, improve the efficiency of web mining, and make the mining results easier to access. We also conduct an experiment on selecting useful words to simulate the realization of the web mining system on the Microsoft.NET platform, which demonstrates the importance of Web service in Web mining.

1 Introduction With the rapid development of online application, the quantities of data stored on the web have increased exponentially since 1990s. As a result of this increase in data quantity, how to discover and obtain useful information faster and more accurate from this vast data resource has become a focus of researchers’ interest. Web mining was studied just under this situation, which refers to the procedure of extracting interesting patterns and knowledge from web resources, such as web contents, web structure and web access. It contains three different data mining tasks: Web Contents Mining, Web Structure Mining, and Web Usage Mining [1]. Now the prospects of Web mining technology have attracted the attention of researchers and commercial organizations. They have developed many mining systems and proposed lots of mining algorithms. However, Web mining is a complex procedure and it still faces many problems. First, as to the Web Contents and Web Structure Mining, most conventional mining algorithms could not get used to the hetero-structured web resources. Because the web resources contain not only structured data in conventional databases, but also non-structured data such as multimedia, sounds, and images. Web mining has extended the objects of data mining from simple and structured data to complicated and semi-structured web data, which hinders those conventional mining algorithms from working effectively. Secondly, as to the Web Usage Mining, usually the usage records of users are not static. Since some clients use local cache and proxies, the web server could only take the information of those proxies, while missing the users’ real information behind them, which prevents catching the behavior of single web user. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 989–994, 2004. © Springer-Verlag Berlin Heidelberg 2004

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Thirdly, Web mining is mostly used by web servers only. So no matter which kind of mining, Web Contents Mining, Web Structure Mining or Web Usage Mining, they all have to be performed by the servers. Therefore, the lack of clear and better design for clients has caused low mining efficiency. Fourthly, now there is contradiction between the large variety of Web mining algorithms and the specialty of their application fields [2]. The users could use those algorithms provided by certain system only, and never could add, delete or organize any of them, which makes the mining systems quite closed and inflexible. Lastly, it is difficult for other systems to process the mining results further, because the formats of most mining results are quite closed. And this closure on the output formats is really bad for the improvements and use of those mining results. So we can think of a new technology nowadays——Web Service. It is a new distributed computing technology and helps solve the problems above.

2 Advantages of Web Service in Web Mining 2.1 The Characters of Web Service Web service is a new distributed computing model on the Internet [3]. It can be used for coupled network environments and provides an interface, which can be accessed by XML message through the network. This interface defines a group of accessible operations, in which functions can be easily realized just by using this standard interface. Figure 1 shows the related standards and architecture [4].

Fig. 1. Web Service Architecture and related standards

Therefore, the key point of Web Service lies in making remote process calling easier and faster by providing a set of Internet standard protocols, such as WSDL, UDDI, SOAP. Meanwhile, it has the compatibility with hetero-structured system platforms, which can eliminate the isolation of information, thus sharing and managing resources over different platforms. 2.2 How to Solve the Problems in Web Mining From the above discussions and explanation, we can design a new Web mining system. This new system follows all the standard protocols already defined, and inte-

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grates various Web mining services based on different kinds of algorithms, operating platforms, and data resources. Figure 2 shows its architecture. The entire system consists of three layers: the Clients Layer, the Server Layer and the Web Mining Service Providing Layer. The Server Layer is its kernel, which is deployed on the network as the form of web service, finding useful mining services from the Web mining Service Providing Layer according to the clients’ particular requests, integrating them with local service, and then providing it to the clients as a whole web service. Obviously, using the web service technology, this new system can easily overcome those problems we encountered in the conventional Web mining process.

Fig. 2. Architecture of a new Web mining System Based on Web Service

1. Web service technology can solve the problem about sharing and managing the hetero-structured data in Web Contents Mining. Because web service is based on the standard XML language, it can integrate hetero-structured data sources and provide structured descriptions to them, thus making those data from different sources easily bonded together. Therefore, the service requesters could obtain the data directly from the web with the original data formats, rather than allowing the original data formats to get lost in the semi-structured description information with various formats. 2. Web service technology can help clients improve efficiency in the Web Usage Mining. In the proposed new system, the clients can call the mining service interface provided by the server conveniently and directly just like calling its local application procedures, which makes the clients not subordinate and passive any more, but as active as the server. So the Web mining is not confined to the server, and changes from the conventional “One-to-Multeity Mining” to the parallel “Multeity-to- Multeity Mining”, which improves the mining efficiency. Meanwhile, by calling the Web mining services, the clients could directly give the feedback of

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the local usage pattern analyses to the server, rather than being screened by those proxies or local cache, which makes tracking the behavior of individual users more easily and plays an important role in building personalized recommendation systems. 3. Web Service technology can help strengthen the specialty of the Web mining algorithms. For example, in the Web Structure Mining, the new system can integrate all those Web Structure Mining algorithms that exist in the form of web services, such as HIT, PageRank, improved HIT and etc, and make them form a unified mining service interface. Then the users could select, add, delete or optimize the algorithms according to their own mining tasks, which forms a custommade mining developing platform and strengthen the specialty of Web mining. 4. Web Service technology can also deal with the results of Web mining effectively. Since the mining results are described and output by the XML language at last, the contents and formats of them are totally separated. The users can figure out the results easily and correctly, use various analyzing tools to visualize them, or make further use of them. Thus this system realizes the sharing of Web mining results over different kinds of systems and platforms.

3 Experiments 3.1 The Implementation of a Simulation System Web service develops very fast nowadays, and many companies have offered various sorts of platforms to design, develop and deploy this new distributed web application. Such as Sun One, IBM’s WebSphere, and Microsoft’s .NET. Now we select the .Net platform from Microsoft to develop the Web mining simulation system. First, we deploy a local web service named “StartWithA” on the local server, which is used to choose the words starting with “A” in certain text. At the same time, we deploy a remote web service named “EndWithD” on another server, which is used to choose the words ending with “D” in certain text. Finally we add its web reference to the local web service.

Fig. 3. The Interface of the simulation system

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Then we can use those two integrated services through the local server at any client machine, only by adding the web reference of the local web service. The working interface of this simulation system is shown in Figure 3. We input all the text into the textbox and click the “Select” button. Then the system can automatically find those two web services we already deployed and call them rapidly. Finally it returns the result we want——all the three words, “and”, “aloud” and “around”, in the text, which both start with “A” and end with “D”. Figure 4 shows the result page.

Fig. 4. The result of selection

3.2 The results Through the process of developing the simulation system we could easily find that when dealing with the real Web mining work, the Web Service technology can not only help the clients by local service, but also integrate a large variety of remote mining services by local server just as fast and convenient as calling local procedure. Meanwhile, by using Web Service as the interface between server and clients, the users could easily write the clients software by themselves, or even integrate all the function provided by this entire system into another system as its subsystem, as long as they conform to the rules when calling the Web Service of this system. Besides, thanks to the B/S (Browser/Server) structure based on the Web Service, there is no need for the clients to worry about the realization of the mining algorithms, the working platforms, the program languages, or the formats of data description. All the service details are transparent to them and they only need to know the address of the local server. The clients get the requests of the users, submit them to the server, and receive the resulting documents returned from the server. Then the users can choose to see the results in a visualized form.

4 Related Work Now there are already some Web mining systems based on Web Service. Such as the Web Service systems based on database—Amazon and Google. Both of them are

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better in the Recall and Precision than some other systems at the same time like Yahoo. Besides, some other network companies have also begun to create certain new services for developers, which can allow the developers access the databases of their companies directly without going through certain application procedures. However, all these services are just based on the elementary data sharing and have not gone deep enough into the data processing and data mining. The TETRIS system, developed by the Fudan University [5], has made great efforts in the open character based on the service integration, from the whole architecture to mining language. It has provided a flexible platform for developing and applying Web mining. But at present this system is not mature enough in practice, and still needs some improvements.

5 Conclusions Web data is so complex and enormous, there are many problems in the Web mining process. We propose the Web Service technology and suggest building a new Web mining system based on it, which can share and manage those semi-structured data from different kinds of platforms, strengthen the specialty of mining algorithms, improve the mining efficiency, and eliminate the closed character of mining results. With the optimization and maturity of Web Service technology, it will surely be used in the Web mining much better. And the various web resources will finally become our treasure, thus making our lives fresher and more vigorous.

References 1. Yun, S., Han, L., Dong, J., Ceh, D.: KDW Survey: Web-based Data Mining. Computer Engineering. 29 (2003) 284-286

2. Zhang, S., Wang, C., Zhou, M., Zou, Y., Wang, W., Shi, B.: TETRIS: An Open Data Mining Application Development Platform Based on Service Integration. Computer Science. 30 (Spp.) (2003) 264-266 3. Zhang, Y., Tang, Y.: The Analysis of Distributed Computing Techniques and Web Service. Modern Computer, 1 (2004) 42-45 4. Kreger, H.: Web Services Conceptual Architecture. http://www-900.ibm.com/developer Works/cn/webservices/ws-wsca/index.shtml, May (2001)

A Collaborative Work Framework for Joined-Up E-Government Web Services
Liuming Lu, Guojin Zhu, and Jiaxun Chen Network & Database Laboratory, Dept. Computer Science, Donghua University, Shanghai 200051, P.R. China [email protected] {gjzhu, jxchen}@dhu.edu.cn

Abstract. One of the main characteristics of e-government is the collaborative work. By the collaborative work we mean that differently functional departments in the government should cooperate with one another in order to accomplish an integrated service required by the citizens. Each functional department works as a part of the integrated service. A web service-based architecture together with a data model of e-documents is proposed to meet the requirements for the collaborative work in e-government. A scenario is given to demonstrate how the suggested architecture works. Keywords: e-government, collaborative work, web service.

1

Introduction

Today’s official business process system lacks the concept of collaboration. By collaboration we mean that differently functional departments in the government should cooperate with one another in order to accomplish an integrated service required by the citizens. Each functional department works as a part of the integrated service. Though a unit of operation in a functional department can be implemented in a service terminal, it sometimes requires cooperation among the departments if a business process involves several departments. In order to meet the requirements for the e-government collaborative work, we propose a collaborative work framework for join-up e-government web services. We firstly wrap the applications in the departments in modular web services. Adopting web services in e-government enables value-added services by defining services to standardize the description, discovery, and invocation of the applications in the departments. Then, we develop the techniques of integrating web services according to required rules to implement the governmental business process. Finally a data model of e-documents for the collaborative work in


This work is partially supported by a grant from Chinese National Natural Science Fund (#60273051) and Shanghai Science and Technology Development Fund (#03DZ05015).

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 995–1001, 2004. c Springer-Verlag Berlin Heidelberg 2004


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e-government is designed.Data standards according to the data model about the definition and description of governmental documents, the business process and application security should be provided for the realization of the interoperability.

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Organizing E-Government Web Services

As Figure 1 shows, basic interactions among e-government web services involve three types of participants: provider, registry, and consumer [1, 2]. Providers include different departments or agencies in the government. The providers publish descriptions of their services, such as operations and network locations in a registry. Consumers, the entities wanting to acquire web services, access the registry to locate services of interest, and the registry returns relevant descriptions, which consumers use to invoke corresponding Web services.

UDDI Registry Find

Publish E-government service

Consumer Message exchange (SOAP)

Provider Service description (WSDL)

Fig. 1. Interactions among e-government web services

Providers describe the operational features of Web services in the Web Services Description Language (WSDL). Each operation has one of four possible modes: – One-way, in which the service receives a message. – Notification, in which the service sends a message. – Request-response, in which the service receives a message and sends a correlated message. – Solicit-response, in which the service sends a message and receives a correlated message. For example, in the collaborative work system of the electronic document transaction a web service offers a request-response operation called gernerateRule. This operation receives a message that includes the document to be processed and returns a message that contains the rule to process the document, such as the involved offices and their executing sequence. WSDL descriptions are stored in a registry based on Universal Description, Discovery, and Integration (UDDI). The registration of web service includes the URL for communicating with this service and a pointer to its WSDL description.

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Dynamic service composition is the process of creating a new integrated service at runtime from a set of web services. This process includes activities that must take place before the actual composition such as locating and selecting service components that will take part in the composition, and activities that must take place after the composition such as registering the new service with a service registry. The main responsibility of the collaborative work system is to facilitate dynamic service composition. The execution of dynamic service composition is centralized in some systems [3]. At the same time the novel techniques involving peer-to-peer execution of services is employed in several systems such as SELF-SERV [4] etc. Although peer-to-peer can lower cost of ownership and cost sharing by eliminating and distributing the maintenance costs and provide anonymity/privacy, it also raises some concerns about security and management. In order to facilitate the management in e-government, we employ the centralized execution mode. Figure 2 shows the architecture of the collaborative work system, which is described as follows in details. – The center server for the e-government collaborative work. The center controller is to manage the running of the collaborative work system. Requester handler is used to receive the request and involved data from the citizens. And the e-document generator is responsible for converting the data from the citizens into the standard data and generating the corre-

E-government Collaborative Work Platform Center Server for E-government Collaborative Work

User Interface

XML Database Server E-document Schema Database

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E-document Generator Transaction Manager

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Microsoft Outlook . . .

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other systems 1

E-document Transaction System

Internet Explorer

Request Handler

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Base Web Service Module

. . .

Informational Security Infrastructure Business Resource Module Database

the Business Process Rule Generator

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the Leader Workstation and Service Terminal Module

Fig. 2. The architecture of the collaborative work system

. . .

. . .

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sponding e-document according to the schema from the e-document schema database. The service locator can be used to look up WSDL descriptions in the UDDI registry for the rule engine. The main responsibility of the rule engine is to execute the rule. The execution contains the receipt of the event to activate the involved rule and the execution of actions that are defined in the rule. The event response module is responsible for abstracting the significant event, encapsulating the event and submitting it to the rule engine. The service invoking module is used to invoke the corresponding web service based on the action from the rule engine. The transaction manager is to guarantee the ACID (atomic, consistent, durable, isolated) features in the execution of the transactions. – XML database server. The XML database server contains an e-document database, an e-document schema database, a UDDI registry, a business rule base, and an access control module. They are described as follows. 1. The UDDI Registry is mainly used to register the collaborated resource such as web services provided by different departments so as to facilitate the service locator to query automatically the required services and the definition of their access interfaces. 2. The e-document schema database is used to store the e-document schemas that are defined in the data standard for the e-government collaborative work. In order to meet the requirements for the collaborative work, the data model in e-documents contains data for business unit requirements, data for controlling the collaborative work, data for ensuring the application security and other data. Data for business unit requirement is provided for business units to implement their corresponding functions. Data for controlling the collaborative work is used in the collaborative work module that contains the components used to integrate the business units, such as the business process rule engine etc. Data for ensuring the application security is used in the application security module whose responsibility is to provide the informational security infrastructure. Other data can include data for index and storage, which facilitates the storage and query of involved data. 3. The e-document database is provided to store e-documents that are instances of the e-document schemas. 4. The access control module is to control the access to the e-document database according to the policy specified in the e-document. 5. The business rule base can store every kind of collaborative rules. Data for controlling the collaborative work in e-documents can be acquired from the business rule base or through the business rule generator, which can also be web service to generate rules. – The informational security infrastructure. The informational security stated here includes identity authentication, data encryption, digital signature, access control etc. The certificate register server,

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the certificate lookup server and authorization center constitute the infrastructure of the informational security. The main responsibility of the three servers is to manage the key for data encryption & decryption and to authenticate the identity of users. – The basic web services module and business resource module. The basic functions provided by the departments are wrapped with web services. And the web services should be registered in UDDI.The module can take Microsoft .Net as its supporting platform and interact with the service invoking module through the message exchange protocol of SOAP. According to the application requirements of the government business, several application systems are built, such as e-document transaction system, conference management system, information report system etc. Every application system is composed by several web services provided by involved departments. How to execute the web services in every system should be directed by the related rule. Business resource module is composed of several databases that store business data for the application systems. – The workstation and service terminal module and user interface. The workstation and service terminal module provides the operation platform for the office clerks. The workstations can be thin workstations, which means that the business logic is put in the service module. User interface can make use of the universal browsing tools such as Internet Explorer, or the office software such as Microsoft Outlook.

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A Scenario: The Application for Projects

Now we take the application for projects as an example to demonstrate how the suggested architecture works. Suppose the application for projects is executed through the collaborative work of several office clerks in related departments. The clerks include the business rule generator, the expert and leader. And the execution sequence is the business process rule generator, the expert and leader. Every function provided by the corresponding department is encapsulated in a web service. And the services are registered in the UDDI registry. We firstly design a special XML Schema used in the scenario according to the data model of e-documents and store the schema in the e-document schema database. When a citizen requests the service of the application for projects, the request handler firstly receives the request and submits it to the center controller, which looks up the corresponding schema in the e-document schema database according to the request. If the center controller finds the schema, it transfers it to the e-document generator, which can generate an e-document based on the XML schema and append some data from the user in the data elements as their values if necessary. Then the e-document is transferred to the center controller, which looks up the rule corresponding to the request

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in the business rule base. If there is no rule in the rule database, the center controller wants to request the rule generator to generate the rule. The following detailed executing process can be described as follows: 1. As is showed in Figure 2, the business process rule generator receives the XML document from the center server. Then he selects the related data elements and fills in them with detailed data. In the case, the content about the next involved clerks and their execution sequence is appended. If necessary, he should encrypt the sensitive content of data elements, and sign with digital signature. Finally he submits the XML document to the center server. 2. The center server firstly validates the validity of the XML document, then disposes of the content of data elements after making sure that the XML document is valid. It should generate the rule according to the related content of the XML document. After making sure that the web services stated in the rule can actually work together, the center controller submits the rule to the rule engine. At the same time it should find the web services in UDDI registry to acquire the relevant descriptions of web services, which can facilitate the following execution for the rule engine. Finally the center server transfers the XML document to the next clerk according to the rule. 3. The expert receives the XML document and fills in the data elements about the expert’s attitude. Then if necessary he should encrypt the appended content and sign. Finally he submits the XML document to the center server. The center server processes it and transfers it to the next clerk, which is the leader in the case. 4. The leader receives the XML document, then decrypts the encrypted data and validates the content if necessary. And he fills in the data elements about the application result. Finally he submits the XML document to the center server. 5. The center server responses to the citizen and stores the e-document in the e-document database.

5

Conclusion

As is illustrated above, the architecture of the collaborative work system for joinup e-government web services together with a data model of e-documents is proposed to meet the requirements for the e-government collaborative work.

References 1. Casati, F., Georgakopoulos, D., and Shan M.: Special Issue on E-Services. VLDB Jour. 24 (2001) 2. Weikum, G.: Special issue on infrastructure for advanced e-services. IEEE Data Engi. Bull. 24 (2001)

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3. Casati, F., Ilnicki, S., Jin, L.J., Krishnamoorthy, V., and Shan, M.C.: Adaptive and dynamic service composition in eFlow. Proc. of the Int. Confe. on Adva. Info. Syst. Engi. (2000) 4. Benatallah, B., DUMAS, M., etc: Declarative Composition and Peer-to-Peer Provisioning of Dynamic Web Services. Proc. of the 18th Inte. Confe. on Data Engi. (2002)

A Novel Method for Eye Features Extraction Zhonglong Zheng, Jie Yang, Meng Wang, and Yonggang Wang Institute of image processing and pattern recognition, Shanghai Jiao Tong University, Shanghai, China, 200030 {zhonglong, jieyang}@sjtu.edu.cn

Abstract. Extraction of the eye features, like the pupil center and radius, eye corners and eyelid contours from the frontal face images often provides us useful cues in many important applications, such as face recognition, facial expression recognition and 3D face modeling from 2D images. Assuming the rough eye window is known, the color information, Gabor features are extracted from the eye window and then these two features and their mutual relationship have been incorporated into the design of our algorithm. Firstly, after the pupil center is detected in H channel of HSV color space, the pupil radius is estimated and refined. Secondly, eye corners are localized using eye-corner filter based on Gabor feature space. Finally, eyelid curves are fitted by spline function. The new algorithm has been tested on our SJTU database and some other pictures taken from the web. The experimental results show that our algorithm has high accuracy and is robust under different conditions.

1 Introduction It is essential to detect precisely facial features and their contours when designing automatic face analysis and processing systems. The detection results could be used for the model-based image coding [1], facial expression recognition [2], 3D face recognition [3] and so on. Generally speaking, the detection of eye features is the first step in a recognition system. The eye features consist of pupil center and its radius, eye corners and eyelid contours. Among these features, pupil center and radius are the features easier to be detected and estimated. As we know, deformable contour model is a well-known method to extract object contour in computer vision. [5] and [6] made an attempt to utilize such algorithm to eye contour extraction. As pointed out in [4], deformable contour model is not optimal and stable in eye contour extraction. To overcome the limitations of deformable models, researchers pay much more attention to several landmark points of eyes other than extracting the complete continuous eye contour. Then the eye contour can be fitted by some kind of functions [8][4]. This paper also adopts such strategy and the results are encouraging. The paper is organized as follows. Based on the assumption that the rough eye window has been detected, Section 2 describes our method in detail: pupil center and radius, eye corners and eyelid contours are precisely detected and estimated step by step. The experimental results are listed in Section 3. The last section draws the conclusion of the paper. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1002–1007, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Extraction of Eye Features Most of the existing detection algorithms for eye features extraction are based on the gray level of the images. However, color information could provide extra cues for detection and recognition. Therefore, the input image for the proposed method is color image and each of them contains a single eye. It is assumed that the approximate location of eye is known from previous rough eye detection step. 2.1 Pupil Center Detection and Radius Estimation Pupil center detection is performed in H channel of HSV color space. Fig 1 shows the original images and the corresponding H channel images. It is interesting that in H channel the pupil is the brightest region comparing with its neighborhoods.

Fig. 1. original image and corresponding H channel image

The location of the pupil center can be derived from the vertical integral projection and horizontal integral projection in Fig 2. The peak points of the projection curves correspond to the coordinates of the pupil center. This method has at least two advantages: one is its simpleness; the other is its robustness.

Fig. 2. location of pupil center by integral projection

Once the approximate location of pupil center is given, a circle with fixed radius is established. The first searching step is circle shift. The operation of this step is to shift the circle in a given neighborhood to obtain a location on which the mean gray

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level of pixels in the circle is the lowest. The second searching step is expansion or shrinking of the circle. The rule of expansion or shrinking is also to minimize the mean gray value of pixels in the circle. In Fig 3, the first row and second row are the location of eyeball before and after the search strategy.

Fig. 3. Location of eyeball before and after the search strategy

2.2 Detection of Eye Corners Here, we propose an eye corner filter based on Gabor feature space for eye corner detection. The Gabor wavelet can be defined as follows

ψ µ ,ν ( z ) =

kµ ,ν

σ

2

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e

( − kµ ,ν

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[e

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− e −σ

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2

/2

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iφµ

(1)

I ( z ) is

Gµ ,ν ( z ) = I ( z ) ∗ψ µ ,ν ( z )

(2)

where z = ( x, y ) and ∗ is the convolution operator. It is obvious that eye corner points are the intersection of the two eyelid curves and the end points of eyelid curves at the same time. Furthermore, the structure is highlighted in Gabor feature space. Motivated by these properties, the paper describes an eye corner filter based on Gabor feature space. The filter is constructed by coefficients at some scales and orientations in Gabor feature space. For example, the filter representing the eye corner near the bridge of the nose is denoted by a 5 × 5 mask. The center of the mask corresponds to the eye corner manually located while other elements of the mask to the neighbors of the eye corner. The values of the elements in the mask are determined by its Gabor representation. Let I ( x, y ) be an eye image,

C ( x, y ) be the 5 × 5 patch image centered at eye corner and Gµ ,ν ( z ) be the Gabor representation of C ( x, y ) ⎛ g 1,1 ⎜ g 2 ,1 G =⎜ ⎜ ... ⎜⎜ ⎝ g 5 ,1

g 1, 2

...

g 2,2 ...

... ...

g 5 ,2

...

g 1,8 ⎞ ⎟ g 2 ,8 ⎟ ... ⎟ ⎟ g 5 ,8 ⎟⎠

(3)

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at five scales and eight orientations. For illumination invariance, G can be normalized as

G' =

G

∑

i, j

gi, j

2

⎛ g '1,1 ⎜ ' g = ⎜ 2,1 ⎜ ... ⎜⎜ ' ⎝ g 5,1

g '1,2 g ' 2,2

... ...

...

...

g '5,2

...

g '1,8 ⎞ ⎟ g ' 2,8 ⎟ ... ⎟ ⎟ g '5,8 ⎟⎠

Let f be the mean value of the first two rows coefficients of G

f =

1 ∑ gi , j n i, j

(4)

'

(5)

n = 16 , i = 1, 2 and j = 1, 2,...,8 . Some Gabor representations, f of C ( x, y ) , are shown in Fig 4.

where

To construct an eye corner (near the bridge of nose) filter, we select 80 corner images described by C ( x, y ) above. The final eye corner (near the bridge of nose) filter is constructed by calculating the average of f

F5×5 =

1 N

N

∑f

i

(6)

i =1

where N = 80 . F5×5 is shown in Fig 5(a).

Fig. 4. Gabor representation of eye corner images

The other eye-corner filter is 7 × 7 in order to contain more information of the corner structure because of its complexity. F7×7 is shown in Fig 5(b). To detect eye corners in an eye image, we need to convolve the Gabor representation of the eye image (the selection of scale and orientation is the same as Gabor representation of eye corner images, and normalized by equation (4) and (5)) with certain filter. In order to reduce the computational cost, the convolution operation is calculated on part of the image because the center and radius of the eyeball are given by previous steps. The corner detection results are shown in Fig 6.

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(a)

(b)

Fig. 5. Eye corner filters

part2

(a) (a)

part1

(b)

(c)

(d)

Fig. 6. Corner detection (a) an eye image on gray level (b) convolution of Gabor representation of part2 in (a) with

F7×7

(c) convolution of Gabor representation of part1 in (a) with

F5×5

(d)

final corner detection result

2.3 Eyelid Curve Fitting

Actually, eye corners are the intersection of the two eyelid curves, and the end points at the same time. Now we only need some medial points to fit the curve. It is advisable to detect the points along the column through the center of pupil in the eye image, denoted by red circle in Fig 7 (a). We use a 7 × 7 window to filter the eye image on gray level: the minimum value in the window is subtracted in order to make the edge more salient. By searching the peak points of column line in Fig 7 (a), we find the medial points. Fitting the eyelid curve with corner points and medial points by spline function, we depict the eyelid curve in Fig 7 (b).

(a)

(b)

Fig. 7. Medial point detection and eyelid curve fitting

3 Experimental Results After obtaining the eye corner filter F5×5 and F7×7 , we apply them to our test dataset that contains more than 700 images, and to some pictures taken from the web. The images are taken under different lighting conditions and some have a slight rotation. Fig 8 shows part of the experimental results. The detected eyeball and eyelid curves are described in red, and eye corners in green.

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The algorithm process is carried out step by step, i.e. if the first step is not accurate, the following detection may be failed. Fortunately, pupil center detection and radius estimation achieve high accuracy over 98%. Thus, the proposed method reached desired performance.

Fig. 8. Part of experimental results

5 Conclusion A robust and accurate algorithm for eye features extraction is proposed in the paper. Firstly, the center of pupil is detected in H channel of HSV space, and then the radius of eyeball is estimated and refined. Secondly, eye corners are detected by the proposed eye-corner filter constructed in Gabor feature space. Finally, based on the results obtained from the previous steps, eyelid curve is fitted by spline function. The proposed methods have shown its good performance in terms of accuracy and robustness, while being straightforward in implementation.

References 1. Zheng N., Song W., Li W.: Image Coding Based on Flexible Contour Model. Machine Graphics Vision 1 (1999) 83-94 2. Brunelli R., Poggio T.: Face Recognition Through Geometrical Features. In: 2nd European Conf. on Computer Vision (1992) 792-800 3. Blanz V., Vetter T.: Face Recognition Based on Fitting a 3D Morphable Model. IEEE trans. on PAMI. 25 (2003) 1063-1075 4. Vezhnevets V., Degtiareva A.: Robust and Accurate Eye Contour Extraction. Proc. Graphicon (2003) 81-84 5. Lam K.M., Yan H.: Locating and Extracting The Coverd Eye in Human Face Image. Pattern Recogntion 29 (1996) 771-779 6. Yin L., Basu A.: Realistic Animation Using Extended Adaptive Mesh for Model Based Coding. In: Proceedings of Energy Minimization Methods in Computer Vision and Pattern Recognition (1999) 315-318 7. Feng G.C., Yuen P.C.: Multi-cues Eye Detection on Gray Intensity Image. Pattern Recognition 34 (2001) 1033-1046 8. Yulle A., Hallinan P., Cohen D.: Feature Extraction from Faces Using Deformable Templates. International Journal of Computer Vision 8 (1992) 99-111

A Q-Based Framework for Demand Bus Simulation Zhiqiang Liu, Cheng Zhu, Huanye Sheng, and Peng Ding Department of Computer Science, Shanghai Jiao Tong University, 200030, Shanghai, China {zqliu, microzc}@sjtu.edu.cn [email protected], [email protected]

Abstract. With the development of telecom, it becomes possible to provide people with Location Based Service (LBS) according to their spatial positions by using mobile equipments. Before using such services, people should evaluate them and make suitable strategies. Demand Bus System is attracting attention as a new public transportation system that provides convenient transportation for special services while solving traffic jams in urban areas. Previous researches focused on the algorithms to the dial-a-ride problem, and few works did on evaluating the usability of the demand bus system. In this paper we proposed a Q-based multi-agent simulation framework for this purpose and implemented a prototype system.

1 Introduction With the development of telecom, it becomes possible to provide people with Location Based Service (LBS) according to their spatial positions by using mobile equipments. Before using such services, people should evaluate them and make suitable strategies. Demand bus system (DBS), also called as demand response system, is thought to be a new way to provide convenient transportation for special services. The user calls a bus center, states the destination and the wanted time period, and then the bus center arranges a suitable bus to pick up the user in some time. It's faster and more convenient than traditional bus, and cheaper than taxi. Different demand bus services had been provided for people all over the world. But people found it's difficult to build perfect demand bus systems to different situations. A rich variety of dial-a-ride problems emerges from the characteristics of the servers, the rides, the metric space, and the objective function. Dial-a-ride problems have been studied extensively in the literature, see for example, Hunsaker and Savelsbergh[1], Diana and Dessouky[2], and Healy and Moll[3].These researches mainly concentrated on the algorithms to solve the problem, and few did on the framework to investigate the effectiveness and the strategy. This has induced the need for suitable methodologies and tools to help in investigating the effectiveness and the strategy of DBS. A useful evaluation tool for achieving these objectives, in particular when lacking real applications is multi-agent based simulation (MABS). In this context, MABS is used as the process of designing and creating a model of a likely or expected public transportation system for conducting numerical experiments. The J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1008–1013, 2004. © Springer-Verlag Berlin Heidelberg 2004

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purpose is to obtain a better understanding of the behaviors of such a system in a given set of conditions, even with uncertain treatment of events. In order to describe the interaction between human and agents, we use the interaction design language-Q, which has been proved to be a good language to build such simulation. In section 2, we propose a Q-based simulation framework. A prototype system using this framework is implemented in section 3. Conclusion and future work are discussed in the last part.

2 DBS Simulation Framework 2.1 Simulation Framework The framework is constructed by three parts (Fig 1): Model designers, Multi-agent system and information resources.

Fig. 1. Q-based Framework for Demand Bus Simulation

To understand complex system, researchers, together with domain experts and stakeholders, would build a model to simulate the phenomenon by using participatory methods. Q language provides a bridge for domain experts and computer experts to share their knowledge on the problem. The detail of Q language will be discussed later. Multi-agent system includes three parts: Q scenario, Q agent adapter and Q agent manager. Q scenario describes agents’ states and actions, which are designed according to the simulation model. Q agent manager is in charge of the management

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of agents and is also the implementation of actions described in scenario. Q agent adapter creates a link between above two parts and also serves as a message layer for the communication between agents. 2.2 Interaction Design Language: Q Some inter-agent protocol description languages, such as KQML and AgenTalk, often regulate an agent’s various actions on the basis of computational model of agent internal mechanisms. Obviously, these agents based on strict computational models have to be designed and developed by computer experts. It is necessary to design a new agent interaction description language, which makes it possible that those noncomputer-professional application designers, such as sales managers and consumers, might write scenarios to describe and model the behaviors of agents, so that a practical multi-agent system can be easily established. Under the background, we start working on Q language [4] - a scenario description language for designing interaction among agents and humans. This kind of scenario-based language is to design interaction from the viewpoint of scenario description, but not for describing agent’s internal mechanisms. Q is highly practical and realistic, which can support many totally different agent systems, such as FreeWalk [5] and Crisis Management [6] for its powerful ability of describing human requests to autonomous agents. So it’s a good language in demand bus system simulation.

3 Demand Bus Shanghai 3.1 The Problem Shanghai is one of the biggest cities in China, which has a population of about 13 Millions. People have to spend lots of time back and forth for work because of the long distance and the bad traffic. Traditional buses have too many stops. In rush-hour, many crowded buses still move along fixed route and stop at every stop even no passenger alights in many stops. With the extension of Shanghai, the city is divided into many small parts with different functions. Some of them are living centers, some are working centers, and others are shopping or entertainment centers. Therefore, it’s possible to use demand bus system as community transportation in Shanghai. 3.2 Simulation Design We suppose that there is only one Bus Center that is in charge of the demand bus system. When it receives user’s request for demand bus service, it will immediately try to find a suitable bus and inform the task. If there is no bus available, the user’s request would be rejected. All buses are treated as independent individuals and can compete for the task to take users. In order to improve the response effect, we designed the multi-agent system according to the Post Price Model [7]. The design process is shown as Fig 2. State transition diagram shows the rules of bus agent will

A Q-Based Framework for Demand Bus Simulation

1011

abide by. At the beginning, when a bus comes into system, it would post its price that means how far it would not like to go, how long its working time is or other conditions. The price is used to find a suitable bus to serve a new request. When a user calls bus center, bus center will find one bus according to buses’ prices and the objective function. The objective function in the simulation is to minimize the total trip distance of all users.

Fig. 2. Illustration of the design process

In the simulation, we supposed that there are no traffic jams; requests for demand bus occur with random frequency in fixed time; departure and destination points are decided randomly and a passenger would use a demand bus and do not transfer between buses. We designed three situations: 1. Multi-Vehicle, Random user requests and the bus acts as a taxi, each time services only for one user. We do such simulation for the purpose of observing the relationship between the service area and the service usability. It should be pointed out that in this case, the numbers of demand buses are equal to those of the user’s requests because we want to decrease the influence of users’ waiting-for-bus time (WBT). We did this simulation in four different scale areas. In each area three different situations are tested, one is 10 requests happen randomly in fixed time period, one is 30 and another is 50. 2. Multi-Vehicle, Random user requests and the bus has unlimited capacity. This simulation aims to find the relationship between the service bus numbers and the service usability. In each area, different amount of bus are used. We observed the average service time, the average WBT and the average transition time. 3. In the last case, conditions are the same as the second simulation except that there are two areas represented as the living center and shopping center separately. User’s origin and destination would be located in the two centers respectively. We

1012

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call this kind of situation as Centralized Position simulation. Three kinds of experiments would be done: in the first case, the distance of two centers is long. In the second, the distance is middle, and in the third, we still use random position. We want to use these experiments to find out the effect of using the demand bus for such situation. 3.3 Experiment Result and Analysis When the amount of demand requests increased (>30) in a large area (400*400), the Average service time increased obviously. Except the influence of the program, it can also be thought that dividing the whole area into small parts can improve the performance of demand bus system.

Fig. 3. The simulation result of experiment 2

In the experiment of second situation, the average service time decreased when the number of demand buses increase. But when the amount of demand buses are enough (in the 200*200 and 400* 400 areas cases, to provide service for 10 users, 4 buses is enough.), the average service time remains unchanged. Among the four results, the average service time is mainly influenced by the WBT. The results are shown in Fig3. In the last experiment, the total distance of all buses with centralized position in the first case is the smallest comparing to the other two. In this case, we can use a small number of buses to serve for the area with similar destinations. It’s suitable for Shanghai which has many communities and many residents having the same situations.

A Q-Based Framework for Demand Bus Simulation

1013

4 Conclusion and Future Work In this paper, we proposed a Q-based multi-agent simulation framework to evaluate the usability of demand bus system. Initial result shows that the system based on such framework can be designed easily and used to evaluate the demand bus system using in Shanghai. Current work is based on the centralized architecture. It’s difficult to re-plan the route and to involve all information of the bus drivers and the demand bus system users in the real system. In our future work, distributed organization would be considered in order that buses can communicate with each other to re-plan some users’ route according to drivers’ and users’ situations. Acknowledgement. This work was supported by Association of International Education, Japan (AIEJ). The authors would thank Prof. Ishida, Dr. Torii and Dr. Murakami in Kyoto University for their help during the conceiving of this paper.

References 1. Hunsaker B., Savelsbergh M.: Efficient feasibility testing for dial-a-ride problems. Operations research letters. 30 (2002) 169-173 2. Diana M., Dessouky M. M.: A new regret insertion heuristic for solving large-scale dial-aride problems with time windows. Transportation Research Part B. 38 (2004) 539–557 3. Healy P., Moll R.: A new extension of local search applied to the Dial-A-Ride Problem. European Journal of Operational Research. 83 (1995) 83-104 4. Ishida T.: Q: A Scenario Description Language for Interactive Agents. IEEE Computer, Vol.35. (2002) 5. Ishida T.: Digital City Kyoto: Social Information Infrastructure for Everyday Life. Communications of the ACM (CACM), Vol. 45, No. 7. (2002) 76-81 6. Ishida T., Nakanishi H., Takata S.: Crisis Management Simulation in Digital City. Journal of the Institute of Systems,Control and Information Engineers. (2002) 7. Buyya R., et al.: Economic Models for Resource Management and Scheduling in Grid Computing. The Journal of Concurrency and Computation: Practice and Experience (CCPE). (2002)

A Q-Based Framework for Demand Bus Simulation Zhiqiang Liu, Cheng Zhu, Huanye Sheng, and Peng Ding Department of Computer Science, Shanghai Jiao Tong University, 200030, Shanghai, China {zqliu, microzc}@sjtu.edu.cn [email protected], [email protected]

Abstract. With the development of telecom, it becomes possible to provide people with Location Based Service (LBS) according to their spatial positions by using mobile equipments. Before using such services, people should evaluate them and make suitable strategies. Demand Bus System is attracting attention as a new public transportation system that provides convenient transportation for special services while solving traffic jams in urban areas. Previous researches focused on the algorithms to the dial-a-ride problem, and few works did on evaluating the usability of the demand bus system. In this paper we proposed a Q-based multi-agent simulation framework for this purpose and implemented a prototype system.

1 Introduction With the development of telecom, it becomes possible to provide people with Location Based Service (LBS) according to their spatial positions by using mobile equipments. Before using such services, people should evaluate them and make suitable strategies. Demand bus system (DBS), also called as demand response system, is thought to be a new way to provide convenient transportation for special services. The user calls a bus center, states the destination and the wanted time period, and then the bus center arranges a suitable bus to pick up the user in some time. It's faster and more convenient than traditional bus, and cheaper than taxi. Different demand bus services had been provided for people all over the world. But people found it's difficult to build perfect demand bus systems to different situations. A rich variety of dial-a-ride problems emerges from the characteristics of the servers, the rides, the metric space, and the objective function. Dial-a-ride problems have been studied extensively in the literature, see for example, Hunsaker and Savelsbergh[1], Diana and Dessouky[2], and Healy and Moll[3].These researches mainly concentrated on the algorithms to solve the problem, and few did on the framework to investigate the effectiveness and the strategy. This has induced the need for suitable methodologies and tools to help in investigating the effectiveness and the strategy of DBS. A useful evaluation tool for achieving these objectives, in particular when lacking real applications is multi-agent based simulation (MABS). In this context, MABS is used as the process of designing and creating a model of a likely or expected public transportation system for conducting numerical experiments. The J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1008–1013, 2004. © Springer-Verlag Berlin Heidelberg 2004

A Q-Based Framework for Demand Bus Simulation

1009

purpose is to obtain a better understanding of the behaviors of such a system in a given set of conditions, even with uncertain treatment of events. In order to describe the interaction between human and agents, we use the interaction design language-Q, which has been proved to be a good language to build such simulation. In section 2, we propose a Q-based simulation framework. A prototype system using this framework is implemented in section 3. Conclusion and future work are discussed in the last part.

2 DBS Simulation Framework 2.1 Simulation Framework The framework is constructed by three parts (Fig 1): Model designers, Multi-agent system and information resources.

Fig. 1. Q-based Framework for Demand Bus Simulation

To understand complex system, researchers, together with domain experts and stakeholders, would build a model to simulate the phenomenon by using participatory methods. Q language provides a bridge for domain experts and computer experts to share their knowledge on the problem. The detail of Q language will be discussed later. Multi-agent system includes three parts: Q scenario, Q agent adapter and Q agent manager. Q scenario describes agents’ states and actions, which are designed according to the simulation model. Q agent manager is in charge of the management

1010

Z. Liu et al.

of agents and is also the implementation of actions described in scenario. Q agent adapter creates a link between above two parts and also serves as a message layer for the communication between agents. 2.2 Interaction Design Language: Q Some inter-agent protocol description languages, such as KQML and AgenTalk, often regulate an agent’s various actions on the basis of computational model of agent internal mechanisms. Obviously, these agents based on strict computational models have to be designed and developed by computer experts. It is necessary to design a new agent interaction description language, which makes it possible that those noncomputer-professional application designers, such as sales managers and consumers, might write scenarios to describe and model the behaviors of agents, so that a practical multi-agent system can be easily established. Under the background, we start working on Q language [4] - a scenario description language for designing interaction among agents and humans. This kind of scenario-based language is to design interaction from the viewpoint of scenario description, but not for describing agent’s internal mechanisms. Q is highly practical and realistic, which can support many totally different agent systems, such as FreeWalk [5] and Crisis Management [6] for its powerful ability of describing human requests to autonomous agents. So it’s a good language in demand bus system simulation.

3 Demand Bus Shanghai 3.1 The Problem Shanghai is one of the biggest cities in China, which has a population of about 13 Millions. People have to spend lots of time back and forth for work because of the long distance and the bad traffic. Traditional buses have too many stops. In rush-hour, many crowded buses still move along fixed route and stop at every stop even no passenger alights in many stops. With the extension of Shanghai, the city is divided into many small parts with different functions. Some of them are living centers, some are working centers, and others are shopping or entertainment centers. Therefore, it’s possible to use demand bus system as community transportation in Shanghai. 3.2 Simulation Design We suppose that there is only one Bus Center that is in charge of the demand bus system. When it receives user’s request for demand bus service, it will immediately try to find a suitable bus and inform the task. If there is no bus available, the user’s request would be rejected. All buses are treated as independent individuals and can compete for the task to take users. In order to improve the response effect, we designed the multi-agent system according to the Post Price Model [7]. The design process is shown as Fig 2. State transition diagram shows the rules of bus agent will

A Q-Based Framework for Demand Bus Simulation

1011

abide by. At the beginning, when a bus comes into system, it would post its price that means how far it would not like to go, how long its working time is or other conditions. The price is used to find a suitable bus to serve a new request. When a user calls bus center, bus center will find one bus according to buses’ prices and the objective function. The objective function in the simulation is to minimize the total trip distance of all users.

Fig. 2. Illustration of the design process

In the simulation, we supposed that there are no traffic jams; requests for demand bus occur with random frequency in fixed time; departure and destination points are decided randomly and a passenger would use a demand bus and do not transfer between buses. We designed three situations: 1. Multi-Vehicle, Random user requests and the bus acts as a taxi, each time services only for one user. We do such simulation for the purpose of observing the relationship between the service area and the service usability. It should be pointed out that in this case, the numbers of demand buses are equal to those of the user’s requests because we want to decrease the influence of users’ waiting-for-bus time (WBT). We did this simulation in four different scale areas. In each area three different situations are tested, one is 10 requests happen randomly in fixed time period, one is 30 and another is 50. 2. Multi-Vehicle, Random user requests and the bus has unlimited capacity. This simulation aims to find the relationship between the service bus numbers and the service usability. In each area, different amount of bus are used. We observed the average service time, the average WBT and the average transition time. 3. In the last case, conditions are the same as the second simulation except that there are two areas represented as the living center and shopping center separately. User’s origin and destination would be located in the two centers respectively. We

1012

Z. Liu et al.

call this kind of situation as Centralized Position simulation. Three kinds of experiments would be done: in the first case, the distance of two centers is long. In the second, the distance is middle, and in the third, we still use random position. We want to use these experiments to find out the effect of using the demand bus for such situation. 3.3 Experiment Result and Analysis When the amount of demand requests increased (>30) in a large area (400*400), the Average service time increased obviously. Except the influence of the program, it can also be thought that dividing the whole area into small parts can improve the performance of demand bus system.

Fig. 3. The simulation result of experiment 2

In the experiment of second situation, the average service time decreased when the number of demand buses increase. But when the amount of demand buses are enough (in the 200*200 and 400* 400 areas cases, to provide service for 10 users, 4 buses is enough.), the average service time remains unchanged. Among the four results, the average service time is mainly influenced by the WBT. The results are shown in Fig3. In the last experiment, the total distance of all buses with centralized position in the first case is the smallest comparing to the other two. In this case, we can use a small number of buses to serve for the area with similar destinations. It’s suitable for Shanghai which has many communities and many residents having the same situations.

A Q-Based Framework for Demand Bus Simulation

1013

4 Conclusion and Future Work In this paper, we proposed a Q-based multi-agent simulation framework to evaluate the usability of demand bus system. Initial result shows that the system based on such framework can be designed easily and used to evaluate the demand bus system using in Shanghai. Current work is based on the centralized architecture. It’s difficult to re-plan the route and to involve all information of the bus drivers and the demand bus system users in the real system. In our future work, distributed organization would be considered in order that buses can communicate with each other to re-plan some users’ route according to drivers’ and users’ situations. Acknowledgement. This work was supported by Association of International Education, Japan (AIEJ). The authors would thank Prof. Ishida, Dr. Torii and Dr. Murakami in Kyoto University for their help during the conceiving of this paper.

References 1. Hunsaker B., Savelsbergh M.: Efficient feasibility testing for dial-a-ride problems. Operations research letters. 30 (2002) 169-173 2. Diana M., Dessouky M. M.: A new regret insertion heuristic for solving large-scale dial-aride problems with time windows. Transportation Research Part B. 38 (2004) 539–557 3. Healy P., Moll R.: A new extension of local search applied to the Dial-A-Ride Problem. European Journal of Operational Research. 83 (1995) 83-104 4. Ishida T.: Q: A Scenario Description Language for Interactive Agents. IEEE Computer, Vol.35. (2002) 5. Ishida T.: Digital City Kyoto: Social Information Infrastructure for Everyday Life. Communications of the ACM (CACM), Vol. 45, No. 7. (2002) 76-81 6. Ishida T., Nakanishi H., Takata S.: Crisis Management Simulation in Digital City. Journal of the Institute of Systems,Control and Information Engineers. (2002) 7. Buyya R., et al.: Economic Models for Resource Management and Scheduling in Grid Computing. The Journal of Concurrency and Computation: Practice and Experience (CCPE). (2002)

A Revision for Gaussian Mixture Density Decomposition Algorithm Xiaobing Yang, Fansheng Kong, and Bihong Liu Artificial Intelligence Institute, Zhejiang University, Hangzhou, China, 310027 [email protected]

Abstract. Gaussian mixture density decomposition (GMDD) algorithm is an approach to the modeling and decomposition of Gaussian mixtures, and it performs well with the least prior knowledge in most case. However, there are still some special cases in which the GMDD algorithm is difficult to converge or can not gain a valid Gaussian component. In this article, a k-means method for Gaussian mixture density modeling and decomposition is studied. Then based on the GMDD algorithm and k-means method, a new algorithm, called k-GMDD algorithm is proposed. It solves the problems of GMDD caused by the symmetry excellent, and consequently makes the applications of GMDD algorithm more extensive.

1 Introduction Finite mixture density modeling and decomposition has been widely applied in variety of important practical situations, such as industrial control [1], machine monitoring [3] and economics [2]. A typical example of application of finite mixture density is the analysis of fisheries data [4]. In this example, for different sex, the mean length of a halibut is approximately different linear function of its age. The age and length of each fish can be measured, but the sex is indistinguishable. Estimating the parameters of the two linear growth curves and determining the sex can be regarded as a problem of finite mixture density modeling and decomposition. A highly robust estimator called model fitting (MF) estimator has been presented by Xinhua Zhuang, Tao Wang and Peng Zhang in 1992 [7]. The MF estimator obtains high robustness through partially but completely modeling the unknown log likelihood function. Using MF estimator, Xinhua Zhuang, Yan Huang, K. Palaniappan and Yunxin Zhao proposed a recursive algorithm called Gaussian mixture density decomposition (GMDD) algorithm for successively identifying each Gaussian component in the mixture. The GMDD algorithm performs well with the least prior knowledge in most case [6]. However, because of some drawbacks, the GMDD algorithm needs still to be improved in order to be more applicable. In this article, a k-means method for Gaussian mixture density modeling and decomposition is studied. Then based on the GMDD algorithm and k-means method, we propose a new algorithm, called k-GMDD algorithm. In the k-GMDD algorithm, the k-means method is used to void the divergence by destroying the symmetry of the data to be decomposed. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1014–1019, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Fundamental Conceptions and GMDD Algorithm Let x1 , x2 ,..., xN be a random sample of completely unclassified observations from n-dimensional Gaussian mixture distribution with q components. If assuming that each observation x j is generated by an unknown Gaussian distribution m( x j ; µ , Σ) with

probability (1 − ε ) plus an unknown outlier distribution h(⋅) with probability ε , the probability density function of x j is given by

1 (1 − ε )exp(− d 2 ( x j )) 2 m( x j ; µ, Σ) = + ε h( x j ) n ( 2π ) | Σ |

(1)

where Σ is the covariance matrix, and d 2 ( x j ) represents the squared Mahalanobis distance of x j from the unknown mean vector µ , i.e. d 2 ( x j ) = ( x j − µ ) ' Σ −1 ( x j − µ )

(2)

If ε = 0 , the density m(⋅; µ , Σ) becomes a pure Gaussian density. Otherwise, if

ε > 0 , m(⋅; µ , Σ) is called a contaminated Gaussian density [5]. The likelihood estimating equations can be written as: N

∑ ∇ µ ln m( x j ; µ , Σ) = 0

(3a)

j =1

N

∑ ∇∑ ln m( x j ; µ , Σ) = 0

(3b)

j =1

where ∇µ and ∇∑ denote respectively differentiations with respect to µ and ∑ . Let g j stands for (exp(−d 2 ( x j ) / 2)) /(( 2π ) n | Σ |) , m j stands for m( x j ; µ , Σ) . Ideally, a sample x j is classified as an inlier if it is realized from g j or as an outlier otherwise (i.e., it comes from h( x j ) ). The probability of a sample x j being an inlier is given by

λj =

(1 − ε ) g j mj

(4)

According to the Bayesian classification rule, if we assume the unknown density function h as follows: h( x1 ) = h( x2 ) = " = h( xn ) = h0

we would get the same output results. Then, (1) can be rewritten as

(5)

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m j = (1 − ε ) g j + ε h0

(6)

∑ ∇ µ ln((1 − ε ) g j + ε h0 ) = 0

(7a)

then (3) can become N

j =1

N

∑ ∇Σ ln((1 − ε ) g j + ε h0 ) = 0

(7b)

j =1

The gradients ∇ µ ln((1 − ε ) g j + ε h0 ) and ∇Σ ln((1 − ε ) g j + ε h0 ) can be derived as 1 2

λ j Σ−1 ( x j − µ ) and − λ j Σ−1{1 − Σ−1 ( x j − µ )( x j − µ ) '} , where λ j = t=

(1 − ε ) g j mj

=

gj gj +t

,

ε h0 . 1− ε Accordingly, the likelihood estimating equations (7) can be written as N

∑ λ j (x j − µ) = 0

(8a)

j =1

N

N

j =1

j =1

∑ λ j − Σ −1 ∑ λ j ( x j − µ )( x j − µ ) ' = 0

(8b)

At each selected partial model “ ts ”, s = 0,1," , L , where t L denotes an upper bound for all potentially desirable partial models, the iterative procedure of GMDD algorithm can be implemented based on (8). In GMDD algorithm, the Kolmogorov-Smirnov (K-S) normality test is used to determine the validity of extracted Gaussian components [6].

3 K-GMDD Algorithm In most case, the GMDD algorithm performs well with the least prior knowledge [6]. However, there are still some special case in which the GMDD algorithm may be hard to converge or can not gain a valid Gaussian component. For example, when there are two Gaussian components with different mean vector µ .But like covariance matrix ∑ and density in n-dimensional space, GMDD may regard them as a whole and be unable to converge or it will get a single Gaussian component which fails to the K-S test. Accordingly, it is still necessary to improve the GMDD algorithm in order to make it be more applicable. K-means method is a well-known and commonly partitioning method. The k-means method takes the input parameter, k, and partitions a set of objects into k clusters so that the resulting intra-cluster similarity is high whereas the inter-cluster similarity is low. Cluster similarity is measured in regard to the mean value of the objects in the cluster, which can be viewed as the cluster’s center.

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K-means works well when the clusters are compact clouds that are rather well separated from each other. It is relatively scalable and efficient in processing large data sets because of its low computational complexity. However, the k-means method can be applied only in few specific cases for some faults of it. For example, it is sensitive to noise and outlier data points since a small number of such data can substantially influence the mean value [3]. In this article, Gaussian mixture density modeling and decomposition with assist of k-means method is studied. Then based on the GMDD algorithm and k-means method, a new algorithm, called k-GMDD algorithm is proposed. In the k-GMDD algorithm, the k-means method is used to void the divergence by destroying the symmetry of the data to be clustered. The k-GMDD algorithm can be described as the following steps: Step 1. Let X be the data set to be clustered, set a threshold N min to decided when end the procedure. Step 2. Execute GMDD algorithm on X until GMDD be unable to converge or can not get a proper Gaussian component, if S ≥ N min , where S is the size of newest data set X new , go to Step 3. Otherwise, return. Step 3. Use k-means method to split X into k sub-dataset X 1 , X 2 ," , X k . Assume

size( X 1 ) ≤ size( X 2 ) ≤ " ≤ size( X k ) , then perform GMDD algorithm on X − X 1 , X − X 2 , " , X − X k in turn until get a valid Gaussian component G. Step 4. Subtract G from X, if S ≥ N min , go to Step 2. Otherwise, return. If the given data set can be decomposed well by GMDD in Step 2 at first time, the algorithm will not execute Step 3, and become pure GMDD algorithm. Step 3 gives a solution to those cases in which GMDD algorithm can not perform well. The input parameter k in Step 3 can be selected randomly in a certain scope. If in some case, given k selected, valid Gaussian component can not be gained, we should have to change the value of k and try to run Step 3 again. The validity of extracted Gaussian components is still determined by the result of K-S test. If the test succeeds, a valid Gaussian component will be determined, and subtracted from the current data set. Then next valid Gaussian component will be identified in the new size-reduced data set. Individual Gaussian components continue to be estimated recursively until the size of a new data set gets too small. The k-GMDD algorithm is effective and robust. It uses GMDD algorithm clustering, and uses k-means method to solve excellently the problems of GMDD caused by the symmetry. Consequently it makes the applications of GMDD algorithm more extensive.

4 Simulation Experiment In order to illustrate the robustness and efficiency, we compare the k-GMDD algorithm with the GMDD algorithm by performing cluster analysis using simulated two-dimensional (2-D) mixture datasets. The generated data consist of three clean Gaussian distribution components under a noisy background consisting of 780 data

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points uniformly distributed. Fig. 1 and Fig. 2 show the performance of the GMDD algorithm and the k-GMDD algorithm.

Fig. 1. The GMDD algorithm can not detect a valid component

Fig. 2. The k-GMDD algorithm detects a valid component

The data values that are assigned to a cluster are marked by “ ∆ ” in the results, and that unassigned to any cluster are marked by “.” symbol. From Figure 1, we can see that it is hard, for the given data set, to converge in GMDD algorithm. On the other hand, the k-GMDD algorithm detected successfully a valid Gaussian component as showed in Figure 2. It is clear that the k-GMDD algorithm will detect easily an other valid Gaussian component after the first gained component having been subtracted from the data set.

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5 Conclusions In this paper a new algorithm called k-GMDD has been proposed for Gaussian mixture density decomposition. This novel algorithm can be robust and effective, which has been illustrated by the simulation experiment. Though the k-GMDD appears to be rather successful, at least by the simulation experiment, there are problems should be further investigated. The value of k may affect badly the performance of the k-GMDD algorithm. Thus, the selection of value of k will be very importable. Application of k-GMDD to high-dimensional data sets is a problem to be researched. Another important topic of k-GMDD is guessing good initializations or reducing the range of random initializations in order to maintain the efficiency of the k-GMDD algorithm. We hope to make some of the above issues the basis of a future investigation.

References 1. Arabie, P., Hubert, L.J., Soete, G. De (eds.): Clustering and Classification, Singapore: World Scientific (1996) 2. Hamermesh, D.S.: Wage bargains, threshold effects, and the phillips curve. In: Quarterly Journal of Economics, vol. 84 (1970) 501-517 3. Han, J., Kamber, M. :Data Mining: Concepts and Techniques, Morgan Kaufmann Publishers, San Francisco (2001) 4. Hosmer, D.W.: Maximum likelihood estimates of the parameters of a mixture of two regression lines. In: Communications in Statistics, vol.3, no. 10 (1974) 995-1005 5. Huber, P.J.: Robust Statistics. New York: Wiley (1981) 6. Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian Mixture Density Modeling, Decomposition, and Applications. In: IEEE Trans. Image Processing, vol. 5, no. 9 (1996) 1293-1302 7. Zhuang, X., Wang, T., Zhang, P.: A Highly Robust Estimator through Partial-Likelihood Function Modeling and Its Application in Computer Vision. In: IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 1 (1992) 19-35

Discretization of Continuous Attributes in Rough Set Theory and Its Application* Gexiang Zhang1,2, Laizhao Hu1, and Weidong Jin2 1

National EW Laboratory, Chengdu 610036 Sichuan, China [email protected] 2 School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China

Abstract. Existing discretization methods cannot process continuous intervalvalued attributes in rough set theory. This paper extended the existing definition of discretization based on cut-splitting and gave the definition of generalized discretization using class-separability criterion function firstly. Then, a new approach was proposed to discretize continuous interval-valued attributes. The introduced approach emphasized on the class-separability in the process of discretization of continuous attributes, so the approach helped to simplify the classifier design and to enhance accurate recognition rate in pattern recognition and machine learning. In the simulation experiment, the decision table was composed of 8 features and 10 radar emitter signals, and the results obtained from discretization of continuous interval-valued attributes, reduction of attributes and automatic recognition of 10 radar emitter signals show that the reduced attribute set achieves higher accurate recognition rate than the original attribute set, which verifies that the introduced approach is valid and feasible.

1 Introduction Rough set theory (RST), proposed by Pawlak [1], is a new fundamental theory of soft computing. [2] RST can mine useful information from a large number of data and generates decision rules without prior knowledge [3,4], so it is used generally in many domains [2,3,5 9]. Because RST can only deal with discrete attributes, a lot of continuous attributes existing in engineering applications can be processed only after the attributes are discretized. Thus, discretization becomes a very important extended research issue in rough set theory. [2,6,7,8] Although many discretization methods, including hard discretization [2,5,6] and soft discretization [7,8], have been presented in rough set theory, the methods are only used to discretize point attribute values (fixed values). However, in engineering applications, especially in pattern recognition and machine learning, the features obtained using some feature extraction approaches usually vary in a certain range (interval values) instead of fixed values because of −

* This work was supported by the National Defence Foundation (No.51435030101ZS0502). J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1020–1026, 2004. © Springer-Verlag Berlin Heidelberg 2004

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several reasons, such as plenty of noise. So a new discretization approach is proposed to process the decision table in which the attributes vary continuously in some ranges.

2 Definition of Generalized Discretization The main point of the existing discretization definition [2] is that condition attribute space is split using selected cuts. The existing discretization methods [2,5-8] always try to find the best cutting set. When the attributes are interval values, it is difficult to find the cutting set. So it is necessary to generalize the existing definition of discretization. The following description gives the generalized discretization definition. Decision system S = 〈U , R, V , f 〉 , where R = A ∪ {d } is attribute set, and the sub-

sets A = {a1 , a2 ,

, am } and {d } are called as condition attribute set and decision

attribute set respectively. U = { x1 , x2 , any ai (i = 1, 2,

, xn } is a finite object set, i.e. universe. For

, m) ∈ A , there is information mapping U → Va , where Va is the i

i

value domain, i.e. min

max

min

max

Va = {[va , va ],[va , va ], i

min

x1

x1

x2

x2

i

i

i

i

min

max

xn

xn

i

i

(1)

,[va , va ]}

max

xj

xj

i

i

Where va , va ∈ R, ( j = 1, 2, , n) . For attribute ai ( ai ∈ A) , all objects in universe U are partitioned using class-separability criterion function J (Va ) and an equivalence relation Ra is obtained, that is, a kind of categorization of universe U is got. Thus, in attribute set A , we can achieve an equivalence relation family P, ( P = {Ra , Ra , , Ra }) composed of m equivalence relations Ra , Ra , , Ra . So P the equivalence relation family P defines a new decision system S = 〈U , R, P P P V , f 〉 , where f ( x ) = k , x ∈ U , k = {0,1, } . After discretization, the original decision system is replaced with the new one. Different class-separability criterion functions generate different equivalence relation families that construct different discrete decision systems. The core of the definition is that the discretization of continuous attributes is regarded as a function that transforms continuous attributes into discrete attributes. The new definition is an extended version of the old one and emphasizes on the separability of different classes in discretization. The definition provides a good way to discretize continuous interval-valued attributes. Additionally, considering the separability of classes in the process of discretization can simplify the structure of classifier and eni

i

1

2

m

1

min

xj

hance accurate recognition rate. If va

i

2

m

max

xj

= va , ( j = 1, 2,

, n) , the discretization of

i

interval-valued attributes becomes the discretization of fixed-point attributes. If the class-separability criterion J (⋅) is a special function that can partition the value domain Va of attribute ai ( ai ∈ A) into several subintervals, that is, the special function i

decides a cutting-point set in the value domain Va , the definition of generalized disi

cretization becomes the common definition of discretization.

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3 Discretization Algorithm The key problem of discretizing interval-valued attributes is to choose a good classsepability criterion function. So a class-sepability criterion function is given firstly in the following description. When an attribute value varies in a certain range, in general, the attribute value always orders a certain law. This paper only discusses the decision system in which the attributes have a certain law. To the extracted features, the law is considered approximately as a kind of probability distribution. Suppose that functions f ( x ) and g ( x ) that are one-dimensional, continuous and non-negative real, are respectively the probability distribution functions of attribute values of two objects in universe U in decision system. The below class-separability criterion function is introduced.

J = 1−

∫ f ( x) g ( x)dx ∫ f ( x)dx ⋅ ∫ g ( x)dx 2

2

(2)

Function J in (2) satisfies the three conditions of class-separability criterion functions [10]: (i) the criterion function value is non-negative; (ii) the criterion function value gets to the maximum when the distribution functions of two classes have nonoverlapping; (iii) the criterion function value equals to zero when the distribution functions of two classes are identical. Because f ( x ) and g ( x ) are non-negative real functions, according to the famous Cauchy Schwartz inequation, we can get

0 ≤ ∫ f ( x) g ( x)dx ≤

∫f

2

( x)dx ⋅

∫ g (x)dx 2

(3)

So the value domain of the criterion function J in (2) is [0,1]. The following description gives the interpretation that function J can be used to justify whether the two classes are separable or not. When the two functions f ( x ) and g ( x ) in (2) are regarded respectively as probability distribution functions of attribute values of two objects A and B in universe U , several separability cases of A and B are shown in figure 1. For all x , if one of f ( x ) and g ( x ) is zero at least, which is shown in Fig. 1(a), A and B are completely separable and the criterion function J arrives at the maximal value 1. If there are some points of x that make f ( x ) and g ( x ) not equal to 0 simultaneously, which is shown in Fig.1(b), A and B are partly separable and the criterion function J lies in the range between 0 and 1. For all x , if f ( x ) = k ⋅ g ( x ) , + k ∈ R , which is shown in Fig.1(c), k = 2 , A and B are unseparable completely and the criterion function J arrives at the minimal value 0. Therefore, it is reasonable that the criterion function J is used to evaluate separability of two classes. According to the above class-separability criterion function, the discretization algorithm of interval-valued attributes in decision system is given as follows. Step 1. Initialization: deciding the number n of objects in universe U and the number m of attributes.

Discretization of Continuous Attributes in Rough Set Theory and Its Application

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Step 2. Constructing decision table: all attribute values are arrayed into a twodimensional table in which all attribute values are represented with an interval values. Step 3. Choosing a little positive number as the threshold Th of class separability. Step 4. For the attribute ai (in the beginning, i = 1 ), all attributes are sorted by the central values from the smallest to the biggest and sorted results are v1 , v2 , , vn . Step 5. The position, where the smallest attribute value v1 in attribute ai is, is encoded to zero (Code=0) to be the initial value of discretization process. Step 6. Beginning with v1 in the attribute ai , the class-separability criterion function value J k of vk and vk +1 ( k = 1, 2, , n − 1) is computed by the sorted order v1 , v2 , , vn in turn. If J k ≥ Th , which indicates the two objects are separable completely, the discrete value of the corresponding position of attribute vk +1 adds 1, i.e. Code=Code+1. Otherwise, J k < Th , which indicates the two objects are unseparable, the discrete value of the corresponding position of attribute vk +1 keeps unchanging. Step 7. Repeating step 6 till all attribute values in attribute ai are discretized. Step 8. If i ≤ m , which indicates there are some attribute values to be discretized, i = i + 1 , the algorithm goes to step 4 and continues until i > m , implying all continuous attribute values are discretized. Step 9. The original decision system is replaced with the discretized one.

f(x)

f(x)

f(x)

g(x) g(x)

(a) J =1

(b) 0< J threshold and height>1 { according to the Cosine similarity formula, the similarity between the classes in classset is calculated; according to the similarity, similar classes are regarded as an element in the set; classset = set; pair= first(set) ; While set≠nil { if the similarity between the classes in pair> threshold then { regard the classes in pair as the subclasses and merge the classes in pair in order to get their parent class called fclass; classset = classset –{pair};//delete the merged classes from classset classset = classset + { fclass };} pair =next(set); } height= height - 1;}} 2.3 DACH Algorithm for Dynamically Maintaining Class Hierarchy How to dynamically merge the classes into class hierarchy becomes more and more important when ontology changes. We propose a new algorithm, DACH, for dynamically maintaining class hierarchy. Its time complexity is O (N), where N is the layer number. The DACH algorithm is described as the following steps: Input: class hierarchy, the merged class Output: merge the class into class hierarchy { set = class hierarchy;

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height =1; using the Cosine similarity formula, calculate the similarity between the merged class and the node in height layer; find the node with the maximal similarity called maxnode; While height threshold then { merge the class into maxnode; store the class in the leaf node;} else store the classes as a leaf node;}

3 Prototype Implementation We adopted the above algorithms in a prototype system PTIDM. Our platform is composed of 2 IBM RS6000 workstations and 2 microcomputers. IBM RS6000 workstations are connected to the ATM network by 155MB/S. The microcomputers are connected to the Ethernet by 10MB/S. All computers are interlinked. We use JAVA program language in order to accomplish platform independence. PTIDM uses DAML+OIL to describe resources and their inter-relations to improve inferential capability. PTIDM can help to acquire ontology information. The CAA algorithm is used to acquire meaningful relationships between different types of instances. Thus, the useful classes may be acquired. According to the similarity between classes, the CCH algorithm is used to create class hierarchy. The DACH algorithm is used to dynamically add the class to a class hierarchy. It is proved that the prototype system has good effect.

4 Related Work Although RDF [4] employs XML to specify semantic networks of information on web pages, there is not any primitive for creating ontology in RDF. Thus it only has a weak idea of ontology. However, some of the Web ontology languages are based on RDF. RDF Schema [5] is improved to some extent. There are some primitives for defining ontology in RDF Schema. In RDF Schema, there is a class hierarchy with multiple inheritances. However, RDF Schema lacks inferential capability. In addition, RDF Schema doesn't maintain effective ontology when ontology changes. In the SHOE language [2], [6], Ontology consists of category and relation definitions. Here classes are called categories. Categories form a simple is-a hierarchy, and slots are binary relations. It also allows relations among instances or instances and data to have any number of arguments. Horn clauses express intensional definitions. SHOE allows all ontologies publicly available on the Web in order to promote interoperability. It also creates some ontologies in specific domain by ontology extension.

A Method of Acquiring Ontology Information from Web Documents

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DAML+OIL [2], [7] employs a different way of defining classes and instances. Besides defining classes and instances declaratively, it use Boolean expressions and the restrictions of class membership to create class definitions. It relies on inference engines to create a class hierarchy and class membership of instances, which are based on the properties of classes and instances. Protégé-2000 [2] provides an integrated environment for editing ontology. It is a conceptual-level ontology editor and knowledge acquisition tool. Thus, developers only consider concepts and relations in the domain that they are modeling. Developers can also customize Protégé-2000 easily to be an editor for a new Semantic Web language.

5 Conclusion Ontology plays an important role on the Semantic Web. Ontology provides a source of shared and well defined terms that can be used in meta-data. In this paper, we propose a method, AOIWD, of acquiring ontology information from Web documents. The AOIWD method employs data mining combined with inference engines to acquire ontology information. In the AOIWD method, we propose the CAA algorithm to create association instances, the CCH algorithm to create class hierarchy and the DACH algorithm to dynamically maintain class hierarchy. The method can find more meaningful relationships and has less human intervention.

Acknowledgement This work is supported by the National Grand Fundamental Research 973 Program of China under No. 2002CB312002, the State Key Laboratory Foundation of Novel Software Technology at Nanjing University under grant A200308 and the Key Natural Science Foundation of Jiangsu Province of China under grant BK2003001.

References 1. Sure, Y. et al. Methodology for Development and Employment of Ontology Based Knowledge Management Applications. SIGMOD Record Vol 31, No 4, December 2002. 2. Noy, N. F. et al. Creating Semantic Web Contents with Protégé--2000. IEEE Intelligent Systems 16(2):60-71, 2001. 3. Agrawal, R. and Srikant, R.. Fast Algorithms for Mining Association Rules. In Proc. of the 20th Int. Conf. on Very Large Databases (VLDB’94), pages 478-499, Santiago, Chile, Sep. 1994. Expanded version available as IBM Research Report RJ9839,June 1994. 4. Lassila, O and Swick, R. R. . Resource Description Framework (RDF) Model and Syntax Specification.W3C Recommendation 22 .www.w3.org/TR/1999/REC-rdf-syntax19990222/ 5. Brickley, D. and Guha,R.V.. Resource Description Framework (RDF) Schema Specification.W3C Candidate Recommendation 27,www.w3.org/TR/2000/CR-rdf-schema20000327.

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6. Heflin, J. and Hendler, J.. Searching the Web with SHOE. In AAAI-2000 Workshop on AI for Web Search. 2000. 7. Hendler, J. and McGuinness, D.L.. “The DARPA Agent Markup Language,” IEEE Intelligent Systems, vol. 16, no. 6, Jan./Feb., 2000, pp. 67–73. 8. Han, L. et al. “A Method of Extracting Information From the Web”. Journal of The China Society for Scientific and Technical Information. Vol.23, No.1. February, 2004, pp. 45-51. 9. Maedche, A. et al. An Infrastructure for Searching, Reusing and Evolving Distributed Ontologies. WWW2003, May 20-24, 2003, Budapest, Hungary.

Adopting Ontologies and Rules in Web Searching Services
He Hu and Xiaoyong Du School of Information, Renmin University of China, Beijing 100872, P.R. China {hehu, duyong}@ruc.edu.cn

Abstract. Keyword-based search has been popularized by Web search services. However, due to the problems associated with polysemy and synonym, users are often unable to get the exact information they are looking for. In this paper, we propose a web search framework in which ontologies and rules are used to deal with the synonym and polysemy problem to gain a better recall and precision performence than the traditional search services. A demonstration system based on Google’s web search APIs is currently under implementation.

1

Introduction

The Web is one of the fastest growing media in the world with millions of pages adding in every day. Buried in this vast, quickly growing collection of documents lies information of interest and use to almost everyone; the challenge is finding it. Currently, search engines are universally employed to find information on the Web. Typically a search engine service works by utilizing keyword (syntactic) matching to find key terms on web sites. Recall and precision are two of the most widely used measures of information retrieval effectiveness for search services. Recall measures how well a service retrieves all the relevant documents, whereas precision measures how well the system retrieves only the relevant documents. There are two main problems impacting the recall and precision level of search services [1]: Problem of polysemy: search services index words, not semantic units; Problem of synonym: search services may miss relevant pages in the answer, just because they apply a different word for the same meaning.

2

Preliminary

2.1

Ontology Approach and Semantic Web

Current search requests must be specified as key words separated by Boolean operators. Search services can only retrieve data on a purely syntactic basis. It


This research was supported by NSFC of China (project number: 604963205)

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1047–1053, 2004. c Springer-Verlag Berlin Heidelberg 2004


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is still not possible to embed domain specific knowledge into the search services’ queries. Ontology approach can solve this problem by providing a semantic foundation in these systems. Tom Gruber [2] has defined ontology as ”a specification of a conceptualization”. Ontologies provide a deeper level of meaning by providing equivalence relations between concepts; they can standardize meaning, description, representation of involved concepts, terms and attributes; capture the semantics involved via domain characteristics, resulting in semantic metadata which forms basis for knowledge sharing and reuse. The Semantic Web has been regarded as the next version of current Web, which aims to add semantics and better structure to the information available on the Web. Underlying this is the goal of making the Web more effective not only for humans but also for automatic software agents. The basic idea is to create an environment for intelligent programs to carry out tasks independently on behalf of the user. Ontologies in fact turn out to be the backbone technology for the Semantic Web; Tim Berners-Lee [3] has portrayed Semantic Web as a layered architecture where ontology layer lies in the middle of the other layers. 2.2

Rule-Based Systems

Research on rule-based systems began in the 1960’s. In the early seventies, Newell and Simon proposed a production system model [4], which is the foundation of the modern rule-based systems. The production model is based on the idea that humans solve problems by applying their knowledge (expressed as production rules) to a given problem represented by problem-specific information. The production rules are stored in the long-term memory and the problem-specific information or facts in the short-term memory. A rule-based system usually consists of: a rule set (the rules to evaluate), a working memory (stores state), a matching scheme (decides which rules are applicable) and a conflict resolution scheme (if more than one rule is applicable, decides how to proceed).

3 3.1

Ontologies Plus Rules for Search Services Ontology Model

The ontology model mainly concentrates on solving synonymy problem. For example, ”plane”, ”aeroplane” and ”airplane” all have the meaning of ”flying machine”; when a Web user include the term ”plane” in his (her) query, our ontology model should automatically take the other two terms into account. The ontology model supported query process is illustrated in Fig. 1: Nicola Guarino[5] has partitioned ontology into three different kinds according to their level of generality. Various ontology-based system adopted this partition, for example, Teknowledge Ontologies[6] use upper ontology as foundation and mid-level ontology as integration framework to support application ontologies creation and utilization. In our Web search framework, the ontology model is comprised of application and domain ontoloies which are based on SUMO top-level ontologies [7].

Adopting Ontologies and Rules in Web Searching Services

T erms we apo n

plane

Synonyms arm arm am e nt o rdnanc e we apo nry

{

airplane ae ro plane

Original Query

F inal Q uery

weapo n & plane arm | arm am e nt | o rdnanc e | we apo nry

}

{

&

1049

airplane | ae ro plane

}

http://www.go o gle .c o m /se arc h? q= we apo n+ plane http://www.go o gle .c o m /se arc h? q= we apo n+ airplane http://www.go o gle .c o m /se arc h? q= we apo n+ ae ro plane http://www.go o gle .c o m /se arc h? q= arm + plane ...

Fig. 1. Query Processing supported by Ontology Model

Unlike the complex ontology structure proposed in [8], the ontology structure of our model is quite simple, ontologies in the framework are represented as hierarchies of terms, and synonymy problem is settled by introducing all the necessary synonymous terms at the same hierarchy level. 3.2

Rule Model

Polysemy problem is the main concern for the design of our rule-based system model. We have built rule-based information filtering systems maintaining user search profiles where the profile consists of a set of filtering rules expressing the users’ information filtering policy, each user has his (her) own tailored rules to filter out irrelevant materials. Our model extends the rule approach proposed in [9], which is explained in more detail in section 5. We have designed following predicates in our rule-based system model. The rules are hard coded, and the filtering process is based on simple conventional HTML structures. The bodies of rules consist of the following predicates standing for relations between terms and HTML tags. ap(region type, word): true if a word appears within a region of region type in a Web page. E.g. ap(title, ”plane”) returns true if ”plane” term appears in title; near(region type, word1, word2, n): This predicate is true if both of words word1 and word2 appear within a sequence of n words somewhere in a region of region type of a Web page. The ordering of the two words is not considered. E.g. near(para, ”plane”, ”ticket”, 4). Many other predicates are omitted here. There are two kinds of filtering rules that users can define in our framework: Preprocessing rules: For tuning search services’ particular behaviors. The actions of preprocessing rules are all supported by search services. They are provided at users’ convenience, an experienced user can enter the rules directly in the search query formulas without the help of preprocessing rules. In our framework, different templates are created for each search service, helping user utilizing all the characteristics of each search service. The framework has built a template handling particular Google characteristics; we will continue to build distinct templates for other search services.

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Postprocessing rules: Operating on fetched Web pages. They are much more flexible than preprocessing rules, and constitute the kernel part of our rulebased model. These rules will apply directly to the (HTML) pages fetched by search services; further filter the result according to users’ special requirements. Postprocessing rules takes web pages as text input and creates output after filtering all the text using all rules in the rule set. The result pages could be greatly shrunk after passing through the users’ filtering rules. Postprocessing rules is consisted of predicates defined above. For example, samepara(”plane”, ”ticket”, ”China”, ”2004”) and near(para, ”plane”, ”ticket”, 4); this rule will ignore all the Web pages unless the words ”plane”, ”ticket”, ”China” and ”2004” appear in the same paragraph, and the words ”plane” and ”ticket” appear within a sequence of 4 words somewhere in a paragraph region of a Web page. The rulebased model is illustrated in the Fig. 2:

Engine -depe ndant tem ple te s

P re proc e ssing R ulle s

Se a rc h E ngine s

P ostproc e ssing R ule s

Fetc he d W eb pa ge s

Result W eb Pages

O ntology M ode l

Fig. 2. Query Processing supported by Ontology Model

4

A Web Search Framework

By fusing the ontology model and rule-based system model of the previous section, we propose a Web search framework illustrated below. The framework puts the tasks of ontology selection (creation) and filtering rules compilation on the side of Web users. Some may argue that the architecture brings too much burden to general Web users; however, we believe it is Web users who bear the semantic meaning in their heads and issue the initial query commands; they deserve more involvement than application developers or ontology (knowledge) engineers in the system. This architecture can guarantee maximal flexibility for the whole Web search application. Moreover, carefully designed User Interfaces and Software Wizards can alleviate the burden of Web users. The structure of our framework and its interactions with Web users and Web search engines is given in Fig. 3:

Adopting Ontologies and Rules in Web Searching Services

O ntology Editing

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Ontology Model

O riginal Q uery

M odified Q uery

Framework UI

We b Us e rs

Filtered Results

Se arch Engine s

S earc h Results

Rule-based Model

F iltering Rules Editing

Web Search Framework Fig. 3. Query Processing supported by Ontology Model

We are building a demonstrator which tests the intuitions proposed above. In recent years, Google has grown to be one of the most popular search engines that are available on the Web. Google Company has made its index available to other developers through a Web services interface [10]. This allows the developers to programmatically send a request to the Google server and get back a response. Currently the service is still in beta version and is for non-commercial use only. It is provided via SOAP (Simple Object Access Protocol) over HTTP and can be manipulated in any way that the programmer pleases, a developer can program in his or her favorite environment - such as Java, Perl, or Visual Studio.NET.

5

Related Works

Haiping Zhu et al. [11] introduce an approach for semantic search by matching RDF graphs. Their approach relies heavily on RDF files and can not process the large number of HTML files on the Web. Roger et al. propose a smart web query (SWQ) method for the semantic retrieval of web data. It uses domain semantics represented as context ontologies to specify and formulate appropriate web queries to search. Their semantic search filters don’t recognize HTML tags and thus can not use the important relations between terms and tags. Masayuki et al. [9] describe a system for collecting Web pages that are relevant to a particular topic through an interactive approach. This system automatically constructs a set of rules to find new relevant pages. Our rule-based model adopts some thoughts proposed in this paper. There are only two rules defined in their paper; our rule-based system extends their work by adding many more rules to provide Web users with more filtering options. Sara Cohen et al. [12] present XSEarch, a semantic search service for XML. XSEarch has a simple query language, suitable for naive users. They also developed advanced indexing techniques to facilitate

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efficient implementation of XSEarch. However, like [11], their approach limits to XML files only. It is inconvenient for Web users to restrict to only XML files. Many systems [11, 12] rely on Semantic Web infrastructure to carry out semantic searches; although Semantic Web is developing rapidly, there are still few RDF or OWL (Web Ontology Language) files available on the Web, with many of them for testing purposes only. To convert current available HTML files into semantic language formats like RDF or OWL requires huge human efforts and will not likely be realized in the near future. Our framework is more practical than theirs in this respect.

6

Conclusion and Future Works

We propose a Web search framework using ontologies and rules. The framework uses ontologies to deal with synonym problem, uses filtering rules to deal with polysemy problem, and thus gains a better recall and precision performance than the traditional search services.

References 1. Han, J.W. and Chang, K.C.-C.: Data Mining for Web Intelligence. IEEE Computer bfseries 35 (2002) 64–70 2. Gruber, T.R.: Toward Principles for the Design of Ontologies Used for Knowledge Sharing, International Journal of Human and Computer Studies, bfseries 43 (1995) 907–928 3. Lee, T.B.: James Hendler and Ora Lasilla, The Semantic Web, The Scientific American, May 2001 4. Newell, A., Simon, H.A.: Human Problem Solving, Prentice-Hall, Englewood Cliffs, New Jersey, 1972 5. Guarino, N.: Formal Ontology in Information Systems, in Proceedings of FOIS’98, Trento, Italy, IOS Press, (1998) 3–15 6. Nichols, D. and Terry, A: User’s Guide to Teknowledge Ontologies, available on-line at http://ontology.teknowledge.com/Ontology User Guide.doc, 2003 7. Niles, I. and Pease, A.: Towards a Standard Upper Ontology, In Proceedings of the 2nd International Conference on Formal Ontology in Information Systems (FOIS2001), 2001 8. Roger, H.L.C., Cecil, E.H.C. and Veda, C.S.: A smart web query method for semantic retrieval of web data, Data & Knowledge Engineering, bfseries 38 (2001) 63–84 9. Okabe, M. and Yamada, S.: Interactive Web Page Filtering with Relational Learning, Web Intelligence, (2001) 443–447 10. Google Corporation, Google Web APIs (beta), http://www.google.com/apis/, 2004

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11. Zhu,H.P., Zhong, J.W., Li J.M. and Yu Y.: An Approach for Semantic Search by Matching RDF Graphs, Proceedings of the Fifteenth International Florida Artificial Intelligence Research Society Conference, AAAI Press, (2002) 450–454 12. Cohen, S., Mamou, J., Kanza, Y. and Sagiv, Y.: XSEarch: A Semantic Search Engine for XML, Proceedings of 29th International Conference on Very Large Data Bases, (2003) 45–56

An Arbitrated Quantum Message Signature Scheme Xin L¨ u1 and Deng-Guo Feng1,2 1

State Key Laboratory of Information Security (Graduate School of Chinese Academy of Sciences), 100039, Beijing, P.R. China [email protected] 2 State Key Laboratory of Information Security (Institute of Software, Chinese Academy of Sciences), 100080, Beijing, P.R. China Abstract. Digital signature is an important task in modern cryptography, which concerns about authenticity, integrity and non-repudiation of data on communication channel. In this paper, an arbitrated quantum digital signature scheme is proposed, in which the receiver verifies the signature with the help of an arbitrator. The most important property of the proposed scheme is that it can sign unknown quantum states. The security of the protocol relies on the quantum one-time-pad and the Greenberger-Horne-Zeilinger (GHZ) triplet particles distributed among communication entities. Security analysis shows that the proposed quantum signature is a secure scheme.

1

Introduction

A major future research theme for cryptography is to weaken the assumptions on which security proofs are based, in particular computational intractability assumptions [1]. Quantum cryptography is one candidate for exploring unconditionally secure cryptography protocols. The idea of introducing quantum mechanics to cryptography can be traced back to Wiesner in 1970s and was published in 1983 [2], which proposed that if single-quantum states could be stored for long periods of time they could be used as counterfeit-proof money. Bennett and Brassard [3] gave the first quantum key distribution protocol, known as BB84, which is provable security [4]. Digital signature and message authentication play the important roles in modern cryptography and are widely used in network communication systems. The purpose of a digital signature scheme is to provide a means for an entity to bind its identity to a piece of information. Many signature schemes could be constructed under some unproven computational assumptions, such as the hard-ness of factoring large integers and finding discrete logarithm, in conventional cryptography. However, Shor’s celebrated quantum algorithm indicated that the cryptography algorithms based on integer factoring related problems were threatened by quantum computers (if constructed in the future)[5]. Exploring more secure cryptography protocols immune to quantum computers is a new topic for the cryptography researchers. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1054–1060, 2004. c Springer-Verlag Berlin Heidelberg 2004


An Arbitrated Quantum Message Signature Scheme

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Gottesman and Chuang proposed a quantum digital signature protocol based on weak quantum one-way functions and claimed that their scheme was secure against quantum attack [7] . The input of that scheme is a classical bits string and the signature keys of the signatory are quantum states. Unfortunately, their signature scheme couldn’t sign general quantum superposition states, but only can deal with quantum basis states. Zeng presented an arbitrated quantum signature scheme in the literature [8], the security of which is due to the correlation of the GHZ triplet states and utilization of quantum one-time pad. In an arbitrated signature scheme, all communications involve a so called arbitrator who has access to the contents of the messages. The security of most arbitrated signature schemes depends heavily on the trustworthiness of the arbitrators[9, 10]. Zeng’s scheme, however, requires that the signed quantum states must be known to the signatory. It seems impossible to sign general unknown quantum messages [7–9, 11]. In this paper, we propose a quantum signature scheme that can sign unknown quantum states. Due to the main properties of quantum information, signing unknown quantum states must ensure that the states can’t be destroyed by the signature process or that the destroyed states can be recovered. In the proposed scheme, a signatory Alice firstly signs some classical bits that are related with the signatory’s secret keys and then uses these classical bits to encrypt and encode her quantum states using quantum stabilizer codes. The receiver verifies the signature with the help of a trusted arbitrator. Alice can’t disavow her signature, because the signature contains her secret keys’ information and this can be confirmed by the arbitrator in the verification phase. For the rest of this paper we assume that the reader is familiar with the basics of quantum cryptography and quantum computation. Further information about quantum cryptography and quantum error correction codes can be found in Ref. [6].

2 2.1

The Proposed Scheme Security Requirements

The proposed scheme involves three entities: a signatory Alice, a receiver Bob, and an arbitrator Trent. The security of the signature scheme depends much on the trustworthiness of the arbitrator who has access to the contents of the messages. The existence of the arbitrator ensures that we can sign unknown quantum messages without Alice’s deceiving. The general requirements for the quantum digital signature scheme discussed in this article should satisfy: 1. Each user (Alice) can efficiently generate her own signature on messages of her choice; 2. A receiver Bob can efficiently verify whether a given string is a signature of another user’s on specific messages with the help of Trent; 3. The signatory can’t disavow the messages that she has signed; 4. It is infeasible to produce signatures of other users’ messages they haven’t signed.

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2.2

The Protocol

Initialization 1. Key distribution. Alice, Bob and Trent agree on some random binary strings KA , KB as their secret keys. KA is shared between Alice and Trent, KB is shared between Trent and Bob. To ensure that the scheme is unconditionally secure, we can generate these keys using quantum key distribution protocols, such as BB84 or EPR protocols [3, 6]. 2. Triplet GHZ states distribution. When Trent receives Alice and Bob’s request for an arbitrated communication, he creates N triplet GHZ state |φ
= |φ1 , · · · , φN
, and 1 |φi
= √ (|000
atb + |111
atb ) (1) 2 where a, t and b correspond to the particle of Alice’s, Trent’s and Bob’s respectively. Trent distributes each of Alice’s and Bob’s GHZ particle to Alice and Bob for each GHZ state. After that, Alice, Bob and Trent each has N particles of GHZ pairs. 3. All the entities know a set of quantum stabilizer cods1 Q = {Q1 , Q2 , · · · , QN }. Alice will select any one of them, such as Qy , to encode her quantum states, but others know nothing about the index y. Signature 1. Alice selects three classical bits strings x, y and t. She constructs a new string as L = (L1 , L2 , · · · , LN ) = (x||y||t), here “||” means concatenation of two bits strings. Alice performs a controlled unitary operation to her GHZ particles according to L. If Li = 1, she executes a bit flip gate X to φi . If Li = 0, she does nothing. After that, the ith GHZ state becomes |φi
when Li = 1 1 (2) |φi
= √ (|100
+ |011
) 2 Alice measures her GHZ qubits and gains N classical bits ωA = ωA1 , ωA2 , · · · , ωAN .

(3)

2. The aim of this step is to transform N -bit classical string L into quantum states |RA
using the secrete key KA distributed in the initial stage. If the i ith bit of KA is zero, namly KA = 0, Alice encodes Li using rectilinear basis i √ . After |0
, |1
. If KA = 1, Alice encodes Li using diagonal basis |±
= |0±|1 2 transformations, Alice has quantum states |RA
= MKA |L
= |lA1
⊗ |lA2
⊗ · · · ⊗ |lAN
1

Introduction about quantum stabilizer cods can be found in the literature [6].

(4)

An Arbitrated Quantum Message Signature Scheme

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3. Supposing Alice has quantum states |ψ
to sign (|ψ
can be unknown to Alice). She firstly encrypts her classical bits L as LA = (xA ||yA ||tA ) using KA and quantumly encrypts (q-encrypts)2 |ψ
as ρ using classical bits xA . Then she encodes ρ according to the quantum stabilizer codes QyA with syndromes tA and obtains quantum states π. Alice encodes her measurement results ωA as quantum states |ωA
using rectilinear basis and encrypts |ωA
together with |RA
as quantum states c1 using KA 3 . After that, she generates a signature s = {π, c1 }. Here, ρ, τ and c1 denote the density matrix of the corresponding quantum states. Alice sends the signature s to Bob and publishes ωA on a public board available only to Bob.

Verification 1. Bob receives the signature s and measures his GHZ particles and obtains ωB = ωB1 , ωB2 , · · · , ωBN . He uses ωA from the public board to recover L as LB = ωA ⊕ ωB = (xB ||yB ||tB ). Here, ⊕ means bit-by-bit XOR of two bits strings. 2. Bob encrypts LB as classical ciphertext c2 using his secrete key KB and sends {s, c2 } to the arbitrator through classical communication channel (for c2 ) and quantum communication channel (for s, s is the density matrix of the signature of quantum state |ψ
) respectively with the same communication sequence number. 3. Trent receives {s, c2 }. He decrypts c2 as classical bits LB and decrypts s as |ωA
and quantum states |RA
using his secrete keys KB and KA respectively. He measures |ωA
using rectilinear basis to obtain ωA = ωA1 , · · · , ωAN and measures his GHZ particles to obtain ωT = ωT1 , · · · , ωTN . The arbitrator uses ωA to recover L as LT1 = ωC ⊕ ωA = (xT1 ||yT1 ||tT1 ). Trent measures i |RA
according to KA and obtains LT2 = (xT2 ||yT2 ||tT2 ). If KA = 0, he i i i
using measures |RA
using rectilinear basis. If KA = 1, he measures |RA diagonal basis. The arbitrator compares LT2 to LB and LT1 . If LT2 = LB , he lets λ1 = 0. Otherwise, λ1 = 1. Adopting the same method, if LT2 = LT1 , he lets λ2 = 0. Otherwise, λ2 = 1. Trent uses KA to encrypts LT1 as LA =  ||tA ) using the same method as Alice does in step 3 of the signature (xA ||yA phase. Trent measures the syndrome t using the stabilizer code QyA
on π and decodes the qubits as ρ. He compares t with tA . If tA = t , he sets λ3 = 0. Otherwise, λ3 = 1. Trent decrypts the quantum states ρ as |ψ
using xA . 4. Trent q-encrypts |ψ
as ρT using classical bits xT2 . Then he encodes ρT according to the quantum stabilizer codes QyT2 with syndromes tT2 and obtains quantum states πT . He encrypts LT2 , λ1 , λ2 , λ3 and πT 2

3

To obtain unconditionally security, we use quantum one-time-pad method [12] and classical one-time-pad to encrypt quantum message and classical message respectively. Supposing KA and KB are long enough to use.

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using KB as classical bits c3 and quantum states δT . He sends c3 and δT to Bob. 5. Bob decrypts c3 and δT as classical strings LT2 , λ1 , λ2 λ3 and quntum states πT using KB . IF λ1 = λ2 = λ3 = 0 and LT2 = LB , he measures the syndrome t using the stabilizer code QyB on πT and decodes the qubits as ρB . Bob compares t with tB . If t = tB , he deciphers the quantum states ρB as |ψ
B and the signature s of quantum states |ψ
is verified. Otherwise, he rejects the signature and stops the protocol.

3 3.1

Security Analysis Correctness

Theorem 1. (Correctness) Supposing all the entities involved in the scheme follow the protocol, then Alice’s signature passes the verification. Proof. The correctness of the scheme can be easily seen by inspection. In the absence of intervention, Alice, Bob and Trent secretly share the GHZ triple states at the end of the initialization phase. Bob recovers Alice’s classical bits string L = (x||y||t) and Trent obtains Alice’s signature |RA
, L and the encoded quantum states π. Trent will correctly verify Alice’s signature and decode Alice’s quantum states and secretly send the verification results to Bob. Bob’s output will be exactly “yes” at the end of the protocol. 3.2

Security Against Forgery

Theorem 2. Other entities can forge Alice’s signature with only a successful probability at most 1 − 2|K1A | . Proof. Supposing that an attacker Eve wants to forger Alice’s signature. Because Eve doesn’t know Alice’s private key KA and doesn’t share GHZ particles with Alice and Trent (GHZ particles are supposed distributed securely in the  initialization phase), she can’t obtain L. If she randomly selects a bits string KA  and KB to execute the protocol, her cheating, will be detected by Trent with an overwhelming probability lager than 1 − 2|K1A | . Here, |KA | means the length of the bits string KA . 3.3

Security Against Repudiation

Alice can’t deny her signature. When dispute between Alice and Bob happens, they will resort to the arbitrator. The signature s contains information about Alice’s secrete key KA , and Trent can confirm this fact in the verification phase. Supposing Alice intercepts the ciphertext c3 and δT that Trent has sent to Bob in the verification phase, she tries to change the signature of her qubits |ψ
to the signature of a new quantum state |ϕ
. Because she knows nothing about Bob and Trent’s secret key KB , she can’t prepare a new legal signature of another quantum messages that passes Bob’s verification.

An Arbitrated Quantum Message Signature Scheme

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Bob can’t deny that he has received Alice’s signature, because he can’t verify the signature without Trent’s help.

4

Conclusion

A quantum digital signature scheme is proposed in this paper. One main feature of the protocol is that the signatory can indirectly sign general unknown quantum messages by signing Alice’s secret keys and the syndromes of stabilizer codes which are used to encrypt and encode the quantum states. The authenticity of the quantum information is obtained by quantum stabilizer codes. The security of the protocol is studied and results show that the proposed signature scheme is a secure signature scheme. An open problem is that it’s still not known whether there exists a general quantum message signature scheme that doesn’t need the presence of an arbitrator. Acknowledgments. This work was supported by the Natural Science Foundation of China under Grant No.60273027; the National Grand Fundamental Research 973 Program of China under Grant No. G1999035802 and the National Science Foundation of China for Distinguished Young Scholars under Grant No.60025205.

References 1. Ueli, M.: Cryptography 2000±10. In: Informatics: 10 Years Back, 10 Years Ahead. Lecture Notes in Computer Science, Vol. 2000, Springer-Verlag, Berlin Heidelberg New York (2001) 63–85. 2. Wiesner, S.: Conjugate coding. SIGACT News. 15 (1983) 78–88. 3. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers Systems and Signal Processing, Bangalore, India (1984) 175–179. 4. Mayers, D.: Unconditional security in quantum cryptography. Journal of the ACM. 48 (2001) 351–406. 5. Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review. 41 (1999) 303–332. 6. Nielson, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, 2000. 7. Gottesman, D., Chuang, I.: Quantum digital signatures. Technical Report, http://arxiv.org/abs/quant-ph/0105032, 2001. 8. Zeng, G., Christoph, K.: An arbitrated quantum signature scheme. Physical Review A. 65 (2002) 0423121–0423126. 9. Lee, H., Hong, C., Kim, H. et al.: Arbitrated quantum signature scheme with message recovery. Physics Letters A. 321 (2004) 295–300. 10. Meijer, H., Akl, S.: Digital Signature Scheme for Computer Communication Networks. In: Advances in Cryptography: Crypto 81, Santa Barbara, California (1981) 65–70.

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11. Barnum, C., Gottesman, D., Smith, A. et al.: Authentication of Quantum Messages. In: Proceedings of 43rd Annual IEEE Symposium on the Foundations of Computer Science, Vancouver, Canada (2002) 449–458. 12. Boykin, P., Roychowdury, V.: Optimal encryption of quantum bits, Physical Review A. 67 (2003) 0423171–0423175.

Fair Tracing Without Trustees for Multiple Banks1 Chen Lin, Xiaoqin Huang, and Jinyuan You Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200030 Shanghai, China {chenlin, huangxq}@sjtu.edu.cn

Abstract. In this paper we present a multiple bank electronic cash system based on group blind signature scheme, which offers a new kind of tracing mechanism. It provides conditional anonymity both for the customers and electronic coins under a judge. The coins can be marked using undeniable signature scheme so that the bank will recognize these coins at deposit. We also use the secret sharing scheme to trace the customer under the permission of a judge. The security of our scheme is analyzed. And compared with other works, our proposed tracing methods offer more privacy and do not need any trusted third parties. Our system is able to prevent from blackmailing, kidnapping, and bank robberies. Also we extend electronic cash system to multiple banks, it is more practical in the real life.

1 Introduction With the development of E-Commence, People can buy merchandise in home and he can pay electronic coins to the shop by the Internet. How to protect the customer’s anonymity and the coin’s validity is an important problem. D. Chaum proposed blind signatures for untraceable payments [1]. However, Von Solms and Naccache [2] have shown that unconditional anonymity may be misused for untraceable blackmailing of customers. Also, unconditional anonymity may ease money laundering, illegal purchases, and bank robberies. Several papers [3] proposed the revocable anonymity methods, where one or more trusted third parties are needed. Kugler and Vogt et al proposed a new kind of tracing mechanism [4,7], which guarantees stronger privacy than other approaches. Their coin tracing can be carried out without the help of any trusted third parties. Their payment system allows tracing, but a traced customer will afterwards detect the fact of being legally or illegally traced. If the tracing turns out to be illegal, the customer can prove this violation of his privacy and the bank can be prosecuted. Paper [4] also gives some useful definitions for coin tracing, owner tracing, legal tracing and illegal tracing. According to these definitions in [4], we introduce a new kind of tracing mechanism, which supports the conditional anonymity, both a customer and a bank can reveal the identity of the customer, none of them can 1

This paper is supported by the National Natural Science Foundation of China under Grant No.60173033.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1061–1066, 2004. © Springer-Verlag Berlin Heidelberg 2004

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reveal it lonely. The bank can trace the coins and the bank can also sign the coins at different marks. The rest of the paper is organized as follows: In Section 2 we present some preliminary works. The implementation of a fair electronic cash system is presented in section 3. The security and anonymity aspects are discussed in section 4. Finally we compare our system with other schemes and give the conclusions.

2 Related Works In this section, we introduce the techniques of group blind signature and secret sharing scheme, which we will use to construct our electronic cash scheme. 2.1 Group Blind Signature Anna Lysyanskaya [5] presents an electronic cash scheme for distributed banks based on group blind signature technique. A group blind signature scheme consists of the following steps: Setup, Join, Sign, Verify and Open. Setup: In this phase, the group manager chooses some security parameters and gets the group’s public key Y = ( n, e, G , g , a, λ , µ ) . Join: If Alice wants to join the group, she picks a secret key x and interacts with the 1

group manager. Then she gets her membership certificate v ≡ ( y + 1) Sign: When a user asks a signing request, the signer signs the message ture is as follows:

e

(mod n) . m , the signa-

gˆ := g~ w , zˆ := ~ zw α

V1 = SKLOGLOGl [α | zˆ = gˆ a ](m)

(1)

V2 = SKROOTLOGl [ β | zˆgˆ = gˆ β ](m) e

m consists of ( gˆ , zˆ,V1 , V2 ) and can be verified by checking correctness of V1 and V2 . Open: Given a signature ( gˆ , zˆ, V1 , V2 ) for a message m , the group manager can Verify: The signature on the message

determine the signer by testing if

gˆ

yp

= zˆ for every group member P (where

y p = log g z P and z P is P ’s membership key). 2.2 Secret Sharing Scheme

(k , n) threshold scheme. We describe it here simply. Suppose p and q are two large primes such that q | ( p − 1) and g is a

In 1979, Shamir [6] proposed a first

generator

g ∈R Z *p of order q . q > n .

Fair Tracing Without Trustees for Multiple Banks

1. Let S (S ∈ Z p ) be a secret value, k be a threshold, and *

We can select x j

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x j ∈ Z *p ( j =1, 2, … n).

= gj.

2. Distributor chooses a random polynomial.

f ( x) = S + a1 x + a2 x 2 + ... + ak −1 x k −1 (mod q). ai (i = 1,2,..., k − 1) ∈R Z *p 3. Distributor distributes 4. Any random k sets of

(2)

x j , D j = f ( x j ) to each user j . ( x j , D j ) of n users can recover secret S from f (x) by k

using Lagrange interpolation equation

f ( x) = ∑ D j j =1

k



l =1,l ≠ j

x − gl . g j − gl

3 Our Proposed Scheme In this section we describe a protocol, which combines secret sharing scheme and group blind signature scheme combined with the Chaum-van Antwerpen undeniable signature [4] in order to make a practical Electronic Cash system. 3.1 Main Idea First of all, we consider a large of banks composing a group. Also there is a group manager. Each bank participating the group can issue Electronic Cash independently. Each bank can sign the Electronic Cash with undeniable signature, which we call it the marked coins. In our system, we consider three parties, customer, merchant and bank. If the blackmailer blackmails the customer, the customer can communicate with the bank notifying the bank the blackmailing event. Then the bank can mark the Electronic Cash and the victim sends the marked coins to the blackmailer. Later, the customer and the bank can decide if these coins can be accepted. Usually the coins are anonymous, but on the condition of blackmailing, the anonymity of the coins can be abolished. We also provide owner-tracing scheme in our system. Owner tracing scheme also allows the authorities to identify customers making an illegal purchase, after the illegal seller has been identified because of suspicious purchase. We use the secret sharing scheme to identify the customers. Only the bank and the merchant can collaborate to identify the customer. None of them can complete it independently. 3.2 Protocol Notations: An RSA public key

(n, e) , where the length of n is at least 2l bits.

l -Security parameter, a cyclic subgroup of Z *p , g , g1 is two generators of Z *p of

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C. Lin, X. Huang, and J. You

order q , where p is a prime and n | ( p − 1) . secret keys and a constant µ > 1.

λ Upper bound on the length of the

Initial Step: As in section 2.1 Setup and Join procedures, a bank P joins a group. The bank picks a secret key

xP ∈R {0,1,...,2 λ − 1} and calculates y P = a xP (mod n) 1

and

z P = g yP . The bank P ’s membership certificate is v ≡ ( y + 1) e (mod n) .

1. Customer requests coin withdrawal to the bank. 2. Bank

selects

random

number

r ∈R Z q* , makes a new generator

α = g1r (mod p) and sends it to the Customer. 3. The bank chooses a random number X as a secret mark and calculates

ω = α X (mod p) . 4. Customer selects a random polynomial

f ( x) = A1 + a1 x(mod q ) , A1 the se-

cret information (Corresponding to the Customer), 5. Customer sends (

a1 ∈R Z *p .

x1 , f ( x1 ) ), g , c0 = g A1 (mod p ) , c1 = g a1 (mod p ) to

x1 ∈ Z P* . A a 6. Customer will send ( x2 , f ( x2 )) , g , c0 = g 1 (mod p ) , c1 = g 1 (mod p ) the Bank. Where

to the merchant later, where

x2 ∈ Z P* .

A1 can be recovered by ( x1 , f ( x1 ) ), ( x2 , f ( x2 )) using Secret Sharing Scheme. By the A1 , the bank can identify the customer later.

7. The secret information

Withdrawal Step: When a customer wants to withdraw a coin from bank P , the bank first asks the user to prove his identity. The customer selects

u1 ∈R Z P ( g u1 g1 ≠ 1 ) and calculates I = g u1 as his identity. Afterwards, I can be used to verify the identity. Also, the customer and the bank generate secret informa-

A1 , secret key X 1 ∈R Z P* , and the public key h = g X1 mod p for the user. These parameters can be preserved in the user’s smart card. A1 Also must be pretion

served in the user’s account in the bank.

m. 2. For every coin, Customer selects δ ∈R Z and calculates α ' = α (mod p ) , 1. The customer sends the bank the user’s identity I and the coin amount * q

δ

ω ' = ω δ (mod p) . m , as in equation (1), the bank signs the message m and the customer gets the group blind signature for m: ( gˆ , zˆ, V1 , V2 ) . 4. Finally, the customer gets the coin: (m, gˆ , zˆ , V1 , V2 , α ' , ω ' ) .

3. For the coin amount

Fair Tracing Without Trustees for Multiple Banks

1065

Pay, Deposit and Verification Step. When customer gives coin to merchant, he also has to give ( x2 , f ( x2 )), g , c0 , c1 to merchant. Then merchant can verify the truth of ?

the shared secret using:

g f ( x 2 ) = c0c1 2 . If it is true, he also has to verify the group x

blind signature as in Section 2.1. If both are passed, then the merchant sends the coin to the bank. The bank verifies group blind signature as the merchant. The bank also ?

verifies ω ' = α ' . If both are passed, the coin is deposited in the merchant’s account and notifies the merchant. The merchant sends the merchandises to the customer. Later, if the authorities find the customer making an illegal purchase, then we can identify the customer by extracting the secret value A1 using the banks ( x1 , f ( x1 )) x

and the customer’s ( x2 ,

f ( x2 )) under the permission of a judger.

f ( x1 ) = A1 + a1 x1 , f ( x2 ) = A1 + a1 x2

(3)

4 Discussion of Security and Anonymity Prevention of Blackmailing. There are three kinds of blackmailing [4]: − Perfect Crime: When the victim is blackmailed, the victim can send an encryption message with secret key X 1 to tell the bank the blackmailing event. The bank sends the marked coin to the customer and the customer sends the marked coin to the blackmailer. − Impersonation: The blackmailer gains access to the victim’s bank account and withdraws coins by him. The blackmailer communicates directly with the bank but cannot observe the victim’s communication with the bank. The customer gives his decryption key to the bank, which can cheat the blackmailer as described in the perfect crime scenario. Kidnapping the Customer: In this scenario a covert channel is needed to inform the bank about the kidnapping. Anonymity of Coins. If the coins are not marked at withdrawal phase, the coins remain anonymous. This means that payments with unmarked coins are unconditional anonymous for customer. In the situation of blackmailing, the marked coins are not anonymous. Anonymity of Customers. In our payment system, we also provide the secret sharing scheme to protect the customer’s anonymity. This is a conditional anonymity. The bank and the customer can collaborate to trace the customer under a judge. When we have two sets of ( x1 , f ( x1 )) ( x2 , f ( x2 )) , we can use secret sharing scheme to identify the customer. Multi-bank Properties. In our system, we adopt the group blind signature scheme to compose a group of banks. Each bank can issue the E-cash and everybody can use the group public key to verify the validness of the coins. If there is some problem about

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the coins, the group manager can identify the identity of the bank. For other people, the coins are anonymous.

5 Comparisons and Conclusions We have proposed a new anonymous payment system based on group blind signature scheme and secret sharing scheme, offering both the coins’ conditional anonymity and the customers’ conditional anonymity. In contrast to other systems with revocable anonymity our system doesn’t need a trusted third party. Our payment system protects private users against blackmailing attacks, by offering a marking mechanism similar to the well-known marking of banknotes. Also our payment system supports the multiple banks, it is very similar to the real life. So our payment system is a practical electronic cash system.

References 1. Chaum, D.: Blind signature for untraceable payments. In Advances in CryptologyCRYPTO’82. Plenum (1983) 199-203 2. Von Solms, B. and Naccache, D.: On blind signatures and perfect crimes. Computers and Security. Vol.11, No.6. (1992) 581-583 3. Davida, G., Frankel, Y., Tsiounis, Y. and Yung, M.: Anonymity control in e-cash systems. In Financial Cryptography-FC’97. Lecture Notes in Computer Science, Vol. 1318. Springer-Verlag, Berlin Heidelberg New York (1997) 1–16. 4. Kugler, D. and Vogt, H.: Marking: A Privacy Protecting Approach Against Blackmailing. PKC 2001, LNCS, Vol.1992. Springer-Verlag, Berlin Heidelberg (2001) 137-152. 5. Lysyanskays, A. and Ramzan, Z.: Group blind signatures: A scalable solution to electronic cash, Financial Cryptography’ 98, LNCS, Vol.1465. Springer-Verlag (1998) 184-197 6. Shamir, A.: How to share a secret, Comm. ACM, Vol.22 (1979) 612-61. 7. Kim, B.G., Min, S.J. and Kim, K.: Fair tracing based on VSS and blind signature without Trustees. http://www.caislab.icu.ac.kr/paper/ 2003/CSS2003/

SVM Model Selection with the VC Bound
Huaqing Li , Shaoyu Wang, and Feihu Qi Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 20030, P. R. China waking [email protected]

Abstract. Model selection plays a key role in the performance of a support vector machine (SVM). In this paper, we propose two algorithms that use the Vapnik Chervonenkis (VC) bound for SVM model selection. The algorithms employ a coarse-to-fine search strategy to obtain the best parameters in some predefined ranges for a given problem. Experimental results on several benchmark datasets show that the proposed hybrid algorithm has very comparative performance with the cross validation algorithm.

1

Introduction

Support vector machine (SVM), due to its powerful learning ability and satisfying generalization ability, is considered to be one of the most effective algorithms for pattern recognition (classification) problems. Generally, it works as follows for binary classification problems: First the training samples are mapped, through a mapping function Φ, into a high (even infinite) dimensional feature space H. Then the optimal separating hyperplane in H is searched. In implementation, the use of kernel functions avoids the explicit use of mapping functions. However, as different kernel functions lead to different SVMs with probably quite different performance, it turns to be very important, yet very hard, to select appropriate types and parameters of kernel functions for a given problem. There are mainly two categories of algorithms for SVM model selection. Algorithms from the first category estimate the prediction error by testing error on a data set which has not been used for training, while those from the second category estimate the prediction error by theoretical bounds. At present, the cross validation algorithm, which falls into the first category, is one of the most popular and robust algorithms employed in literatures [3, 4]. Though some theoretical bounds have been explored [2, 6], the use of the Vapnik Chervonenkis (VC) bound is less reported [5]. However Burges pointed out that, despite its looseness, the VC bound can be very predictive for SVM model selection [1]. In this paper, we propose two algorithms that use the VC bound for SVM model selection. The algorithms employ a coarse-to-fine search strategy to obtain the optimal SVM parameters. Experimental results on several benchmark


This work is supported by the National Natural Science Foundation of China (No. 60072029).

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1067–1071, 2004. c Springer-Verlag Berlin Heidelberg 2004


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datasets demonstrate that the proposed hybrid algorithm slightly outperforms the cross-validation algorithm. The rest of the paper is organized as follows: Section 2 introduces the VC bound and shows how to make it practical for use. The SVM model selection algorithms are described in Section 3. In Section 4, experimental results are presented and analyzed. Finally, conclusions are given in Section 5.

2

The VC Bound

The VC bound is given by Vapnik [1]:
  h(log(2l/h) + 1) − log(η/4) R(α) ≤ Remp (α) + . l where R(α) is the generalization error, Remp (α) is the training error, h is the VC dimension, l is the size of the training set, η is a user-determined parameter, 0 ≤ η ≤ 1. With probability 1 − η, the above bound holds. The main difficulty of using the VC bound lies in determining the VC dimension. Burges suggested to ease this difficulty by using the following bound on the VC dimension instead of the dimension itself [1]: h≤

2 Dmax 2 +1 . Mmin

where Dmax is the maximal diameter of a set of gap tolerant classifiers, Mmin is the minimal margin of the same set of classifiers. Then the only thing left is to estimate Dmax . This problem can be described as follows [1]: Given a training set of data points Xi and a function Φ which maps the data points from the original space to a feature space H, we wish to compute the radius of the smallest sphere in H which encloses the mapped training data. The corresponding formulation is Minimize subject to:

R2 ,

R2 − Φ(Xi ) − C2 ≥ 0

(1) ∀i .

where C is the (unknown) center of the sphere in H. As the problem resembles that of SVMs training, algorithms for the latter can be modified to solve (1) [5].

3

SVM Model Selection Algorithms

In this paper, we investigate model selection for SVMs with the radius basis function (RBF) kernel. The RBF kernel is defined as: K(Xi , Xj ) = exp(−σ(Xi − Xj 2 )) . Hence there are mainly two parameters to be tuned, the penalty parameter C and the kernel parameter σ.

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For algorithms that can not employ gradient-descent based method to obtain the optimal parameters, Chung et al. recommended the use of an exhaustive grid-search strategy in some predefined parameter ranges [2]. They also pointed out that trying exponentially growing sequences of C and σ was a practical method to identify good parameters (for example, C = 2−5 , 2−3 , . . . , 215 , σ = 2−15 , 2−13 , . . . , 23 ). However, a standard grid-search is very computational expensive when dealing with even moderate problems. In [4], Staelin proposed a coarse-to-fine search strategy based on ideas from design of experiments. Experimental results showed that it was robust and worked effectively and efficiently. The strategy can be briefly described as follows: Start the search with a very coarse grid covering the whole search space and iteratively refine both the grid resolution and search boundaries, keeping the number of samples roughly constant at each iteration. In this paper, a similar search strategy like this is employed for the algorithms proposed. 3.1

Algorithm 1: The Fixed-C Algorithm

Empirically we find that, when employing the VC bound for SVM generalization error estimation, searching simultaneously for the optimal values of C and σ always results in poor SVM models. This is due to the effect the parameter C has on the SVM margin, which is inclined to lead to a very small C. Thereby, we’d better prefix C to some appropriate value and merely search for the optimal value of σ. In [5], Li et al. showed that a relative large C, e.g. 2048, could work for most cases. Note that the fixed-C algorithm has a pleasing byproduct — only one parameter is needed to be tuned. 3.2

Algorithm 2: The Hybrid Algorithm

In SVMs training, the penalty parameter C is very important. It balances the training error and the capacity of the machine. However, the fixed-C algorithm suggests a constant C for all problems. This, to some extent, is unreasonable. Therefore, we propose a hybrid algorithm, which works as follows: First the fixed-C algorithm is performed to choose the optimal value of σ. Then, with σ fixed, the cross validation algorithm is performed to obtain a better C.

4

Experiments

Experiments are carried out on several benchmark datasets1 to investigate the performance of the proposed algorithms. The search is done in the log2 -space of both parameters. The parameter ranges are log2 C ∈ {−5, −4, . . . , 15} and log2 σ ∈ {−15, −14, . . . , 3}. Totally five iterations are performed for both the fixed-C algorithm and the fixed-σ cross validation algorithm. At each iteration five points uniformly distributed in the latest range are examined. LIBSVM [3] 1

Dr. Chih-Jen Lin from National Taiwan University kindly shares these datasets with us.

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is employed for SVMs training and testing, as well as model selection with the cross validation algorithm. Model selection with the fixed-C algorithm is done with a module developed by us with C ++ (Ref. [5] for more details). The experimental results are shown in Table 1. Where c-ratio stands for the cross validation ratio, t-ratio is the test ratio on the corresponding test datasets, bound is the minimal bound obtained by the fixed-C algorithm with a prefixed C of 2048. Datas in the first three columns of the cross validation algorithm are taken from [4]. Algorithm 2 has the same σ with algorithm 1. Table 1. Performance comparison of algorithms on several datasets Data sets banana diabetes image ringnorm splice Titanic twonorm waveform

Cross Validation [4] log2 C log2 σ c-ratio t-ratio 11.25 -1.5 93 87.39 5.62 -10.5 79.7 76.33 8.44 -4.6 96.5 97.92 7.19 -3.47 98.75 98.20 12.19 -7.97 87.8 89.52 -1.25 -1.5 80.67 77.08 1.87 -6.00 98 97.07 1.56 -5.16 93.5 89.63

Algorithm 1 log2 σ bound t-ratio 0.75 124.14 85.88 -1.78 0.30 72.67 0.75 1.03 96.24 -3.47 0.77 98.20 -5.44 1.15 89.89 -15.0 0.72 77.43 -3.75 0.92 96.64 -2.91 1.07 88.43

Algorithm 2 log2 C c-ratio t-ratio 0 92.25 88.73 -1.25 76.28 75.0 1.88 95.38 96.34 -2.5 98.75 98.43 0.94 87.6 89.93 9.06 80.0 77.43 -2.5 97.25 97.61 0.31 92.0 88.85

From Table 1, we can see that on five datasets the hybrid algorithm behaves best. On the rest three datasets the cross validation algorithm obtains best test ratios. While the fixed-C algorithm only has satisfying performance on datasets titanic and splice. It is interesting to note that, although the test ratios of the cross validation algorithm and algorithm 2 are very comparative, the obtained C and σ may differ widely, e.g. on datasets banana and titanic. Another interesting thing is to compare the computational cost of the three algorithms. To make things simple, we assume that no cache technique like the one used in [4] is employed. Obviously 125 samples need to be examined with the cross validation algorithm to select the best C and σ, while only 25 samples with the fixed-C algorithm and 50 samples with the hybrid algorithm. This makes the hybrid algorithm more appealing.

5

Conclusion

Model selection is very important for a support vector machine (SVM). Several algorithms have been explored in literatures to select appropriate SVM parameters for a given problem. In this paper, we investigate the use of the Vapnik Chervonenkis (VC) bound for SVM model selection. Two algorithms, the fixedC algorithm and the hybrid algorithm, are proposed. Experimental results on several benchmark datasets show that the hybrid algorithm has very comparative, if not better, performance than the cross validation algorithm. Moreover,

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the computational cost of the former is much less than the latter, which makes it more appealing. Future research directions include: (1) Extend current work with other types of kernel functions, such as the polynomial kernel and the sigmoid kernel. (2) Combine the proposed algorithms with other algorithms to obtain even better SVM models. For example, we can use the proposed algorithms to select better initial values for other gradient-descent based algorithms, e.g. those using the radius margin bound.

References 1. Burges, C.J.: A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery. 2 (1998) 121–267 2. Chung, K.-M., Kao, W.-C., Sun, T., Wang, L.-L., Lin, C.-J.: Radius Margin Bounds for Support Vector Machines with the RBF Kernel. Neural Computation. 11 (2003) 2643–2681 3. Chang, C.-C., Lin, C.-J.: LIBSVM: A Library for Support Vector Machines. (2002) Online at http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf 4. Staelin, C.: Parameter Selection for Support Vector Machines. (2003) Online at http://www.hpl.hp.com/techreports/2002/HPL-2002-354R1.pdf 5. Li, H.-Q., Wang, S.-Y., Qi, F.-H: Minimal Enclosing Sphere Estimation and Its Application to SVMs Model Selection. IEEE Intl. Symposium on Neural Networks. (2004) to appear 6. Chapelle, O., Vapnik, V., Bousquet, O., Mukherjee, S: Choosing Multiple Parameters for Support Vector Machines. Machine Learning. 46 (2002) 131-159

Unbalanced Hermite Interpolation with Tschirnhausen Cubics Jun-Hai Yong and Hua Su School of Software, Tsinghua University, Beijing 100084, P. R. China [email protected]

Abstract. A method for constructing a cubic Pythagorean hodograph (PH) curve (called a Tschirnhausen cubic curve as well) satisfying unbalanced Hermite interpolation conditions is presented. The resultant curve interpolates two given end points, and has a given vector as the tangent vector at the starting point. The generation method is based on complex number calculation. Resultant curves are represented in a B´ezier form. Our result shows that there are two Tschirnhausen cubic curves fulfilling the unbalanced Hermite interpolation conditions. An explicit formula for calculating the absolute rotation number is provided to select the better curve from the two Tschirnhausen cubic curves. Examples are given as well to illustrate the method proposed in this paper. Keywords: Hermite; Pythagorean hodograph; Absolute rotation number.

1

Introduction

Hermite interpolation problem is a fundamental problem in computer aided geometric design (CAGD)[1], and has numerous applications in a lot of areas such as robotics (for path planning), computer graphics, and computer-aided design (CAD) [2]. Yong and Cheng [1] make a good summarization on recent research directions on this problem. A lot of attentions have been paid to build geometric Hermite curves [3–7 et al.] with a low degree, high order geometric continuity and high order approximation accuracy. Another research direction is to combine Hermite interpolation with Pythagorean hodograph condition [8–12 et al.] The research in this paper belongs to this direction. A parametric polynomial curve satisfying the Pythagorean hodograph (PH) condition has at least the following benefits, (1) the arc length could be expressed in a polynomial form, and (2) both the curvature and the offset curve are rational. In this research direction, current research focuses on balanced Hermite interpolation conditions with a PH curve, i.e., constructing a PH curve to interpolate two given end points and take two given vectors as the tangent vectors at the end points. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1072–1078, 2004. c Springer-Verlag Berlin Heidelberg 2004


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Up to now, no literature could be found about unbalanced Hermite interpolation with a PH curve. The endpoint position requirement is the same between the balanced Hermite interpolation and the unbalanced one, while the unbalanced Hermite interpolation has the tangent vector requirement only at one end point, i.e., only a vector is given, which should be the tangent vector of the resultant curve at an end point, for example, at the starting point. Unbalanced Hermite interpolation problem is frequently required in a lot of practical applications as well. For example, the curves of this kind could be two end segments of a composition curve, which could be a sketch in the mechanical design or a contour in a GIS (geographic information system). To construct either of the two end segments of the composition curve is usually to build a curve fulfilling unbalanced Hermite interpolation conditions. The resultant curve, which is an end segment of composition curve, should match the tangent condition at one end point to satisfy the C1 continuity requirement of the composition curve. At the other end point of the resultant curve, the tangent condition is often unnecessary. PH curves with balanced Hermite interpolation conditions could fulfill the unbalanced Hermite interpolation conditions as well. However, Farouki and Neff [9] point out that Quintics are the simplest PH curves with balanced Hermite interpolation conditions. In this paper, we show that a cubic PH curve (called a Tschirnhausen cubic curve as well) is enough to build a PH curve with unbalanced Hermite interpolation conditions. Complex number theory is used to generate the Tschirnhausen cubic curve fulfilling the unbalanced Hermite interpolation conditions. We find that there are totally two resultant Tschirnhausen cubic curves. An absolute rotation number is used to automatically find out a better one from the two resultant curves. An explicit formula is given to calculate the absolute rotation number. The remaining part of the paper is arranged as follows. According to complex number theory, Section 2 presents the method for generating Tschirnhausen cubics, which are the simplest polynomial curves with the Pythagorean hodograph property, to match the unbalanced Hermite interpolation requirements. We find that there are totally two resultant Tschirnhausen cubic curves. Based on the absolute rotation number, a method for selecting a better curve from the two resultant Tschirnhausen cubic curves is provided in Section 3. The formula for calculating the absolute rotation number is given in this section as well. Some examples and some concluding remarks are provided in the last section.

2

Unbalanced Hermite Interpolation

As shown in Figure 1, this section provides a method for constructing a Tschirnhausen cubic curve P(t) such that P(0)=A, P(1)=D and P (0)=T, where A and D are two given points, and T is a given vector. The resultant curve P(t) is presented in a B´ezier form. According to the interpolation property of a B´ezier curve, A and D should be two control points of P(t). Assume

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z2

C

B z1

z3

P(t)

D

A Fig. 1. Unbalanced Hermite interpolation with Tschirnhausen cubic curve P(t)

that the other two control points are B and C, respectively. Then, the B´ezier form of P(t) is P(t) = AB0,3 (t) + BB1,3 (t) + CB2,3 (t) + DB3,3 (t), where Bi,3 (t)(i = 0, 1, 2, 3) are Bernstein basis functions. Our method is based on complex number calculation, i.e., values of A, B, C, D, T and P(t) are given by complex numbers. For convenience, for any complex number z, let arg(z) ∈ (−π, π] represent the angle from the positive real axis to z, where counterclockwise and clockwise rotations give positive and negative values, respectively. In this paper, we do not consider the degenerated cases that A = D, or T = D − A, or T = 0. For convenience of presentation, we take these assumptions for granted. With complex analysis, we have the following theorem. Theorem 1. There are two Tschirnhausen cubics satisfying the unbalanced Hermite interpolation conditions. Proof. Let z1 = B − A, z2 = C − B and z3 = D − C, as shown in Figure 1, then we have (1) z1 + z2 + z3 = D − A, and the tangent vector of P(t) at the starting point is P (0) = 3z1 = T.

(2)

Reference [8] points out that a B´ezier curve P(t) is a Tschirnhausen cubic curve if and only if z1 z3 = z22 .

(3)

Substituting Equations (2) and (3) into Equation (1), we obtain that z2 is a root of 9z22 + 3Tz2 + T(3A − 3D + T) = 0.

(4)

Unbalanced Hermite Interpolation with Tschirnhausen Cubics

Therefore, z2 has two possible values. Additionally, we have z1 = z3 =

3z22 T

1075 T 3

and

from the above equations. Thus, the resultant cubic B´ezier curve P(t) is 3z2

2 determined by the control points A, B = A+z1 = A+ T 3 , C = D−z3 = D− T , and D. Because z2 has two possible values, C has two possible positions. Hence, we obtain the conclusion in Theorem 1.  

The above proof also provides the method for producing the resultant curves. The method for automatically choosing a better one from the two resultant curves is given in the next section.

3

Absolute Rotation Number

Absolute rotation number here is used to select a better curve from two resultant Tschirnhausen cubics. Experience shows that the curve with a better shape is the one with the smaller absolute rotation number in two resultant Tschirnhausen cubics. The value of the absolute rotation number of a given curve is the result of 2π dividing the total absolute rotation angle of the curve tangent vector along the curve. Some more details about the absolute rotation number could be found in Reference [9]. In this paper, an explicit formula for calculating the absolute rotation number of a Tschirnhausen cubic curve is proposed here. It is based on the following lemma. Lemma 1. Let a Tschirnhausen cubic curve P(t) be given in a cubic B´ezier form with four control points A, B, C and D. And let z1 = B − A, z2 = C − B and z3 = D − C. Then, the rotation direction of the curve P(t) at the starting
point P(0) is the same as the rotation direction from z1 to z2 , i.e., if arg zz21 < 0, the rotation direction of P(t) at P(0) is clockwise; otherwise, it is counterclockwise. The above lemma could be proved with the definition of the curvature of a B´ezier curve and the difference property of a B´ezier curve. Those properties of a B´ezier curve could be found in a lot of textbooks about computer graphics or CAGD such as Reference [13]. And then, the explicit formula for calculating the absolute rotation number of a Tschirnhausen cubic curve is given by the following theorem. Theorem 2. The absolute rotate number of a Tschirnhausen cubic curve P(t) is given by    1 z2  Rabs = arg , (5) π z1  where the notations here just follow those in Lemma 1. Proof. According to the derivative property of a B´ezier curve, the directions of the tangent vectors of P(t) at the starting point and at the ending point are

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the same as the directions of z1 and z3 , respectively. References [10] and [11] have shown that a Tschirnhausen cubic curve does not have any inflection point or cusp. Therefore, 2πRabs is the absolute angle from z1 to z3 along the curve P(t). From Equation (3), we have that z2 is on the line, which bisects the angle from z1 to z3 . Lemma 1 shows that the rotation direction of P(t) at the starting point P(0) is the same as the rotation direction from z1 to z2 . Therefore, we obtain that z2 exactly bisects the angle from z1 to z3 along the direction of P(t). Hence, 2πRabs is twice of the absolute angle from z1 to z2 . Thus, we have the conclusion in Theorem 2.  

4

Example and Conclusions

An example is presented here to illustrate the method proposed in this paper. It is shown in Figure 2, where the two given end points are A = 0 and D = 1, and the tangent vector at A is T = 0.25 + 0.25i. As shown in Figure 2(a), there are two Tschirnhausen cubics matching the above unbalanced Hermite interpolation requirements. They are drawn in solid and in dashed, respectively. The four control points of the solid one are 0, 0.25 + 0.25i, 0.6469 + 0.2747i and 1. And the four control points of the dashed one are 0, 0.25 + 0.25i, −0.3969 − 0.0247i and 1. Figures 2(b) and 2(c) illustrate the Gauss maps of the solid curve and the dashed curve, respectively. As shown in the curves, z2 bisects the angle from z1 to z3 along the direction of the resultant curve. The solid curve whose absolute rotation number is 0.2302 has a better shape than the dashed curve whose absolute rotation number is 0.8778. One more example is given in Figures 3. The curves are built with the method provided in the proof of Theorem 1. The degree of the resultant curves fulfilling the unbalanced Hermite interpolation requirement is only 3, while the degree of the PH curves satisfying the balanced Hermite interpolation requirement is at least 5 [9]. The Gauss maps illustrate the bisection property of z2 . Absolute rotation numbers could be calculated according to Theorem 2 in Section 3. The

T z1 B

z2

C

z2

z3 P(t) P(t)

z1 C

A (a)

z3

z1 z2

z3

z2

z3

D (b)

(c)

Fig. 2. Example 1: (a) two resultant Tschirnhausen cubics; (b) Gauss map of the solid Tschirnhausen cubic curve; (c) Gauss map of the dashed Tschirnhausen cubic curve

Unbalanced Hermite Interpolation with Tschirnhausen Cubics T

C

z2

z1

z3 B

z1

z2

P(t) A

z2

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z3

z1 z2

D

z3

z3 C (a)

(b)

(c)

Fig. 3. Example 2: (a) two resultant Tschirnhausen cubics; (b) Gauss map of the solid Tschirnhausen cubic curve; (c) Gauss map of the dashed Tschirnhausen cubic curve

absolute rotation numbers of the solid curve and the dashed curve in Figure 3(a) are 0.4873 and 0.6744, respectively. Those examples (see Figures 2 and 3) show that the resultant curve (solid in figures) with the smaller absolute rotation number has a better shape than the other resultant curve (dashed in figures).

Acknowledgements The research was supported by Chinese 863 Program (2003AA4Z3110) and 973 Program (2002CB312106). The first author was supported by a project sponsored by SRF for ROCS, SEM (041501004), and a Foundation for the Author of National Excellent Doctoral Dissertation of PR China (200342).

References 1. Yong, J.H. and Cheng, F.: Geometric Hermite curves with minimum strain energy. Computer Aided Geometric Design 21 (2004) 281–301 2. Yong, J.H. and Zheng, W.: Geometric method for Hermite interpolation by a class of PH quintics. Journal of Computer Aided Design & Computer Graphics (to appear) 3. de Boor, C., H¨ ollig, K., and Sabin, M.: High accuracy geometric Hermite interpolation. Computer Aided Geometric Design 4 (1987) 269–278 4. H¨ ollig, K. and Koch, J.: Geometric Hermite interpolation. Computer Aided Geometric Design 12 (1995) 567–580 5. H¨ ollig, K. and Koch, J.: Geometric Hermite interpolation with maximal order and smoothness. Computer Aided Geometric Design 13 (1996) 681–695 6. Reif, U.: On the local existence of the quadratic geometric Hermite interpolant. Computer Aided Geometric Design 16 (1999) 217–221 7. Schaback, R.: Optimal geometric Hermite interpolation of curves. In Dahlen, M., Lyche, T., and Schumaker, L.L., eds.: Mathematical Methods for Curves and Surface II. (1998) 1–12 8. Farouki, R.T.: The conformal map of the hodograph plane. Computer Aided Geometric Design 11 (1994) 363–390 9. Farouki, R.T. and Neff, C.A.: Hermite interpolation by Pythagorean hodograph quintics. Mathematics of Computation 64 (1995) 1589–1609

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10. Farouki, R.T. and Sakkalis, T.: Pythagorean hodographs. IBM Journal of Research and Development 34 (1990) 736–752 11. Meek, D.S. and Walton, D.J.: Geometric Hermite interpolation with Tschirnhausen cubics. Journal of Computational and Applied Mathematics 81 (1997) 299–309 12. Meek, D.S. and Walton, D.J.: Hermite interpolation with Tschirnhausen cubic spirals. Computer Aided Geometric Design 14 (1997) 619–635 13. Piegl, L. and Tiller, W.: The NURBS Book. Springer, Berlin (1995)

An Efficient Iterative Optimization Algorithm for Image Thresholding Liju Dong1,2 and Ge Yu1 1

School of Information Science and Engineering, Northeastern University, Shenyang 110004, China 2 School of Information Science and Engineering, Shenyang University, Shenyang 110044, China [email protected], [email protected]

Abstract. Image thresholding is one of the main techniques for image segmentation. It has many applications in pattern recognition, computer vision, and image and video understanding. This paper formulates the thresholding as an optimization problem: finding the best thresholds that minimize a weighted sum-of-squared-error function. A fast iterative optimization algorithm is presented to reach this goal. Our algorithm is compared with a classic, most commonly-used thresholding approach. Both theoretic analysis and experiments show that the two approaches are equivalent. However, our formulation of the problem allows us to develop a much more efficient algorithm, which has more applications, especially in real-time video surveillance and tracking systems.

1 Introduction Image segmentation plays a very important role in many tasks of pattern recognition, computer vision, and image and video retrieval. Many approaches have been proposed in the literature [1–5]. Image thresholding is one of the most important techniques for image segmentation. Its goal is to automatically find one or more thresholds from the histogram of the image under study. The thresholds divide the image into two or more regions each with similar gray levels. Among many thresholding techniques, the Otsu’s method [6] is considered as the most commonly-used one in the survey papers [1–5]. It is also ranked as the best and fastest global thresholding technique in [2] and [3]. In applications such as real-time video surveillance and recognition systems, and image and video retrieval and understanding from large databases, it is desirable to develop as fast algorithms as possible for a task. This paper proposes an efficient approach to image thresholding. We formulate the thresholding as a discrete optimization problem: finding the best thresholds that minimize a weighted sum-of-squarederror objective function. A fast iterative optimization algorithm is proposed to reach this goal based on the histogram. We compare our approach with the Otsu’s method. Both theoretic analysis and experiments show that the two methods yield the same segmentation results but our algorithm is much faster. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1079–1085, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 The New Approach 2.1 Formulation of the Problem The goal of image thresholding is to divide the pixels of an image into two or more regions with similar gray levels, which is similar to data clustering where data are partitioned into clusters with similar properties. Therefore, the widely used sum-ofsquared-error criterion in data clustering [7] is modified in this paper to be the objective function of the segmentation. Suppose that there are L gray levels {0,1,..., L − 1} in an image. Let nl denote the number of pixels at level l . If an image contains three different objects each with exactly the same gray level (an ideal case), there will be only three non-zero nl , l ∈ {0,1,..., L − 1} , in the histogram of this image (see Fig. 1(a)). However, the practical histogram of a real image with three objects always has much more non-zero nl on it. These gray levels spread on the histogram in a wide range, as shown in Fig. 1(b). Thus we formulate the image segmentation as finding the clusters on the histogram such that the total deviation of the gray levels from their corresponding cluster centers (centroids) is minimized (see Fig. 1(c)). More formally, we give the following formulation. nl

S1

nl l

0

L-1

l 0

L-1

0

(b)

(a)

S2

x

m1

S3

x

t1

m2 (c)

t2

l x m3 L-1

Fig. 1. (a) An ideal histogram with only three non-zero gray levels. (b) A practical histogram with three clusters. (c) One partition of three clusters of the gray levels, S 1 , S 2 , S 3 , where the centroids of the clusters are m1 , m2 and m3 , and the two thresholds are t1 and t 2

Definition 1. Suppose that the histogram of an image is divided into c clusters (disjoint subsets) S1 , S 2 ,..., S c , as shown in Fig. 1(c). Let m1 , m2 ,..., mc be the centroids of these clusters. The image thresholding problem is to search for the partition such that the objective function c

f (m1 , m2 ,..., mc ) = ∑∑ nl (l − mi ) 2 .

(1)

i =1 l∈S i

is minimized. The c − 1 thresholds t1 , t2 ,..., tc−1 can be obtained from the final partition S1 , S 2 ,..., S c . We call f (m1 , m2 ,..., mc ) a weighted sum-of-squared-error function, where nl serves as a weighting factor. The centroids are calculated by mi =

1 di

∑n l ，d = ∑n l

l∈S i

i

l∈S i

l

，1 ≤ i ≤ c .

(2)

An Efficient Iterative Optimization Algorithm for Image Thresholding

For convenience, let

f i = ∑ nl (l − mi ) 2 .

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(3)

l∈Si

which is the weighted sum of squared errors in cluster Si . Assume that a grey level k currently in cluster S i is tentatively moved to cluster S j . Then m j changes to m *j , mi changes to mi* , f j changes to f j* , and f i changes *

to f i* , where m *j , mi* , f j* , and f i can, after some mathematical manipulation, be derived as

m *j = m j + f j* = f j +

(k − m j ) n k

d j + nk

d j nk (k − m j ) 2 d j + nk

, mi* = mi −

(k − mi )nk d i − nk

(4)

, f i* = f i −

d i nk ( k − mi ) 2 . d i − nk

(5)

From (5) , we see that the transfer of gray level k from cluster Si to S j can reduce f (m1 , m2 ,..., mc ) if 2 d i nk (k − mi ) 2 d j nk ( k − m j ) > d i − nk d j + nk

(6)

If the reassignment of the gray level k is profitable, the greatest decrease in f ( m1 , m2 ,..., mc ) is obtained by choosing the cluster for which the value d j nk (k − m j ) 2 /(d j + nk ) is minimal. The above equations and analysis lead to the algorithm presented in the next section. 2.2 The Iterative Algorithm

1. Select an initial partition of c clusters S1 , S 2 ,..., S c of the L gray levels on the histogram and calculate m1 , m2 ,..., mc and d1 , d 2 ,..., d c 2. changed ← No 3. for k = 0,1,..., L − 1 do 4. if d i ≠ nk (suppose k ∈ Si currently) then

5.

6.

⎧ d i nk ( k − mi ) 2 q=i ⎪ ⎪ d i − nk Compute rq = ⎨ 2 ⎪ d q n k ( k − mq ) q≠i ⎪ d q + nk ⎩ if rj ≤ rq , j ≠ i, ∀q then (move k to S j )

7.

Update m j and mi with (4)

8.

d i ← d i − nk ; d j ← d j + nk ; changed ← Yes

9. if changed = Yes goto Step 2

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10. else Find c − 1 thresholds from the final partition S1 , S 2 ,..., S c 11. Return the thresholds This algorithm reflects the idea of iteratively improvement in minimizing the objective function f (m1 , m2 ,..., mc ) as described in Section 2.1. The optimization procedure repeats until no further improvement is obtained. A good initial partition can reduce the number of iterations. Let the smallest and largest non-zero gray levels on the histogram be lmin and lmax , respectively. A good initial partition can be obtained by equally dividing [l min , lmax ] into c clusters. It is not difficult to find the computational complexity of the algorithm. Step 1 or Step 10 can be computed in O (L) time. The main computation is in Steps 3 to 8, which requires O (cL) time. Therefore, the algorithm runs in O (cLQ ) time with Q being the number of iterations, which is the number of times Step 2 is visited. From our experiments, we find that Q < 15 in general. 2.3 Comparison with the Otsu’s Method

Otsu proposed his method, from the viewpoint of statistical theory, by maximizing a function σ B2 (t1 , t 2 ,..., tc −1 ) , the detail of which can be found in [6]. In fact, our method and the Otsu’s method are equivalent in essence. Theorem 1. If σ B2 (t1 , t 2 ,..., t c −1 ) is maximized by a partition S1 , S 2 ,..., S c , then f ( m1 , m2 ,..., mc ) in (1) is minimized by the same partition, and vice versa.

The proof can be found in [8]. The optimal thresholds t1 , t2 ,..., tc−1 in the Otsu’s method are obtained by exhaustive search on the histogram. Its computational complexity is O ( cLc ) [8]. Obviously, the complexity O (cLQ ) of our new algorithm is much less, where L = 256 and Q < 15 in general.

3 Experimental Results Our algorithm is implemented in C and runs on a 1 GHz Pentium III PC. For comparison, we also implement the Otsu’s method. More than 80 images have been used to test them. Many of the images are gathered from the web sites on the internet, such as the one in [9] where a number of public image and video databases are available. For an application of image thresholding, how many clusters are divided from the histogram is application dependent. Most practical applications classify the gray levels on the histogram into two or three clusters. In all the experiments, the two algorithms obtain the same result for each image. Here we give two of them. Fig. 2(a) is an infrared image. The two-cluster segmentation result by the two algorithms is very good. The thermal infrared image shown in Fig. 3(a) from a surveillance system cannot be handled with one threshold as illustrated in Fig. 3(b). However, the two algorithms can obtain satisfactory result (Fig. 3(c)) by finding the two thresholds 60 and 150.

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(a)

(b)

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(c)

Fig. 2. (a) An infrared image. (b) The two-cluster segmentation result by our or the Otsu’s algorithm. (c) Histogram of the image in (a)

(a)

(b)

(c)

(d)

Fig. 3. (a) A thermal infrared image. (b) Bad two-cluster segmentation. (c) Good three-cluster segmentation where the clusters are denoted by three gray levels. (d) Histogram of image in (a)

Next we compare the computational time taken by the two algorithms. As mentioned in the last section, theoretically, the new algorithm with complexity O (cLQ ) is much more efficient than the Otsu’s algorithm with complexity O (cLc ) . The experiments show that generally Q < 10 and Q < 15 when the new algorithm carries out two-cluster and three-cluster segmentation, respectively. Table 1 gives the average running time for each algorithm to handle one image in the cases of segmentation with one threshold and two thresholds. Table 1. Comparison of the average running time by the two algorithms (in second)

Algorithm New algorithm Otsu’s algorithm

One threshold 0.0001 0.0011

Two thresholds 0.0008 0.17

From Table 1, we see that both algorithms can find one threshold quickly on an image, and the new algorithm is one order of magnitude faster than the Otsu’s. For three-cluster segmentation, the Otsu’s algorithm requires 0.17 second to deal with one image, while our algorithm spends only 0.0008 second, which is more than 200 times faster than the Otsu’s.

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In many real-time automatic video surveillance and tracking systems, there are 30 frames per second usually. Image segmentation is only part of the processing in these systems. Therefore, in order to reach the goal of processing 30 images within 1 second, the time that is allowed to perform segmentation for one image is much less than 0.03 second. In this case, our algorithm is still fast enough for the job, but the Otsu’s algorithm is not qualified.

4 Conclusions Image segmentation by thresholding is the classic technique that is still used widely in many applications of pattern recognition and computer vision. The main advantage is its simplicity and good efficiency, which is a crucial requirement in most real-time systems. We have presented a new efficient optimization approach to image thresholding. The algorithm iteratively minimizes a weighted sum-of-squared-error objective function, which is expected to finally generate good segmentation of gray levels on the histogram. Our approach is essentially equivalent to the Otsu’s method, which is popular and ranked as the best and fastest global thresholding technique in the survey papers [2] and [3]. However, the new formulation of the segmentation in this paper allows us to develop an even far more efficient algorithm. The complexity O (cLQ ) of the new algorithm is much lower than the complexity O (cLc ) of the Otsu’s, where c is the number of clusters, L = 256 , and Q < 15 in general. A number of experiments have been conducted to test our algorithm and the Otsu’s algorithm. While the two algorithms yield the same segmentation results, our algorithm is more than 10 times and 200 times faster for two-cluster and three-cluster segmentation, respectively. Therefore, our algorithm is more efficient and has more applications, especially in real-time video surveillance and tracking systems.

References 1. Sankur, B., Sezgin, M.: A survey over image thresholding techniques and quantitative performance evaluation. Journal of Electronic Imaging. (to appear). 2. Trier, O.D., Jain A.K.: Goal-directed evaluation of binarization methods. IEEE Trans. Pattern Anal. Machine Intell. 17 (1995) 1191–1201. 3. Trier, O.D., Taxt, T.: Evaluation of binarization methods for document images. IEEE Trans. Pattern Anal. Machine Intell. 17 (1995) 312–315. 4. Pal, N.R., Pal, S.: A review on image segmentation techniques. Pattern Recognition. 26 (1993) 1277–1294. 5. Sahoo, P.K., et al.: A survey of thresholding techniques. Comput. Vis. Graph. Image Process. 41 (1988) 233–260. 6. Otsu, N.: A threshold selection method from grey-level histograms. IEEE Trans. Syst., Man, Cybern. 8 (1979) 62–66. 7. Theodoridis, S., Koutroumbas, K.: Pattern Recognition. Academic Press, London (2003).

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8. Dong L.: An iterative algorithm for image thresholding. Technical Report #20031225, Department of Communications Engineering, Shengyang University, China, 2003. 9. Computer vision test images: http://www-2.cs.cmu.edu/~cil/v-images.html.

Computing the Sign of a Dot Product Sum Yong-Kang Zhu, Jun-Hai Yong, and Guo-Qin Zheng School of Software, Tsinghua University, Beijing 100084, P. R. China [email protected] {yongjh, gqzheng}@tsinghua.edu.cn

Abstract. A real number usually cannot be exactly represented by a floating-point number in a computer. Namely, a floating-point number frequently stands for any real number in a specific interval. In this paper, we present a method for computing the sign of a dot product sum. Each initial datum that is a floating-point number is considered as an interval. With interval analysis and floating-point summation methods, an explicit formula for calculating the minimal interval of a dot product sum is presented. Error analysis and some examples are provided as well. Keywords: Floating-point arithmetic; Rounding error; Interval analysis.

1

Introduction

Sums of floating-point numbers are ubiquitous in scientific computing [1]. Moreover, geometric algorithms are frequently dependent on the sign of a finite sum or a dot product sum [2, 3]. Many people have devoted to studying floating-point summation. In 1999, Anderson [4] presents a floating-point summation method, which iteratively uses the reduction algorithm that makes a cancellation between a positive summand and a negative one, until all the summands have the same sign. This cancellation is exact, which is proved in the paper [4]. And then, using compensated summation method to sum up the remaining summands that have the same sign. Thus, this method could exactly compute the sign of the sum of n floating-point numbers. In the same year, Ratschek and Rokne [3] give a method, named ESSA (Exact Sign of Sum Algorithm), for exactly calculating the sign of a sum of a finite set of floating-point numbers. These two methods are exact when the initial data are just the values of those floating-point summands. However, a real number frequently cannot be exactly represented by a computer floating-point number, due to the length limit of its mantissa. Hence, even if the floating-point computation is exact, the result may be unreliable. Take A = 1.1, B = 9.7, C = −10.8, and S = A+B +C as an example. It seems obvious that the sign of S is zero. If A, B, C are represented by floating-point arithmetic, such as IEEE 754 double, then the sign obtained by either of the above two summation methods is negative, which is different from the expected result. In practice, the correct result could be obtained by comparing the sum with a very tiny positive number, ε. If |s| < ε, then the result could be set zero, where s is the exact sum J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1086–1092, 2004. c Springer-Verlag Berlin Heidelberg 2004


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of all the floating-point numbers. But how to choose an appropriate value of ε is difficult and partially depends on the average magnitude of initial data. A method to calculate the sign of a dot product sum with consideration of the uncertainty of the initial data is presented in this paper. Each floatingpoint number is represented by an interval, which is the minimal interval that contains the possible real value this floating-point number represents. Then, interval analysis method [5] is used to sum up the intervals to decide the sign. Sections 2 defines the representation error of initial data, and tells how to use an interval to represent a floating-point number. In Section 3, the minimal interval of a product between two floating-point numbers is calculated, and the sign of a dot product sum is computed. Examples and conclusions are given in Section 4.

2

Representation Error

In this paper, only fixed-length floating-point arithmetic is considered. We use β to represent the base (sometimes called the radix), use t to represent the precision, and use the fl(a ◦ b) (where ◦ ∈ {+, −, ·, /}) to represent the floatingpoint arithmetic. And if x is a real number, then fl(x) means the floating-point value of x. Additionally, floating-point overflow and underflow are not taken into account. Error of the example in Section 1 is caused by the reason that real numbers 1.1, 9.7, and −10.8 cannot be exactly represented by IEEE 754 double. This type of error is defined as representation error: if x is a real number, then the representation error er of x satisfies er = x − fl(x). There are two ways to let the program know whether initial data have representation error. The first one is that all initial data are given with flags, each of which tells whether the corresponding datum is exactly represented. The other way is an estimated method: the representation error is decided by analyzing the mantissa of the floating-point number. Assume x is the initial datum that is a real number. If the last nm digits of fl(x)’s mantissa are all zero, then we estimate that x = fl(x). Otherwise, x = fl( x), which means representation error occurs. This method is based on the assumption that if a floating-point number exactly represents a real number, then the precision of it is less than the length of its mantissa. If IEEE 754 double (β = 2, t = 53) is used, then 4 ≤ nm ≤ 8 is recommended in practice. If x = fl( x), then there exists a tiny positive floating-point number , which satisfies x ∈ [fl(x) − , fl(x) + ]. If the floating-point arithmetic is correctly rounded, then the minimal  is 12 ulp(x). Otherwise, the minimal  is 1ulp(x). Here, ulp means unit in last place [6]. In this paper, we assume the floatingpoint arithmetic is correctly rounded [7], so we have  = 12 ulp(x). If x = fl(x), then the floating-point number fl(x) is represented by the interval, [fl(x), fl(x)].

3

Calculating the Sign

In this section, a method that decides the sign of a dot product sum, S =
n i=1 Ai Bi (Ai and Bi are real numbers), is presented. Because each initial

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datum, Ai or Bi , is represented
n by an interval, the dot product sum S is in a certain interval, namely S = i=1 Ai Bi ∈ [S, S]. The sign of S is determined by analyzing the interval. Firstly, we consider that how to obtain the interval of the product of two real numbers. Given two real numbers A and B, and let a = fl(A) and b = fl(B). Without losing generality, we assume that A > 0 and B > 0. If both a and b have representation error, then we have A ∈ [a − a , a + a ], and B ∈ [b − b , b + b ], where a = 12 ulp(a) and b = 12 ulp(b). According to interval analysis [5], we obtain AB ∈ [a − a , a + a ] · [b − b , b + b ] = [ab − ab − ba + a b , ab + ab + ba + a b ].

(1)

The algorithms are often implemented on a machine using IEEE 754 Standard binary floating-point arithmetic [8]. Real numbers in programs are represented by two types: f loat (t=24, β=2) or double (t=53, β=2), which are correctly rounded. Here we consider how to calculate the interval (1) with IEEE 754 Standard. The IEEE 754 way of expressing a floating-point number d is d = ±d0 .d1 d2 . . . dt−1 × β ed ,

(2)

where each di is an integer and satisfies 0 ≤ di ≤ β − 1, ed is the exponent of d, d0 is the hidden bit, d0 = 0 for normalized numbers, and the partd1 d2 . . . dt−1 is called the mantissa of d. So a and b could be calculated by a = 12 ulp(a) = 2ea −t and b = 12 ulp(b) = 2eb −t . Thus, according to Equation (1) we have AB ∈ [ab − o − p + q, ab + o + p + q], where o = b2ea −t , p = a2eb −t , q = 2ea +eb −2t . If a does not have representation error, then a = 0, whence o = 0 and q = 0. If b does not have representation error, then b = 0, whence p = 0 and q = 0. Since the exact value of the product of two floating-point numbers can be represented by a sum of two floating-point numbers [9, 10], ab could be exactly computed by ab = c + d, where c and d are two floating-point numbers. Lemma 1. The minimal intervals that contain the value of AB are: ⎧ [(c + d + q) − (+o + p), (c + d + q) + (+o + p)], when a > 0, b > 0; ⎪ ⎪ ⎨ [(c + d − q) − (−o + p), (c + d − q) + (−o + p)], when a > 0, b < 0; AB ∈ [(c + d − q) − (+o − p), (c + d − q) + (+o − p)], when a < 0, b > 0; ⎪ ⎪ ⎩ [(c + d + q) − (−o − p), (c + d + q) + (−o − p)], when a < 0, b < 0. (3) And these intervals can be exactly obtained with floating-point numbers. Proof. According to interval analysis [5], the interval of Equation (1) is the minimal interval that contains the product of A and B, where A is any real number that a could represent, and B is any real number that b could represent. Thus, the intervals of Equation (3) are minimal as well. The value of o = b2ea −t could be obtained by adding ea −t to the exponent of b without floatingpoint computation. And the value of p = a2eb −t could be obtained by adding eb −t to the exponent of a without floating-point computation. And the value of

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q = 2ea +eb −2t could be gained by constructing a new floating-point number with mantissa being set zero and exponent being set ea + eb − 2t. Thus, c, d, o, p and q can be exactly stored in five floating-point numbers, which means the intervals of Equation (3) could be exactly represented with floating-point numbers. According to the intervals of Equation (3), the interval of Ai Bi could be expressed as the form [(g1i + g2i + g3i ) − (g4i + g5i ), (g1i + g2i + g3i ) + (g4i + g5i )].
n Theorem 1. The minimal interval that contains S = i=1 Ai Bi is:  n  n   S∈ ((g1i + g2i + g3i ) − (g4i + g5i )), ((g1i + g2i + g3i ) + (g4i + g5i )) . i=1

i=1

(4) And the signs of two boundaries of the interval can be calculated exactly. Proof. According to Lemma 1 and interval analysis, the
interval of Equation n (4) is the minimal interval that contains the result of S = i=1 Ai Bi . Since two boundaries of this interval are both a sum of 5n floating-point numbers, the signs of them could be exactly figured out by Anderson’s floating-point summation method [4] or ESSA method [3]. Then, the sign of S could be obtained by analyzing the signs of two boundaries of the above interval. The resulting sign ss could be obtained as follows:
n 1. Calculate the sign of i=1 (g1i + g2i + g3i ), say s1 ; 2. If s1 > 0, then
n (a) Calculate the sign of i=1 ((g1i + g2i + g3i ) − (g4i + g5i )), say s2 ; (b) If s2 > 0, then let ss = 1. Otherwise, let ss = 0; 3. If s1 < 0, then
n (a) Calculate the sign of i=1 ((g1i + g2i + g3i ) + (g4i + g5i )), say s3 ; (b) If s3 < 0, then let ss = −1. Otherwise, let ss = 0; 4. If s1 = 0, then let ss = 0. Corollary 1. Assume the minimal interval of S is [S, S]. If S and S have the same sign, then the sign of S can be obtained exactly by the above method. If S and S have opposite signs, then the sign obtained by the above method is zero. Proof. According to Theorem 1, [S, S] could be exactly obtained. If S and S have the same sign, then we have S > 0 or S < 0. Thus, the above method can produce the exact sign of S. Otherwise, the sign obtained by the method is zero. With the corollary, if two boundaries of the interval have different signs, the sign of S is set zero. In this case, the actual sign of S is indefinite, because zero falls into the minimal interval of S. There is no error in calculating the sign of the minimal interval. Therefore, this uncertainty is only determined by the limitation of floating-point representation, namely the representation error due to length limit of mantissa. The error analysis of our method is given in the following theorem.

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Theorem 2. When initial data have no representation errors, the error of our method is zero. Assume the sign obtained by our method is ss . 1. If S = 0, then ss = 0, i.e. the error of the method is 0. 2. If S = 0and ss = ,0then the error of the method is 0. 3. If S = 0and ss = 0, then the error of the method is e = |S|. ∆ ], ∆ , S+ Let ∆ be the length of the interval of Equation(4), we have S ∈ [S− 2 2 ∆ ≤ . Therefore, the error where S ≈ S. If S = 0 andss = 0, then we have |S| 2 ∆ only possibly occurs when S is very close to ∆ 2 or |S| < 2 . Assume δi is the interval length of the minimal intervals of Equation(3), we have δ2i = |o| + |p|. Let ai = fl(Ai ) and bi = fl(Bi ). So, the interval length ∆ of Equation(4) satisfies n n n   ∆  δi = (|ai 2ebi −t | + |bi 2eai −t |) = 2−t (mai + mbi )2eai +ebi = 2 i=1 i=1 i=1

< n2ew −t+2 = 2n · ulp(w),

(5)

where mai and mbi are mantissas of ai and bi , and ew = max (eai + ebi ), w = max (|ai bi |), for all i = 1, 2, · · · , n. Thus, if |S| < 2n · ulp(w) is satisfied, then the sign of S calculated by our method may be wrong. Compensated summation [11] produces a relative error of at most nu (u is the unit roundoff) when all the summands have the same sign [1]. It can be used as a tool to accelerate our method when the sign is apparently not zero. Using compensated summation method, all the positive summands are accumulated to s+ , and all the negative summands are accumulated to s− , where s+ and s− are floating-point numbers. If |s+ + s− | > nu, the sign can be obtained directly. Otherwise, the exact summation method is called to calculate the sign of the boundaries of the interval.

4

Examples and Conclusions

Some examples and some concluding remarks are provided in this section. The floating-point arithmetic used in our examples is IEEE 754 double. The first example contains six initial data: 1.1, −0.1, 2.3, 9.8, 9.7, and −22.8. Our new method obtains that the sign of the sum with the six numbers is zero, which matches the sign of the real sum, while Anderson’s method [4] and ESSA method [3] produce negative signs against the real value. The second example is an application of the method proposed in this paper. It determines whether two line segments intersect. The testing problem could be converted into calculating signs of several dot product summations [2]. If the signs could be computed exactly, then the testing result is reliable. In this example, the new method, say M3 , is compared with the other two methods. The first method, say M1 , converts each coordinate into an integer (ex. 0.34 into 34), and then calculates the signs of those dot product summations with the integer arithmetic. It could always produce exact results. The second method,

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say M2 , uses instances of Java’s “class BigDecimal” to represent the floatingpoint values of coordinates (ex. fl(0.34)), and then calculates the signs with a Java program. It could avoid the error of floating-point computations, but it neglects the representation error of initial data. 1,000,000 random tests are carried out. In each intersection test, eight coordinates of the four end points of the two given line segments are randomly selected from an array, whose elements belong to {0.00, 0.01, · · ·, 0.99}. We find that M3 always gives the same results as M1 does, while M2 produces different results 197 times. The experiment shows that the two given line segments intersect at an ending point when the differences occur. This example illustrates that the method could well deal with some singular cases. Thus, the proposed method for calculating the sign of a dot product sum can deal with the representation error of initial data. The method uses an interval, which is as compact as possible, to represent each floating-point number. The minimal interval of the dot product sum is then obtained to determine the the sign of the resulting dot product sum. The accuracy of our method is demonstrated with Theorem 2 in this paper.

Acknowledgements The authors appreciate the comments and suggestions of the anonymous reviewer. The research was supported by Chinese 863 Program (2003AA4Z3110) and 973 Program (2002CB312106). The second author was supported by a project sponsored by SRF for ROCS, SEM (041501004), and an FANEDD(200342).

References 1. Higham, N.J.: The accuracy of floating point summation. SIAM Journal on Scientific Computing 14 (1993) 783–799 2. Gavrilova, M. and Rokne, J.: Reliable line segment intersection testing. ComputerAided Design 32 (2000) 737–745 3. Ratschek, H. and Rokne, J.: Exact computation of the sign of a finite sum. Applied Mathematics and Computatoin 99 (1999) 99–127 4. Anderson, I.J.: A distillation algorithm for floating-point summation. SIAM Journal on Scientific Computing 20 (1999) 1797–1806 5. Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs, NJ (1966) 6. Higham, N.J.: Accuracy and Stability of Numerical Algorithms. second edn. SIAM. Philadelphia (2002) 7. Jaulin, L., Kieffer, M., Didrit, O., and Walter, E.: Applied Interval Analysis. Springer (2001) 8. ANSI/IEEE New York: IEEE Standard for Binary Floating-Point Arithmetic, Standard 754-1985. (1985)

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9. Masotti, G.: Floating-point numbers with error estimates. Computer-Aided Design 25 (1993) 524–538 10. Priest, D.M.: Algorithms for arbitrary precision floating point arithmetic. In Kornerup, P. and Matula, D.W., eds.: Proceedings of the 10th IEEE Symposium on Computer Arithmetic, IEEE Computer Society Press, Los Alamitos, CA (1991) 132–143 11. Kahan, W.: Further remarks on reducing truncation error. Communications of the ACM 8 (1965) 40

Bilateral Filter for Meshes Using New Predictor Yu-Shen Liu1 , Pi-Qiang Yu1 , Jun-Hai Yong2 , and Hui Zhang2 , and Jia-Guang Sun1,2 1

2

Department of Computer Science and Technology, Tsinghua University, Beijing 100084, P. R. China [email protected] School of Software, Tsinghua University, Beijing 100084, P. R. China

Abstract. A new predictor of bilateral filter for smoothing meshes is presented. It prevents shrinkage of corners. A major feature of mesh smoothing is to move every vertex along the direction determined by the mean curvature normal with speed defined by the predictor. It prevents unnatural deformation for irregular meshes. In order to remove the normal noise, we use adaptive Gaussian filter to smooth triangle normals.

1

Introduction

Nowadays, mesh smoothing or mesh denoising, whose goal is to adjust vertex positions so that the overall mesh becomes smooth while mesh connectivity is kept, is an important process for many digital geometry applications. Removing noise while preserving important features currently is an active area of research. Many mesh smoothing algorithms have been developed in the last few years. Taubin [9] pioneered λ|µ algorithm to solve the shrinkage problem caused by Laplacian smoothing. Desbrun et al. [2] extended this approach to irregular meshes using mean curvature flow. However, these techniques are isotropic, and therefore diffuse shape features. Feature-preserving mesh smoothing was recently proposed. Methods presented in [6, 7, 10] achieve this goal by first smoothing the normal field, and then updating vertex positions to match the new normals. The extension from image smoothing to mesh smoothing was explored in [1, 3, 4, 8]. The bilateral filter, which is an alternative edge-preserving image filter [11], has been extended to mesh smoothing in different ways [1, 3, 4]. Since the bilateral filter is simple, fast and well feature-preserving, it is a good choice for smoothing and denoising. However, the bilateral filter is sensitive to the initial normals, and tends to round off corners, which may result in unnatural deformation for irregular meshes. In this paper, we present a new predictor of bilateral filter which avoids corner shrinkage. This predictor depends on normals of both a vertex and its nearby triangles. We first smooth mesh normals. Then, we move every vertex along the J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1093–1099, 2004. c Springer-Verlag Berlin Heidelberg 2004


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direction determined by the mean curvature normal with speed defined by the new predictor. The major contributions of our work are as follows. - The new predictor preserves both sharp edges and corners. - Combination of the new predictor and the method of normal improvement prevents unnatural deformation for highly irregular meshes.

2

Bilateral Filter for Meshes

A bilateral filter is an edge-preserving filter introduced in image processing for smoothing images [11]. It has been extended to mesh smoothing in different ways [1, 3, 4]. Let M be a input mesh with some additive noise, and let s and p be two points on M. Jones [5] introduces the concept of predictor (Πp (s)), which defines the denoised position of s due to p. The bilateral filter for meshes is defined as
f (||p − s||)g(||Πp (s) − s||)Πp (s) E(s) =

p∈N (s)




f (||p − s||)g(||Πp (s) − s||)

,

(1)

p∈N (s)

where N (s) is a neighborhood of s, and the weight of p depends on both the spatial distance ||p − s|| and the signal difference ||Πp (s) − s||. A spatial weight Gaussian f of width σf and an influence weight Gaussian g of width σg are often chosen in practice. Let ns be the normal at s, and let np be the normal at p. Here we formally define a displacement signed-distance ds from a current position s to the predictor Πp (s). Fleishman et al. [3] have proposed an extension of bilateral filter to meshes. Their predictor can be written by Πp (s) = s + ((p − s) · ns )ns ,

(2)

where p is a vertex in the neighborhood of s. It is illustrated in Fig. 1(a). The predictor does not introduce tangential vertex drift. However, it tends to move vertices along the normal direction to round off corners as shown in Fig. 3(b). Considering the case in which the point s is a corner, Fleishman et al.’s predictor moves great distance from s to Πp (s) as shown in Fig. 2(a).

s ns

p

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Ð p (s)

p

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Fig. 1. (a) Fleishman et al.’s predictor. (b) Jones et al.’s predictor. (c) Our predictor

Bilateral Filter for Meshes Using New Predictor

s

ns

p

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Ð p (s)

np

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Ð p (s)

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Fig. 2. s is a corner. (a) Fleishman et al.’s predictor. (b) Jones et al.’s predictor. (c) Our predictor

Independently, Jones et al. [4] present a similar algorithm. Their approach projects the central vertex s onto the planes of nearby triangles, while that of Fleishman et al. project nearby vertices onto the tangent plane of the central vertex s. The predictor of Jones et al. can be written by Πp (s) = s + ((p − s) · np )np ,

(3)

where p is the centroid of a triangle in the neighborhood of s. It is illustrated in Fig. 1(b). In Fig. 2(b), Jones et al.’s predictor moves a little distance from s to Πp (s) when s is a corner. However, since s does not move along the direction of normal ns , it may introduce tangential vertex drift. This produces unnatural deformation for irregular meshes as shown in Fig. 4(e). 2.1

New Predictor of Bilateral Filter

To avoid unnatural deformation arising from the predictors of Fleishman et al. and Jones et al., we present a new predictor that considers both the vertex normal and its nearby triangle normals. Our approach moves the central vertex s to the tangent planes of nearby triangles along the direction of the normal ns . The new predictor prevents corner shrinkage and tangential vertex drift. Our predictor satisfies Πp (s) = s + dsns

and

(Πp (s) − p)np = 0,

where p is the centroid of a triangle in the neighborhood of s. By solving the above equations, we obtain Πp (s) = s + (

(p − s) · np )ns . n s · np

(4)

It is illustrated in Fig. 1(c). Since our predictor moves vertices along the normal direction, no vertex drift occurs. Due to the combination with nearby triangle normals, corners can be preserved. We consider the case where the point s is a corner. Compared with Fleishman et al.’s predictor which tends to round off corners as shown in Fig. 2(a), our predictor is able to preserve corners as

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(a)

(b)

(c)

Fig. 3. Smoothing of CAD-like model with large noise. (a) Input noisy model. (b) Fleishman et al.’s result (5 iterations). (c) Our result (5 iterations)

(a)

(d)

(b)

(e)

(c)

(f)

(g)

Fig. 4. (a) A torus with different sampling rates. (b) A magnified view of a part of the torus. (c) The torus with additive Gaussian noise in both vertex positions and normals. (d) Fleishman et al.’s method deforms the initial shape. (e) Jones et al.’s method smoothes well but slightly deforms the initial shape. (f) Mean curvature flow smoothes well. (g) Our method smoothes well as (f)

shown in Fig. 2(c). In Fig. 3 we show the smoothing results of a CAD object. In Fig. 3(b), the corners are rounded off by Fleishman et al.’s predictor, while they are preserved by our new predictor as shown in Fig. 3(c). Compared with Jones et al’s predictor which introduces tangential vertex drift as shown in Fig. 2(b), our predictor moves vertices along the normal direction as shown in Fig. 2(c). Fig. 4(e) shows the result of vertex drift. Our result achieves better smoothing with respect to the shape as shown in Fig. 4(g).

3

Improving and Smoothing Normals

Fleishman et al. compute the normal at a vertex as the weighted average (by the area of the triangles) of the normals to the triangles in the 1-ring

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neighborhood of the vertex, where the normal direction depends on the parameterization defined by the areas of the neighborhood triangles. Moving vertex along this direction may result in unnatural deformation for highly irregular meshes (see Fig. 4(d)). To overcome this problem, we use the mean curvature normal. According to [2], a good estimation of the mean curvature normal at vertex p is given by 1
Hn(p) = (cot αi + cot βi )(qi − p), (5) 4A i∈V (p)

where A is the sum of the areas of the triangles around p, V (p) is the set of adjacent vertex indexes to p, qi corresponds to the ith adjacent vertex to p, and αi and βi are the two angles opposite to the edge pqi . In this paper, we use the unit vector n(p) = ||Hn Hn|| as the normal at vertex p instead of the normal used by Fleishman et al.. Roughly speaking, our smoothing schemes consist of moving every vertex along the direction determined by the mean curvature normal of Equation (5), with speed defined by the new predictor of Equation (4). This prevents unnatural deformation for irregular meshes (see Fig. 4(g)). Our predictors are also based on the normals of the nearby triangles. Since the normals are sensitive to noise [4], we smooth normals by adaptive Gaussian filter applied to triangle normals [7].

4

Results and Discussion

We demonstrate our results in Figs. 4-5. The execution time is reported on a Pentium IV 1.70GHz processor with 256M RAM excluding that of loading meshes. All meshes are rendered with flat shading. In Table 1, we indicate model sizes, the number of iterations, running time, and the parameters. The σf and

(a)

(b)

(c)

(d)

(e)

Fig. 5. Results of smoothing the dinosaur model. (a) Input noisy model. (b) A magnified view of (a). (c) Fleishman et al.’s result. (d) Jones et al.’s result. (e) Our result. Notice that details such as the skeletons are better preserved by our method, while flat regions are equivalently smoothed

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Fig. Verts. Iterations

Dinosaur 5(c) 56K 5(d) 5(e)

Time σf

σg

3 1.2s Interactive Interactive non-iterative 22.5s 4.0 0.2 3 7.8s 4.0 0.2

σg are expressed as ratios of the mean edge length used by Jones et al.’s [4]. Fig. 4 shows a comparison for smoothing a irregular mesh with other algorithms. In Fig. 5, we compare our result to the results of other bilateral filter algorithm for the dinosaur model. We have presented a novel predictor of bilateral filter which prevents shrinkage of corners. Based on this predictor and the mean curvature normal, we introduced a new mesh smoothing method which prevents unnatural deformation for irregular meshes. In the future, we wish to find a way to automatically select parameters used in bilateral filter such that smoothing is adaptively achieved. Acknowledgements. The research was supported by Chinese 973 Program (2002CB312106). The third author was supported by the project sponsored by SRF for ROCS, SEM (041501004) and FANEDD (200342).

References 1. Choudhury, P., Tumblin, J.: The trilateral tilter for high contrast images and meshes. Proc. of the Eurographics Symposium on Rendering (2003) 186-196 2. Desbrun, M., Meyer, M., Schr¨ oder, P., and Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In SIGGRAPH’99 Conference Proceedings (1999) 317-324 3. Fleishman, S., Drori, I., and Cohen-Or, D.: Bilateral mesh denoising. In SIGGRAPH’ 03 Conference Proceedings (2003) 950-953 4. Jones, T., Durand, F., and Desbrun, M.: Non-iterative, feature-preserving mesh smoothing. In SIGGRAPH’ 03 Conference Proceedings (2003) 943-949 5. Jones, T.: Feature preserving smoothing of 3D surface scans. Master’s Thesis, Department of Electrical Engineering and Computer Science, MIT (2003) 6. Ohtake, Y., Belyaev, A., and Bogaevski, I.: Mesh regularization and adaptive smoothing. Computer-Aided Design 33 (2001) 789-800 7. Ohtake, Y., Belyaev, A., and Seidel, H.P.: Mesh smoothing by adaptive and anisotropic gaussian filter applied to mesh normal. In Vision, modeling and visualization (2002) 203-210 8. Shen, Y., Barner, K.E.: Fuzzy vector median-based surface smoothing. IEEE Transactions on Visualization and Computer Graphics 10 (2004) 252-265

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9. Taubin, G.: A signal processing approach to fair surface design. In SIGGRAPH’95 Conference Proceedings (1995) 351-358 10. Taubin, G.: Linear Anisotropic mesh filtering. Tech. Rep. IBM Research Report RC2213 (2001) 11. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In Proc. IEEE Int. Conf. on Computer Vision (1998) 836-846

Scientific Computing on Commodity Graphics Hardware Ruigang Yang University of Kentucky, Lexington KY 40506, USA [email protected] http://www.cs.uky.edu/~ryang

Abstract. Driven by the need for interactive entertainment, modern PCs are equipped with specialized graphics processors (GPUs) for creation and display of images. These GPUs have become increasingly programmable, to the point that they now are capable of efficiently executing a significant number of computational kernels from non-graphical applications. In this introductory paper we first present a high-level overview of modern graphics hardware’s architecture, then introduce several applications in scientific computing that can be efficiently accelerated by GPUs. Finally we list programming tools available for application development on GPUs.

1

Introduction

As the mass-market emphasis in computing has shifted from word processing and spreadsheets to interactive entertainment, computer hardware has evolved to better support these new applications. Most of the performance-limiting processing today involves creation and display of images; thus, a new entity has appeared within most computer systems. Between the system’s general-purpose processor and the video frame buffer, there is now a specialized Graphic Processing Unit (GPU). Early GPUs were not really processors, but hardwired pipelines for each of the most common rendering tasks. As more complex 3D-transformations have become common in a wide range of applications, GPUs have become increasingly programmable, to the point that they now are capable of efficiently executing a significant number of computational kernels from non-graphical applications. A GPU is simpler and more efficient than a conventional PC processor (CPU) because a GPU only needs to perform a relatively simple set of array processing operations (but at a very high speed). Many problems in scientific computing, such as physically-based simulation, information retrieval, and data mining, can boil down to relatively simple matrix operations. This characteristic makes these problems ideal candidates for GPU acceleration. In this introductory paper we first present a high-level overview of modern graphics hardware’s architecture and its phenomenal development in recent years. Then we introduce a large array of non-graphical computational tasks, in J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1100–1105, 2004. c Springer-Verlag Berlin Heidelberg 2004


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particular, linear algebra operations, that have been successfully implemented on GPUs and obtained significant performance improvements. Finally we list programming tools available for application development on GPUs. Some of them are designed to allow programming GPUs with familiar C-like constructs and syntax, without worrying about the details of the hardware. They hold the promise of bringing the vast computational power in GPUs to the broad scientific computing community.

2

A Brief Overview of GPUs

In this section, we will explain the basic architecture of GPUs and the potential advantages of using GPUs to solve scientific problems. 2.1

The Rendering Pipeline

GPUs are dedicated processors designed specifically to handle the intense computational requirements of display graphics, i.e., rendering texts or images over 30 frames per second. As depicted in Figure 1, a modern GPU can be abstracted as a rendering pipeline for 3D computer graphics (2D graphics is just a special case) [1].

Geometric primitives

Vertex Processing

Rasterization

Fragment Processing

Frame buffer

Fig. 1. Rendering Pipeline

The inputs to the pipeline are geometric primitives, i.e., points, lines, polygons; and the output is the framebuffer–a two-dimensional array of pixels that will be displayed on screen. The first stage operates on geometric primitives described by vertices. In this vertex-processing stage vertices are transformed and lit, and primitives are clipped to a viewing volume in preparation for the next stage, rasterization. The rasterizer produces a series of framebuffer addresses and color values, each is called a fragment that represents a portion of a primitive that corresponds to a pixel in the framebuffer. Each fragment is fed to the next fragment processing stage before it finally alters the framebuffer. Operations in this stage include texture mapping, depth test, alpha blending, etc. 2.2

Recent Trend in GPUs

Until a few years ago, commercial GPUs, such as the RealityEngine from SGI [2], implement in hardware a fixed rendering pipeline with configurable parameters.

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As a result their applications are restricted to graphical computations. Driven by the market demand for better realism, the current generation of commercial GPUs such as the NVIDIA GeForce FX [3] and the ATI Radeon 9800 [4] added significant programmable functionalities in both the vertex and the fragment processing stage(stages with double-lines in Figure 1). They allow developers to write a sequence of instructions to modify the vertex or fragment output. These programs are directly executed on the GPUs to achieve comparable performance to fixed-function GPUs. In addition to programable functionalities in modern GPUs, their support for floating point output has been improving. GPUs on the market today support up to 32-bit floating point output. Such a precision is usable for many diverse applications other than computer graphics.

10000

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Fig. 2. A graph of performance increase over time for CPUs and GPUs. GPU performance has increased at a faster rate than CPUs. (Data courtesy of Anselmo Lastra)

GPUs have also demonstrated a rapid improvement in performance during the past few years. In Figure 2, we plot the performance increase of both GPUs and commodity Central Processor Units (CPUs). Similar to the number of integer operations per second for CPUs, a typical benchmark to gauge a GPU’s performance is the number of triangles it can process every second. We can see that GPUs have maintained a performance improvement rate of approximately 3X/year, which exceeds the performance improvement of CPUs at 1.6X/year. This is because CPUs are designed for low latency computations, while GPUs are optimized for high throughput of vertices and fragments [5]). Low latency on memory-intensive applications typically requires large caches, which use a large silicon area. Additional transistors are used to greater effect in GPU architectures because they are applied to additional functional units that increase throughput [6].

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1103

Applications of GPUs for General-Purpose Computation

With the wide deployment of inexpensive yet powerful GPUs in the last several years, we have seen a surge of experimental research in using GPUs for tasks other than rendering. For example, Yang et. al. have experimented with using GPUs to solve computer visions problems [7, 8]; Holzschuch and Alonso to speed visibility queries [9]; Hoff et. al. to compute generalized Voronoi Diagrams [10] and proximity information [11]; and Lok to reconstruct an object’s visual hull given live video from multiple cameras [12]. Each of these applications obtained significant performance improvements by exploiting the speed and the inherent parallelism in modern graphics hardware. For the scope of this paper, we introduce several representative approaches to accelerate linear algebra operations on GPUs. Larsen and McAllister present a technique for large matrix-matrix multiplies using low cost graphics hardware [13]. The method is an adaptation of the technique from parallel computing of distributing the computation over a logically cube-shaped lattice of processors and performing a portion of the computation at each processor. Graphics hardware is specialized in a manner that makes it well suited to this particular problem, giving faster results in some cases than using a general-purpose processor. A more complete and up-to-date implementation of dense matrix algebra is presented by Morav´anszky [14]. The paper of Bolz et al. shows two basic, broadly useful, computational kernels implemented on GPUs: a sparse matrix conjugate gradient solver, and a regular-grid multigrid solver [15]. Performance analysis with realistic applications shows that a GPU-based implementation compares favorable over its CPU counterpart. A similar framework for implementation of linear algebra operators on GPUs is by Kr¨ uger and Westermann [16], which focuses on sparse and banded matrices. There are many other algorithms for scientific computing that have been implemented on GPUs, including FFT [17],level set [18, 19], and various types of physically-based simulations [20–22]. Interested readers are referred to http://www.gpgpu.org for other general-purpose applications on GPUs.

4

GPU Programming Languages

While many non-graphical applications on GPUs have obtained encouraging results by exploiting GPU’s fast speed and high bandwidth, the development process is not trivial. Many of the existing applications are written using low level assemble languages that are directly executed on the GPU. Therefore, novice developers are faced with a steep learning curve to master a thorough understanding of the graphics hardware and its programming interfaces, namely OpenGL [1] and DirectX [23]. Fortunately, this is rapidly changing with several high-level languages available. The first is Cg – a system for programming graphics hardware in a C-like

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language[24]. It is, however, still a programming language geared towards rendering tasks and tightly coupled with graphics hardware. There are other high-level languages, such as Brook for GPUs and Sh, which allow programming GPUs with familiar constructs and syntax, without worrying about the details of the hardware. Brook extends C to include simple dataparallel constructs, enabling the use of the GPU as a streaming coprocessor. Sh is a metaprogramming language that offers the convenient syntax of C++ and takes the burden of register allocation and other low-level issues away from the programmer. While these languages are not fully mature yet, they are the most promising ones to allow non-graphics researchers or developers to tap into the vast computational power in GPUs.

5

Conclusion

The versatile programmability and improved floating-point precisions now available in GPUs make them useful coprocessors for scientific computing. Many non-trivial computational kernels have been successfully implemented on GPUs to receive significant acceleration. As graphics hardware continues to evolve at a faster speed than CPUs and more “user-friendly” high-level programming languages are becoming available, we believe communities outside computer graphics can also benefit from the fast processing speed and high bandwidth that GPUs offer. We hope this introductory paper will encourage further thinking along this direction.

Acknowledgments The author would like to thank Hank Dietz for providing some of the materials in this paper. This work is supported in part by fund from the office of research at the University of Kentucky and Kentucky Science & Engineering Foundation (RDE-005).

References 1. Segal, M., Akeley, K.: The OpenGL Graphics System: A Specification (Version 1.3) (2001) http://www.opengl.org. 2. Akeley, K.: RealityEngine Graphics. In: Proceedings of SIGGRAPH. (1993) 3. NVIDIA Corporation: GeForce FX (2003) http://www.nvidia.com/page/fx desktop.html. 4. ATI Technologies Inc.: ATI Radeon 9800 (2003) http://www.ati.com/ products/radeon9800. 5. Lindholm, E., Kilgard, M., Moreton, H.: A User Programmable Vertex Engine. In: Proceedings of SIGGRAPH. (2001) 149–158 6. Harris, M.: Real-Time Cloud Simulation and Rendering. PhD thesis, Department of Computer Science, University of North Carolina at Chapel Hill (2003)

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7. Yang, R., Welch, G.: Fast Image Segmentation and Smoothing Using Commodity Graphics Hardware. Journal of Graphics Tools, special issue on HardwareAccelerated Rendering Techniques 7 (2003) 91–100 8. Yang, R., Pollefeys, M.: Multi-Resolution Real-Time Stereo on Commodity Graphics Hardware. In: Proceedings of Conference on Computer Vision and Pattern Recognition (CVPR). (2003) 211–218 9. Holzschuch, N., Alonso, L.: Using graphics hardware to speed-up visibility queries. Journal of Graphics Tools 5 (2000) 33–47 10. III, K.E.H., Keyser, J., Lin, M.C., Manocha, D., Culver, T.: Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware. In: Proceeding of SIGGRAPH 99. (1999) 277–286 11. III, K.E.H., Zaferakis, A., Lin, M.C., Manocha, D.: Fast and simple 2d geometric proximity queries using graphics hardware. In: 2001 ACM Symposium on Interactive 3D Graphics. (2001) 145–148 ISBN 1-58113-292-1. 12. Lok, B.: Online Model Reconstruction for Interactive Virtual Environments. In: Proceedings 2001 Symposium on Interactive 3D Graphics, Chapel Hill, North Carolina (2001) 69–72 13. Larsen, E.S., McAllister, D.K.: Fast Matrix Multiplies using Graphics Hardware. In: Proceeding of Super Computer 2001. (2001) ´ am Morav´ 14. Ad´ anszky: Dense Matrix Algebra on the GPU. In: Shaderx2: Shader Programming Tips & Tricks With Directx 9. Wordware (2003) 15. Bolz, J., Farmer, I., Grinspun, E., Schrder, P.: Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid. ACM Transactions on Graphics (SIGGRAPH 2003) 22 (2003) 16. Krger, J., Westermann, R.: Linear Algebra Operators for GPU Implementation of Numerical Algorithms. ACM Transactions on Graphics (SIGGRAPH 2003) 22 (2003) 17. Moreland, K., Angel, E.: The FFT on a GPU. In: SIGGRAPH/Eurographics Workshop on Graphics Hardware 2003 Proceedings. (2003) 112–119 18. Strzodka, R., Rumpf, M.: Level set segmentation in graphics hardware. In: Proceedings of the International Conference on Image Processing. (2001) 19. Lefohn, A.E., Kniss, J., Hansen, C., Whitaker, R.T.: Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware. In: Proceedings of IEEE Visualization. (2003) 20. Harris, M., Baxter, W., Scheuermann, T., Lastra, A.: Simulation of Cloud Dynamics on Graphics Hardware. In: Proceedings of Graphics Hardware. (2002) 92 – 101 21. Kim, T., Lin, M.: Visual Simulation of Ice Crystal Growth. In: Proceedings of ACM SIGGRAPH / Eurographics Symposium on Computer Animation 2003. (2003) 92 – 101 22. S.Tomov, M.McGuigan, R.Bennett, G.Smith, J.Spiletic: Benchmarking and Implementation of Probability-Based Simulations on Programmable Graphics Cards. Computers & Graphics (2004) 23. Microsoft: DirectX (2003) http://www.microsoft.com/windows/directx. 24. NVIDIA: Cg: C for Graphics (2002) http://www.cgshaders.org/.

FIR Filtering Based Image Stabilization Mechanism for Mobile Video Appliances Pyung Soo Kim Mobile Platform Lab, Digital Media R&D Center, Samsung Electronics Co., Ltd, Suwon City, 442-742, Korea Phone : +82-31-200-4635, Fax : +82-31-200-3975 [email protected]

Abstract. This paper proposes a new image stabilization mechanism based on filtering of absolute frame positions for mobile video appliances. The proposed mechanism removes undesired motion effects in real-time, while preserving desired gross camera displacements. The well known finite impulse response (FIR) filter is adopted for the filtering. The proposed mechanism provides the filtered position and velocity that have good inherent properties. It is shown that the filtered position is not affected by the constant velocity. It is also shown that the filtered velocity is separated from the position. Via computer simulations, the performance of the proposed mechanism is shown to be superior to the existing Kalman filtering based mechanism.

1

Introduction

In recent years, video communication and processing play a significant role in mobile video appliances such as mobile phones, handheld PCs, digital consumer camcorders, and so on. Thus, a camera becomes an inherent part to acquire video images. However, image sequences acquired by a camera mounted on a mobile video appliance are usually affected by undesired motions causing unwanted positional fluctuations of the image. To remove undesired motion effects and to produce compensated image sequences that expose requisite gross camera displacements only, various image stabilization mechanisms have been mainly used for the computation of ego-motion [1], [2], the video compression [3], the estimation and tracking of moving mobiles [4]-[7]. In this paper, the image stabilization mechanism for the estimation and tracking of moving mobiles will be considered. Recently, the motion vector integration (MVI) in [4] and the discrete-time Fourier transform (DFT) filtering in [5] are developed. However, in the MVI mechanism, the filtered position trajectory is delayed owing to filter characteristics imposing larger frame shift than actually required for stabilization, in which stabilization performance is degraded. The DFT filtering based mechanism is not suited for real-time application since off-line processing is required. Therefore, in recent, the image stabilization mechanism using the Kalman filtering has been made by posing the optimal filtering J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1106–1113, 2004. c Springer-Verlag Berlin Heidelberg 2004


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problem due to the compact representation and the efficient manner [6], [7]. However, the Kalman filter has an infinite impulse response (IIR) structure that utilizes all past information accomplished by equaling weighting and has a recursive formulation. Thus, the Kalman filter tends to accumulate the filtering error as time goes. In addition, the Kalman filter is known to be sensitive and show even divergence phenomenon for temporary modeling uncertainties and round-off errors [8]-[11]. Therefore, in the current paper, an alternative image stabilization mechanism is proposed. The proposed mechanism gives the filtered absolute frame position in real-time, removing undesired motion effects, while preserving desired gross camera displacements. For the filtering, the proposed mechanism adopts the well known finite impulse response (FIR) filter that utilizes only finite information on the most recent window [10], [11]. The proposed mechanism provides the filtered velocity as well as the filtered position. These filtered position and velocity have good inherent properties such as unbiasedness, efficiency, time-invariance, deadbeat, and robustness due to the FIR structure. It is shown that the filtered position is not affected by the constant velocity. It is also shown that the filtered velocity is separated from the position. These remarkable properties cannot be obtained from the Kalman filtering based mechanism in [6], [7]. Via numerical simulations, the performance of the proposed mechanism using the FIR filtering is shown to be superior to the existing Kalman filtering based mechanism. The paper is organized as follows. In Section 2, a new image stabilization mechanism is proposed. In Section 3, remarkable properties of the proposed mechanism are shown. In Section 4, computer simulations are performed. Finally, conclusions are made in Section 5.

2

FIR Filtering Based Image Stabilization Scheme

The following fourth order state space model for the image stabilizer is constructed as shown in [6], [7] : x(i + 1) = Ax(i) + Gw(i), z(i) = Cx(i) + v(i) where x(i) =




(1)




 xp (i) wp (i) II I0 , w(i) = , A= , G= , C = [I 0]. 0I 0I xv (i) wv (i)

The state xp (i) = [xp1 xp2 ]T represents horizontal and vertical absolute frame position and the state xv (i) = [xv1 xv2 ]T represents the corresponding velocity in the frame i acquired by a camera mounted on a mobile platform. The process noise w(i) and observation noise v(i) are a zero-mean white noise with covariance Q and R, respectively. Note that noise covariances Q and R can be determined via experiments or left as a design parameter. The main task of the proposed image stabilization mechanism is the filtering of absolute frame positions in real-time, removing undesired motion effects, while

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preserving desired gross camera displacements. For the filtering, the well known FIR filter in [10], [11] is adopted. For the state-space model (1), the FIR filter x ˆ(i) processes linealy the only finite observations on the most recent window [i − M, i] as the following simple form: 

x ˆp (i) Hp = HZM (i) = x ˆ(i) = ZM (i) (2) Hv x ˆv (i) where the gain matrix H and the finite observations ZM (i) are represented by 

H = [h(M ) h(M − 1) · · · h(0)], 

T

T

(3) T

T

ZM (i) = [z (i − M ) z (i − M + 1) · · · z (i)] .

(4)

Hp and Hv are the first 2 rows and the second 2 rows of H, respectively. The algorithm for filter gain coefficients h(·) in (3) is obtained from the following algorithm as shown in [10], [11]: h(j) = Ω −1 (M )Φ(j)C T R−1 ,

0 ≤ j ≤ M,

where Φ(l + 1) = Φ(l)[I + A−T Ω(M − l − 1)A−1 GQGT ]−1 A−T , Ω(l + 1) = [I + A−T Ω(l)A−1 GQGT ]−1 A−T Ω(l)A−1 + C T R−1 C, with Φ(0) = I, Ω(0) = C T R−1 C, and 0 ≤ l ≤ M − 1. Note that gain matrices Hp and Hv require computation only on the interval [0, M ] once and is timeinvariant for all windows. The finite observations ZM (i) in (4) can be represented in the following regression form: ZM (i) = LM xp (i − M ) + NM Xv (i) + GM Wp (i) + V (i)

(5)

where Xv (i), Wp (i), V (i) have the same form as (4) for xv (i), wp (i), v(i), and matrices LM , NM , GM are defined by ⎤ ⎤ ⎡ ⎤ ⎡ ⎡ I 0 0 ··· 0 0 0 0 ··· 0 0 ⎥ ⎥ ⎢ ⎥ ⎢ ⎢  ⎢I ⎥  ⎢I 0 ··· 0 0⎥  ⎢I 0 ··· 0 0⎥ L M = ⎢ . ⎥ , N M = ⎢ . . . . . ⎥ , GM = ⎢ . . . . . ⎥ . ⎣ .. ⎦ ⎣ .. .. .. .. .. ⎦ ⎣ .. .. .. .. .. ⎦ I

3

I I ··· I 0

I I ··· I 0

Remarkable Properties

Ultimately, the filtered absolute frame position x ˆp (i) is obtained from (2) as follows: x ˆp (i) = Hp ZM (i).

(6)

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The filtered position x ˆp (i) has good inherent properties of unbiasedness, efficiency, time-invariance and deadbeat since the FIR filter used provides these properties. The Kalman filter used in [6], [7] does not have these properties unless the mean and covariance of the initial state is completely known. Among them, the remarkable one is the deadbeat property which the filtered position x ˆp (i) tracks the actual position xp (i) exactly in the absence of noises. The deadbeat property gives the following matrix equality as shown in [10], [11]: ⎤ ⎡ C ⎢ CA ⎥ ⎥ ⎢ H ⎢ . ⎥ = AM ⎣ .. ⎦ CAM and then





M  

Hp ¯M = I M I LM N Hv 0 I T

¯M = [0 I 2I · · · M I] . Therefore, the following matrix equalities are where N obtained: ¯M = M I, Hv LM = 0, Hv N ¯M = I, Hp LM = I, Hp N

(7)

which gives following remarkable properties. It will be shown in the following theorem that the filtered position x ˆp (i) in (6) is not affected by the velocity when the velocity is constant on the observation horizon [i − M, i] Theorem 1. When the velocity is constant on the observation window [i−M, i], the filtered position x ˆp (i) in (6) is not affected by the velocity. Proof. When the velocity is constant as x ¯v on the observation window [i − M, i], the finite observations ZM (i) in (5) can be represented in  ¯v for [i − M, i]} ZM (i){xv (i) = x ¯M x = LM xp (i − M ) + N ¯v + GM Wp (i) + V (i). (8) Then, the filtered position x ˆp (i) is derived from (6)-(8) as x ˆp (i) = Hp ZM (i)

¯M x ¯v + GM Wp (i) + V (i) = Hp LM xp (i − M ) + N

¯M x ¯v + Hp GM Wp (i) + V (i) = Hp LM x(i − M ) + Hp N

¯v + Hp GM Wp (i) + V (i) . = xp (i − M ) + M I x

(9)

From (1), the actual position xp (i) can be represented on [i − M, i] as follow:  ¯v for [i − M, i]} xp (i){xv (i) = x ¯ M Wp (i) ¯v + G (10) = xp (i − M ) + M I x

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P.S. Kim



¯ M = I I · · · I 0 . Thus, using (9) and (10), the error of the filtered where G position x ˆp is

¯ M Wp (i), x ˆp (i) − xp (i) = Hp GM Wp (i) + V (i) − G which does not include the velocity term. This completes the proof. The velocity itself can be treated as variable which should be filtered. In this case, the filtered velocity is shown to be separated from the position term. Theorem 2. The filtered velocity x ˆv (i) in (2) is separated from the position term. Proof. The filtered velocity x ˆv (i) is derived from (2) and (7) as x ˆv (i) = Hv ZM (i)

= Hv LM xp (i − M ) + NM Xv (i) + GM Wp (i) + V (i)

= Hv NM Xv (i) + GM Wp (i) + V (i) which does not include the position term. This completes the proof. Above remarkable properties of the proposed FIR filtering based mechanism cannot be obtained from the existing Kalman filtering based mechanism in [6], [7]. In addition, as mentioned previously, the proposed mechanism has the deadbeat property, which means the fast tracking ability of the proposed mechanism. Furthermore, due to the FIR structure and the batch formulation, the proposed mechanism might be robust to temporary modeling uncertainties and to roundoff errors, while the Kalman filtering based mechanism might be sensitive for these situations. The noise suppression of the proposed mechanism might be closely related to the window length M . However, although the proposed mechanism can have greater noise suppression as the window length M increases, too large M may yield the long convergence time of the filtered position and velocity, which degrades the filtering performance of the proposed mechanism. This illustrates the proposed mechanism’s compromise between the noise suppression and the tracking speed of the filtered position and velocity. Since M is an integer, fine adjustment of the properties with M is difficult. Moreover, it is difficult to determine the window length is systematic ways. In applications, one way to determine the window length is to take the appropriate value that can provides enough noise suppression.

4

Computer Simulations

The performance of the proposed FIR filtering based image stabilization mechanism is evaluated via a numerical simulation. It was already shown in [7] that the Kalman filtering based mechanism outperforms the MVI mechanism of [4] for the ‘bike’ sequence acquired by a consumer camcorder mounted on the rear carrier of a moving motorcycle. Therefore, in this paper, the proposed FIR filtering

Image Stabilization Mechanism for Mobile Video Appliances

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based mechanism will be compared with the Kalman filtering based mechanism for the same ‘bike’ sequence of [7]. Note that the Kalman filtering with an IIR structure provides a minimum variance state estimate x ˆ(i), called the one-step predicted estimate, with the estimation error covariance P (i) as shown in [12]: ˆ(i)), x ˆ(i + 1) = Aˆ x(i) + [AP (i)C T (R + CP (i)C T )−1 ](z(i) − C x −1 T −1 −1 T T P (i + 1) = A[P (i) + C R C] A + GQG .

Horizontal position 80

Displacement

60 40 20 0 −20 −40 −60

0

20

40

60

80

100

120

140

160

180

200

120

140

160

180

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Vertical position 150

Displacement

100

50

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−50

0

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40

60

80

100

Fig. 1. Actual horizontal and vertical positions

Horizontal position (Kalman) 5

4

4 RMS Error

RMS Error

Horizontal position (Proposed) 5

3 2 1 0

3 2 1

50

100

150

0

200

50

3

2.5

2.5

2 1.5 1 0.5 0

150

200

Vertical position (Kalman)

3

RMS Error

RMS Error

Vertical position (Proposed)

100

2 1.5 1 0.5

50

100

150

200

0

50

Fig. 2. Filtered position

100

150

200

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P.S. Kim Horizontal velocity (Kalman) 0.2

0.15

0.15 RMS Error

RMS Error

Horizontal velocity (Proposed) 0.2

0.1

0.05

0

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0.05

50

100

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0.06

0.05

0.05

0.04

0.04

0.03 0.02 0.01 0

150

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Vertical velocity (Kalman)

0.06

RMS Error

RMS Error

Vertical velocity (Proposed)

100

0.03 0.02 0.01

50

100

150

200

0

50

100

150

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Fig. 3. Filtered velocity

The existing Kalman filtering based mechanism assumes that a priori information is exactly known, although this assumption would be unpractical [10]. Thus, the initial state estimate is taken by x ˆ(i0 ) = [0 0 0 0]T as shown in [7]. On the other hand, the proposed FIR filtering based mechanism doesn’t require the initial state estimate as shown in (2). The window length is taken by M = 20. For both mechanisms, noise covariances are taken by Q = 0.1 and R = 100 as [7]. To make a clearer comparison, thirty Monte Carlo runs are performed and each single run lasts for 200 samples. Actual horizontal and vertical positions used in one of thirty runs are plotted in Fig. 1. Fig. 2 and 3 show root-mean-square (RMS) errors of the filtered position and velocity. For both filtered position and velocity, simulation results show that the performance of the proposed FIR filtering based mechanism is superior to the existing Kalman filtering based mechanism.

5

Concluding Remarks

This paper has proposed a new image stabilization mechanism based on filtering of absolute frame positions for mobile video appliances. The proposed mechanism removes undesired motion effects in real-time, while preserving desired gross camera displacements. The well known FIR filter is adopted for the filtering. The proposed mechanism provides the filtered position and velocity that have good inherent properties. It is shown that the filtered position is not affected by the constant velocity. It is also shown that the filtered velocity is separated from the position. Simulation results show that the performance of the proposed FIR filtering based mechanism is superior to the existing Kalman filtering based mechanism.

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References 1. Irani, M., Rousso, B., Peleg, S.: Recovery of ego-motion using image stabilization. In: Proc. IEEE Int. Conf. on Computer Vision and Pattern Recognition. (1994) 454–460 2. Rousso, B., Avidan, S., Shashua, A., Peleg, S.: Robust recovery of camera rotation from three frames. In: Proc. IEEE Int. Conf. on Computer Vision and Pattern Recognition. (1996) 796–802 3. Kwon, O., Chellappa, R., Morimoto, C.: Motion compensated subband coding of video acquired from a moving platform In: Proc. IEEE Int. Conf. on Computer Vision and Pattern Recognition. (1995) 2185–2188 4. Engelsberg, A., Schmidt, G.: A comparative review of digital image stabilising algorithms for mobile video communications. IEEE Trans. Consum. Electron. 45 (1999) 591–597 5. Erturk, S., Dennis, T.J.,: Image sequence stabilisation based on DFT filtering. IEE Proc. Vis. Image Signal Process. 147 (2000) 95–102 6. Censi, A., Fusiello, A., Roberto, V.: Image stabilization by features tracking. In: Proc. of Int. Conf. Image Analysis and Processing. (1999) 665–667 7. Erturk, S., Dennis, T.J.,: mage sequence stabilisation based on Kalman filtering of frame positions IEE Proc. Vis. Image Signal Process. 37 (2001) 1217–1219 8. Fitzgerald, R.J.: Divergence of the Kalman filter. IEEE Trans. Automat. Contr. 16 (1971) 736–747 9. Schweppe, F.: Uncertain Dynamic Systems. Englewood Cliffs, NJ:Prentice-Hall (1973) 10. Kwon, W.H., Kim, P.S., Park, P.: A receding horizon Kalman filter for discretetime invariant systems. IEEE Trans. Automat. Contr. 44 (1999) 1787–1791 11. Kwon, W.H., Kim, P.S., Han, S.H.: A receding horizon unbiased FIR filter for discrete-time state space models. Automatica. 38 (2002) 545–551 12. Kalman, R.E., Bucy, R.S.: New results in linear filtering and prediction theory Trans. ASME J. of Basic Engr. 83 (1961) 95–108

p-Belief Communication Leading to a Nash Equilibrium Takashi Matsuhisa
Department of Liberal Arts and Sciences, Ibaraki National College of Technology, Nakane 866, Hitachinaka-shi, Ibaraki 312-8508, Japan [email protected]

Abstract. A pre-play communication in the p-belief system is presented which leads to a Nash equilibrium of a strategic form game through messages. In the communication process each player predicts the other players’ actions under his/her private information with probability at least p. The players communicate privately their conjectures through message according to the communication graph, where each player receiving the message learns and revises his/her conjecture. The emphasis is on that any topological assumptions on the communication graph are not required in the theorem. Keywords: p-Belief system, Nash equilibrium, Communication, Protocol, Conjecture, Non-corporative game. AMS 2000 Mathematics Subject Classification: Primary 91A35, Secondary 03B45. Journal of Economic Literature Classification: C62, C78.

1

Introduction

This article relates equilibria and distributed knowledge. In game theoretical situations among a group of players, the concept of mixed strategy Nash equilibrium has become central. Yet little is known about the process by which players learn if they do. This article will give a protocol run by the mutual learning leading to a mixed strategy Nash equilibrium of a strategic form game from the epistemic point of belief revision system. We show that Main Theorem. Suppose that the players in a strategic form game have the p-belief system with a common prior distribution. In a communication process of the game according to a protocol with revisions of their beliefs about the other


Partially supported by the Grant-in-Aid for Scientific Research(C)(2)(No.14540145) in the Japan Society for the Promotion of Sciences.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1114–1120, 2004. c Springer-Verlag Berlin Heidelberg 2004


p-Belief Communication Leading to a Nash Equilibrium

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players’ actions, the profile of their future predictions induces a mixed strategy Nash equilibrium of the game in the long run. Let us consider the following protocol: The players start with the same prior distribution on a state-space. In addition they have private information given by a partition of the state space. Beliefs are posterior probabilities: A player p-believes (simply, believes) an event with 0 < p ≤ 1 if the posterior probability of the event given his/her information is at least p. Each player predicts the other players’ actions as his/her p-belief of the actions. He/she communicates privately their p-beliefs about the other players’ actions through messages, and the receivers update their p-beliefs according to the messages. Precisely, the players are assumed to be rational and maximizing their expected utility according to their p-beliefs at every stage. Each player communicates privately his/her p-belief about the others’ actions as messages according to a communication graph as a protocol,1 and the receivers update their private information and revise their p-beliefs. The main theorem says that the players’ predictions regarding the future pbeliefs converge in the long run, which lead to a mixed strategy Nash equilibrium of a game. The emphasis is on the two points: First that each player’s prediction is not required to be common-knowledge among all players, and secondly that the communication graph is not assumed to be acyclic.

2

The Model

Let Ω be a non-empty finite set called a state-space, N a set of finitely many players {1, 2, . . . n} at least two (n ≥ 2), and let 2Ω be the family of all subsets of Ω. Each member of 2Ω is called an event and each element of Ω called a state. Let µ be a probability measure on Ω which is common for all players. For simplicity it is assumed that (Ω, µ) is a finite probability space with µ full support.2 2.1

p-Belief System3

Let p be a real number with 0 < p ≤ 1. The p-belief system associated with the partition information structure (Πi )i∈N is the tuple N, Ω, µ, (Πi )i∈N , (Bi )i∈N  consisting of the following structures and interpretations: (Ω, µ) is a finite probability space, and i’s p-belief operator Bi is the operator on 2Ω such that Bi E is the set of states of Ω in which i p-believes that E has occurred with probability at least p ; that is, Bi E := {ω ∈ Ω | µ(E | Πi (ω)) ≥ p }. We note that when p = 1 the 1-belief operator becomes knowledge operator.

1 2 3

When a player communicates with another, the other players are not informed about the contents of the message. That is; µ(ω)
= 0 for every ω ∈ Ω. Monderer and Samet [5].

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2.2

Game on p-Belief System4

By a game G we mean a finite strategic form game N, (Ai )i∈N , (gi )i∈N  with the following structure and interpretations: N is a finite set of players {1, 2, . . . , i, . . . n} with n ≥ 2, Ai is a finite set of i’s actions (or i’s pure strategies) and gi is an i’s payoff function of A into IR, where A denotes the product A1 ×A2 ×· · ·×An , A−i the product A1 × A2 × · · · × Ai−1 × Ai+1 × · · · × An . We denote by g the n-tuple (g1 , g2 , . . . gn ) and by a−i the (n − 1)-tuple (a1 , . . . , ai−1 , ai+1 , . . . , an ) for a of A. Furthermore we denote a−I = (ai )i∈N \I for each I ⊂ N . A probability distribution φi on A−i is said to be i’s overall conjecture (or simply i’s conjecture). For each player j other than i, this induces the marginal distribution on j’s actions; we call it i’s individual conjecture about j (or simply i’s conjecture about j.) Functions on Ω are viewed like random variables in the probability space (Ω, µ). If x is a such function and x is a value of it, we denote by [x = x] (or simply by [x]) the set {ω ∈ Ω| x(ω) = x}. The information structure (Πi ) with a common prior µ yields the distribution on A × Ω defined by qi (a, ω) = µ([a = a]|Πi (ω)); and the i’s overall conjecture defined by the marginal distribution qi (a−i , ω) = µ([a−i = a−i ]|Πi (ω)) which is
viewed as a random variable of φi . We denote by [qi = φi ] the
intersection [q (a ) = φ (a )] and denote by [φ] the intersection i −i a−i ∈A−i i −i i∈N [qi = φi ]. Let gi be a random variable of i’s payoff function gi and ai a random variable of an i’s action ai . i’s action ai is said to be actual at a state ω if ω ∈ [ai = ai ]; and the profile aI = (ai )i∈I is said to be actually played at ω if ω ∈ [aI = aI ] :=
i∈I [ai = ai ] for I ⊂ N . The payoff functions
g = (g1 , g2 , . . . , gn ) are said to be [gi = gi ]. Let Exp denote the actually played at a state ω if ω ∈ [g = g] := i∈N expectation defined by Exp(gi (bi , a−i ); ω) := gi (bi , a−i ) qi (ω)(a−i ). a−i ∈A−i

A player i is said to be rational at ω if each i’s actual action ai maximizes the expectation of his actually played payoff function gi at ω when the other players actions are distributed according to his conjecture qi (· ; ω). Formally, letting gi = gi (ω) and ai = ai (ω), Exp(gi (ai , a−i ); ω) ≥ Exp(gi (bi , a−i ); ω) for every bi in Ai . Let Ri denote the
set of all of the states at which an player i is rational, and R the intersection j∈N Rj . 2.3

Protocol5

We assume that the players communicate by sending messages. Let T be the time horizontal line {0, 1, 2, · · · t, · · ·}. A protocol is a mapping Pr : T → N × N, t → (s(t), r(t)) such that s(t) =r(t). Here t stands for time and s(t) and r(t) are, respectively, the sender and the receiver of the communication which takes place at time t. We consider the protocol as the directed graph whose vertices are the set of all players N and such that there is an edge (or an arc) from i to j if and only if there are infinitely many t such that s(t) = i and r(t) = j.

4 5

Aumann and Brandenburger [1]. C.f.: Parikh and Krasucki (1990).

p-Belief Communication Leading to a Nash Equilibrium

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A protocol is said to be fair if the graph is strongly-connected; in words, every player in this protocol communicates directly or indirectly with every other player infinitely often. It is said to contain a cycle if there are players i1 , i2 , . . . , ik with k ≥ 3 such that for all m < k, im communicates directly with im+1 , and such that ik communicates directly with i1 . The communications is said to proceed in rounds if there exists a time m such that for all t, Pr(t) = Pr(t + m). 2.4

Communication on p-Belief System

A pre-play communication process π p (G) with revisions of players’ conjectures (φti )(i,t)∈N ×T according to a protocol for a game G is a tuple π p (G) = Pr, (Πit )i∈N , (Bit )i∈N , (φti )(i,t)∈N ×T  with the following structures: the players have a common prior µ on Ω, the protocol Pr among N , Pr(t) = (s(t), r(t)), is fair and it satisfies the conditions that r(t) = s(t + 1) for every t and that the communications proceed in rounds. An n-tuple (φti )i∈N is a profile of player i ’s individual conjecture at time t. The information structure Πit at time t is the mapping of Ω into 2Ω for player i that is defined inductively as follows: If i = s(t) is a sender at t, the message sent by i to j = r(t) is Wit (ω) = [gi ] ∩ [φti ] ∩ Rit . – Set Πi0 (ω) = Πi (ω). – Assume that Πit is defined. It yields the distribution qti (a, ω) = µ([a = a]|Πit (ω)). Whence • Rit denotes the set of all the state ω at which i is rational according to his conjecture qti (· ; ω); that is, each i’s actual action ai maximizes the expectation of his payoff function gi being actually played at ω when the other players actions are distributed according to his conjecture qti (· ; ω) at time t.6 • Qti denotes the partition of Ω induced by qti (· ; ω), which is decomposed into the components Qti (ω) consisting of all of the states ξ such that qit (· ; ξ) = qit (· ; ω): • Gi denotes the partition {[gi = gi ], Ω \ [gi = gi ]} of Ω, and Rti the partition {Rit , Ω \ Rit }: • Wit denotes the join Gi ∨ Qti ∨ Rti that is the refinement of the three partitions Gi , Qti and Rti . Therefore the message sent by the sender i is Wit (ω) = [gi ] ∩ [φti ] ∩ Rit if ω ∈ [gi ] ∩ [φti ] ∩ Rit . Then: 6

Formally, letting gi = gi (ω), ai = ai (ω), the expectation at time t, Expt , is t defined by Exp (gi (ai , a−i ); ω) := gi (ai , a−i ) qti (a−i , ω). A player i is a−i ∈A−i

said to be rational according to his conjecture qti (· , ω) at ω if for all bi in Ai , Expt (gi (ai , a−i ); ω) ≥ Expt (gi (bi , a−i ); ω).

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– The revised partition Πit+1 at time t + 1 is defined as follows: • If i is a receiver of a message at time t + 1 then Πit+1 (ω) = Πit (ω) ∩ t Ws(t) (ω). • If not, Πit+1 (ω) = Πit (ω). It is of worth noting that (Πit )i∈N is a partition information structure for every t ∈ T . Let Bit be the p-belief operator corresponding to Πit defined by Bit E = {ω ∈ Ω | µ(E | Πit (ω)) ≥ p }. We require the additional condition that:
t t t for every t ∈ T . 7 The specification is that each i∈N Bi ([gi ] ∩ [φi ] ∩ Ri ) =∅ player p-believes his/her payoff, rationality and conjecture at every time t. We denote by ∞ a sufficient large τ such that for all ω ∈ Ω, qτi (· ; ω) = qτi +1 (· ; ω) = τ ∞ qτi +2 (· ; ω) = · · ·. Hence we can write qτi by q∞ i and φi by φi .

3

The Result

We can now state the main theorem: Theorem 1. Suppose that the players in a strategic form game G have the pbelief system with µ a common prior. In the pre-play communication process π p (G) according to a protocol among all players in the game with revisions of their conjectures (φti )(i,t)∈N ×T there exists a time ∞ such that for each t ≥ ∞, the n-tuple (φti )i∈N induces a mixed strategy Nash equilibrium of the game. Proof. We shall briefly sketch the proof based on the below proposition: Proposition 1. If the protocol in π p (G) is not acyclic then for any players ∞ i, j ∈ N , both the conjectures q∞ i and qj on A × Ω must coincide; that is, ∞ q∞ (a; ω) = q (a; ω) for all (a; ω) ∈ A × Ω. i j Proof of Theorem | (i, j) = Pr(t) for some t ∈ T }
1:
Set Γ (i) = { j ∈ N ∞ and [φ∞ ] := i∈N a−i ∈Ai [q∞ (a ; ∗) = φ −i i i (a−i )]. For each i ∈ N , denote ∞ ∞ Fi := [gi ] ∩ [φ ] ∩ R . It is noted that Fi =∅. We can plainly observe the first point that µ([a−j = a−j ] | Fi ∩Fj ) = φ∞ j (a−j ). for each i ∈ N , j ∈ Γ (i) and for every a ∈ A. Then summing over a−i , we can observe that µ([ai = ai ] | Fi ∩ Fj ) = φ∞ j (ai ) for any a ∈ A. In view of Proposition 1 it can be observed that φ∞ j (ai ) is independent of the choices of every j ∈ N other than i. We set the probability distribution σi on Ai by σi (ai ) := φ∞ j (ai ), and set the profile σ = (σi ). Therefore all the other players j than i agree on the same conjecture σj (ai ) = φ∞ j (ai ) about  i. We shall observe the second point that for every a ∈ i∈N Supp(σi ), φ∞ i (a−i ) = σ1 (a1 ) · · · σi−1 (ai−1 )σi+1 (ai+1 ) · · · σn (an ): In fact, viewing the definition of σi ∞ we shall show that φ∞ this it suffices to i (a−i ) = k∈N \{i} φi (ak ). To verify  ∞ ∞ (a ) show that for every k = 1, 2, · · · , n, φi (a−i ) = φ∞ −I k i k∈Ik \{i} φi (ak ) : We prove it by induction on k. For k = 1 the result is immediate. Suppose it is 7

where we denote [gi ] := [gi = gi ], [φti ] :=


a−i ∈Ai

[qti (a−i ; ∗) = φti (a−i )].

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true for k ≥ 1. On noting the protocol is fair, we can take the sequence of sets of players {Ik }1≤k≤n with the following properties: (a) I1 = {i} ⊂ I2 ⊂ · · · ⊂ Ik ⊂ Ik+1 ⊂ · · · ⊂ Im = N :  (b) For every k ∈ N there is a player ik+1 ∈ j∈Ik Γ (j) with Ik+1 \ Ik = {ik+1 }. Take j ∈ Ik such that ik+1 ∈ Γ (j), and set Hik+1 := [aik+1 = aik+1 ]∩Fj ∩Fik+1 . It can be verified that µ([a−j−ik+1 = a−j−ik+1 ] | Hik+1 ) = φ∞ −j−ik+1 (a−j ). Dividing µ(Fj ∩ Fik+1 ) yields that µ([a−j = a−j ] | Fj ∩ Fik+1 ) = φ∞ ik+1 (a−j )µ([aik+1 = aik+1 ] | Fj ∩ Fik+1 ). ∞ t Thus φ∞ j (a−j ) = φik+1 (a−j−ik+1 )φj (aik+1 ); then summing over aIk ∈ AIk we ∞ ∞ obtain φj (a−Ik ) = φik+1 (a−Ik −ik+1 )φ∞ j (aik+1 ). In view of Proposition 1 it can ∞ ∞ be plainly observed that φ∞ (a ) = φ −I k i i (a−Ik −ik+1 )φi (aik+1 ), as required. On noting that all the other players i than j agree on the same conjecture σj (aj ) = φ∞ i (aj ) about j, we can conclude that each action ai appearing with positive probability in σi maximizes gi against the product of the distributions σl with l =i. This implies that the profile σ = (σi )i∈N is a mixed strategy Nash equilibrium of G, in completing the proof.  

4

Concluding Remarks

Many authors have studied the learning processes modeled by Bayesian updating. E. Kalai and E. Lehrer [2] (and references therein) indicate increasing interest in the mutual learning processes in games that leads to equilibrium: Each player starts with initial erroneous belief regarding the actions of all the other players. They show that the two strategies converges to an ε-mixed strategy Nash equilibrium of the repeated game. As for as J.F. Nash [6]’s fundamental notion of strategic equilibrium is concerned, R.J. Aumann and A. Brandenburger [1] give epistemic conditions for mixed strategy Nash equilibrium: They show that the common-knowledge of the predictions of the players having the partition information (that is, equivalently, the S5-knowledge model) yields a Nash equilibrium of a game. However it is not clear just what learning process leads to the equilibrium. The present article aims to fill this gap. Our real concern is with what learning process leads to a mixed strategy Nash equilibrium of a finite strategic form game from epistemic point view. As we have observed, in the pre-play communication process with revisions of players’ beliefs about the other actions, their predictions induces a mixed strategy Nash equilibrium of the game in the long run. We have proved this assertion in the pbelief system. Matsuhisa [3] established the same assertion in the S4-knowledge model. Furthermore Matsuhisa [4] showed a similar result for ε-mixed strategy Nash equilibrium of a strategic form game in the S4-knowledge model, which highlights an epistemic aspect in Theorem of E. Kalai and E. Lehrer [2].

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References 1. Aumann, R. J., and Brandenburger, A.: Epistemic conditions for mixed strategy Nash equilibrium, Econometrica 63 (1995) 1161–1180. 2. Kalai E., and Lehrer, E.: Rational learning to mixed strategy Nash equilibrium, Econometrica 61 (1993) 1019–1045. 3. Matsuhisa, T.: Communication leading to mixed strategy Nash equilibrium I, T. Maruyama (eds) Mathematical Economics, Suri-Kaiseki-Kenkyusyo Kokyuroku 1165 (2000) 245–256. 4. Matsuhisa, T.: Communication leading to epsilon-mixed strategy Nash equilibrium, Working paper (2001). The extended abstract was presented in the XIV Italian Meeting of Game Theory and Applications (IMGTA XIV), July 11-14, 2001. 5. Monderer, D., and Samet,, D.: Approximating common knowledge with common beliefs, Games and Economic Behaviors 1 (1989) 170–190. 6. Nash J. F.: Equilibrium points in n-person games, Proceedings of the National Academy of Sciences of the United States of America 36 (1950) 48–49. 7. Parikh R., and Krasucki, P.: Communication, consensus, and knowledge, Journal of Economic Theory 52 (1990) 178–189.

p-Belief Communication Leading to a Nash Equilibrium Takashi Matsuhisa
Department of Liberal Arts and Sciences, Ibaraki National College of Technology, Nakane 866, Hitachinaka-shi, Ibaraki 312-8508, Japan [email protected]

Abstract. A pre-play communication in the p-belief system is presented which leads to a Nash equilibrium of a strategic form game through messages. In the communication process each player predicts the other players’ actions under his/her private information with probability at least p. The players communicate privately their conjectures through message according to the communication graph, where each player receiving the message learns and revises his/her conjecture. The emphasis is on that any topological assumptions on the communication graph are not required in the theorem. Keywords: p-Belief system, Nash equilibrium, Communication, Protocol, Conjecture, Non-corporative game. AMS 2000 Mathematics Subject Classification: Primary 91A35, Secondary 03B45. Journal of Economic Literature Classification: C62, C78.

1

Introduction

This article relates equilibria and distributed knowledge. In game theoretical situations among a group of players, the concept of mixed strategy Nash equilibrium has become central. Yet little is known about the process by which players learn if they do. This article will give a protocol run by the mutual learning leading to a mixed strategy Nash equilibrium of a strategic form game from the epistemic point of belief revision system. We show that Main Theorem. Suppose that the players in a strategic form game have the p-belief system with a common prior distribution. In a communication process of the game according to a protocol with revisions of their beliefs about the other


Partially supported by the Grant-in-Aid for Scientific Research(C)(2)(No.14540145) in the Japan Society for the Promotion of Sciences.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1114–1120, 2004. c Springer-Verlag Berlin Heidelberg 2004


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players’ actions, the profile of their future predictions induces a mixed strategy Nash equilibrium of the game in the long run. Let us consider the following protocol: The players start with the same prior distribution on a state-space. In addition they have private information given by a partition of the state space. Beliefs are posterior probabilities: A player p-believes (simply, believes) an event with 0 < p ≤ 1 if the posterior probability of the event given his/her information is at least p. Each player predicts the other players’ actions as his/her p-belief of the actions. He/she communicates privately their p-beliefs about the other players’ actions through messages, and the receivers update their p-beliefs according to the messages. Precisely, the players are assumed to be rational and maximizing their expected utility according to their p-beliefs at every stage. Each player communicates privately his/her p-belief about the others’ actions as messages according to a communication graph as a protocol,1 and the receivers update their private information and revise their p-beliefs. The main theorem says that the players’ predictions regarding the future pbeliefs converge in the long run, which lead to a mixed strategy Nash equilibrium of a game. The emphasis is on the two points: First that each player’s prediction is not required to be common-knowledge among all players, and secondly that the communication graph is not assumed to be acyclic.

2

The Model

Let Ω be a non-empty finite set called a state-space, N a set of finitely many players {1, 2, . . . n} at least two (n ≥ 2), and let 2Ω be the family of all subsets of Ω. Each member of 2Ω is called an event and each element of Ω called a state. Let µ be a probability measure on Ω which is common for all players. For simplicity it is assumed that (Ω, µ) is a finite probability space with µ full support.2 2.1

p-Belief System3

Let p be a real number with 0 < p ≤ 1. The p-belief system associated with the partition information structure (Πi )i∈N is the tuple N, Ω, µ, (Πi )i∈N , (Bi )i∈N  consisting of the following structures and interpretations: (Ω, µ) is a finite probability space, and i’s p-belief operator Bi is the operator on 2Ω such that Bi E is the set of states of Ω in which i p-believes that E has occurred with probability at least p ; that is, Bi E := {ω ∈ Ω | µ(E | Πi (ω)) ≥ p }. We note that when p = 1 the 1-belief operator becomes knowledge operator.

1 2 3

When a player communicates with another, the other players are not informed about the contents of the message. That is; µ(ω)
= 0 for every ω ∈ Ω. Monderer and Samet [5].

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2.2

Game on p-Belief System4

By a game G we mean a finite strategic form game N, (Ai )i∈N , (gi )i∈N  with the following structure and interpretations: N is a finite set of players {1, 2, . . . , i, . . . n} with n ≥ 2, Ai is a finite set of i’s actions (or i’s pure strategies) and gi is an i’s payoff function of A into IR, where A denotes the product A1 ×A2 ×· · ·×An , A−i the product A1 × A2 × · · · × Ai−1 × Ai+1 × · · · × An . We denote by g the n-tuple (g1 , g2 , . . . gn ) and by a−i the (n − 1)-tuple (a1 , . . . , ai−1 , ai+1 , . . . , an ) for a of A. Furthermore we denote a−I = (ai )i∈N \I for each I ⊂ N . A probability distribution φi on A−i is said to be i’s overall conjecture (or simply i’s conjecture). For each player j other than i, this induces the marginal distribution on j’s actions; we call it i’s individual conjecture about j (or simply i’s conjecture about j.) Functions on Ω are viewed like random variables in the probability space (Ω, µ). If x is a such function and x is a value of it, we denote by [x = x] (or simply by [x]) the set {ω ∈ Ω| x(ω) = x}. The information structure (Πi ) with a common prior µ yields the distribution on A × Ω defined by qi (a, ω) = µ([a = a]|Πi (ω)); and the i’s overall conjecture defined by the marginal distribution qi (a−i , ω) = µ([a−i = a−i ]|Πi (ω)) which is
viewed as a random variable of φi . We denote by [qi = φi ] the
intersection [q (a ) = φ (a )] and denote by [φ] the intersection i −i a−i ∈A−i i −i i∈N [qi = φi ]. Let gi be a random variable of i’s payoff function gi and ai a random variable of an i’s action ai . i’s action ai is said to be actual at a state ω if ω ∈ [ai = ai ]; and the profile aI = (ai )i∈I is said to be actually played at ω if ω ∈ [aI = aI ] :=
i∈I [ai = ai ] for I ⊂ N . The payoff functions
g = (g1 , g2 , . . . , gn ) are said to be [gi = gi ]. Let Exp denote the actually played at a state ω if ω ∈ [g = g] := i∈N expectation defined by Exp(gi (bi , a−i ); ω) := gi (bi , a−i ) qi (ω)(a−i ). a−i ∈A−i

A player i is said to be rational at ω if each i’s actual action ai maximizes the expectation of his actually played payoff function gi at ω when the other players actions are distributed according to his conjecture qi (· ; ω). Formally, letting gi = gi (ω) and ai = ai (ω), Exp(gi (ai , a−i ); ω) ≥ Exp(gi (bi , a−i ); ω) for every bi in Ai . Let Ri denote the
set of all of the states at which an player i is rational, and R the intersection j∈N Rj . 2.3

Protocol5

We assume that the players communicate by sending messages. Let T be the time horizontal line {0, 1, 2, · · · t, · · ·}. A protocol is a mapping Pr : T → N × N, t → (s(t), r(t)) such that s(t) =r(t). Here t stands for time and s(t) and r(t) are, respectively, the sender and the receiver of the communication which takes place at time t. We consider the protocol as the directed graph whose vertices are the set of all players N and such that there is an edge (or an arc) from i to j if and only if there are infinitely many t such that s(t) = i and r(t) = j.

4 5

Aumann and Brandenburger [1]. C.f.: Parikh and Krasucki (1990).

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A protocol is said to be fair if the graph is strongly-connected; in words, every player in this protocol communicates directly or indirectly with every other player infinitely often. It is said to contain a cycle if there are players i1 , i2 , . . . , ik with k ≥ 3 such that for all m < k, im communicates directly with im+1 , and such that ik communicates directly with i1 . The communications is said to proceed in rounds if there exists a time m such that for all t, Pr(t) = Pr(t + m). 2.4

Communication on p-Belief System

A pre-play communication process π p (G) with revisions of players’ conjectures (φti )(i,t)∈N ×T according to a protocol for a game G is a tuple π p (G) = Pr, (Πit )i∈N , (Bit )i∈N , (φti )(i,t)∈N ×T  with the following structures: the players have a common prior µ on Ω, the protocol Pr among N , Pr(t) = (s(t), r(t)), is fair and it satisfies the conditions that r(t) = s(t + 1) for every t and that the communications proceed in rounds. An n-tuple (φti )i∈N is a profile of player i ’s individual conjecture at time t. The information structure Πit at time t is the mapping of Ω into 2Ω for player i that is defined inductively as follows: If i = s(t) is a sender at t, the message sent by i to j = r(t) is Wit (ω) = [gi ] ∩ [φti ] ∩ Rit . – Set Πi0 (ω) = Πi (ω). – Assume that Πit is defined. It yields the distribution qti (a, ω) = µ([a = a]|Πit (ω)). Whence • Rit denotes the set of all the state ω at which i is rational according to his conjecture qti (· ; ω); that is, each i’s actual action ai maximizes the expectation of his payoff function gi being actually played at ω when the other players actions are distributed according to his conjecture qti (· ; ω) at time t.6 • Qti denotes the partition of Ω induced by qti (· ; ω), which is decomposed into the components Qti (ω) consisting of all of the states ξ such that qit (· ; ξ) = qit (· ; ω): • Gi denotes the partition {[gi = gi ], Ω \ [gi = gi ]} of Ω, and Rti the partition {Rit , Ω \ Rit }: • Wit denotes the join Gi ∨ Qti ∨ Rti that is the refinement of the three partitions Gi , Qti and Rti . Therefore the message sent by the sender i is Wit (ω) = [gi ] ∩ [φti ] ∩ Rit if ω ∈ [gi ] ∩ [φti ] ∩ Rit . Then: 6

Formally, letting gi = gi (ω), ai = ai (ω), the expectation at time t, Expt , is t defined by Exp (gi (ai , a−i ); ω) := gi (ai , a−i ) qti (a−i , ω). A player i is a−i ∈A−i

said to be rational according to his conjecture qti (· , ω) at ω if for all bi in Ai , Expt (gi (ai , a−i ); ω) ≥ Expt (gi (bi , a−i ); ω).

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– The revised partition Πit+1 at time t + 1 is defined as follows: • If i is a receiver of a message at time t + 1 then Πit+1 (ω) = Πit (ω) ∩ t Ws(t) (ω). • If not, Πit+1 (ω) = Πit (ω). It is of worth noting that (Πit )i∈N is a partition information structure for every t ∈ T . Let Bit be the p-belief operator corresponding to Πit defined by Bit E = {ω ∈ Ω | µ(E | Πit (ω)) ≥ p }. We require the additional condition that:
t t t for every t ∈ T . 7 The specification is that each i∈N Bi ([gi ] ∩ [φi ] ∩ Ri ) =∅ player p-believes his/her payoff, rationality and conjecture at every time t. We denote by ∞ a sufficient large τ such that for all ω ∈ Ω, qτi (· ; ω) = qτi +1 (· ; ω) = τ ∞ qτi +2 (· ; ω) = · · ·. Hence we can write qτi by q∞ i and φi by φi .

3

The Result

We can now state the main theorem: Theorem 1. Suppose that the players in a strategic form game G have the pbelief system with µ a common prior. In the pre-play communication process π p (G) according to a protocol among all players in the game with revisions of their conjectures (φti )(i,t)∈N ×T there exists a time ∞ such that for each t ≥ ∞, the n-tuple (φti )i∈N induces a mixed strategy Nash equilibrium of the game. Proof. We shall briefly sketch the proof based on the below proposition: Proposition 1. If the protocol in π p (G) is not acyclic then for any players ∞ i, j ∈ N , both the conjectures q∞ i and qj on A × Ω must coincide; that is, ∞ q∞ (a; ω) = q (a; ω) for all (a; ω) ∈ A × Ω. i j Proof of Theorem | (i, j) = Pr(t) for some t ∈ T }
1:
Set Γ (i) = { j ∈ N ∞ and [φ∞ ] := i∈N a−i ∈Ai [q∞ (a ; ∗) = φ −i i i (a−i )]. For each i ∈ N , denote ∞ ∞ Fi := [gi ] ∩ [φ ] ∩ R . It is noted that Fi =∅. We can plainly observe the first point that µ([a−j = a−j ] | Fi ∩Fj ) = φ∞ j (a−j ). for each i ∈ N , j ∈ Γ (i) and for every a ∈ A. Then summing over a−i , we can observe that µ([ai = ai ] | Fi ∩ Fj ) = φ∞ j (ai ) for any a ∈ A. In view of Proposition 1 it can be observed that φ∞ j (ai ) is independent of the choices of every j ∈ N other than i. We set the probability distribution σi on Ai by σi (ai ) := φ∞ j (ai ), and set the profile σ = (σi ). Therefore all the other players j than i agree on the same conjecture σj (ai ) = φ∞ j (ai ) about  i. We shall observe the second point that for every a ∈ i∈N Supp(σi ), φ∞ i (a−i ) = σ1 (a1 ) · · · σi−1 (ai−1 )σi+1 (ai+1 ) · · · σn (an ): In fact, viewing the definition of σi ∞ we shall show that φ∞ this it suffices to i (a−i ) = k∈N \{i} φi (ak ). To verify  ∞ ∞ (a ) show that for every k = 1, 2, · · · , n, φi (a−i ) = φ∞ −I k i k∈Ik \{i} φi (ak ) : We prove it by induction on k. For k = 1 the result is immediate. Suppose it is 7

where we denote [gi ] := [gi = gi ], [φti ] :=


a−i ∈Ai

[qti (a−i ; ∗) = φti (a−i )].

p-Belief Communication Leading to a Nash Equilibrium

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true for k ≥ 1. On noting the protocol is fair, we can take the sequence of sets of players {Ik }1≤k≤n with the following properties: (a) I1 = {i} ⊂ I2 ⊂ · · · ⊂ Ik ⊂ Ik+1 ⊂ · · · ⊂ Im = N :  (b) For every k ∈ N there is a player ik+1 ∈ j∈Ik Γ (j) with Ik+1 \ Ik = {ik+1 }. Take j ∈ Ik such that ik+1 ∈ Γ (j), and set Hik+1 := [aik+1 = aik+1 ]∩Fj ∩Fik+1 . It can be verified that µ([a−j−ik+1 = a−j−ik+1 ] | Hik+1 ) = φ∞ −j−ik+1 (a−j ). Dividing µ(Fj ∩ Fik+1 ) yields that µ([a−j = a−j ] | Fj ∩ Fik+1 ) = φ∞ ik+1 (a−j )µ([aik+1 = aik+1 ] | Fj ∩ Fik+1 ). ∞ t Thus φ∞ j (a−j ) = φik+1 (a−j−ik+1 )φj (aik+1 ); then summing over aIk ∈ AIk we ∞ ∞ obtain φj (a−Ik ) = φik+1 (a−Ik −ik+1 )φ∞ j (aik+1 ). In view of Proposition 1 it can ∞ ∞ be plainly observed that φ∞ (a ) = φ −I k i i (a−Ik −ik+1 )φi (aik+1 ), as required. On noting that all the other players i than j agree on the same conjecture σj (aj ) = φ∞ i (aj ) about j, we can conclude that each action ai appearing with positive probability in σi maximizes gi against the product of the distributions σl with l =i. This implies that the profile σ = (σi )i∈N is a mixed strategy Nash equilibrium of G, in completing the proof.  

4

Concluding Remarks

Many authors have studied the learning processes modeled by Bayesian updating. E. Kalai and E. Lehrer [2] (and references therein) indicate increasing interest in the mutual learning processes in games that leads to equilibrium: Each player starts with initial erroneous belief regarding the actions of all the other players. They show that the two strategies converges to an ε-mixed strategy Nash equilibrium of the repeated game. As for as J.F. Nash [6]’s fundamental notion of strategic equilibrium is concerned, R.J. Aumann and A. Brandenburger [1] give epistemic conditions for mixed strategy Nash equilibrium: They show that the common-knowledge of the predictions of the players having the partition information (that is, equivalently, the S5-knowledge model) yields a Nash equilibrium of a game. However it is not clear just what learning process leads to the equilibrium. The present article aims to fill this gap. Our real concern is with what learning process leads to a mixed strategy Nash equilibrium of a finite strategic form game from epistemic point view. As we have observed, in the pre-play communication process with revisions of players’ beliefs about the other actions, their predictions induces a mixed strategy Nash equilibrium of the game in the long run. We have proved this assertion in the pbelief system. Matsuhisa [3] established the same assertion in the S4-knowledge model. Furthermore Matsuhisa [4] showed a similar result for ε-mixed strategy Nash equilibrium of a strategic form game in the S4-knowledge model, which highlights an epistemic aspect in Theorem of E. Kalai and E. Lehrer [2].

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T. Matsuhisa

References 1. Aumann, R. J., and Brandenburger, A.: Epistemic conditions for mixed strategy Nash equilibrium, Econometrica 63 (1995) 1161–1180. 2. Kalai E., and Lehrer, E.: Rational learning to mixed strategy Nash equilibrium, Econometrica 61 (1993) 1019–1045. 3. Matsuhisa, T.: Communication leading to mixed strategy Nash equilibrium I, T. Maruyama (eds) Mathematical Economics, Suri-Kaiseki-Kenkyusyo Kokyuroku 1165 (2000) 245–256. 4. Matsuhisa, T.: Communication leading to epsilon-mixed strategy Nash equilibrium, Working paper (2001). The extended abstract was presented in the XIV Italian Meeting of Game Theory and Applications (IMGTA XIV), July 11-14, 2001. 5. Monderer, D., and Samet,, D.: Approximating common knowledge with common beliefs, Games and Economic Behaviors 1 (1989) 170–190. 6. Nash J. F.: Equilibrium points in n-person games, Proceedings of the National Academy of Sciences of the United States of America 36 (1950) 48–49. 7. Parikh R., and Krasucki, P.: Communication, consensus, and knowledge, Journal of Economic Theory 52 (1990) 178–189.

Color Image Vector Quantization Using an Enhanced Self-Organizing Neural Network 1

Kwang Baek Kim and Abhijit S. Pandya

2

1

Dept. of Computer Engineering, Silla University, S. Korea Div. of Information and Computer Engineering, Silla University, S. Korea Dept. of Computer Science and Engineering, Florida Atlantic University, U.S.A [email protected] 2

Abstract. In the compression methods widely used today, the image compression by VQ is the most popular and shows a good data compression ratio. Almost all the methods by VQ use the LBG algorithm that reads the entire image several times and moves code vectors into optimal position in each step. This complexity of algorithm requires considerable amount of time to execute. To overcome this time consuming constraint, we propose an enhanced selforganizing neural network for color images. VQ is an image coding technique that shows high data compression ratio. In this study, we improved the competitive learning method by employing three methods for the generation of codebook. The results demonstrated that compression ratio by the proposed method was improved to a greater degree compared to the SOM in neural networks.

1 Introduction Computer Graphics and Imaging applications have started to make inroads into our everyday lives due to the global spread of Information technology. This has made image compression an essential tool in computing with workstations, personal computers and computer networks [1]. Compression can also be viewed as a form of classification, since it assigns a template or codeword to a set of input vectors of pixels drawn from a large set in such a way as to provide a good approximation of representation. A color Image is composed of three primary components. The most popular choices of color primaries are (R, G, B), (Y, I, Q), and (Y, U, V). The Y component represents the brightness and IQ (IV) components represent the chrominance signals. In this paper, we considered color images in the (R, G, B) domain with a color of one pixel determined by three primary components, the red(R), green (G) and blue (B). Each component is quantized to 8 bits, hence 24 bits are needed to represent one pixel. The number of palette elements to be represented by 24 bits is 224 , but all of colors are not used to represent one image. So it is possible to compress the pixel color of the real image. It is also necessary to compress the pixel color because of the limitation of disk space and the transmission channel bandwidth [2]. In the compression methods introduced until now, the image compression by Vector Quantization (VQ) is most popular and shows a good data compression ratio. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1121–1126, 2004. © Springer-Verlag Berlin Heidelberg 2004

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Most methods by VQ use the LBG algorithm developed by Linde, Buzo, and Gray [2]. But this algorithm reads an entire image several times and moves code vectors into optimal position in each step. Due to the complexity of the algorithm, it takes considerable time to execute. To overcome this time consuming constraints, we propose an enhanced self-organizing vector quantization method for color images.

2 Enhanced Self-Organizing Neural Network 2.1 VQ Using a Self-Organizing Feature Map

The Self-Organizing Feature Map has been found to serve as a good algorithm for codebook generation. The SOM algorithm, which is derived from an appropriate stochastic gradient decent scheme, results in a natural clustering process in which the network performs competitive learning to perceive pattern classes based on data similarity. Smoothing of vector elements does not take place in this unsupervised training scheme. At the same time, since it doses not assume an initial codebook, the probability of getting stranded in local minima is also small. The investigations for high quality reconstructed pictures have led us to the edge preserving self-organizing map. This greatly reduces the large computational costs involved in generating the codebook and finding the closest codeword for each image vector. However, from practical experience, it is observed that additional refinements are necessary for the training algorithm to be efficient enough for practical applications [3]. The SOM technique can display, in a single grey level image, the most significant clustering of data in an n-dimensional feature space, without confusing clusters that are distinct in the feature space [4]. This is possible because points which are far apart in the feature space can map to the same grey level, quantized to the same map node, only if the distribution of data near them is very sparse [5]. Thus, the points far apart in grey level belong to different significant clusters. However, this conventional method leaves a large amount of neurons under-utilized after training [6]. 2.2 Enhanced SOM Algorithm for Color Image Vector Quantization

In this paper, we improved the SOM algorithm by employing three methods for the efficient generation of codebook. First, the error between the winner node and the input vector and the frequency of the winner node are reflected in the weight adaptation. Second, the weight is adapted in proportion to the present weight change and the previous weight change as well. Third, in the weight adaptation for the generation of the initial codebook, the weight of the adjacent pixel of the winner node is adapted together. In the proposed method, the codebook is generated by presenting the entire image only two times. In the first step, the initial codebook is generated to reflect the distribution of the given training vectors. The second step uses the initial codebook and regenerates the codebook by moving to the center within the decision region. To generate the precise codebook, it needs to select the winner node correctly and we have to consider the real distortion of the code vector and the input vector. For this management, the measure of the frequency to be selected as winner node and the

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distortion for the selection of the winner node in the competitive learning algorithm are needed. We use the following equation in the weight adaptation. wij (t + 1) = wij (t ) + α ( xi − wij (t ))

α = f (e j ) +

1 fj

(1)

α is the learning factor between 0 and 1 and is set between 0.25 and 0.75 in general. ( xi − wij (t )) is an error value and represents the difference between the input vector and the representative code vector. This means weights are adapted as much as the difference and it prefers to adapt the weight in proportion to the size of the difference. Therefore, we use the normalized value for the output error of the winner node that is converted to the value between 0 and 1 as a learning factor. f (e j ) is the normalization function that converts the value of e j to the value between 0 and 1, e j is the output error of the j th neuron, and f j is the frequency for the j th neuron as the winner. The above method considers only the present weight change and does not consider the previous weight change. So in the weight adaptation, we consider the previous weight change as well as the present one’s. This concept corresponds to the momentum parameter of BP. Based on the momentum factor, the equation for the weight adaptation is as follows: wij (t + 1) = wij (t ) + δ ij (t + 1)

(2)

δ ij (t + 1) = α ( xi − wij (t )) + αδ ij (t )

(3)

The algorithm is detailed below: 1. Initialize the network. i.e., initialize weights ( wij ) from the n inputs to the output nodes to small random values. Set the initial neighborhood, N c to be large. Fix the convergence tolerance limit for the vectors to be a small quantity. Settle maximum number of iterations to be a large number. Divide the training set into vectors of size n × n . 2. Compute the mean and variance of each training input vector. 3. Present the inputs xi (t ) . 4. Compute the Euclidean distance d j between the input and each output node j , given by, d j = f j × d ( x, wij (t ))

(4)

Where f j is the frequency of the j th neuron being a winner. Select the minimum distance. Designate the output node with minimum d j to be j * . 5. Update the weight for node j * and its neighbors, defined by the neighborhood size N c . The weights are updated:

if i ∈ N c (t ) f j* = f j* + 1

(5)

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(6)

δ ij* (t + 1) = α (t + 1)( xi − wij* (t )) + α (t + 1)δ ij* (t )

(7)

α (t + 1) = f (e j* ) +

e j* =

1 f j*

1 n −1 ∑ xi (t ) − wij* (t ) n i =0

(8)

(9)

if i ∉ N c (t )

wij (t + 1) = wij (t )

(10)

The neighborhood N c (t ) decreases in size as time goes on, thus localizing the area of maximum activity. And f (e j ) is normalization function. 6. Repeat by going to step 2 for each input vector presented, till a satisfactory match is obtained between the input and the weight or till the maximum number of iterations are complete.

3 Simulation Simulation was performed on a personal computer using C++ builder to evaluate the proposed method. Digitized color images of the (R, G, B) domain and a resolution of 128 x 128 were used for the simulation. Fig.1 shows various images used for simulation.

(a) Image1: A card

(b) Image2: A cell image

Fig. 1. Original images used for simulation

Based on simulation results, we can see that the proposed method makes the codebook 5 times faster than the LBG algorithm for the vector quantization. Moreover, the performance of the proposed method is better than the conventional VQ algorithm. That is, the proposed method shows higher data compression ratio than the conventional VQ algorithm. The LBG algorithm reads the entire image data several times and moves code vectors into optimal position in each step. This repetitive process shows the block effect by which the image is recovered. Often in an image, adjacent pixels tend to have similar color and compose a color block. This means that one image is composed of such block. We adapt the weight of adjacent pixels of the winner node together in case

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of generating the initial codebook. In the proposed method, if an input block and the adjacent pixel have a similarity pixel, the neighboring is adapted. The equation for measuring the similarity is as follows where xk is the adjacent pixel. | xi − xk |< Escrit

(11)

That is, if the difference of an input vector from the adjacent pixel is less than Escrit which is a criterion for admission, then the neighboring pixel is adapted. Here, the Escrit was set to 0.0001. The enhanced self-organizing vector quantization for color images proposed in this paper can decrease the number of times the entire image data is read. Table 1 show the size of the codebook file for the LBG Algorithm, the conventional SOM and the enhanced self-organizing vector quantization for color images. Table 1. Size of codebook by VQ (byte) Algorithms Images Image1 Image2

LBG

SOM

Enhanced SOM

30064 49376

32208 52080

31968 51648

To Measure a degree of distortion of the reproduction vector, a mean square error (MSE) is generally used. Table 2, which shows the MSE values of images created by using the LBG algorithm, the conventional SOM and the enhanced SOM and from Fig. 2 through 3. Consequently, the transmission time and the memory space reduced than LBG algorithm. Table 2. Comparison of MSE (Mean Square Error) for compressed images Algorithms Images Image1 Image2

LBG

SOM

Enhanced SOM

15.2 14.5

13.1 11.3

11.2 10.8

Fig. 2 and Fig. 3 show respectively recovered images for original images of Fig. 1. This contribution proposed an improved SOM algorithm. It improves compression and replay rate of image by the codebook dynamic allocation than the conventional SOM algorithm.

(a) SOM

(b) Enhanced SOM

(c) LBG Algorithm

Fig. 2. The recovered image for Image1

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(a) SOM

(b) Enhanced SOM

(c) LBG Algorithm

Fig. 3. The recovered image for Image2

4 Conclusion The proposed method in this paper can be summarized method as follows: Using the enhanced SOM algorithm, the output error concept is introduced into the weight adaptation and the momentum factor is added. The simulation results show that the enhanced SOM algorithm for color image compression produces a major improvement in both subjective and objective quality of the decompressed images. The proposed method is apt to real time application because the codebook is created by reading whole image only twice. Generally, the procreation of the codebook is difficult work in vector quantization of color image. Therefore, we propose a new method that uses enhanced SOM learning algorithm to increase the compression and replay ratio. In the future study, we plan to develop a novel VQ using the fuzzy membership function.

Acknowledgment This article was supported by the research grant 2004 of Silla University.

References [1] Rabbani, M., Jones, P. W.: Digital Image Compression Technique. Spie. Optical Engineering Press. (1991) 144-169 [2] Gray, R. M.: Vector Quantization. IEEE ASSP Magazine. (April 1984) 4-29 [3] Liza, J., Kaimal, M. R.: A Self Organizing Neural Network for Second Generation Image Coding. Proceedings of TAINN. (1999) 130-137 [4] Seo, S., Bode, M., Obermayer, K.: Soft Nearest Prototype Classification. IEEE Trans. Neural Networks. 14(2) (2003) 390-398 [5] Oehler, K. L., Gray, R. M.: Combining Image Compression and Classification using Vector Quantization. IEEE Multimedia. (1997) 36-45 [6] Madeiro, F., Vilar, R. M., Fechine, J. M., Aguiar Neto, B. G.: A Slef-Organizing Algorithm for Vector Quantizer Design Applied to Signal Processing. International Journal of Neural Systems. 9(3) (1999) 219-226

Alternate Pattern Fill Xiao-Xin Zhang1,2 , Jun-Hai Yong1 , Lie-Hang Gong2 , Guo-Qin Zheng1 , and Jia-Guang Sun1,3 2

1 School of Software, Tsinghua University, Beijing 100084, P. R. China Department of Mechanical Engineering, PLA University of Science and Technology, Nanjing 210007, P. R. China 3 Department of Computer Science and Technology, Tsinghua University, Beijing 100084, P. R. China

Abstract. An algorithm for alternate pattern fill on arbitrary line segments, circular arcs and elliptical arcs is proposed in this paper. The algorithm creates an external loop which is a minimal loop that contains a given point. And then, all loops that delimit the nested regions for the alternate pattern fill inside the external loop are built. The loop detection is based on a new method for searching the leftmost edges. It requires only values of positions, tangent vectors, curvature radii, and the first derivatives of curvature radii at intersection points and areas of circles and ellipses. After all necessary loops are built, the given pattern is filled in the nested loops inside the external loop. Filling the given pattern in this paper is simplified into filling line segment patterns on some parallel lines.

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Introduction

Pattern fill is a process of tiling the interior of a closed region with a repetitive pattern. It is a fundamental problem in a lot of fields [1, 2]. In practical applications, a closed region may contain some other closed regions. Thus, alternate pattern fill may be required. Alternate pattern fill is a process of filling nested closed regions alternately. Up to now, in literature about pattern fill [1] or about loop detection [3, 4], boundaries of closed regions are usually represented by polygons. Most of the methods for pattern fill are scan-line methods or their mutations. Those pattern fill algorithms have some limitations in practical applications. Firstly, boundaries of closed regions often consist of some curves. Those curves have to be converted into line segments. The number of line segments may be gigantic when the precision is critical. Space cost may become too large. Secondly, the pattern fill algorithms assume that the valences of all vertices in boundaries of closed regions should be exactly 2. However, in a geographic map, a river usually has two different end points, from a mountain to another larger river or an ocean. In this paper, the assumption on valences of vertices is not required any longer. Boundaries of closed regions are composed of line segments, circular arcs and elliptical arcs. Curves of other kinds such as spline curves are converted into J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1127–1133, 2004. c Springer-Verlag Berlin Heidelberg 2004


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arc splines [5] rather than polygonal curves. Experience [5] shows that the number of arcs in the resultant arc splines is much less than the number of line segments in the resultant polygonal curves after conversion. Circular arcs and elliptical arcs are selected here because they are widely used in computer aided design. The algorithm proposed in this paper is quite different from scan-line method. It consists of three main steps: preprocess, loop detection and filling patterns. These steps will be explained in the following sections.

2

Preprocess

Before building loops, a preprocess is performed on the given edge set E. All edges are converted into line segments, circular arcs or elliptical arcs if they are not[5]. Then, all line segments (or circular arcs or elliptical arcs), which are overlapped, are combined into a line segment (or a circular arc or an elliptical arc). Finally, closed circular arcs or elliptical arcs are divided into two equivalent circular arcs or elliptical arcs. Thus, after the preprocess, all edges in E have some uniform properties. All edges are line segments, circular arcs or elliptical arcs, the number of intersection points of any two edges in E is finite, and every edge in E exactly has two distinguished vertices.

3

Searching Leftmost Edge

The loop detection in this paper is based on searching the leftmost edge from E with respect to a given directed edge e. We define an edge is on the left side of another edge at a given point as follows. Definition 1. Given a point ps , and two edges e1 and e2 , the point ps is the ending point of e1 and on the edge e2 . e1 and e2 are line segments, circular arcs or elliptical arcs. Let T1 and T2 be the tangent vectors of e1 and e2 at ps , respectively. e1 is on the left side of e2 at ps if and only if one of the following cases is matched. Case 1. T1 is on the left side of T2 . Case 2. T1 and T2 have the same direction. e1 is a circular arc or an elliptical arc. The center point of e1 is on the left side of T1 . And e2 is a line segment, or the center point of e2 is on the right side of T1 if e2 is not a line segment. Case 3. T1 and T2 have the same direction. e1 is a line segment, and e2 is a circular arc or an elliptical arc. The center point of e2 is on the right side of T1 . Case 4. T1 and T2 have the same direction. e1 and e2 are circular arcs or elliptical arcs. And both center points of e1 and e2 are on the left side of T1 . Let ri , ri and si (i = 1 and 2) be the curvature radii, the first derivatives of the curvature radii, and the areas of ei , respectively. If the values of (r1 , r1 , s1 ) and (r2 , r2 , s2 ) are not the same, the first

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different value in (r1 , r1 , s1 ) is smaller than the first different value in (r2 , r2 , s2 ). Case 5. T1 and T2 have the same direction. e1 and e2 are circular arcs or elliptical arcs. And both center points of e1 and e2 are on the right side of T1 . Let ri , ri and si (i = 1 and 2) be the curvature radii, the first derivatives of the curvature radii, and the areas of ei , respectively. If the values of (r1 , r1 , s1 ) and (r2 , r2 , s2 ) are not the same, the first different value in (r1 , r1 , s1 ) is larger than the first different value in (r2 , r2 , s2 ). In Definition 1, we use the following values: positions, tangent vectors, the curvature radii, the first derivatives of the curvature radii, and areas to judge whether an edge is on the left side of another edge at a given point. From above definition, we can search the leftmost edge from the given edge set E with respect to a given directed edge e. The leftmost edge is just sought in the order mentioned above. Additionally, an edge may be divided into some subedges. A subedge could be considered as an ordinary edge in the algorithm. For convenience and without confusion, a subedge is called an edge as well in this paper.

4

Loop Detection

The loop detection here is to build loops using edges in a given edge set E for the following main step of filling patterns. At first, an external loop is created. Then, other loops are made subsequently. A point p is given to identify an external loop, which is the minimal loop among all loops that contain the given point p and are built by edges in the given edge set E. In order to avoid confusion, it is usually required that the point p is not on any edge in E. Other loops built for the alternate pattern fill are the nested loops inside the external loop. Here, we do not need to know how the loops are nested. The alternate pattern fill in the next section will identify the nesting hierarchy. The loop detection in this paper is an iterative procedure of building loops. Therefore, the following provides the algorithm for building a loop from a given edge e. It is based on searching the leftmost edge in the previous section. Algorithm 1. Building a loop from a given edge e and a given edge set E. (Note that e should be in the loop, and that some edges in E, which cannot form loops, will be removed from E.) Input: an edge set E after the preprocess, and an edge e. Output: a loop L searched from a given edge e built by e and edges in E. 1. Let both the edge set Es and the loop L contain exactly an element e. Let ecur = e be the current edge. 2. Search the leftmost edge e with the inputs E and ecur . Then we obtain the trimmed leftmost edge e∗ and the trimmed current edge e at the intersection point.

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3. If the output of Algorithm 1 is null, then go to Step 5. Otherwise, go to the next step. 4. Replace the first element in L with e. Add e∗ into L and Es respectively. (Note that e∗ becomes the first element of L and Es after insertion.) If the edges in L form a loop L1 , then let L = L1 , and go to Step 6 (end of the algorithm). Otherwise let ecur = e∗ , and go to Step 2. 5. Remove ecur from Es and E, and remove the first element of L from L. If L contains no element, then go to Step 6 (end of the algorithm). Otherwise, let ecur be the first element of Es , and go to Step 2. 6. End of Algorithm 1. By calling the Algorithm 1, we can build the external loop with respect to the point p using edges in E. The input edge e is constructed as follows. Find a point q on an edge in E such that q is furthest from p along the direction of x-axis. Let E1 be the set of the edges in E, which have intersection points with the line segment from p to q. Sort edges in E1 in the “leftmost” order. The first element in E1 is set as input edge e of Algorithm 1. If the external loop can not be built from the first element, then the next element is set as input. Then we can find all loops that delimit the nested regions inside the external loop. The algorithm is as follows. The edge closest to the point p is set as input edge e of Algorithm 1. If the loop can be built by Algorithm 1, then the loop is appended to the loop set SL . The edges encountered during search are removed from E2 which is a set of all edges in E and is inside the external loop Lext . The procedure is repeated until E2 is empty.

5

Filling Patterns

After producing all loops needed by the alternate pattern fill, patterns will alternately be tiled on the nested regions delimited by those loops. Before patterns are filled, it should be known how a pattern is defined and required to be repeated. Usually a given pattern is very small, so we can decompose or approximate a pattern with several line segments. This
paper  uses the following values to repx0 resent a “line segment pattern”. α and determine a line passing through 0
 y

 cos(α) ∆x x0 and with the direction . makes the above line become sin(α) y0
∆y  x0 + i∆x a cluster of parallel lines passing through and with the direction y0 + i∆y
 cos(α) , where i are integers. Each i ∈ Z corresponds to a line in the cluster sin(α) of the parallel lines. The sequence of real numbers determines the lengths of the line segments and the breaks. They are repeated along the parallel lines as shown in the Figure 1. As shown in Figure 1, pattern fill could be simplified into line segment pattern fill. For each parallel line, let the set Si be initiated as a set with all intersection

Alternate Pattern Fill

(a)

(b)

(c)

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(d)

Fig. 1. Pattern fill of stars (a) is simplified into pattern fill of line segments (b, c, d)

points between the parallel line and the edges in the external loop Lext and in the loop in SL . If any edge overlaps the parallel line, then Si just stores the starting point and the ending point of the edge. If two or more edges have the same intersection points with the parallel line, Si records all of them. Si is adjusted for some singular cases shown in Figure 2 as follows. As shown in Figure 2(a), if some edges are tangent with the parallel line, and the tangent points are not vertices of the edges , then remove those tangent points from Si . In the cases shown in Figure 2(b) and Figure 2(c) , two neighboring edges in a loop intersect the parallel line at the join point of the two neighboring edges. If they do not cross the parallel line at the join point(for example, Figure 2(b)), then remove the join point twice from Si . If they cross the parallel line(for example, Figure 2(c)), then the join point is removed from Si only once. The case that any edge overlaps the parallel line (for examples, Figures 2(d) and 2(e)) could be simplified into the cases in Figures 2(b) and 2(c). The method is to ignore the edge that overlaps the parallel line so that the previous edge and the following edge become two “neighboring” edges in the loop.

(a)

(b)

(c)

(d)

(e)

Fig. 2. Some singular cases (edges are in solid, and the parallel line is dashed)

Suppose that Si = {p1 , p2 , · · · , pm } after all the singular cases as shown in Figure 2 are processed. Then, the line segments are drawn from p1 to pm along the parallel line according to the given values for the line segment pattern fill. The line segments between p2k and p2k+1 , where k are an integer, and 2 ≤ 2k < 2k + 1 ≤ m, are trimmed or removed. The line segments on the edges, which overlap the parallel line, are trimmed or removed as well. In other words, the line segments for filling pattern are drawn on the parallel line from p2k−1 to p2k , and not on the edges of the given edge set.

6

Example and Conclusions

Figure 3 give a practical example. It is a drawing of a toy tractor. The point labelled with p in the figure is used to identify the regions for the alternate

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p

(a)

(b)

Fig. 3. Example 2(a drawing of a toy tractor): (a) before alternate pattern fill; (b) after alternate pattern fill

pattern fill. In this example, there are vertices which valences are 1. Some curves are NURBS curves.They are converted into arcs during the preprocess stage. The figure shows that the method in the paper could well deal with it. The algorithm for alternate pattern fill in this paper has been implemented in our commercial CAD software OpenCAD. The example in the paper is produced with the software OpenCAD as well. The algorithm for alternate pattern fill in the paper could deal with not only line segments but also circular arcs and elliptical arcs. Curves of other kinds will be converted into circular arcs. Edges in the given edge set could be arbitrary. The valences of vertices in the given edge set have no constrain. The loop detection in this paper is based on searching the leftmost edges. While searching the leftmost edges, we only calculate some values at intersection points and areas of ellipses or circles if necessary. Additionally, pattern fill is simplified into line segment pattern fill in this paper.

Acknowledgements The research was supported by Chinese 863 Program (2003AA4Z3110) and 973 Program (2002CB312106). The second author was supported by a project sponsored by SRF for ROCS, SEM (041501004), and FANEDD(200342).

References 1. Angel, E.: Computer Graphics. Addison-Wesley Publishing Company, New York (1990) 2. Praun, E., Hoppe, H., Webb, M., and Finkelstein, A.: Real-Time Htching. In: Proceedings of SIGGRAPH. (2001) 581–586 3. Gujar, U. and Nagendra, I.: Construction of 3D Solid Objects from Orthographic Views. Computer & Graphics 13 (1989) 505–521

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4. Satoh, S., Hiroshi, M., and Sakauchi, M.: An Efficient Extraction Method for Closed Loops Using a Graph Search Technique. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 78 (1995) 583–586 5. Yong, J.H., Hu, S.M., and Sun, J.G.: A Note on Approximation of Discrete Data by G1 Arc Splines. Computer-Aided Design 31 (1999) 911–915

A Boundary Surface Based Ray Casting Using 6-Depth Buffers Ju-Whan Song1 , Ou-Bong Gwun2 , Seung-Wan Kim2 , and Yong-Guk Kim3 1

3

School of Liberal Art, Jeonju University, Jeonju, Jeonbuk, Korea [email protected] 2 Division of Electronics and Information Engineering, Chonbuk National University, Jeonju, Jeonbuk, Korea {obgwun, kswsamson}@chonbuk.ac.kr School of Computer Engineering, Sejong University, Seoul, Korea [email protected]

Abstract. This paper focuses on boundary surface based ray casting. In general the boundary surface based ray casting is processed in two stages. In the first stage, boundary surfaces are found and stored into buffers. In the second stage, the distance between the viewpoint and the voxels of the area of interest is calculated by projecting boundary surfaces on the view plane, and then the traverse of the volume data space with the distance is started. Our approach differs from the general boundary surface ray casting in its first stage. In contrast to the typical boundary surface based ray casting where all boundary surfaces of volume data are stored into buffers, in our proposal, they are projected on the planes aligned to the axis of volume data coordinates and these projected data are stored into 6-depth buffers. Such a maneuver shortens the time for ray casting, and reduces memory usage because it can be carried out independently from the amount of the volume data.

1

Introduction

Boundary surface based ray casting enables a ray to traverse the voxels of the area of interest directly without traversing the front voxels of this area. It makes voxel traversing fast because the voxels of areas of no interest do not need to be traversed. It is necessary to know the exact distance between a view plane and a boundary surface while traversing voxels in the boundary surface based ray casting. For that purpose, Zuiderveld et al. make a map representing the distance from the viewpoint to the nearest possible voxels of the area of interest area and use the map for voxel traversing[6]. In Polygon Assisted Ray Casting(PARC) algorithm, Sobierajski et al. find the polygons of the boundary surfaces that surround the possible voxels of interested area in the preprocessing and then project the polygons of boundary surfaces on the view plane by Z-buffer algorithm to find the distance in the main J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1134–1140, 2004. c Springer-Verlag Berlin Heidelberg 2004


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processing[3]. The performance of PARC algorithm for the case of a boundary surface with many polygons is degraded as the projection time of the polygons is increased[3]. In boundary cell based rendering, Wan et al. find the boundary cells that surround the region of interest and store these boundary cells in the vector table[4]. The algorithm is only effective for small volume data of less than 1283 . In this paper, we propose a new boundary surface based ray casting. The algorithm is different from the above algorithms: first, the boundary surface data are once stored in 6-depth buffers by projecting boundary surfaces on the XY, YZ, ZX planes of volume data coordinates; second, projection of boundary surfaces is performed using an incremental algorithm.

2

6-Depth Buffers

In this paper, we propose a novel boundary surface ray casting, in which the distances from a view plane to voxels of area of interest are calculated using depth buffers aligned in 3 directions in the volume data space and volume data are represented by 3 dimensional arrays of cube. In the volume data space, we can define volume data coordinates in which the coordinates axes are principle edges of it as illustrated in Fig. 1. In the coordinates, we build total 6-depth buffers: 2 buffers (near and far) for each direction x, y and z, respectively. Boundary surface data are stored in the 6-depth buffers by projection. The resolution of the depth buffer for each direction is identical to the resolution of the volume data space for each direction. The far and near depth values for the boundary surface are found by shooting a ray from each plane (XY, YZ, XZ) and calculating the location of the intersection point between a the boundary surface and a ray. They are calculated only once and stored in the head of volume data because the near and far depth values of boundary surface are independent on any viewpoint. The following algorithm finds the near depth values of Z direction on the XY plane. Depth values perpendicular to X, Y directions can be found using a similar method. for all pixels(i, j) on the XY view plane{ Z(i, j) = inf ; /* initialize z buffer with maximum value*/ } for all pixels(i, j) on the XY view plane{ spawn a ray(i, j); traverse cell of the ray(i, j) through the volume data space; if( Ray(i, j) meets boundary surface cell for the first time){ find the distance from XY viewplane to the boundary surface cell; Z(i, j) = the distance; } }

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6-Depth Buffers Creation

In Section 2, the depth values are stored in 6-depth buffers if it assumed that the view coordinates are the same as the volume data coordinates. However, changing the viewpoint requires transformation of the near and far depth values of 6-depth buffers. The near depth values from the viewpoint can be calculated by projecting the values of the front 3 depth buffers among 6-depth buffers on a view plane. Fig. 2 illustrates this process. The far depth values of a viewpoint can be calculated using a similar method.

Fig. 1. The concept of 6-depth buffers

Fig. 2. Finding of the depth value for a viewpoint

The following pseudo code describes the algorithm, in which a location (x, y, z) in the X direction buffer among 6-depth buffers is transformed into a location (x, y, z) of view coordinates, for (yd = 0; yd < ny - 1; yd++) for(zd = 0; zd < nz - 1; zd++) xv, yv, vv = view_transform(x_buffer(yd, zd), yd, zd); } } Where view transform (x buffer((yd, zd), yd, zd) is found as follows[5]: 


xv yv zv

=

cosαcosβ cosαsinβsinθ − sinαcosθ cosαsinβcosθ + sinαsinθ sinαcosβ sinαsinβsinθ + cosαcosθ sinαsinβcosθ − cosαsinθ −sinβ cosβsinθ cosβcosθ

xd yd zd

(1)

Where ny-1, nz-1 is the volume resolution of y, z direction, respectively, and xd, yd, zd is the location of volume data coordinates, respectively, and xv, yv, zv is the location of view coordinates, respectively.

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Though the above algorithm represents the transformation from a location of volume data coordinates to a location of view coordinates for x direction, the transformation of a location for y (or z direction) can be obtained in a similar way. The above algorithm is calculated by the incremental algorithm. The first value [xv, yv, zv] is calculated by (1) but the next values [xv, yv, zv+1] or [xv, yv+1, zv+1] are calculated by adding step increment into [xv, yv, zv] or [xv, yv, zv+1].

4

Potential Problems and Their Remedy

We encounter two potential problems with the present approach. The first problem is caused because the footprint of the cells projected on the view plane is smaller than the pixel size as shown in Fig. 3. In this case, some parts of boundary cells not covered by the projected cell are created. The second problem is caused by the insufficient number of depth buffers used to store the boundary surface of the area of interest. When the shape of a boundary surface is concave, then some boundary cells of volume data space cannot be sampled in the 6-depth buffers as shown in Fig. 4. In such a case, holes are generated when view direction changes. Fig. 5 shows the holes generated by the above two problems.

Fig. 3. Holes caused by smaller cell foot print than pixel size

Fig. 4. Holes caused by insufficient number of depth buffer in 2 dimensions

In our case, we remedy this problem as follows. If there is a hole during the process of view transformation of depth buffers, we search the depth values of 4-neighbor pixels of the hole and set the nearest depth value of them as the depth value of the hole. If there are no depth values in the 4-neighbor pixels, we expand the search area. If several depth values from more than one depth buffer are overlapped, the nearest depth value among them is selected and stored into the depth buffer for the view plane. Fig. 6 shows that holes are removed by this method.

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Fig. 5. Holes caused by smaller cell foot print than pixel size and insufficient number of depth buffers: Black points in the image represent holes

Fig. 6. Boundary surface modified by larger cell foot print than original cell footprint: Holes disappeared

Fig. 7. Skull images of digital man by common ray casting, PARC algorithm, and proposed algorithm

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Results and Algorithm Comparison

The proposed algorithm is compared to the common ray casting as well as PARC algorithm on a PC platform. In PARC, x, y, z value of cells (polygon) correspond to the boundary surfaces in the depth buffer. When the number of cells consisting of boundary surfaces is n, and x, y, z component of one cell is represented with 2 bytes; PARC requires nx3x2 bytes memory space. The proposed algorithm always requires the memory space of twice the number of XY, YZ, ZX plane resolution of volume data space regardless of boundary surface complexity, because we know 2 components among x, y, z component from a depth buffer. We have evaluated the result image using the performance measures: MAE (Mean Absolute Error) and RMSE (Root Mean Square error)[2]. Table 1 and Fig. 7 show the experiment results for the CT data of digital man[1]. The size of additional memory of PARC algorithm is 1,493,868 bytes and the size of additional memory for the proposed algorithm is 786,432 bytes. The ray casting time of common ray casting, PARC algorithm and the proposed algorithm is 6.345, 1.221 and 0.582 seconds, respectively. The speed-up ratios of the proposed algorithm to common ray casting and PARC algorithm is 10.902:1

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Table 1. Ray casting time and speed-up ratio of skull images of digital man †Com. ‡PARC §Prop. Additional Memory Capacity(bytes) 0 1,493,868 786,432 Ray Casting Time(seconds) 6.345 1.221 0.582 Speed-up Prop.:Com. 10.902 : 1 Ratio Prop.:PARC 2.098 : 1 Differences of MAE 0.014029(Com. to Prop.), 0.007124(PARC to Prop.) Result Images RMSE 0.078967(Com. to Prop.), 0.035247(PARC to Prop.) †Com.: Common ray casting algorithm ‡PARC: PARC algorithm §Prop.: Proposed algorithm

and 2.098:1. The difference of the image generated by common ray casting and the proposed algorithm when measuring MAE and RMSE is 0.014029, 0.078967 respectively. Those by PARC algorithm and the proposed algorithm is 0.007124, 0.035247, respectively. The image generated by the proposed algorithm is very similar to common ray casting. However, the image generated by the proposed algorithm is more similar to the image generated by PARC algorithm than the image generated by common ray casting.

6

Conclusions

In this paper, we proposed a boundary surface based ray casting, implemented it on a PC, and compared it to common ray casting algorithm and PARC algorithm. In contrast to the typical boundary surface based ray casting where all boundary surfaces of volume data are stored into buffers, in our proposal, they are projected on the planes aligned to the axis of volume data coordinates and these projected data are stored into 6-depth buffers. Such a maneuver shortens the time for ray casting, and reduces memory usage because it can be carried out independently from the amount of the volume data. In a future study, we plan to make our algorithm faster by structuring the data in the 6-buffers.

References 1. http://www.nlm.nih.gov/research/visible/visible human.html. NLM the Visible Human Project 2. Kim, K., Wittenbrink, C. M., Pang, A.: Extended specifications and test data Sets for Data Level Comparisons of Direct Volume Rendering Algorithms. IEEE Transactions on Visualization and Computer Graphics 7 (2001) 299–317 3. Sobierajski, L. M., Avila, R. S.: A Hardware Acceleration Method for Volumetric Ray Tracing. IEEE Visualization 95 (1995) 27–34 4. Wan, M., Bryson, S., Kaufman, A.: Boundary cell-based acceleration for volume ray casting. computers & graphics 22 (1999) 715–721

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5. Yang, S., Wu, T.: Improved Ray-casting Algorithm for Volume visualization. SPIE Visualization and Data Analysis 4665 (2002) 319–326 6. Zuiderveld, K. J., Koning, A. H. J., Viergever, M. A.: Acceleration of ray-casting using 3D distance transforms. SPIE Visualization in Biomedical Computing 1808 (1992) 324–334

Adaptive Quantization of DWT-Based Stereo Residual Image Coding
Han-Suh Koo and Chang-Sung Jeong

Department of Electronics Engineering, Korea University, 1-5ka, Anam-dong, Sungbuk-ku, Seoul 136-701, Korea {hskoo, csjeong}@korea.ac.kr Abstract. General procedure for stereo image coding is to use disparity compensated prediction methods and code residuals separately. Although the characteristics of stereo residuals are different from those of common images, JPEG-like methods which are applied to monocular images are used frequently and less research has been devoted to residual image coding. The focus of this paper is to make stereo image coding more efficient by speculating the characteristics of the residual image. By measuring the edge tendency of residual image, our method modifies the quantization matrix adaptively using discrete wavelet transform.

1

Introduction

A stereo pair is two images which are captured at slightly different positions. Due to the advances in 3D technology, stereo image compression is becoming a crucial research field for various applications that includes teleconferencing, visualization, and robotics. Most stereo image coding algorithms take advantages of disparity estimation and compensation used for compression of monocular image sequences include block matching to predict one image from the other one. Reference image is coded independently, and target image is predicted from reference one. The residual which is the error between actual and predicted target image is coded successively using a suitable transform coder. Although the characteristics of disparity-compensated stereo residuals are different from that of common images, less research has been devoted to residual image coding and JPEG-like methods including Discrete Cosine Transforms (DCT) which are used to compress common monocular images are generally employed. In this paper, we designed a new stereo residual image coding algorithm which uses wavelet transform. Considering the features of residual images, we proposed a new Discrete Wavelet Transforms (DWT) quantization matrix emphasizing vertical or horizontal structures according to the edge strength of stereo residual image. Our algorithm can adjust entries of quantization matrix in view of the edge tendency.




This work was partially supported by the Brain Korea 21 project in 2004 and KIPAInformation Technology Research Center. Corresponding author.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1141–1147, 2004. c Springer-Verlag Berlin Heidelberg 2004


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Related Researches

DCT-based compressions have been popular so far for monocular image coding, and JPEG-like DCT-based schemes are also frequently used for stereo image residual because they can be easily combined with existing monocular image coding methods. Lately DWT-based compressions attract much attention in image coding research field because they provide many useful features and better performance than DCT-based schemes [1]. Related with this report, stereo image coding algorithms based on wavelet transform have been presented by many researchers [2–4]. As for coding of stereo residuals, mixed image transform coder which uses DCT on the well matched blocks by block matching and Haar filtering on the occluded blocks was proposed [5]. However JPEG coding which uses DCT is a de facto standard and many systems built on JPEG are already used in various applications. Queiroz et al. proposed the JPEG-like DWT image coder known as DWTJPEG [6]. They incorporated DWT into the JPEG baseline system for coding general images by designing a new block-scanning order and quantization matrix into JPEG coder block. Nayan et al. showed that DWT-JPEG is superior to DCT in stereo residual coding [7]. By JPEG-like approach, it does not require full-image buffering nor imposes a large complexity increase. Moellenhoff and Maier presented two special properties for disparity compensated stereo residual images [8, 9]. First, in case that disparity compensation is performed well, much of the residual image has intensity values near zero. Second, the remaining contents are narrow vertical edges because of strictly horizontal apparent motion between the two views. They proposed Directional DCT quantization matrix based on anticipated DCT energy distribution to emphasize the linear structure in the image. However optimal quantization matrix for various image condition caused by the baseline of two cameras and a characteristic of subjects cannot be determined easily because DCT quantization matrix is confined within local 8×8 areas. Determining a unified matrix is difficult and finding individual one for each local area is not adequate in rate’s aspect within traditional JPEG framework.

3

A DWT Coding of Stereo Residual Image

Most stereo image coding algorithms use block-based disparity estimation and compensation to predict one of stereo pair from the counterpart. One image is coded and transmitted independently using conventional methods for monocular images and the other one is compensated and coded using disparity vectors and residuals. Disparity vectors are coded losslessly by Differential Pulse Code Modulation (DPCM) followed by Variable Length Coding (VLC). Because error-free stereo image pair can hardly be constructed by disparity-compensated prediction, residual errors should be coded to get better results.

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A DWT-JPEG has been proposed to provide better coding performance. However, DWT-JPEG quantization matrix does not guarantee the best performance in stereo residual image coding because it was not designed considering the condition of stereo images. The characteristics of disparity-compensated stereo residuals are different from those of normal images. As mentioned in Sect. 2, Moellenhoff and Maier surveyed two special properties for disparity-compensated stereo residuals. Applying these features, they proposed a quantization matrix for DCT coding of stereo residual images emphasizing the horizontal structures in local 8×8 areas. However we found that the quantization process using this matrix might raise some argument under particular conditions. Because previous method uses a fixed quantization matrix based on anticipated DCT energy distribution, it can not be adapted to various conditions arisen by geometry of cameras and objects. Residual images may have various edge tendency and distribution according to the image type or the performance of disparity compensated prediction. Based on arguments from DWT-JPEG and Directional DCT, we designed a new stereo residual image coding scheme. Our scheme takes advantage of features of previous works. Figure 1 is an overall flow diagram of our scheme. In ordinary block-based coding scheme, DCT coefficients are grouped within common spatial location and each of them indicates different subbands. While, in DWT, coefficients indicate different spatial locations in common subband. Because overall distribution of intensity in residual image is easily considered by DWT approach, adaptive schemes according to image conditions are devised by DWT rather than DCT. Following DWT to input residuals, the coefficients are reordered by DWT-JPEG scanning [6]. Coefficients in the same location, but different subbands are grouped together in a block like DCT coefficients in JPEG. For each reordered block, adaptive quantization is processed using the 8×8 matrix defined by Q = A(Q
− 1) + 1, (1) ⎡

(1)

(1)

(1)

(1)

ck−3 dk−3 dk−2 dk−2 dk−1 ⎢ . ⎢ (2) (3) (1) (1) ⎢ dk−3 dk−3 dk−2 dk−2 .. ⎢ . ⎢ (2) (2) (3) (3) ⎢ dk−2 dk−2 dk−2 dk−2 .. ⎢ (2) (2) (3) (3) (1) ⎢d k−2 dk−2 dk−2 dk−2 dk−1 Q
= ⎢ ⎢ d(2) · · · · · · d(2) d(3) ⎢ k−1 k−1 k−1 ⎢ . .. .. ⎢ . . . ⎢ . ⎢ . . . ⎢ . .. .. ⎣ . (2) (2) (3) dk−1 · · · · · · dk−1 dk−1

⎤ (1) · · · · · · dk−1 .. ⎥ ⎥ . ⎥ .. ⎥ ⎥ . ⎥ (1) ⎥ · · · · · · dk−1 ⎥ ⎥. (3) · · · · · · dk−1 ⎥ ⎥ .. ⎥ ⎥ . ⎥ .. ⎥ ⎥ . ⎦ (3) · · · · · · dk−1

(2)

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Fig. 1. Flow diagram of proposed stereo residual image coder

In the matrix Q
, entry ck−3 for DC quantization is set as 2 like Directional DCT for stereo residual. Because intensity of residual image is usually small, DC quantization is done with small value. Entries representing diagonal edges are fixed to the value of that of DWT-JPEG because our scheme is also based (3) (3) (3) on DWT. Accordingly, entries dk−1 , dk−2 , and dk−3 are set as 55, 12, and 7 respectively. To determine the entries for vertical and horizontal edges, we defined following metric, (3)

(3)

(3) d(l) m = dm−1 + (dm − dm−1 ) × (1 −

El ), E1 + E2

(3)

where m is a level of wavelet tree and El is the energy of subband l of the highest l level. We called E1E+E as an edge tendency αl at subband l. By this scheme, 2 smaller factors are assigned to subbands having stronger edge tendency. That is, directional quantization coefficients can be adaptively determined according to the directionality of stereo residual image. In (1), A is a positive value used as a scaling factor to control the bit rate, and bold constants are matrices that act like a constant. Constant matrices are used to avoid quantization failure when A is a decimal fraction. Quantized entries are encoded in Run-Length Encoding (RLE) block. After encoding process, disparity vector, DWT coefficients, and horizontal edge tendency are transmitted to decoder along with information of first view. Decoder reconstructs stereo image pair using information from encoder. Decoding procedure is virtually reverse order of encoding. Quantization matrix is constructed with edge tendencies. One is transmitted αl and the other is calculated via (1 − αl ). Wavelet coefficients are restored with the matrix.

4

Experimental Results

We compared our algorithm with DWT-JPEG scheme because the focus of this paper is to evaluate the performance of adaptive quantization matrix in DWT. Figure 2 are stereo images experimented in this paper. The size of test image is 512×512 with 256 gray levels intensity. In all of our experiments, the size of block for disparity compensated prediction and residual coder is chosen to be 8×8 pixels. For DWT, Haar bases were used in our experiments. Search range for finding disparity vectors is confined to 8 pixels for left margin and 4 pixels for right margin. Residuals between original right image and estimated image which is assembled by disparity vectors are coded using residual coder. Using (3), adaptive quantization matrix for each test set is constructed. Entries

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of quantization matrix Q
is filled with coefficients which are determined from edge tendencies. We compared Peak Signal-to-Noise Ratio (PSNR) differences of ours named Directional DWT with DWT-JPEG. PSNR is calculated between original right image and the reconstructed image from decoder. Results are compared objectively in Fig. 3. Scaling factor A used in this experiment ranged from 0.6 to

(a)

(b)

(c)

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Fig. 2. Experimental image sets (a) Ball image (real) (b) Cone image (synthetic) (c) Apple image (real) (d) Pentagon image (real) cone

25

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Fig. 3. Performance evaluation of Directional DWT with DWT-JPEG using plots of PSNR (a) Ball image (b) Cone image (c) Apple image (d) Pentagon image

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1.4 and discretely varied in 0.1 step. Scaling factor is also multiplied to quantization matrix of DWT-JPEG. Graphs show that PSNR performance varies linearly according to the variation of scaling factor A. Experimental results under various scaling factor demonstrate that Directional DWT performs better than DWT-JPEG through all the observed bit rates though it is not optimized. We can validate that improvements of coding efficiency are achieved by adaptive quantization. Concerning bit allocation, Directional DWT and DWT-JPEG require bandwidth for disparity vectors and DWT coefficients. In addition to commonly required information, Directional DWT consumes memory to save edge tendency. However Directional DWT shows better performance than DWT-JPEG regardless of additional memory consumption because compression efficiency of Directional DWT is excellent to offset the differences.

5

Conclusion and Future Work

In this paper, we proposed a DWT-based algorithm to code stereo residual image. Our system adopted DWT-JPEG scheme because DWT is known to be superior to DCT in coding efficiency and DWT-JPEG is able to be incorporated into the JPEG framework. Considering edge tendency of residual image, our strategy adaptively modifies quantization matrix to get improved coding efficiency. By experiments with stereo images, we showed that our scheme outperforms compared with previous DWT-based coding. For future work, we will test various wavelet filter banks and optimize our algorithm to get the best performance.

References 1. Xiong, Z., Ramchandram, K., Orchard, M. T., and Zhang, Y. Q.: A Comparative Study of DCT- and Wavelet-Based Image Coding. IEEE T. Circ. Syst. Vid. 9 (1999) 692–695 2. Jiang, Q., Lee, J. J., and Hayse, M. H.: A Wavelet Based Stereo Image Coding Algorithm. Proc. IEEE Int. Conf. Acoust. Speech 6 (1999) 3157–3160 3. Xu, J., Xiong, Z., and Li, S.: High Performance Wavelet-based Stereo Image Coding. IEEE Int. Symp. Circ. Syst. 2 (2002) 273–276 4. Palfner, T., Mali, A., and Muller, E.: Progressive Coding of Stereo Images using Wavelets and Overlapping Blocks. Proc. IEEE Int. Conf. Image Process. 2 (2002) 213–216 5. Frajka, T., Zeger, K.: Residual Image Coding For Stereo Image Compression. Opt. Eng. 42 (2003) 182–189 6. de Queiroz, R., Choi, C. K., Huh, Y., and Rao, K. R.: Wavelet Transforms in a JPEG-Like Image Coder. IEEE T. Circ. Syst. Vid. 7 (1997) 419–424

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7. Nayan, M. Y., Edirisinghe, E. A., and Bez, H. E.: Baseline JPEG-Like DWT CODEC for Disparity Compensated Residual Coding of Stereo Images. Proc. Eurographics UK Conf. (2002) 67–74 8. Moellenhoff, M. S., Maier, M. W.: DCT Transform Coding of Stereo Images for Multimedia Applications. IEEE T. Ind. Electron. 45 (1998) 38–43 9. Moellenhoff, M. S., Maier, M. W.: Transform Coding of Stereo Image Residuals. IEEE T. Image Process. 7 (1998) 804–812

Finding the Natural Problem in the Bayer Dispersed Dot Method with Genetic Algorithm Timo Mantere Department of Information Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland [email protected]

Abstract. This paper studies how the built-in natural weakness in the image processing algorithm or system can be searched and found with the evolutionary algorithms. In this paper, we show how the genetic algorithm finds the weakness in the Bayer’s dispersed dot dithering method. We also take a closer look at the method and identify why this weakness is relatively easy to find with synthetic images. Moreover, we discuss the importance of comprehensive testing before the results with some image processing methods are reliable.

1

Introduction

An image processing system or algorithm may contain some built-in natural weaknesses that normal testing with relatively few standard test images may not reveal. The image-processing researcher may be satisfied with his algorithm if he gets good results with just a few standard test images (Lena, Baboon, etc.). The test image choice has a big influence on the results. This is clearly demonstrated in [1] by selecting an appropriate five-image subset from a 15-image test set, any one of the six Gamut Mapping Algorithms (GMA) tested could appear like the best one. They studied 21 research papers on GMAs and found out that these papers have represented results by using only 1 to 7 test images. The general belief that the system really operates satisfactorily with all possible images requires more extensive testing. In software testing the software system is usually tested with a much larger test data set. Software faults can be searched and found with automatic testing by e.g. random search or evolutionary algorithms. Software test data is given as input and the test results are analyzed from the output. In paper [2] we used image-processing software as a test example. We sent synthetic images to the system and measured how close the processed result images were to the original. In other words, we tested the quality of image processing software. In the case of image processing software the fault we find may not be caused by badly written software, but instead by the image-processing algorithm implemented in it. We also state [2, 3] the importance of extensive testing and explain why it is better to use a large number of simulated test images instead of just standard test images. In study [2] we did not analyze what caused the target software to process the J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1148–1154, 2004. c Springer-Verlag Berlin Heidelberg 2004


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worst test data (hardest images) as badly as it did. The purpose of this is paper is to go back and analyze what made the tested image processing software behave badly with our synthetic test images. Genetic algorithms (GA) [4] are population-based computerized optimization methods that use the Darwinian evolution [5] of nature as a role model. The solution base of the problem is encoded to individuals. These individuals are tested against our problem, which is represented as a fitness function. The better the fitness value of the individual, the better is its chance to survive and be selected as a parent for new individuals. By using crossover and mutation operations GA creates new individuals. In crossover we select the genes for a new chromosome from each parent using some pre-selected practice, e.g. onepoint, two-point or uniform crossover. In mutation we change random genes of the chromosome either randomly or using some predefined strategy. Dithering or digital halftoning [6] is a method where we reduce the number of tones in the image and present the result image with less colors or gray tones. The aim is to do dithering so that the resulting images do not contain any disturbing artifacts or moir´e [7]. In this paper, the original images contain 256 possible gray tones and the resulting images are bi-level images, i.e. they can only have white and black pixels. The method we use is the thresholding with the Bayer [8] dispersed dot ordered threshold matrix. Image comparison between original and dithered images is a difficult problem. Much research has been done in this area and several methods of how this should be done have been proposed. Usually the methods try to adapt the human eye visual transformation (HVT) function. The human eye is a kind of lowpass filter that averages the perception from small details. In this paper we use the lowpass filter model based on HVT [9]. The image comparison is done by using Normalized Root Mean Squared Error (NRMSE) [10] difference metric (1), after lowpass filtering dithered images.
 N −1 M −1 2  i=0 j=0 [I0 (i, j) − Ir (i, j)] N RM SE =  N −1 M −1 2 i=0 j=0 [I0 (i, j)]

(1)

There is still some active research applying Bayer’s method, e.g. [11] uses the Bayer method as a starting point to develop a dithering algorithm for threedimensional printing. According to [11], the dispersed dot dither can avoid undesirable low frequency textures in the constant regions and is therefore preferred in applications for 3D printing. Different kinds of pictures may be dithered in the most satisfactory way with different halftoning techniques, e.g. hand drawings are totally different than natural images [12], and therefore require different algorithms. We also recognized the fact that different subsets of images are better halftoned with different error-diffusion coefficients when we applied co-evolution to optimize error-diffusion coefficients together with the test images [3]. There are some formerly identified weaknesses in Bayer’s method, but despite that it is widely used in digital halftoning, and images that have been halftoned with it are easily recognized from the quasi-period cross-hatch pattern artifacts [12]

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that this method produces in the display. This artifact is usually seen as a major weakness in this technique that is otherwise fast and powerful.

2

The Proposed Method

The proposed method (Fig. 1) consists of a genetic algorithm that generates parameter arrays. These parameter arrays are used by an image producer application that generates synthetic test images. Images are then sent to the image processing application that halftones the input image using Bayer’s ordered dither method and outputs the result image. The image comparator subprogram in GA reads the pixels from the original test image and halftoned result image and compares them. The comparison value is used by GA as a fitness value.

Fig. 1. GA-based image processing software quality testing system

The GA chromosome consists of 217 floating-point numbers, and 210 of them are divided into 30 groups of 7 parameters. They are used to generate 30 basic image components; the 7 parameters define their type (lines, rectangles, ovals, or ASCII characters), position, size, colors, and transparency. One parameter defines the overall image background tone. The last six are used to generate chaotic stripes, 3 for vertical and 3 for horizontal stripes. These 3 parameters for chaotic data are value a = [2, 4], and the initial value x0 = [0, 1] of Verhulst equation [13]: xn+1 = a×xn ×(1−xn ), the third parameter is the offset, i.e. how many xn values are bypassed in the beginning. Two chaotic data fillings enable us to generate diagonal stripes and sort of squared artifacts (crossing stripes) to the test image. We used chaotic data to make images more varied, and because its appearance can be controlled by parameters, unlike random data.

3

Experimental Results

We run tests with both GA and random search methods in order to verify that GA really does learn and adapt to the problem parameters, and results are not due to just random luck. The GA parameters in this case were: population 60,

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elitism 50%, mutation percentage 3%, crossover rate 50%, with uniform/singlepoint crossover ratio 50/50. The test runs with both the GA and the random method were 200 generations long. With random search the “generation” means as many new random test images as new individuals in one GA generation. Figure 2 shows the development of the highest fitness value with GA and random search, as a function of generations, in the best and worst test runs out of 10 with each method. Fig. 2 shows typical GA development, and it clearly outperforms random search in this problem. We believe that the reason why it is possible to generate such synthetic images that their darkness changes so dramatically (Fig. 3) during the halftoning process is a natural weakness in the Bayer method. Let us try to identify it.

Fig. 2. The development of GA-based optimization and random search while searching harder test images, in the best (high) and the worst test runs (low)

The initial numbers 0, 1, 2, 3 for the Bayer matrix are put as D(2)= [ 03 21 ]. 0 8 2 10 4 14 6 The larger matrix is accomplished by (2), e.g. D(4) = 12 3 11 1 9 , where 15 7 13 5   20 36 24 40 ]. We can calculate that in D (16) (column) = 30 and (row) = [   the (column) = 2040, but the (row) = [1360, 2720]. At first we suspected that the differences between row sums enable the image darkness to change so dramatically. However, the stripes in our test images (Fig. 3) were clearly vertical, which seems to indicate that there is a different explanation. A closer look reveals that the threshold (or image) values in the vertical columns create this phenomena. When we go through all possible 16×16pixel one-tone gray images, tones 0 to 255, and threshold them with the Bayer method we saw that the resulting tone values start to change unevenly in the result image rows and columns.

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Fig. 3. Examples of GA-generated test images and their halftone result images



D

(n)

(2)

(2)

4D(n/2) + D00 U (n/2) 4D(n/2) + D01 U (n/2) = (2) (2) 4D(n/2) + D10 U (n/2) 4D(n/2) + D11 U (n/2)

 (2)

If we have a one-tone image where every pixel value is 128, the Bayer method generates an output image where all row and column sums are equal to 2040 (in a 16 × 16 area) and white and black pixels alternate. With a one-tone image, tone=64, the method produces images where every other row and every other column is equal to zero and the rest equal to 2040, this means that every other column is totally black and in every other the black and white pixels alternate. With a one-tone image, tone=192, the method generates an output image where every other row and column is completely white, and in the rest the black and white pixels alternate. These differences mean that if we generate a test image where in every other vertical column all pixels are tone=64 and in every other tone=192, the result image with the Bayer method is exactly the same as with one-tone images, with tone=192 or tone=64, depending on the order of stripes. In other words we have generated a half gray image, but our result image is either 64 tones too dark or too light.

4

Conclusions and Discussion

We demonstrated that synthetic test images could be used to find problematic image features that the tested image processing system is not capable of processing satisfactorily. The genetic algorithm is an optimization method that adapts to the system and “learns” those parameters that generate high fitness function values. In this case the GA learned the natural weakness in the Bayer matrix and was able to generate synthetic test images that cause high tone changes.

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In addition, it also learned such image patterns that cause some image components to totally disappear, and also in some cases ghost image artifacts to appear. We used simulated images and saw that they have the power to find some problems that commonly used standard test images do not discover. As far as we know, no one has reported problems with the Bayer method similar to the ones we found. This can be due to the fact that the method is usually used with natural images. Natural images do not have as large artificial variations, which is probably why it operates well with the subset of natural images. However, we can see that a general method such as this is often used with totally different kinds of images [11, 12]. Testing an image processing system or algorithm with just a few standard test images is not sufficient for assuming that works with all images. We suggest that the system must be tested with an extensive number of test images, both natural and synthetic, before we can fully trust that the system operates sufficiently. We have also implemented other halftoning methods to the image processing software and found out that other methods seem to have some natural built-in weaknesses as well. The weakness of the commonly used Floyd-Steinberg error diffusion method [14] seems to be its delayed response to the high contrast changes in the borders. Our GA-based test system utilized that problem by generating synthetic images that had many feature borders with large tone changes. In this paper we do not design better halftoning methods. But we believe that testing with synthetic test images is also helpful when designing or improving halftoning methods.

References 1. Morovic, J., Wang, Y.: Influence of test image choice on experimental results. In: Proc. of 11th Color Imaging Conference, Scottsdale, AR, Nov. 3-7 (2003) 143-148. 2. Mantere, T. Alander, J.T.: Testing halftoning methods by images generated by genetic algorithms. Arpakannus 1, FAIS, Espoo, Finland (2001) 39-44. 3. Mantere, T., Alander, J.T.: Testing digital halftoning software by generating test images and filters co-evolutionarily. In: Proc. of SPIE 5267: Intelligent Robots and Computer Vision XXI, Providence, RI, Oct. 27-30 (2003) 257-268 4. Holland, J.: Adaptation in Natural and Artificial Systems. The MIT Press (1992) 5. Darwin, C.: The Origin of Species. Oxford Univ. Press, London (1859) 6. Kang, H.: Digital Color Halftoning. SPIE Press, Bellingham, WA (1999) 7. Lau, D., Ulichney, R., Arce, G.: Blue- and green-noise halftoning models. IEEE Signal Processing Magazine, July (2003) 28-38 8. Bayer, B.: An optimum method for two-level rendition of continuous-tone pictures. In: Proc. of IEEE Int. Conf. on Communications 1, NY, June 11-13 (1973) 11-15 9. Sullivan, J. Ray, L., Miller, R.: Design of minimum visual modulation halftone patterns. IEEE Transactions on Systems, Man, and Cybernetics 21(1), (1991) 10. Fienup J.: Invariant error metrics for image reconstruction. Applied Optics 36(32), (1997) 8352-8357 11. Cho, W., Sachs, E., Patrikalaikis, N., Troxel, D.: A dithering algorithm for local composition control with 3D printing. Computer-Aided Design 35 (2003) 851-867

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12. Savazzi, E.: Algorithms for converting photographs of fossils to ink drawings. Computers&Geosciences 22(10), (1996) 1159-1173 13. Addison, P.: Fractals and Chaos. Philadelphia Inst. of Physics Publishing (1997) 14. Floyd, R., Steinberg, L.: An adaptive algorithm for spatial gray-scale. In: Proc. of Social Information Display 17(2), (1976) 75-78

Real-Time Texture Synthesis with Patch Jump Maps Bin Wang, Jun-Hai Yong, and Jia-Guang Sun Tsinghua University, Beijing 100084, P. R. China

Abstract. This paper presents a real-time method for synthesizing texture. The algorithm consists of two stages: a preprocess stage and a real-time synthesis stage. In the preprocess stage, jump lists are built for each texture patch in the input sample texture and all the jump lists are stored in patch jump maps. In the synthesis stage, we synthesize the output texture with the aid of stored patch jump maps. Experiments show 200-500 frames of 256 × 256 high quality textures can be produced within a second.

1

Introduction

Texture synthesis is an important technique in computer graphics and computer vision nowadays. Among lots of texture synthesis algorithms, the methods based on Markov Random Field(MRF) have been intensively investigated recently. Leung and Efros [2] present a nonparametric sampling algorithm which synthesizes the output texture pixel by pixel. A year later, Wei and Levoy [8] significantly accelerate Leung and Efors’s algorithm using Gaussian pyramid and tree-structured vector quantization search method. By using the coherence between the neighborhoods of pixels, Ashikhmin [1] presents a method for synthesizing nature texture. Unlike Wei and Levoy who search the whole input texture, Ashikhmin only checks several candidate pixels to find the best-fit pixel for current output position. Ashikhmin’s algorithm takes only 0.1 seconds to generate a 256 × 256 texture. It can produce high-quality result for some special textures, such as flower, grass and bark, but is not suitable for other textures, especially textures with regular structures. Zelinka and Garland [10] present the (pixel) jump map method towards real-time texture synthesis. They first find several similar pixels for every pixel in the input texture in the analysis stage, and the algorithm does not calculate the distance of the neighborhood anymore in the synthesis stage. It just randomly chooses a pixel according to the probability in the jump list. The jump map algorithm is very fast, taking only 0.03 − 0.07 seconds to produce a texture with the size 256 × 256. However, the behavior of the jump map method is similar to Ashikhmin’s algorithm. Although it can generate high quality synthesized results for stochastic sample textures, it meets trouble while synthesizing structured textures. In this paper, we present a real-time texture synthesis method based on patch jump maps as an extension to the jump map technique. The method has two J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1155–1160, 2004. c Springer-Verlag Berlin Heidelberg 2004


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merits over the old jump map algorithm. First, it can produce much better results for the structured textures than the old one. Second, it takes only 0.0020.005 seconds to generate a 256 × 256 texture, about 10 times faster than the old one.

2

Patch Jump Maps

Our algorithm fits in the category of patch-based texture synthesis method. Unlike the pixel-based method mentioned in section 1, patch-based methods attempt to copy a selected region from the input texture each time otherwise a pixel. Xu et al. [9] apply cat map chaos transformations to transform a randomly selected patch to a new position and use a simple cross-edge filter to smooth the block boundaries. Efros and Freeman [3] improve Xu’s method through an image quilting operation, which tries to find a minimum error boundary cut within the overlap region of two patches. Kwatra el al. [4] present graphcut method as an extension to the image quilting algorithm to make the method more flexible. Liang et al. [5] use patch-based sampling strategy to choose the best-fit texture patch from the input sample, paste it into the output texture and perform feather blending in the boundary zones. Wang et al. [7] extend Liang’s method to multisources 2D directional texture synthesis.

(b)

(a) Fig. 1. Illustration of texture analysis

As shown in figure 1(a), suppose A, B and C are three already synthesized patches(size = WD ×WD ) in the output texture. The “L-Shape” zone Eout (width = WE ) hatched with white lines is the boundary zone of the already pasted patches and ED is the boundary zone of candidate patch D(size = WD × WD ) from sample texture. While pasting D to the target position of the output texture, the two boundary zones would overlap. So a standard patch-based sampling algorithm is to find a patch D in the input texture such that its boundary zone ED matches Eout . That means the distance between Eout and ED should be below a given threshold. L2 norm [5] is used as the comparison distance metric,

Real-Time Texture Synthesis with Patch Jump Maps


 A 1  d(Eout , ED ) =  (pi − piD )2 , Ω i=1 out

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(1)

where Ω is the number of pixels in the boundary zone, piout and piD are the pixel values in the boundary zone. The boundary comparison for patch-based sampling is a time-consuming operation. Liang et al. use optimized kd-tree, quadtree pyramid and principal components analysis(PCA) to get a good performance. However, we find the algorithm could be much faster if applying the jump map techniques to the patch-based sampling algorithm. Take figure 1 as an example for the constructing of jump map. A strategy for generating the jump map is to use the boundary zone as a whole neighborhood. However, as shown in figure 1(a), Eout is composed of part α (the top-right corner of patch A), part β (the top boundary of patch B) and part γ (the right boundary of patch C). So to be more natural, we decompose the boundary zone into three parts and build a jump map for each of them. Suppose patch S is the target patch, and we will build its jumps for the β part of its boundary zone. Let dmax denote the distance threshold and T denote another patch in the sample texture. If the distance between the corresponding part of the boundary zones dβ (ES , ET ) < dmax , then patch T would be considered as a jump of patch S for the boundary part β. Suppose we have found a jump list which contains k jumps for part β of the patch S by searching the whole input texture(Figure 1(b) shows three jumps of them, β0 , β1 and β2 ), then the probability for each jump in the list is calculated as follows: pi =

Ωβ d βi (1 − ), k ∗ Ωt dmax

(2)

where Ωβ is the number of pixels in the β part of the boundary zone, Ωt = Ωα + Ωβ + Ωγ and dβi represents the distance between βi and β. After all the jump lists are constructed for each patch in the sample texture, we store them as a patch jump map for β part. In a similar way, we build jump maps for α and γ parts, such that three jump maps(called α, β and γ maps) are obtained for an input sample texture. A brute force search method to construct a jump map usually takes a very long time and is unacceptable. Since the distance metric is actually a vector comparison operation, some existing algorithm could be employed to accelerate the search procedure. We first use PCA method to reduce a high dimension vector1 , and then use an optimized kd-tree to find the matching vectors. With the accelerated algorithm, building a jump map for a 256 × 256 sample texture only takes several minutes.

1

The original dimension is A × c in our application, where c is the channels of color and it could be reduced to about 25% while retaining 97% original variance.

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Texture Synthesis with Patch Jump Maps

We have built three patch jump maps for a sample texture and now let’s illustrate how to synthesize a texture with the patch jump maps. The algorithm is briefly summarized as follows.

(a)

(b)

(c)

Fig. 2. Illustration of texture synthesis

1. Split the output texture into n × n patches (patch size = WD × WD ). Assign every patch a type id (tid ). For the patch in the left bottom corner, set its tid = −1. Assign 0 to the lowest patches and assign 1 to the left patches. For all other patches, set tid = 2. 2. Randomly choose a texture patch from the input sample texture. Paste it to the left bottom corner of the output texture. Record the sample(source) position of every pixel in the output texture. 3. Synthesize the patches with a scan line order, from bottom to top, from left to right. 4. Construct a candidate texture patch set ΨD for the current patch to be synthesized. If the patch’s id is 0, then only the γ boundary part of already synthesized patch need to be matched(see figure 2(a)). Let (x, y) denote the origin pixel(left bottom corner)’s coordinate of the current patch, the pixel left to it is (x−1, y). Since (x−1, y) has been already synthesized, we suppose its source pixel is (sx, sy). Therefore, the patch with the origin (sx + 1, sy) in the input sample texture and its jumps from the γ map form a candidate set ΨD for the current patch. Similarly, if the patch’s id is 1 and the origin point is (x, y)(see figure 2(b)), then the patch with the origin (sx, sy + 1) and its jumps from the β maps form ΨD , where (sx, sy) is the source pixel of position (x, y − 1). If the patch’s id is 2(see figure 2(c)), then ΨD are constructed by the jumps from all the three jump maps. 5. Select one texture patch from ΨD according to the jump probability. Paste it to the position of current patch and record the sample position of every pixel in the output texture. 6. Repeat steps 3, 4, and 5 until the output texture is fully covered. 7. Perform feather blending (algorithm sees [6]) in the boundary zones.

Real-Time Texture Synthesis with Patch Jump Maps

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Results and Conclusions

We present a real-time texture synthesis algorithm in this paper by combining the merits of jump map technique and patch-based sampling method. We first generate three different jump maps for a sample texture off-line and then synthesize texture by constructing candidate set ΨD from the jump maps dur-

Fig. 3. Comparison among pixel jump map method(left), our method(middle) and patch-based sampling method(right)

Fig. 4. Some more synthesis examples. In each example, the small(left) image is the input sample texture and the large(right) image is the output texture

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ing runtime. The synthesis results of our algorithm are better than the pixel jump map method and are comparable with the patch-based sampling method. Moreover, our algorithm is the fastest one among the three algorithms. It takes 0.002-0.005 seconds2 to output a 256 × 256 synthesized texture. We also find that if the candidate jumps in each jump list are limited to a fixed number, the performance of the algorithm is non-sensitive to the size of input sample texture. Figure 3 shows a comparison of our algorithm with pixel jump map method [10] and the patch-based sampling method [5]. We can see that the quality of our results is almost as good as that of the patch-based sampling algorithm and is better than that of the pixel jump map especially for the structured texture. Figure 4 shows some more synthesis results of our algorithm, all the results are 256 × 256, the patch size is 16 × 16 and the width of the boundary zone is set to 4 pixels while building jump maps.

Acknowledgements The research was supported by Chinese 863 Program (2003AA4Z3110) and 973 Program (2002CB312106). The second author was supported by a project sponsored by SRF for ROCS, SEM (041501004), and FANEDD(200342).

References 1. Ashikhmin M.: Synthesizing natural textures. In Proceedings of the Symposium on Interactive 3D graphics (2001) 217–226 2. Leung T., Efros A.: Texture Syntheis by Non-parametric Sampling. In Proceedings of ICCV’99 (1999) 1033–1038 3. Efros A., Freeman W. T.: Image Quilting for Texture Synthesis and Transfer. In Proceedings of SIGGRAPH’01 (2001) 341–346 4. Kwatra V., Schodl A., Essa I., Turk G., Bobick A.: Graphcut textures:image and video synthesis using graph cuts. ACM Transactions on Graphics 22 (2003) 277– 286 5. Liang L., Liu C., Xu Y.-Q., Guo B., Shum H.-Y.: Real-time texture synthesis by patch-based sampling. ACM Transactions on Graphics 20 (2001) 127–150 6. Szeliski R., Shum H.-Y.: Creating Full View Panoramic Mosaics and Environment Maps. In Proceedings of SIGGRAPH’97 (1997) 251–258 7. Wang B., Wang W.-P., Yang H.-P., Sun J.-G.:Efficient example-based painting and synthesis of 2d directional texture. IEEE Transactions on Visualization and Computer Graphics 10 (2004) 266–277 8. Wei L.-Y., Levoy M.: Fast texture synthesis using tree-structured vector quantization. In Proceedings of SIGGRAPH’00 (2000) 479–488 9. Xu Y.-Q., Guo B., Shum H.-Y.: Chaos mosaic: Fast and memory efficient texture synthesis. In Tech. Rep. 32, Microsoft Research Asia (2000) 10. Zelinka S., Garland M.: Towards Real-Time Texture Synthesis with the Jump Map. In Proceedings of thirteen eurographics workshop on Rendering (2002) 2

All the experiments data in this paper are obtained on a PC with 2GHz Pentium IV CPU.

Alternation of Levels-of-Detail Construction and Occlusion Culling for Terrain Rendering Hyung Sik Yoon1 , Moon-Ju Jung2 , and JungHyun Han3,
1

3

School of Information and Communications Engineering, Sung Kyun Kwan University, Korea 2 Samsung SDS, Korea Department of Computer Science and Engineering, Korea University, Korea

Abstract. Terrain data set is essential for many 3D computer graphics applications. This paper presents a general framework for real-time terrain walk-through application, where the LOD(levels of detail) construction and occlusion culling are alternately selected depending on the terrain geometry. For highly occluded areas, only the occlusion culling is enabled. For less occluded areas, only the LOD rendering is enabled. A small piece of pre-computed information helps the renderer alternate the two methods. The experiment results demonstrate significant savings in rendering time.

1

Introduction

Terrain rendering occupies an important part in many 3D computer graphics applications such as games, and speed-up techniques are crucial because computing resources should also be assigned to other tasks such as 3D character/avatar rendering. The most popular representation for terrain data is uniformly sampled height field, a set of height/elevation data sampled in a regular grid. In terrain rendering, the LOD(levels of detail) algorithms are popular that select only a subset of the height field points and produce a coarser mesh from the subset [1] [2] [3] [4] [5] [6]. A well-known speed-up technique in the computer graphics field is occlusion culling, which removes the portions of the scene that are occluded and cannot contribute to the final image [7] [8]. Its application to terrain rendering has also been reported [9] [10]. In terrain walk-through applications, this paper proposes to alternately select between the LOD construction and occlusion culling depending on the terrain geometry.

2

Hierarchical Structures of Height Field Data

The smallest representable mesh consists of 3 × 3 vertices, called a block, as depicted in Figure 1-(a). The simplification procedure considers 5 vertices (top,


Corresponding Author.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1161–1167, 2004. c Springer-Verlag Berlin Heidelberg 2004


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Fig. 1. A quadtree block and its simplification

bottom, left, right and center) for removal. If all of them are removed, we have two possible triangulations in Figure 1-(b). Figure 2-(a) shows the results of two successive stages of complete simplification. The simplification strategy is compatible with the quadtree structure [11]. Given (2k + 1) × (2k + 1) vertices, the quadtree will have k levels. A node of the quadtree corresponds to a block. There can exist 12 triangles in a block, as depicted in Figure 2-(b). A certain simplified block is composed of a subset of the 12 triangles. To describe the status of a block, we use a structure Block, where each triangle in Figure 2-(b) is associated with a 1-bit flag, which indicates its presence/absence.

TL

TR

T

LT

RT

LB

RB

L BL

level 2

level 1 (a) Quadtree levels

BR

R B

level 0 (b) 12 possible triangles in a block

Fig. 2. Quadtree levels and triangle indices

A block is divided into 4 quadrants, and each quadrant is labeled as depicted in Figure 3-(a). Let us see the indexing scheme. The white-vertex block in Figure 3-(a) is positioned inside quadrant 3 (11(2) ) of the quadtree level 1, and is quadrant 2 (10(2) ) of level 2. Therefore, its index is 1110(2) =14(10) . The parent-child relations between blocks are found by shift operations on the indices. A separate array of Block structures is maintained for a quadtree level, and therefore we have k arrays as shown in Figure 3-(b).

3

Occlusion Culling

Occlusion culling requires the terrain data to be rendered in front-to-back order. Before a block is rendered, it should be checked if previously drawn blocks occlude the current block. Therefore, those blocks closer to the viewpoint should

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Fig. 3. Block indices and quadtree structure

be rendered first. Figure 4-(a) shows that, given the viewpoint in quadrant 0, the front-to-back ordering is (0,2,1,3). Depending on which quadrant the viewpoint lies in, 4 different orderings are needed. They are stored in a look-up table. In the quadtree structure, each quadrant is recursively traversed and rendered, and the front-to-back ordering should be enforced on all descendants of the quadrant. For example, quadrant 0 in Figure 4-(a) has 4 children as shown in Figure 4-(b), and the correct ordering among the children should be determined. For the purpose, we use the following classifications based on the viewpoint position: the viewpoint’s quadrant (quadrant 0 in Figure 4-(a)), the diagonal quadrant (quadrant 3), and the adjacent quadrant (quadrants 1 and 2). – The Viewpoint’s Quadrant: The ordering is “retrieved from the look-up table.” As shown in Figure 4-(b), the viewpoint is now in quadrant 1, and the look-up table is accessed to retrieve (1,3,0,2). – The Diagonal Quadrant: All descendants of this quadrant simply follow the ordering of their parents, i.e. (0,2,1,3) obtained in Figure 4-(a). Two-level results are illustrated in Figure 4-(d).

2

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(a) 2 0

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(e)

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(f)

3 1

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(g)

Fig. 4. Front-to-back traversal

(h)

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– The Adjacent Quadrant: Between quadrants 1 and 2 in Figure 4-(a), let us discuss with quadrant 2. The ordering depends on whether the viewpoint is in the right-hand side or in the left-hand side with respect to the quadrant center. As illustrated in Figure 4-(e), the viewpoint is in the right-hand side, and (1,3,0,2) is chosen. If it were in the left-hand side, (0,2,1,3) would be chosen, as shown in Figure 4-(f). (The case of quadrant 1 is shown in Figure 4-(g).) Distinguishing between left- and right-hand sides is done simply by checking the index of the viewpoint’s quadrant in the ‘same’ quadtree level. The quadtree nodes are rendered in the front-to-back order, and occlusion culling is performed. Occlusion culling is done using hardware visibility query. Contemporary graphics hardware supports such visibility query. For a block, its top-most edges of axis-aligned bounding box (AABB) are used for occlusion query. If occlusion query result is ‘0,’ the block is taken as ‘occluded.’

4

Rendering Process

One of the most promising LOD algorithms has been reported in [5]. We have implemented their algorithms in the proposed framework. However, suppose a mountain area with high occlusion where only a small subset of (near-side) faces contributes to the final image. Then, the efforts to construct an LOD for the entire area are all in vain. On the other hand, suppose a plain area with few occlusions. In such a case, the cost for occlusion test, which we call occlusion culling overhead, significantly degrades the overall rendering performance. Our strategy based on these observations is to choose between LOD construction and occlusion culling such that the chosen method should produce a higher frame rate than the other. A small piece of pre-computed information, named LOM (LOD or Oocclusion culling guide Map), is generated by pre-rendering the scene twice: one with LOD only, and the other with occlusion culling only. Between the two results, a faster one is selected and recorded into the LOM. The ideal but infeasible method to generate a LOM would be to pre-render the scene at all possible positions and directions of the terrain surface. Instead, we have sampled 8 directions (N, E, W, S, NW, NE, SW and SE) ‘for every vertex position’ of the height field data set. The 8 directions are parallel to the xy-plane, and good for walk-through applications. As we need a 1-bit information for each direction, 1-byte additional information for LOM is needed at each vertex. LOM-guided rendering is simple. For a walk-through path, the vertex nearest to the current position is retrieved, and the direction (out of 8 sampled directions) is selected which is closest to the viewing direction. If the bit is 0, only LOD construction is enabled. If 1, only occlusion culling is enabled.

Alternation of LOD Construction and Occlusion Culling

5

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Test Results and Discussion

We have implemented the proposed algorithms on a PC with an Intel 2.4GHz Pentium 4 CPU, 512MB memory, and two NVIDIA graphics cards: GeforceFX 5900 and GeforceFX 5200. Figure 5-(a) is for a case with an open view. Only LOD is enabled. The top view shows various levels of detail. Figure 5-(b) is for a highly occluded view. Only occlusion culling is enabled. The top view shows only the rendered blocks. The gray area inside the view frustum is taken by the blocks culled out through occlusion culling. Due the occluding blocks near the viewpoint (drawn as a white ellipse), most of the blocks which are relatively far from the viewpoint do not have a chance to enter the rendering pipeline. Figure 6 shows the frame rate graphs for 4 cases of rendering: (1) with the finest-resolution original data (with none of speed-up techniques), (2) with LOD construction only, (3) with occlusion culling only, and (4) with alternation of LOD construction and occlusion culling, guided by the LOM. The results in Figure 6-(a) are obtained using GeforceFX 5900, and those in (b) are using GeforceFX 5200. Note that the LOM-guided alternation takes the higher frame rate between the LOD-only rendering and occlusion-culling-only rendering. Therefore, the stable frame rate of the LOD-only case is almost always guaranteed. The occlusion-culling-only rendering produces a higher frame rate than the LOD-only case. Note that the relatively higher frame rate is obtained due to

(a) An open view rendered with LOD only

(b) A highly occluded view with occlusion culling only

Fig. 5. Rendering results

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Fig. 6. Frame rate graphs

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high occlusion, and the occluding triangles are usually at the near-plane side of the view frustum. Then, the polygonal silhouette of the terrain is revealed, which is quite annoying. The extra computing power can be used to smooth it by using interpolation or subdivision surface techniques. Both of the LOM-guided and LOD-only cases will then show similar frame rates, but the image qualities are quite different.

6

Conclusion

This paper presents a general framework for real-time terrain walk-through application, where the LOD construction and occlusion culling are alternately selected depending on the terrain geometry. The experiment results with current implementations demonstrate significant savings in rendering time. Future research issues include designing more effective LOM structure, incorporating silhouette smoothing techniques into the framework, etc.

Acknowledgements This work was supported by grant No. 1999-2-515-001-5 from the Basic Research Program of the Korea Science and Engineering Foundation.

References 1. Lindstrom, P., Koller, D., Ribarsky, W., Hodges, L.F., Faust, N., Turner, G.A.: Real-time, continuous level of detail rendering of height fields. In: SIGGRAPH. (1996) 109–118 2. Duchaineau, M.A., Wolinsky, M., Sigeti, D.E., Miller, M.C., Aldrich, C., MineevWeinstein, M.B.: ROAMing terrain: real-time optimally adapting meshes. In: IEEE Visualization. (1997) 81–88 3. Rottger, S., Heidrich, W., Slussallek, P.: Real-time generation of continuous levels of detail for height fields. In: Proc. 6th Int. Conf. in Central Europe on Computer Graphics and Visualization. (1998) 315–322 4. Pajarola, R.B.: Large scale terrain visualization using the restricted quadtree triangulation. In: IEEE Visualization. (1998) 19–26 5. Lindstrom, P., Pascucci, V.: Terrain simplification simplified: A general framework for view-dependent out-of-core visualization. IEEE Transactions on Visualization and Computer Graphics 8 (2002) 239–254 6. Pajarola., R.: Overview of quadtree-based terrain triangulation and visualization.(technical report, university of california irvine). (2002) 7. Pantazopoulos, Ioannis; Tzafestas, S.: Occlusion culling algorithms: A comprehensive survey. In: Journal of Intelligent and Robotic Systems: Theory and Applications. Volume 35. (2002) 123–156 8. Daniel Cohen-Or, Yiorgos L. Chrysanthou, C.T.S.F.D.: A survey of visibility for walkthrough applications. In: IEEE Transations on Visualization and Computer Graphics. Volume 9. (2003) 412–431

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9. Stewart, A.J.: Hierarchical visibility in terrains. In: Eurographics Rendering Workshop. (1997) 217–228 10. Lloyd, B., Egbert, P.: Horizon occlusion culling for real-time rendering of hierarchical terrains. In: IEEE Visualization. (2002) 403–410 11. Samet, H.: The quadtree and related hierarchical data structures. In: ACM Computing Survey. Volume 16. (1984) 99–108

New Algorithms for Feature Description, Analysis and Recognition of Binary Image Contours Donggang Yu and Wei Lai Swinburne University of Technology, PO Box 218, Hawthorn,VIC 3122, Australia

Abstract. In this paper, some new and efficient algorithms are described for feature description, analysis and recognition of contours. One linearization method is introduced . The series of curvature angle, linearity, and bend angle between two neighboring linearized lines are calculated from the starting line to the end line. The series of structural points are described. The useful series of features can be used for shape analysis and recognition of binary contours.

1

Introduction

The description of binary image contour plays an important role for the shape analysis and recognition of image. line segment, curvature angle of lines, the bend angle, and convexity and concavity of the bend angles are useful features to analyze the shape of binary image contour. Many methods and algorithms are developed for the description of contours in the past [1-4]. However, these descriptions cannot form series of sets, or the inter contour of a binary image can not be processed based on these algorithms [3], which make the analysis and understanding of contour shape difficult. Also, no one uses difference code to describe and extract these series of features because there are some spurious contour points. The methods proposed in this paper can make it possible. Some useful structural points are defined to analyze and recognize contour shape. The relevant algorithms are described in Section 2. Finally, a conclusion is given.

2

The Linearization and Description Features

Let the starting point of an binary image be the upper-left corner. Freeman code is used, and the contours are 8-connected. The chain code set of contour k is represented as: Ck = {c0 , c1 ...ci , ...cn−1 , cn }

(1)

where i is the index of the contour pixels. The difference code, di , is defined as: di = ci+1 − ci . J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1168–1174, 2004. c Springer-Verlag Berlin Heidelberg 2004


(2)

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Fig. 1. Original image, contours, smooth following and linearization of two handwritten digits 7

In smoothed contours, |di | equals 0 or 1 [4]. Two samples are shown in Figs. 1(3) and 1(6). 2.1

The Curvature Angle of a Linearized Line

The curvature angle is defined as the direction angle between the x coordinate axis and lse , and the angle is formed with starting from the direction of the x coordinate axis to the direction of linearized line, which is determined by the line’s element codes, in anti-clock. Let

ln ln
(3) ∆x =
xln k [0] − xk [nk − 1]


∆y =
ykln [0] − ykln [nln k − 1]

(4)

in Fig. 2. Let  curve be the curvature angle, then it is found as follows (corresponding four quadrants) (see Fig. 2): Case 1: If cdir1 and cdir2 are chain codes 0, 1 or 2 (the first quadrant), then curve = (180◦ /π) se, where





se = tag −1 (

∆y ). ∆x

(5)

Case 2: If cdir1 and cdir2 being chain code 4, 5 or 6 (the third quadrant), then  curve = 180◦ + (180◦ /π) se based on Equation (5) and Fig. 2. Similarly, the curvature angles can be found in the second and Fourth quadrants. Case 5: There are eight special cases which are shown in Fig. 3, and  curve is found as follows: (1) If its cdir1 is chain code 4,  curve = 180◦ for the case in Fig. 3(1). (2) If its cdir1 is chain code 0,  curve = 360◦ (0◦ ) for the case in Fig. 3(2). Similarly, the curvature angles of other six cases can be found based on Figs. 3(3-8).

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|α−β| β

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(3)

Fig. 2. Finding the curvature angle of linearized lines

line[j+1]

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Fig. 4. Finding the bend angle between two neighboring linearized lines

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Fig. 5. Detection pattern of the bend angle property

The Bend Angle and Its Property

The bend angle of linearized lines is defined as the angle between the line j and the line [j + 1]. It can be calculated based on Fig. 4. a. The Bend Angle of Linearized Lines Let  curve[j] and  curve[j + 1] be the curvature angle of lines j and [j + 1] respectively, and ∆[j, j + 1] be their curvature angle difference, then ∆[j, j + 1] =  curve[j] −  curve[j + 1],

(6)

where  curve[j] is α,  curve[j + 1] is β, and ∆[j, j + 1] is |α − β| in Fig. 4 respectively. Let  angle[j] be the bend angle between lines j and [j + 1], then it can be found based on following equation (see Fig. 4): 

angle[j] = 180◦ − |∆[j, j + 1]| .

(7)

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b. The Property of Bend Angle of Linearized Lines Let lcdir1 [j] and lcdir2 [j] be the first and second element codes of the line j, and lcdir1 [j + 1] and lcdir2 [j + 1] be the first and second element codes of the line [j + 1] respectively. Thirty two detection patterns of the bend angle property (convex or concave) can be found, here only eight patterns are shown in Fig. 5. One detection rule can be described as follows: If lcdir1 [j] is code 0 and lcdir2 [j] is code 1 (see Figs. 5(1) and 5(5)), or lcdir1 [j] is chain code 1 and lcdir2 [j] is chain code 0 (see Figs. 5(2) and 5(6)), then – If is – If is

lcdir1 [j + 1] is chain code 2 or lcdir2 [j + 1] is chain code 2, then  angle[j] convex (see Figs. 5(1-2)). lcdir1 [j + 1] is chain code 7 or lcdir2 [j + 1] is chain code 7, then  angle[j] concave (see Figs. 5(5-6)).

Similarly, other rules can be found based on other twenty eight patterns. Based on the above algorithms, series of description features of two sample images (see Figs. 1(3) and 1(6)) can be found from starting point to end point, and shown in Table 1. These series of features can be constructed as a feature vector. For example, the vector of a series of curvature and bend angles of the contour in Fig. 1(3) is: 200◦ 110◦ → 270◦ 74◦ → 15◦ 119◦ → 315◦ 96◦ → 231◦ 96◦ → 315◦ 81◦ → 53◦ 71◦ → 161◦ 140◦ (see Table 1(1)). For Fig. 1(6), the similar vector can be found. These feature vectors can describe the series of directions (concave or convex), and it is shown in Fig. 1(7). Also, the feature vectors of sample images in Figs. 7-9 can be found. 2.3

Structural Points of Smoothed Contours

The structural points are some special points which can be used to represent convex or concave change in the direction of chain codes between two neighboring lines along the contour. Their definition and detection are based on the structure patterns of element codes of two lines. Assume that line[ln] is the current line and that line[ln − 1] is the previous line. Definition 1. The convex point in the direction of code 4 (represented with the character “∧”). If the element codes 3, 4 and 5 occur successively as a group of neighborhood linearized lines, then one convex point can be found as follows: if cdir1 of line[ln] is code 4, cdir2 is code 5 and the direction chain code of the last pixel of line[ln − 1] is code 3, then the first pixel of the current line line[ln] is a convex point which is represented with “∧”. Definition 2. The concave point in the direction of code 4 (represented with the character “m”). If the element codes 5, 4 and 3 occur successively as a group of neighborhood linearized lines, then one concave point can be found as follows:

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Code 4

Code 0

(1) Convex Point (^) (in the Code 4)

(2) Concave Point (m) (in the Code 4)

(3) Concave Point ($) (in the Code 4)

(4) Convex Point (v) (in the Code 4)

Code 2

Code 6 (5) Convex Point ([) (in the Code 6)

(6) Concave Point (]) (in the Code 6)

(7) Convex Point ()) (in the Code 2)

(8) Concave Point (() (in the Code 2)

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(11) Concave Point in the Code 1 (O)

(12) Convex Point in the Code 1 (o)

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(16) Concave Point in the Code 3 (t) * *

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Fig. 7. Example of one handwritten digit 3

if cdir1 of line[ln] is code 4, cdir2 is code 3 and the direction chain code of the last pixel of line[ln − 1] is code 5, then the first pixel of the current line, line[ln], is a concave point which is represented with “m”. Similar to Definitions 1-2, other structural points can be defined and found. These points are convex points “v”, “[’, “)”, “F”, “o”, “T”, “s”, and concave points “$”, “]”, “(”, “f”, “O”, “t” and “S” which are shown in Fig. 6 respectively. These structural points describe the convex or concave change in different chain code directions along the contour, and they can therefore be used to represent the morphological structure of contour regions. For the outer contour in Fig. 7(5) there is a series of structural points: “∧” → “F” → “[”→ “s”→ “v” (convex) → “$” →“S” →“]” → “f” (concave) → “F”→ “[”→ “s”→ “v” (convex) → “$” →“S” →“]” → “f”→ “m”(concave) “∧” → “F” → “[”→ “s”→ “v”→ “o”→ “)”→ “T”→ “∧” (convex). Each convex or concave change consists of a group of convex or concave structural points respectively. For example, the first convex change of the above series consists of convex structural points “∧”, “F”, “[”, “s”, and “v”. For the outer contour in Fig. 8(5 ), the series of structural points is: “∧” → “F” → “[”→ “s” (convex) →“S” →“]” → “f” (concave) → “F”→ “[”→ “s” (convex) →“S” →“]” → “f”→ “m”(concave) “∧” → “F” → “[”→ “s”→ “v”→ “o”→ “)” (convex) → “(” (concave) → “T”→ “∧” (convex). There are similar concave changes which contain a group of points “S” and “]” (concave morphological change in chain codes 7 and 6) in both above vectors of structural points. If recognized object images are digit based on prior infor-

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Fig. 8. Original image, contour, smooth following, linearization, and structural points of another handwritten digit 3

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Fig. 9. Example of one lily flower image

mation, then two images are recognized as handwritten digit 3. This is because there is such a morphological structure pattern (two group of points “S” and “]”) on the smoothed contours of all type of digits 3 (both print and handwritten digits 3). For the outer contour in Fig. 9(5), the series of structural points is: “∧” → “F” → “[” (convex) → “]” → “f” (concave) → “F”→ “[”→ “s” (convex) → “S” (concave) → “s”→ “v” (convex) → “$” (concave) → “v”→ “o”→ “)” (convex) → “(”→ “O” (concave) → “o”→ “)”→ “T” (convex) → “t”→ “(” (concave) → “)”→ “T”→ “∧” (convex) → “m” (concave) →“∧” (convex). It is clear, the outer contour is six angles because of six pairs of convex and concave change. If flower images are recognized, it can be recognized as lily flower. For most sorts of lily flower there are six petals which are constructed by sixangles. Also, the series set of linearized lines, curvature and bend angles give the detail of contour analysis for each convex or concave change.

3

Conclusion

An efficient and new method has been developed to linearize the smoothed contours and to find the series of structural features of linearized lines of contours based on the structure analysis of difference chain code. All features, linearity, curvature and bend angles, and structural points can be use to analyze contours, and to recognize contour shape. Compare our algorithm with other methods [1-4], the best useful contribution is that some series of structural features of linearized lines of contours are found based on our algorithm, but other methods not. Also, these ordered series of structural features (the input of a pro-

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cessing system) make shape analysis and recognition of contours possible. These algorithms have been used in the recognition of document and GIS images. Acknowledgement. This work is supported by the Australia Research Council SPIRT grant (C00107573).

References 1. Moktarian, F., Mackworth, A. K. A Theory of Multiscale Curvature-Based Shape Representation for Planer Curvature Angles. IEEE Trans. Pattern Analysis Mach. Intell. 14 (8), (1992) 789–805 2. Fu, A. M. N., Yan, H., Huang K. A Curvature Angle Bend Function Based Method to Characterize Contour Shapes. Patt. Recog. 30 (10), (1997) 1661–1671 3. Sonka, M., Hlavac, V. and Boyle R., “Image Processing, Analysis and Machine Vision,” Chapman & Hall Computing, Cambridge, 1993. 4. Yu, D., Yan, H. An efficient algorithm for smoothing binary image contours. Pro. of ICPR’96. 2 , (1996) 403–4

A Brushlet-Based Feature Set Applied to Texture Classification Tan Shan, Xiangrong Zhang, and Licheng Jiao National Key Lab for Radar Signal Processing and Institute of Intelligent, Information Processing, Xidian University, Xi’an, 710071, China [email protected]

Abstract. The energy measures of Brushlet coefficients are proposed as features for texture classification, the performance of which to texture classification is investigated through experiments on Brodatz textures. Results indicate that the high classification accuracy can be achieved, which outperforms widely used classification methods based on wavelet.

1 Introduction The analysis of texture image plays an important role in image processing. Much work has been done to develop proper representations that are effective to texture analysis during the last several decades [1][2][3]. Recently, two spatial-frequency techniques were introduced, namely, Gabor filters [4] and wavelet transforms [5][6], both of which have achieved considerable success in texture classification. Especially, the texture image analysis methods based on wavelet have received more and more attention in that the energy measures of the channels of the wavelet decomposition were found to be very effective as features for texture analysis. It is well known that the orientation is an important characteristic of texture. Unfortunately, the separable 2-D wavelet transform provides only few orientations other than horizontal, vertical and diagonal ones. Many researchers have been dedicating to the problem, and hope to develop certain new mathematical tool which can provides more orientation information of image than wavelet does [8][9]. In paper [10], the author introduced a new system called brushlet, which is a new kind of analysis tool for directional image. And the ability of brushlet to analyze and describe textural patterns was well demonstrated by compressing richly textured images efficiently in paper [10]. In this paper, we show how the brushlet provide efficient features for texture image classification. This paper is organized as follows. First, the brushlet transform is discussed briefly. And in section 3, energy measure of brushlet coefficients as texture feature is presented. Then, in the section 4, the effectiveness of brushlet energy measure is investigated experimentally. Finally, the conclusions are drawn in section 5. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1175–1180, 2004. © Springer-Verlag Berlin Heidelberg 2004

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2 Brushlet Transform We will briefly explain the construction of brushlet. A detailed exposition on brushlet may be found in [10]. Brushlet is constructed in the Fourier domain by expanding the Fourier transform n =+∞

of a function into orthonormal basis. Consider a cover R = ∪ n =−∞ [an , an +1 ) , and write

ln = an +1 − an , cn = (an +1 − an ) / 2 . Let r be a ramp function such as if t ≤ −1

⎧0 r (t ) = ⎨ ⎩1

if t ≥ 1

.

(1)

And r 2 (t ) + r 2 (−t ) = 1, ∀t ∈ ℜ . Let ν is the bump function supported on [−ε , ε ] t

t

ν (t ) = r ( )r (− ) . ε ε And bn is the windowing function supported on [− ln ⎧ ⎪ 2 t+ 2 ) ⎪r ( 2 ⎪ ⎪ bn (t ) = ⎨ 1 ⎪ ln ⎪ ⎪ 2 −t + 2 ) ⎪r ( ⎪⎩ 2

Write e j , n =

1 ln

exp(−2iπ j

if if

if

(2) ln l −ε, n +ε], 2 2

ln l − ε,− n + ε) 2 2 ln ln t ∈ [− + ε , − ε ) . 2 2

t ∈ [−

t ∈[

(3)

ln l − ε, n + ε) 2 2

x − an ) . Then, for ∀j , n ∈ Z , the collection ln

u j , n (t ) = bn ( x − cn )e j , n ( x) + υ ( x − an )e j , n (2an − x) − υ ( x − an +1 )e j , n (2an +1 − x) .

(4)

is an orthonormal basis for L2 ( R ) . Let f ∈ L2 ( R) . Expanding fˆ , which is the Fourier transform of f , into the basis u , we have fˆ = fˆ u . Then we take the inverse Fourier transform

∑

j ,n

n, j

n, j

f = ∑ fˆn , j wn , j .

(5)

where wn , j is the inverse Fourier transform of un , j .Obviously, the collection {wn, j , n, j ∈ Z } is an orthonormal basis for f ∈ L2 ( R) . We call wn , j brushlet. Brushlet can be extended to two dimensions case through separable tensor products. Let

∪

j =+∞ j =−∞

[ x j , x j +1 ) and

∪

k =+∞ k =−∞

[ yk , yk +1 ) denote two partitions of R , write

h j = x j +1 − x j and lk = yk +1 − yk , then the sequence wm, j ⊗ wn , k is an orthonormal basis for L2 ( R 2 ) too, namely, the brushlet in two dimensions.

A Brushlet-Based Feature Set Applied to Texture Classification

1177

3 Energy Measures of Brushlet Coefficients Brushlet transform is of multilevel-type structure as wavelet packet, which can be performed using finer and finer tiling in Fourier plane. The brushlet wm, j ⊗ wn , k can extract effectively orientation information of texture. In fact, wm, j ⊗ wn , k is an oriented pattern oscillating with the frequency (( x j + x j +1 ) 2, ( yk + yk +1 ) 2) and localized at (m h j , n lk ) . The size of the pattern is inversely proportional to the size of the analyzing window, h j × lk in the Fourier space. For the one-level extension, the Fourier plane is divided into four quadrants denoted by Q1i ( i = 1, 2,3, 4 ) first. Then, each one of four quadrants is expanded into four sets of brushlets having the parameter set as follows: x0 = −128, x1 = 0, x2 = 127 and similarly y0 = −128, y1 = 0, y2 = 127 (for the case image is of size 256 × 256 ). The four sets of brushlets have the orientation (π 4) + k (π 2) , k = 0,1, 2,3 , as shown in Fig.1. (a). Since the input image is real, the coefficients are antisymmetric with respect to the origin. When expanding function in L2 ( R 2 ) into two-level brushlet, each quadrant of Q1i ( i = 1, 2,3, 4 ), created in the onelevel decomposing, is divided into four quadrants again. So, sixteen quadrants are created, denoted by Q2i , i = 1, 2...16 , then the brushlet coefficients in each Q2i is expanded into orthonormal basis um, j ⊗ un , k . The sixteen sets of brushlet have twelve different orientations as shown in Fig.1. (b). The orientations (π 4) + k (π 2) , k = 0,1, 2,3 are associated with two different orientations. Note that the sixteen quadrants of brushlet coefficients are antisymmetric with respect to the origin again, as the same as one-level decomposing of brushlet.

(a)

(b)

Fig. 1. (a) Orientation of one-level brushlet extension (b) Orientation of two-level brushlet extension

Since the 2-D brushlet is orthonormal basis in L2 ( R 2 ) , obviously, for ∀f ∈ L2 ( R 2 ) we have the Parseval relation

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f

2 2

= ∑ fˆn , j n, j

2

.

(6)

2

where fˆn, j is the brushlet coefficients being the same as in (5). We define an energy measure as El ,i =

∑

2

fˆn , j (k1 , k2 ) , which is used to represent

k1 , k2

the energy of the ith quadrant of the lth level decomposing, where k1 , k 2 is the index of brushlet coefficient in each quadrant. Therefore, we have

E= f

2 2

= ∑ El ,i for ∀l .

(7)

i

Our strategy is to compute the energy measures associated with each quadrant first. The energy pattern distributed in brushlet domain should provide unique information and support a representation for texture classification. Thus, a features vector for texture classification consists of a set of energy values. Due to the antisymmetric of the brushlet coefficients, we only compute the energy measure of upper half of Fourier plane. Consequently, in the case of one-level decomposing, the energy feature vector of dimension 2 is obtained; in the case of two-level decomposing, a feature vector of dimension 8 is obtained; and in the case of l level decomposing the dimension of the feature vector is 2 × 4l −1 . Exactly as the techniques based on wavelet, one can also define different energy measure as the texture feature, for example, the Norm1 Energy 1 N Measure, E = ∑ CK . N k =1

4 Experimental Results Experiments are carried out to test the performance of energy measures of brushlet for texture classification. Focusing on the effectiveness of the energy measure itself as texture features, the simple classifier, K-NN is used. And the experiments are carried out on test data set from the Brodatz album, which consists of 112 natural textures. Each texture has been digitized, and was stored as a 640 × 640 , 8 bit/pixel digital image. In our experiment, each of the selected texture is divided into 25 nonoverlapping subsamples of size 128 × 128 , 10 for training and 15 for test. Note many of the textures in the Brodatz album are not homogeneous, which usually contaminate the performance of classification algorithm seriously [11]. In some sense, the existing of these textures makes the comparison between different algorithms insignificant. Some examples of such textures are shown in Fig.2. By removing 34 inhomogeneous texture images from the whole album, a test data set of 78 textures is created. And the whole test data set is of 1950 subsamples. The 34 removed texture is listed as follows: D005, D007 D013, D030, D031), D036, D038, D040, D042, D043, D044, D045, D054, D058, D059, D061, D063, D069, D079, D080, D088, D089, D090, D091, D094, D096, D097, D098, D099, D100, D102, D103, D106, D108, D110.

A Brushlet-Based Feature Set Applied to Texture Classification

1179

Fig. 2. Examples of inhomogeneous textures in Brodatz album Row 1: D042, D043, D044, D045, Row2: D058, D059, D090, D091

Table 1. 78 textures classification accuracy with Norm1 Energy Measure based on different decomposing method

Brushelt based energy measures

DWT based energy measures

UDWT based energy measures

93.33%

90.85%

92.48%

For comparison, the energy measures based on decimated and undecimated wavelet transform (DWT and UDWT) with three-level decomposing are used for texture classification too. And the wavelet energy measures with Norm1 Energy Measure is extracted from the channels of the wavelet decomposition, as was widely used in the literature for texture analysis [5][6][7]. The Daubechies-6 filter is used for both DWT and UDWT. The results of classification are summarized in Table.1. The experimental results show that the performance of energy measures of brushlet outperforms that of the other two substantially.

5 Conclusion The performance of brushlet for texture image classification is investigated in this paper. And we have described how the energy measures of brushlet provide efficient features for texture image classification. And the high performance of the new texture feature results from more orientations provided by brushlet coefficients. As has demonstrated by experiments, the new textual features work better than that based on wavelet energy measure. Undoubtedly, Brushlet provides a new mathematic tool for image processing. Other potential application includes texture segment, object identification and image fusion etc.

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References 1. Robert, M.H., Shanmugan, K., Dinstein, I.H.: Texture Feature for Image Classification. IEEE Trans. on SMC. 6 (1973) 610–621 2. Chellappa, R., Chatterjee, S.: Classification of Textures Using Gaussian Markov Random Fields. IEEE Trans. on ASSP. 4 (1985) 959–963 3. Mao, J., Jain, A.K.: Texture Classification and Segmentation Using Multiresolution Simultaneous Autoregressive Models. Patt. Recog.. 2 (1992) 173–188 4. Teuner, A., Pichler, O., Hosticka, B.J.: Unsupervised Texture Segmentation of Images Using Tuned Matched Gabor Filters. IEEE Trans. on Image Processing. 4 (1995) 1549– 1560 5. Chang, T., Kuo, C.C.J.: Texture Analysis and Classification with Tree-structured Wavelet Transform. IEEE Trans. on Image Processing. 2 (1993) 429–441 6. Unser, M.: Texture Classification and Segmentation Using Wavelet Frames. IEEE Trans. on Image Processing. 4 (1995) 1549–1560 7. Laine, A., Fan, J.: Texture Classification by Wavelet Packet Signatures. IEEE Trans. on Pattern Anal. Machine Intell.. 15 (1993) 1186–1191 8. Donoho, D.L.: Orthonormal Ridgelets and Linear Singularities. SIAM J. Math Anal. 31 (2000) 1062–1099 9. Pennec, E.L., Mallat, S.: Image Compression With Geometrical Wavelets. IEEE Int. Conf. Image Processing. 1 (2000) 661–664 10. Meyer, F.G., Coifman, R.R.: Brushlets : A Tool for Directional Image Analysis and Image Compression. Applied and Computational Harmonic Analysis. 4 (1997) 147–187 11. Haley, G.M., Manjunath, B.S.: Rotation-Invariant Texture Classification Using A Complete Space-Frequency Model. IEEE Trans. on Image Processing. 8 (1999) 255–269

An Image Analysis System for Tongue Diagnosis in Traditional Chinese Medicine Yonggang Wang, Yue Zhou, Jie Yang, and Qing Xu Institute of Image Processing & Pattern Recognition, Shanghai Jiaotong University, Shanghai, China, 200030 {yonggangwang, zhouyue, jieyang, xuqing}@sjtu.edu.cn

Abstract. We introduced a computer-aider tongue examination system, which can reduce the large variation between the diagnosis results of different doctors and quantize the tongue properties automatically in traditional Chinese medicine (TCM) diagnosis. Several key issues and algorithms in this system are discussed, involving some newly proposed image analysis techniques: i) a new tongue color calibration scheme is proposed to overcome the drawbacks of the previous method; ii) a gradient vector flow (GVF) snake based model integrating the chromatic information of the tongue image is used to extract the tongue body; iii) an unsupervised segmentation method of color-texture regions is adopted to quantitatively analyze the distribution of the substance and the coat on the tongue surface. The experimental results show that the presented system has a great deal of potential for the tongue diagnosis.

1

Introduction

In traditional Chinese medicine (TCM), the examination of tongue is one of the most important approaches to retrieving significant physiological information on human body. TCM doctors use information of the tongue colors, the distribution of the coat, the degree of wetness and the shape of the patient’s tongue to determine his syndrome and body condition. However, the process of tongue diagnosis, highly relying on the subjective experience and knowledge of the doctors or experts, has impeded the development of TCM to some extent. Moreover, most of the precious experience and cases in traditional tongue diagnosis could not be retained quantitatively. Therefore, it is necessary to build an objective diagnosis system for the examination of tongue. Recently, several tongue diagnosis systems [1–3] based on image analysis have been developed for the purpose of the diagnosis and treatment of patients, providing a new research approach for tongue diagnosis characterization. However, these systems do not realize completely automatic analysis of the tongue, i.e. need some tiresomely interactive operations. Moreover, their accuracy in recognizing substance and coat colors in the tongue is usually limited. To overcome these drawbacks, we develop a new automatic tongue diagnosis system based on several newly proposed image analysis techniques in this paper. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1181–1186, 2004. c Springer-Verlag Berlin Heidelberg 2004


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The paper is organized as follows. Section 2 introduces the architecture of our system. Section 3 discusses the image analysis algorithms involved in this system. Section 4 tests the total system and Section 5 contains the conclusions.

2

System Implementation

The system we designed consists of image acquisition part and software part. The image acquisition part provides a stable and consistent sampling environment, which has several main components as follows: light source, color CCD camera, computer and dark chest with face supporting structure. A Canon-G5 CCD digital camera is used without distinct color distortion and with a high resolution of 1024×768 pixels. The camera is mounted to the side of the dark chest, opposite to and on the horizontal line with the face supporting device. Four standard light sources with 5000K color temperature are fixed at the front of the chest. As an image analysis unit, a Dell Dimension8200 workstation is adopted. The software part consists of a tongue image analysis module and a database module. The image analysis module includes various algorithms of tongue image processing, such as color calibration, tongue body extraction, quantitative analysis of the substance and the coat of a tongue, and so on. The database module is established to store and manage tongue images and the patient’s information.

3 3.1

Tongue Image Analysis Color Calibration

The purpose of color calibration here is to keep the consistency and the repeatability of the colors transmitted from camera to monitor. In [4], an online color calibration method integrating color evaluation with colorimetric matching was proposed to calibrate the tongue’s colors. In the work, several consistent color patches are designed and mounted inside the dark chest. They will be recorded simultaneously when any patient’s tongue is captured. To get the standard data of those patches, several subjects’ tongue images are captured and rendered on the monitor together with the patches. The experienced doctors adapt the tristimulus values of the tongue image in order to make the rendered tongue look the same as the real tongue, and thus the patches’ colors are also adjusted together with the tongue. The adapted color values of the patches are extracted and considered as the standard data. For a tongue image to be calibrated, a polynomial model will be established between the color values of the patches in this image and the standard data. Finally, this model will be used to correct the current tongue image. Our scheme is based on this work. In the process of retrieving the standard data, however, the method has the following disadvantages: i) The adapted colors of all patches will lean toward the same orientation when the tongue image is adjusted. The isotropic adaption does not agree with the fact that the patches have different color shifts. ii) Putting the tongue out for a long time will make the subject tired and thereby affect

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the operation. Accordingly, we adapt the rendered color patches directly with the real patches when collecting the standard data. This improvement leads to nonlinear shifts of the patches’ color values and a flexible operation. Parts of color patches which we use are shown in Fig. 1. These patches, designed by the experienced doctors, contain most of the usual colors of the substance and the coat. They will be used in the following process of tongue color recognition too.

Fig. 1. Parts of color patches

3.2

Tongue Body Extraction

In the computerized tongue analysis, extracting the tongue body automatically and correctly out of its background is critical to the further processing. Unfortunately, due to the weak edge and the color similarity between the tongue and the lip, the traditional methods, e.g. region growing and gradient based edge detection, fail to segment the whole tongue body. Recently, active contour or snake models, incorporating a global view of edge detection by assessing continuity and curvature, have been utilized to extract the tongue body [3, 5]. In [3], a dual-snake model was proposed to deal with the initialization problem existing in the original snakes. The model was tested through an experiment with 400 tongue images and the correct rate came to 88.89%. Pang et al. [5] suggested a bi-elliptical deformable contour (BEDC) scheme for tongue segmentation, which combined a bi-elliptical deformable template and an active contour model. Due to the nature of the snake models, these methods i) still depend on the subjective interference, ii) neglect the color information in tongue image, and iii) have limited accuracy. In our work, we propose a new model based on chromatic partition and gradient vector flow (GVF) snake. At first, chromatic information is used to differentiate tongue from lip and face skin in a coarse scale. Then we adopt the GVF snake to further find the exact edge of the tongue. The GVF snake is a novel snake model proposed recently by Xu and Prince [6], which can effectively solve the two main problems of the original snakes, i.e. sensitivity to initial contour and poor convergence to boundary concavities. 3.3

Quantitative Analysis of Substance and Coat

In the tongue image, the colors of the tongue substance can be classified into light pink, rose pink, red, purple, etc. while the coat colors can be classified into white, yellow, brown, black, etc. Generally, a tongue body image is divided into five parts as shown in Fig. 2. According to the TCM principles, the condition of the different parts indicates the heath information of their corresponding organs of human body. The purpose of quantitative analysis here is to estimate the distribution of substance (and coat) of each color class in each part of the tongue. Most researches have adopted supervised classifiers, e.g. SVM and supervised

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Fig. 2. Five parts of a tongue corresponding to the health condition of different organs

FCM [2, 4], to recognize the colors of the tongue image. These classifiers omit the spatial correlation in the tongue image so as to have poor classification accuracy. Moreover, a great number of samples are required to train the classifiers. It can be observed that the tongue image is a typical kind of color-texture image and has locally different color distribution. Following this logic, we partition a tongue image into various regions, each of which has homogenous properties such as colors and textures. Then we represent the colors in each region quantitatively so that the distribution of the substance and the coat can be obtained. JSEG is a new method for unsupervised segmentation of color-texture images presented by Deng and Manjunath [7]. This method involves two steps: color quantization and spatial segmentation. After the first step, the image pixels are represented by their corresponding color class labels. In the second step, a criterion for “good” segmentation is applied to local windows in the class-map, resulting in the so called “J-image”. A region growing method is then used to segment the image based on the multiscale J-images. For each homogenous region obtained through applying the JSEG to the tongue body image, we determine its color class label by virtue of those color patches mentioned in the color calibration section. The minimum distance classifier is used after calculating the statistics between each patch and the region. Finally, we cover the mask given in Fig. 2 on the tongue image and thereby, the color distribution of the substance and the coat will be achieved.

4

Experimental Results

We have developed a prototype implementation of the system and applied it to some samples randomly chosen from our database. The database contains thousands of tongue images. In this section, we will present some useful results.

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Fig. 3. A color calibration example: (a) an original tongue image and (b) its result

(a)

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Fig. 4. (a) is an original tongue image; (b), (c) and (d) are the results obtained through tongue body extraction, JSEG-based partition and color recognition of the substance and the coat, respectively

The results through the color calibration method proposed in this paper basically satisfy the TCM doctors who evaluate the system. Fig. 3 is an example of color calibration. Obviously, the original tongue image with a color shift to red has been corrected very well. In our segmentation experiments, the satisfactory results account for about 93% of the total 1500 tongue images. We also carry out color recognition and quantitative analysis of the substance and the coat with these tongue images. More than 90% recognition results are satisfactory when compared with the results determined by doctors. Fig. 4 shows the results through applying the techniques of tongue extraction, JSEG-based partition and recognition of substance and coat colors, respectively, to a sample image. Note that in Fig. 4, we use pseudocolors to represent different types of substance and coat.

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Conclusions

We have developed a tongue diagnosis supporting system based on image analysis. The system can provide lots of important information for tongue diagnosis in traditional Chinese medicine. Several key issues in tongue image analysis are described, namely, color calibration, tongue body extraction and quantitative analysis of the substance and the coat. The experimental results show that the system has a great deal of potential for computerized tongue diagnosis. In the next stage, pulse state information will be integrated with the tongue analysis to provide a qualitatively diagnostic result.

References 1. Chiu, C.C.: A novel approach based on computerized image analysis for traditional chinese medical diagnosis of the tongue. Computer Methods and Programs in Biomedicine 61 (2000) 77–89 2. Zhao, Z.X., Wang, A.M., Shen, L.S.: An automatic tongue analyzer of chinese medicine based on color image processing. In: The 4th Int. Conf. on Electronic Measurement and Instruments Conf. Proc., Harbin, China (1999) 830–834 3. Wang, Y.G.: Research on pragmatizing the tongue image analysis instrument of traditional chinese medicine. Master’s thesis, Beijing Polytechnic University (2001) 4. Wang, Y.G., Wang, A.M., Shen, L.S.: A study of colour reproduction method of colour image. China Illuminating Engineering Journal 12 (2000) 4–10 5. Pang, B., Wang, K., Zhang, D., et al: On automated tongue image segmentation in chinese medicine. In: IEEE Int. Conf. on Image Processing. Volume I., Rochester NY (2002) 616–619 6. Xu, C., Prince, J.L.: Snakes, shapes, and gradient vector flow. IEEE Trans. on Image Processing 7 (1998) 359–369 7. Deng, Y., Manjunath, B.S.: Unsupervised segmentation of color-texture regions in images and video. IEEE Trans. on Pattern Anal. and Machine Intell. 23 (2001) 800–810

3D Mesh Fairing Based on Lighting and Geometric Conditions for Interactive Smooth Rendering Seung-Man Kim and Kwan H. Lee Gwangju Institute of Science and Technology(GIST), 1 Oryong-dong, Puk-gu, Gwangju, 500-712, South Korea {sman, lee}@kyebek.kjist.ac.kr

Abstract. In this paper, we propose a fairing method of 3D rough meshes based on illuminations and geometric conditions for smooth rendering. In applications of interactive graphics such as virtual reality or augmented reality, rough meshes are widely used for fast optical interactions owing to their simple representation. However, in vertex-based shading, rough meshes may produce non-smooth rendering results; Distinct normal vectors and comparatively longer distance between consecutive vertices increase the difference of radiances. In order to improve the smoothness of the rendering results, the difference of radiances among vertices should be minimized by considering lighting conditions as fairing parameters. We calculated illuminations using diffuse lighting models at each vertex. Then normalized illumination is linearly integrated with the curvedness to prevent the shape distortion. By adapting integrated values to Laplacian weight factors, the difference of radiances is minimized and rendering result is improved, while maintaining the important curved shapes of the rough meshes. The proposed method also improves the compactness of triangles. The comparative study of our method with other existing fairing schemes has been discussed. We also applied our method to arbitrarily simplified meshes for demonstration.

1 Introduction With the technological advancement of 3D scanners, scanned models are being widely used for several areas of computer graphics and geometric modeling. However the complexity of meshes has increased much faster than the advancement of graphics hardware techniques. Because of hardware limitations, it is necessary to reduce the amount of data by simplifying dense meshes in order to display geometric meshes in real time. Unlike previous studies that consider only geometric conditions, we propose a lighting dependent fairing method for rough meshes, which is constrained by a curvature-based curvedness. Many fairing algorithms are based on the concept of Laplacian since the storage and computational cost are almost linearly proportional to the number of vertices[1,2,3,4,5]. Also geometric conditions, such as valences, parameters of the transfer function, edge lengths and triangle areas, are used as weight factors to keep the shrinking problems from occurring during mesh fairing. Although the rough meshes, espeJ. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1187–1194, 2004. © Springer-Verlag Berlin Heidelberg 2004

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cially simplified ones, are well faired based on geometric conditions, non-smooth rendering may occur, since simplified meshes have different levels of importance determined by lighting conditions in the rendering process. The importance level means the difference of radiances between vertices. The region where radiances have a high variation in the mesh has a higher level of importance. In a vertex-based rendering, the radiance computed at each vertex corresponds to the color of the vertex and inner pixels of the triangle are interpolated from the color of its vertices. High difference of radiances causes undesirable rendering effects to the inside triangles of meshes, especially in highly simplified meshes. Klein[6], Xia[7] proposed illumination dependent refinement method of multiresolution meshes. The method considered only the normal deviation between different levels of detail as refinement metric in the simplification process. If meshes are faired based on only geometric conditions, triangles in the region of the high importance can be ignored during mesh fairing or vice versa. In addition, simplified meshes have discrete structures and they consist of a small number of triangles, so that they have much higher difference of radiances than dense meshes. Therefore, for smooth rendering with simplified models in real time, we propose a new fairing method that considers lighting conditions as well as geometric conditions.

2 Lighting Dependent Fairing with Geometric Constraints 2.1 Lighting Conditions Radiances are used to render the objects with two separated components of a specular and a diffuse term. We have chosen the Phong shading model and Lambertian(ideally diffuse) reflection properties due to its simplicity[8]. Equation(1) represents radiances that consider only the diffuse reflection. G G 1 k d md I j ni • li , j 2 j =1 ri , j

{

n

Li = ∑

(

)}

(1)

In equation(1), Li is the radiance at vertex pi on the meshes, kd is the diffuse reflection coefficient, md is material properties of the object representing the color value, Ij G is the intensity of light sources and G n is the number of light sources. And ni represents a normal vector at each vertex, li , j is the unit directional vector from vertex pi to the light source(j), and ri,j is the distance between a vertex and a light source. We assume that objects are Lambertian surfaces and a point light source is used for the convenience of visual comparisons, hence the radiance can be defined as below: G G I ni • li Ei = ri 2

(

)

(2)

Here, kd is set to 1 since surfaces are purely diffuse and md is assumed to have a uniform value(here set to 1). From the assumption, radiances(L) are determined by irradiance(E) that is proportional to the light intensity and the inverse of the squared

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distance(inverse square law). It is also highly affected by the angle of inclined surfaces(cosine’s law) in terms of normal vectors and directional lighting vectors. 2.2 Geometric Constraints While lighting conditions are used as fairing weights, the fairing metric is constrained by the curvedness in order to prevent an undesirable distortion or a loss of important curved shapes. By using the constraint of the curvedness, the movement of vertices in high curvature regions is restricted, since the curvedness represents curved areas in the meshes. In order to use the curvedness R = (κ 12 + κ 22 ) / 2 as the constraint of the fairing metric, we should compute the sum of squared principal curvatures κ1 and κ2. The curvature might not be defined at vertices properly because meshes are actually comprised of flat triangles, i.e., the mesh is not C2differentiable. Therefore we assume that the mesh is a piecewise linear approximation of an unknown continuous surface. The curvatures can be estimated only by using information of the triangular mesh itself[9]. Instead of calculating principal curvatures directly to get the curvedness, we compute the Gaussian curvature K=κ1κ2 and the mean curvature H=(κ1 +κ2)/2 since the curvedness can be expressed by R = 2 H 2 − K . The Gaussian curvature of a vertex is related to angles and face areas that are connected to that vertex. The mean curvature H is derived by applying Steiner formula to the triangulated polyhedral surface [10] as shown in Fig. 1.

Fig. 1. Geometric parameters

Here, A is the sum of neighboring triangle’s area(fi) of a vertex, k is the number of neighboring faces, and φ represents the angle at a vertex. ei is a length of the edge, and di is determined by a dihedral angle which can be calculated at edge ei using normal vectors of two adjacent triangles.

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2.3 Modified Laplacian Fairing Operator Laplacian fairing techniques are generally based on the membrane energy minimization. For a parametric surface S:P=P(u,v), the membrane energy functional(Em) is: 1 Em ( S ) = ∫ (Pu2 + Pv2 ) dS 2 S Where, u and v are parameters of parametric surface(S). In minimizing the membrane energy functional, its derivatives correspond to the Laplacian operator L(P): L ( P ) = Puu + Pvv . For a discrete mesh, the Laplacian operator L(Pi) at vertex pi can be linearly approximated[11]. ni −1

L( pi ) = wi , j ∑ ( p j − pi ) i =0

wi,j is general Laplacian weight factors and pj is neighboring vertices of pi and ni is the number of vertices in the mesh. For each vertex, a lighting dependent weight wi is defined by the linear combination of the normalized curvedness(R) and irradiance(E) in equation(3).

wi = µ

Ei R + (1 − µ ) i , 0 ≤ µ ≤ 1 E max Rmax

(3)

Emax and Rmax are the maximum value of E and R respectively. µ is the weight parameter that controls lighting effects and geometric constratins. Newly defined fairing operator L(pi) and a faired vertex(p'i) are in equation(4).

L( pi ) =

1 n−1 ∑ wi, j ( p j − pi ) , pi′ = pi + λL( pi ) wsum j=0

(4)

n −1

where wi , j = wi − w j , w = ∑ w and wi , j ≥ 0 . sum i, j j =0

wi,j is the difference of weights at each edge which consists of a vertex and its neighboring vertex, and n is the number of neighboring vertices of pi. wsum is the summation of all wi,j.

Fig. 2. Schematic diagram of lighting dependent fairing for rough meshes

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Fig. 2 shows a schematic diagram of mesh fairing that minimizes the difference of irradiances. The operator L(pi) gathers the vertices in the direction of the marked arrows shown in the figure into the region where the difference of irradiance is high.

3 Results and Comparisons We implemented our proposed method using Visual C++ and OpenGL graphics library on Window 2000 platform with Pentium 4 processor(1.5GHz, 512 memory). In order to manage arbitrary mesh data, an efficient data structure is necessary for a fast access to geometric information and connectivities. A half-edge data structure has been widely used for arbitrary meshes [12]. It provides fast, constant-time access to one-ring neighborhood of a vertex. Since the half-edge stores the main connectivity information and always has the same topology; vertices, edges and faces are types of constant size [13]. In the experiment, geometric conditions such as the Gaussian curvature, the mean curvature and the curvedness are computed at compile time in order to reduce a computational load in run time since those parameters are fixed. Whereas, since lighting conditions change dynamically, the computation of lighting conditions and the fairing process are performed at run time as shown in Fig. 3.

Input Input rough rough mesh mesh

Compute parameters Gaussian Gaussian curvature curvature Mean Mean curvature curvature Curvedness Curvedness Irradiance Irradiance

Compute Compute Laplacian Laplacian weights weights

Lighting Lighting dependent dependent Laplacian Laplacian fairing fairing

Fig. 3. Flowchart for implementation of lighting dependent mesh fairing

We applied the lighting dependent fairing method to the simplified Stanford bunny model with 800 vertices. Fig. 4 shows fairing results according to the weight parameter(µ). Fig. 4(b) shows fairing weights are determined by the curvedness only, and fig. 4(c) by only radiances. In the experiment, by setting the weight parameter as 0.5 heuristically(fig. 4(d)), we can keep the bunny model from being distorted and appearing small cracks. As a result, the rendering result shows a smoother surface. In Fig. 5, we set up the weight parameter(µ) and the scaling factor(λ) to 0.5 and 0.7 respectively. The wireframe model of the bunny clearly shows our results with better compactness of triangles, especially in the leg of the bunny. Overall shape is also refined and improved smoothly. In the case of the textured bunny, the mesh is spherically parameterized and mapped by uniform shape of a texture. In the original textured bunny, the textured images are distorted where the triangles of the bad compactness occur. However for the bunny faired by our method, the distortion decreases since the compactness of triangles is refined by minimizing the difference of the radiance.

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(a)original

(b)µ=1

(c)µ=0

(d)µ=0.5

Fig. 4. Fairing results by weight parameters(µ)

(a) Original bunny model

(b) Faired model Fig. 5. Fairing results in enhanced rendering quality and parameterization

Fig. 6 shows the computation time for different level of details for the bunny model. The computation time linearly depends on the number of vertices. Based on the graph, the proposed method can be applicable to real time visualization. We compared our results with different methods(the Laplacian flow, mean curvature flows, and Loop subdivision). Laplacian flow method improves geometric smoothness, but there are problems such as shape shrinkage and loss of details. In order to improve smoothness, our method also prevents from distortion of the shape by using the curvedness as fairing constraints. Fig. 7 shows numerical comparison results by the subdivision sampling scheme [14] that is used to compare the distance between a faired mesh and an original one. The diagonal length of bunny’s bounding box is 0.658mm.

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Fig. 6. Computation time

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Fig. 7. Numerical comparisons

4 Conclusions We have proposed a new, lighting dependent fairing method to improve the quality of rendering by enhancing the smoothness of meshes. We use weighted Laplacian to minimize the difference of radiances between consecutive vertices. In addition, the curvedness is used as constraints for retaining curved parts of the meshes. By applying our method to arbitrarily simplified meshes, the rendering result is improved along with triangle’s compactness. As a result of advanced compactness, the distortion of textures is reduced. Our method adopts a half-edge data structure and the Laplacian operator that supplies constant time access to one-ring neighborhood vertices. The proposed fairing method can be used for real time applications. The proposed method can be further developed by optimizing the determination of the weight parameter and the scaling. It is also desired to use the estimated lighting conditions from the real world as weight factors for realistic rendering.

References 1. Taubin, G.: A Signal Processing Approach to Fair Surface Design. SIGGRAPH 95 Proceedings (1995) 351-358 2. Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.-P.: Interactive Multi-resolution Modeling on Arbitrary Meshes. SIGGRAPH 98 Proceedings (1998) 105-114 3. Fujiwara, K.: Eigenvalues of Laplacians on a Closed Riemannian Manifold and its Nets. Proceedings of the AMS, 123 (1995) 2585-2594 4. Desbrun, M., Meyer, M., Schroder, P., Barr, A.H.: Implicit Fairing or Irregular Meshes Using Diffusion and Curvature flow. SIGGRAPH99 Proceedings (1999) 317-324 5. Guskov, I., Sweldens, W.: Multiresolution Signal Processing for Meshes. SIGGRAPH 99 Proceedings (1999) 324-334 6. Klein, R., Schilling, A., Straßer, W.: Illumination Dependent Refinement of Multiresolution Meshes. In Proceeding of Computer Graphics International, IEEE Computer Society Press (1998) 680-687 7. Xia, J.C., Jihad, E., Varshney, A.: Adaptive Real-Time Level-of-detail-based Rendering for Polygonal Models. IEEE Transactions on Visualization and Computer Graphics, Vol. 3. No. 2 (1997) 8. Moller, T. A., Haines, E.: Real-time Rendering 2nd Edition. A K Peters (2002)

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9. Dyn, N., Hormann, K., Kim, S.J., Levin, D.: Optimizing 3D Triangulations using Discrete Curvature Analysis. Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, Nashville (2000) 135-146 10. Lyche, T., Schumaker, L.: Mathematical Methods for Curves and Surfaces. Vanderbilt University Press (2001) 135-146 11. Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., Stuetzle, W.: Multiresolution Analysis of Arbitrary Meshes. SIGGRAPH 95 Proceedings (1995) 173-182 12. Lutz, K.: Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces. Proc. 14th Annual ACM Symp. on Computational geometry (1998) 13. Botsch, M., Steinberg, S., Bischoff, S., Kobbelt, L.: OpenMesh-a Generic and Efficient Polygon Mesh Data Structure. OpenSC Symposium (2002) 14. Cignoni, P., Rocchini, C., Scopigno, R.: Metro : Measuring Error on Simplified Surfaces. Computer Graphics Form, Vol. 17. No. 2. (1998) 167-174

Up to Face Extrusion Algorithm for Generating B-Rep Solid Yu Peng1 , Hui Zhang2 , Jun-Hai Yong2 , and Jia-Guang Sun1,2 1

Department of Computer Science and Technology, Tsinghua University, Beijing 100084, P. R. China [email protected] 2 School of Software, Tsinghua University, Beijing 100084, P. R. China Abstract. Up to face extrusion (UTFE) is an effective operation to extrude the profile from a sketch plane to a selected face. An up to face extrusion algorithm is presented in this paper. The algorithm first generates the trimmed extrusion through a simple body-surface Boolean operation method, and then generates the resultant solid through a regularized Boolean operation between the original solid and the trimmed extrusion. The algorithm has been implemented in a commercial geometric modeling software system TiGems. Examples are given to illustrate the algorithm.

1

Introduction

Feature-based design emerges as the fundamental design paradigm of geometric model systems. In feature-based geometric modeling system, the user designs with a vocabulary of design elements that are grouped into proto-features based on a planar profile, such as protrusion and cut. When the proto-feature is generated, the resultant solid is built using regularized Boolean operations and the feature operators, i.e., a protrusion is the regularized union, and a cut is the regularized subtraction. Let S be a closed profile in the sketch plane P. S consists of a set of closed planar curves defining the interior and exterior. The extrusion of S is defined to a solid obtained as follows. The profile S is swept perpendicularly to P, up to a parallel plane P
, resulting in one or more ruled surfaces which we called side face(s). The interior of the contour in P and in P
defines the planar faces that, together with the side faces, bound a solid. A blind extrusion is determined by a dimension d specifying the depth of the extrusion and a direction paralleling the normal of the sketch plane. Up to face extrusion (UTFE) is an operation that extrudes the profile from the sketch plane to the selected face. Chen et al. [3] presented an algorithm to build ‘from-to feature’, which is a sweep that begins at a face designated as ‘from’ and ends at a face designated ‘to’. In their algorithm, the direction of extrusion must be given by user explicitly, and the method for extending curved surfaces are not given when the ‘from face’ or the ‘to face’ does not completely intersect the generated feature. Fig. 1 gives an example of UTFE. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1195–1200, 2004. c Springer-Verlag Berlin Heidelberg 2004 

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S2

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S1

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Fig. 1. Up to face extrusion: (a) Original solid. (b) Planar curves S1 , S2 and selected face F. (c) Trimmed extrusion. (d) Resultant solid after UTFE

This paper gives a new UTFE algorithm. The direction of extrusion is determined automatically, and the method of face extension is proposed. A bodysurface Boolean operation algorithm is also presented. In this paper, a solid is assumed to be 2-manifold using B-rep, i.e., it is closed topologically and has no isolated faces or edges. Each face of the solid has a surface geometrical data to represent its geometrical shape, and a set of loops (one counterclockwise outer loop and several clockwise inner loops) in 2D parameter domain of the surface to define its boundary. In UTFE, the generated proto-feature is a trimmed extrusion (see Fig. 1(c)), whose top face has the same surface geometrical data as the selected face. The main features of our algorithm are the following. • Generate the trimmed extrusion. • Generate the resultant solid using the Boolean operations between the original solid and the trimmed extrusion. The second step addresses the problem of regularized Boolean operations on two solids, which is outside the scope of this paper but can be found in references [1, 8, 9, 11]. Therefore, we only discuss the first step in the remainder of the paper. In order to generate the trimmed extrusion, we first generate a blind extrusion with a large depth. The blind extrusion has the same direction as the UTFE, and the depth of the extrusion is large enough to intersect the selected face. The selected face should be extended if it does not completely intersect the blind extrusion. There are three problems in trimmed extrusion generation. The first one shows how to choose the direction and the depth. The second one shows how to extend the selected face. The last one shows how to generate the trimmed extrusion through the trimmed curves and trimmed surface. In the following sections, each problem is explained in detail.

2

Compute Extrusion Direction and Depth

We call the bottom planar face of a blind extrusion a base face, which is bounded by the curves in the sketch plane. A feature line of a blind extrusion is defined by P(t) = P0 + N · t, where t ∈ (−∞, +∞), P0 is an arbitrary point which lies on a curve of the base face, and N is the normal vector of the sketch plane.

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Likewise, we define a feature line to represent the selected face. The feature line of a selected face depends on its geometrical surface data. We illustrate the feature lines of some analytic surfaces shown in Fig. 2, respectively. The feature line of plane surface is the projection of the feature line of the selected face (see Fig. 2(a)). The feature line of cylinder surface coincides with the central axis of cylinder (see Fig. 2(b)). The feature line of sphere surface goes through the centre of sphere and is perpendicular to the feature line of the corresponding blind extrusion (see Fig. 2(c)). We find a point P1 on the feature line of the blind extrusion and a point P2 on the feature line of the selected face, where the distance between P1 and P2 equals the distance between the two feature lines. Thus, the direction of the blind extrusion is defined by N1 = P1 − P0 . The distance between P0 and P1 is denoted by d. In this paper, the depth of blind extrusion is given by 2d + f (s), where f (s) is a function with respect to the selected face. For example, f (s) equals zero for plane surface, the radius of circle for cylinder surface, and the radius of sphere for sphere surface. Fig. 3 shows an example of a blind extrusion generation with respect to a plane surface, and P1 coincides with P2 in this case.

l1 N O

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Fig. 2. Feature lines of analytic surfaces are denoted by l1 , and feature lines of blind extrusions are denoted by l2 . The normal vector of plane is denoted by N, and the center of sphere is denoted by O. (a) Feature line of plane surface. (b) Feature line of cylinder surface. (c) Feature line of sphere surface F

l2 l1

P2 P1

2d

d

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Fig. 3. Blind extrusion generation: Feature line of selected face is denoted by l1 , and feature line of blind extrusion is denoted by l2 . (a) Planar curves S1 , S2 and selected face F. (b) Calculation of direction and depth. (c) Blind extrusion

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Face Extension

The method of face extension depends on the geometrical surface data of the face. It should be noted that, unlike the faces of analytic surfaces, there is no unique way to extend faces of free-form surfaces. For this reason, the free-form face extension is not handled in this paper. We handle the plane surface extension and some conic surface extensions. The examples of face extension are shown in Fig. 4. The selected face of each example is denoted by F, and the planar curves are denoted by S. For a plane surface F as shown in Fig. 4(a), we project the 2D bounding box, which includes all the curves of sketch plane, onto the selected plane in the direction of the blind extrusion. The extended face is defined by a face, which is bounded by the projected 2D bounding box (see thick black rectangle in Fig. 4(a)). For a cylinder surface F as shown in Fig. 4(b), we first calculate the bounding box of the blind extrusion (see gray cuboid wire-frame in Fig. 4(b)). Next we translate the feature line l1 of the selected cylinder surface, where the translated line l2 goes through P1 defined in Section 2. Then we project l2 onto top face of the bounding box (see l3 in Fig. 4(b)) and calculate Q1 and Q2 on l3 . Finally we project Q1 and Q2 onto l1 and get Q
1 and Q
2 . The extended face is bounded by two circles, which uses Q
1 and Q
2 as two centers, respectively. Note that a sphere surface bounds a closed region, so we use the boundary of the entire surface in 2D parameter domain as the boundary of the extended face (see Fig. 4(c)).

F

F

F Q1

Q2

Q '1

P 2 Q '2 P1

l3 l1 l2

Q1 Q 2 l3

S

S

S

P0

(a)

(b)

(c)

Fig. 4. Face extension for plane surface, cylinder surface and sphere surface: (a) Extended face bounded by thick black rectangle. (b) Extended face bounded by thick black cylinder wire-frame. (c) Extended face bounded by thick black sphere wire-frame

4

Body-Surface Boolean Operations

Before the body-surface Boolean operation, we should determine whether the UTFE is illegal. We project the contour of the extended face onto sketch plane. If the projected contour contains all curves of the sketch plane, the UTFE is legal. Otherwise the UTFE is illegal. The side faces of the blind extrusion are denoted by Fi , where 1 ≤ i ≤ n, n is the number of the faces of the blind extrusion

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solid. In the literature, extensive research have resulted in grand algorithms for Boolean operations on surfaces or non-manifold solid [4, 7, 10]. In this paper, the body-surface Boolean operation consists of three steps. 1. Calculate the trimmed intersection curves between Fi and the extended face and form loops in 2D parameter domain for them. 2. Subdivide Fi and the extended face to some trimmed faces by the loops and classify the trimmed faces of the extended face. 3. Generate the trimmed extrusion. The first step addresses the problem of curve/surface and surface/surface intersection, which is outside the scope of this paper but can be found in references [2, 5, 6]. In Step 2, we create the trimmed faces by the loops obtained in Step 1. Each trimmed face includes an outer loop and several inner loops and has the same geometrical surface data as the original face. Every trimmed face of the extended face is classified into one of the following three types based on inclusion relation with respect to the closed region of the blind extrusion: Class In, Class Out, Class On. Now we describe the third step in more detail. We use a face array to store the bounding faces of the trimmed extrusion. First, we add the base face to the face array. Next, for each trimmed face of Fi , we add the trimmed face, which shares one bounding edge of the base face, to the face array. Finally, for each trimmed face of extended face that is classified by Class In, we search for the one that is nearest to the base face of the blind extrusion. Add the nearest trimmed face to the face array. Thus, the trimmed extrusion is obtained through the face array.

5

Examples and Conclusions

The algorithm has been implemented in a commercial geometric modeling software system TiGems and greatly enhances the capability for creating an extrusion feature. Fig. 5 shows two examples of UTFE using our algorithm.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 5. Examples of UTFE: (a)-(c) is an example of up to sphere surface extrusion, and (d)-(f) is an example of up to cylinder surface extrusion. (a) Original solid, selected face and profile. (b) Trimmed extrusion. (c) Resultant solid. (d) Original solid, selected face and profile. (e) Trimmed extrusion. (f) Resultant solid

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We present a UTFE algorithm in this paper. The extrusion direction is determined automatically. The methods of face extension of some analytic surfaces are given, and a simple body-surface Boolean operation algorithm is presented to generate the trimmed extrusion solid.

Acknowledgements The research was supported by Chinese 863 Program (2003AA4Z3110) and Chinese 973 Program (2002CB312106). The third author was supported by a project sponsored by SRF for ROCS, SEM (041501004), and a Foundation for the Author of National Excellent Doctoral Dissertation of PR China (200342).

References 1. Arbab, F.: Set models and Boolean operations for solids and assemblies. IEEE Computer Graphics & Applications 10 (1990) 76-86 2. Barnhill, R. E., Kersey, S. N.: A marching method for parametric surface/surface intersection. Computer Aided Geometric Design 7 (1990) 257-280 3. Chen, X. P., Hoffmann, C. M.: Towards feature attachment. Computer-Aided Design 27 (1995) 695-702 4. Granados, M., Hachenberger, P., Hert, S., Kettner, L., Mehlhorn, K., Seel, M.: Boolean operations on 3D selective Nef complexes: Data structure, algorithms, and implementation. In Proc. 11th Annu. European Sympos. Algorithms, LNCS 2832 (2003) 654-666 5. Krishnan, S., Manocha, D.: Efficient representations and techniques for computing B-Reps of CSG models with NURBS primitives. In:Woodmark J, eds. Set-theoretic Solid Modeling Techniques and Applications. Winchester, UK: Information Geometers Ltd. (1996) 101-122 6. Manocha, D., Krishnan, S.: Algebraic pruning: a fast technique for curve and surface inter section. Computer Aided Geometric Design 14 (1997) 823-845 7. Marcheix, D., Gueorguieva, S.: Topological operators for non-manifold modeling. Proeedings of the Third International Conference in Central Europe on Computer Graphics and Visualisation 1 (1995) 173-186 8. M¨ antyl¨ a, M.: Boolean operations of 2-manifolds through vertex neighborhood classification. ACM Transactions on Graphics 5 (1986) 1-29 9. Requicha, A. A. G., Voelcker, H. B.: Boolean operations in solid modeling: boundary evaluation and merging algorithms. Proceedings of the IEEE 70 (1985) 30-44 10. Satoh, T., Chiyokura, H.: Boolean operations on sets using surface data, ACM SIGGRAPH: Symposium on Solid Modeling Foundations and CAD/CAM Applications, Austin, Texas, USA. (1991) 119-127 11. Zhu, X. H., Fang, S. F., Bruderlin, B. D.: Obtaining robust Boolean set operations for manifold solids by avoiding and eliminating redundancy. In: Proceedings of the 2nd ACM Symbosium on Solid Modeling, Montreal, Canada (1993)

Adaptive Model-Based Multi-person Tracking Kyoung-Mi Lee Department of Computer Science, Duksung Women’s University, Seoul 132-714, Korea [email protected] http://www.duksung.ac.kr/~kmlee

Abstract. This paper proposes a method for tracking and identifying persons from video image frames taken by a fixed camera. The majority of conventional video tracking surveillance systems assumes a likeness to a person’s appearance for some time, and existing human tracking systems usually consider short-term situations. To address this situation, we use an adaptive background and human body model updated statistically frame-by-frame to correctly construct a person with body parts. The formed person is labeled and recorded in a person’s list, which stores the individual’s human body model details. Such recorded information can be used to identify tracked persons. The results of this experiment are demonstrated in several indoor situations.

1 Introduction With recent advances in computer technology real-time automated visual surveillance has become a popular area for research and development. In a visual surveillance system, computer-based image processing offers means of handling image frames generated by large networks of cameras. Such automated surveillance systems can monitor unauthorized behavior or long-term suspicious behavior and warn an operator when unauthorized activities are detected [2,3]. However, tracking approaches as applied to video surveillance systems must deal adequately with the problems caused by the non-rigid form of the human body and the sensitivities of such systems to dynamic scenes. Tracking people based on images using a video camera plays an important role in surveillance systems [1,5]. A popular approach of tracking using a fixed camera consists of three steps: background subtraction, blob formation, and blob-based person tracking. To look for regions of change in a scene, a tracking system builds a background model as a reference image and subtracts the monitored scene from the reference frame. However, background subtraction is extremely sensitive to dynamic scene changes due to lighting and extraneous events. Blob formation involves grouping homogeneous pixels based on position and color. However, it is still difficult to form blobs of individual body parts using such spatial and visual information since color and lighting variations causes tremendous problems for automatic blob formation algorithms. The tracking human body parts is performed by J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1201–1207, 2004. © Springer-Verlag Berlin Heidelberg 2004

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relating body parts in consecutive frames [8,9]. Such correspondence-based approaches work well for cases with no occlusion, but are unable to decide upon a person identity if a human body is occluded. In addition, most existing surveillance systems consider only immediate unauthorized behaviors. In this paper, we propose a framework to track and identify multiple persons in a fixed camera situation with illumination changes and occlusion. Section 2 presents an adaptive background model which is updated with on-line recursive updates in order to cope with illumination changes. In Section 3, blob formation at the pixel-level and a hierarchical human body model at blob-level are proposed. During tracking, the proposed human body model is adaptively updated on-line. Section 4 describes, in terms of the blob and human model, multi-person tracking. Experimental results based on several scenarios and conclusions are presented in Section 5.

2 Adaptive Background Modeling To detect moving persons in video streams, background subtraction provides the most complete feature data, but it is unfortunately extremely sensitive to dynamic scene changes due to lighting and other extraneous events. To overcome this situation, during tracking, the reference image should be compensated according to the lighting conditions present in the scene. In this paper, we build the adaptive background model, using the mean ( µ B ) and standard deviation ( σ B ) of the background. At the pixel level, let It represent the intensity value in the t-th frame. At time t, a change in pixel intensity is computed using Mahalanobis distance δ n :

δt =

I t − µ Bt

(1)

σ Bt

where µ Bt and σ Bt are the mean and standard deviations of the background at time t, respectively. µ B0 is initially set to the first image, µ B0 = I 0 , and σ B0 is initialized by 0. For each pixel, Eq. (1) is evaluated to separate background as δ t ≤ θ t , where θ t is a difference threshold observed from the sequence of images prior to t. θ 0 is initially set to the largest distance and multiplied at each time step by a decay constant 0 < γ < 1 until it reaches a minimum. Whenever a new frame I t arrives, a pixel in the frame is tested to classify background or foreground (moving persons). If a pixel satisfies δ t ≤ θ t at time t, the adaptive background model ( µ Bt and σ Bt ) is updated as follows [6]:

µ Bt = α t −1 µ Bt −1 + (1 − α t −1 )I t , and σ = α W + (1 − α t −1

t B

where W = {σ

} + {µ

}

t −1

){µ

t −1 B t −1 B

t B

−I

},

(2)

t 2

. α t −1 = N where N Bt −1 means the number of N +1 frames participating in the background model to time t-1. t −1 2 B

t B

−µ

t −1 2 B

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3 Blob-Based Person Modeling Before tracking persons, they should be initialized when they start to appear in the video. We construct same colored regions from a foreground image and build a hierarchical human body model. In Sec. 4, this person model will be used for tracking and for identification. 3.1 Blob Formation for Person Tracking The foreground image derived from adaptive background subtraction (Sec. 2) is applied to find candidate human body parts. To group segmented foreground pixels into a blob and to locate the blob on a body part, we use a connected-component algorithm which calculates differences between intensities between a pixel and its neighborhoods. However, it is difficult to form perfect individual body parts using such a color-based grouping algorithm since color and lighting variations causes tremendous problems for automatic blob formation algorithms. Therefore, small blobs are merged into large blobs and neighboring blobs that share similar colors are further merged together to overcome over-segmentation generated by initial grouping, which is largely due to considerable illumination changes across the surfaces of coherent blobs. Two adjacent blobs will be merged if the intensity difference is smaller than a threshold. Then, some blobs are removed according to criteria, such as, too small, too long, or too heterogeneous incompact blobs. Each blob contains information such as an area, a central position, a bounding box, and a boundary to form a human body. After completing blob formation, blobs are classified to skin-area and non-skinarea since skin area is important for person detection and tracking. The skin color similarity of a blob Bi is evaluated as follows: P(Bi | skin ) =

∑ P(x | skin)

x∈ Bi

Area(Bi )

(3)

where P(x|skin) is the skin color similarity of a pixel x, which is calculated by [7]. Area(Bi) means an area of Bi defined by a pixel number in Bi. If the skin similarity of a blob is larger than a predefined threshold, the blob is considered a skin blob. 3.2 Human Modeling for Multi-person Tracking As a person can be defined as a subset of blobs, which correspond to body parts, blobs in a frame should be assigned to corresponding individuals to facilitate multiple individual tracking. The person formation algorithm first computes a blob adjacency graph, where each node represents a blob. The criterion of adjacency is based on a minimum distance computed between the associated bounding boxes of each blob. A distance between the vertices of the bounding boxes is computed much faster than adjacency in the pixel domain [4]. The merging criterion between bounding boxes of adjacent blobs is based on a maximum allowed distance. Let P0 be a subset of blobs Bi. The set of potential person areas is built iteratively, starting from the P0 set and its adjacent graph. The set P1 is obtained by merging compatible adjacent blobs of P0.

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(a)

(b)

(c)

(d)

Fig. 1. A hierarchical person model: (a) Bounding region in the high level after background subtraction, (b) three body parts in the middle level, (c) skin blobs in the low level, and (d) a hierarchical human body model applied to a video image frame

Then, each new set of merged blob Pk is obtained by merging the set of merged blob Pk-1 with the original set P0. Finally, a candidate person CPn contains the built sets of merged blob Pk, i.e., CPn = ∪ Kk=0 Pk , n=1…N where N is the number of persons. Each candidate person CPn is formed with a unique label and information on the person, such as, the number of blobs, height, width, centroid, and an adjacent graph of blobs. To match blobs to body parts, we use a hierarchical human model (Fig. 1). First, we assumed that all individuals in the video are upright or in a slightly skewed standing position. The high level of the model contains a whole human model and its information (Fig. 1(a)). After grouping at the pixel-level, each merged blob is displayed as an average color. Depending on the relative position in a candidate person Pk, each blob is assigned to one of three categories in the middle level: the head, the upper body, and the lower body (Fig. 1(b)). If a category in the middle level contains two more blobs, these blobs are tested for skin similarity to classify the blobs as skin or non-skin area at the low level using Eq. (3) (Fig. 1(c)). The person model is defined by 3 categories and their geometrical relations in the middle level, and as 6 classes and their geometrical and color relations in the low level as follows:

( {

}{

}{

CPn = Rn0 , C n1 , Rn1 , C n2 , Rn2 , C n3 , Rn3

})

(4)

0

where R means a relation among three parts. Cnj and Rnj mean a set of blobs and their relationships of the j-th body part of CPn , respectively. 3.3 Adaptive Human Modeling The goal of this paper is to observe existing persons exiting, new persons entering, and previously observed persons re-entering a scene. Since a person is tracked using the model defined by Eq. (4), human body model information is stored to track multiple-persons and to determine whether a specified person has appeared. Even though the total motion of a person is relatively small between frames, large changes

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in the color-based model can cause simple tracking to fail. To resolve this sensitivity of color-model tracking, we compare the current model to a reference human model. During tracking, the reference model should be compensated according to the scenes lighting conditions. Thus, the reference human model has to adapt to slow change such as illumination changes by model updating. To maintain a dynamic environment with continually arriving frames, we use online clustering. Let a person CPnt −1 represented by an average ( µ nt −1 ) and a deviation ( σ nt −1 ), which are computed up to time t-1 and new blobs Bit and their relations Brit are formed in frame t. The minimum difference between the person model CPnt −1 (Eq. (4)) and the new blobs Bit is computed as follows: ⎛ B t − µ t −1,C j n ⎜ i d nt = min ⎜ Cj j =1 3 σn ⎜ ⎝

p

⎞ ⎛ Br t − µ t −1, R j n ⎟ ⎜ i ⎟ + min ⎜ Rj j =0 4 σn ⎟ ⎜ ⎠ ⎝

p

⎞ ⎟ ⎟ ⎟ ⎠

(5)

where µ nt −1,C and µ nt −1,R mean a set of averages of blobs and relations in the j-th body j

j

part at time t-1, respectively. σ nt −1,C and σ nt −1,R a set of deviations of blobs and relations, respectively. If the minimum distance is less than a predefined threshold, the proposed modeling algorithm adds blobs Bit and relations Brit to corresponding j

j

adaptive person model ( µ nt −1,C and µ nt −1,R ) and updates the adaptive model by recalculating their center and uncertainties [6]. j

j

4 Model-Based Multi-person Tracking Tracking people poses several difficulties, since the human body is a non-rigid form. After forming blobs, a blob-based person tracking maps blobs from the previous frame to the current frame, by computing the distance between blobs in consecutive frames. However, such a blob-based approach for tracking multiple persons may cause problems due to the different number of blobs in each frame: blobs can be split, merged, even disappear or be newly created. To overcome this situation, many-to-many blob mapping can be applied [9]. While these authors avoided situations where blobs at time t-1 are associated to a blob at time n, or vice versa, they adopted a variant of the multiagent tracking framework to associate multiple blobs simultaneously. In this paper, we assume that persons CPnt −1 have already been tracked up to frame t-1 and new blobs Bit are formed in frame t. Multi-persons are then tracked as follows: Case 1: If Bi is included in Pk, the corresponding blob in Pk is updated with Bi. Case 2: If a blob in Pk is separated into several blobs in frame t, the blob in Pk is updated with one blob in frame t and other blobs at time t are appended into Pk. Case 3: If several blobs in Pk are merged into Bi, one blob in Pk is updated with Bi and other blobs are removed from Pk.

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Case 4: If Bi is included in Pk but the corresponding blob does not exist, Bi is added to Pk. Case 5: If Bi is not included in Pk, the blob is considered as a newly appearing blob and thus a new person is added to the person list (Sec. 3.2). where including a region into a person with a bounding box means the region overlaps over 90% to the person. Corresponding a blob to the adaptive person model is computed using Eq. (5). In addition to simplify the handling of two lists of persons and blobs, the proposed approach can keep observe existing persons exiting, new persons entering, and previously monitored persons re-entering the scene. One advantage of the proposed approach is to relieve the burden of correctly blobbing. Even though a blob can be missed by an illumination change, person-based tracking can retain individual identity using other existing blobs. After forming persons (Sec. 5), the number of blobs in a person are flexibly changeable. The proposed approach can handle over-blobbing (Case 2) and under-blobbing (Case 3) problems.

5 Results and Conclusions The proposed multi-person tracking approach was implemented in JAVA (JMF), and tested in Windows 2000 on a Pentium-IV 1.8 GHz CPU with a memory of 512 MB. For 320×240 frames, videos were recorded using a Sony DCR-PC330 camcoder.

(a) Entering

(b) Occlusion

(c) Exiting

(d) Reentering

Fig. 2. Experimental results using adaptive person models

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The number of persons the algorithm can handle simultaneously and the duration a specific person’s information can be held by the algorithm are not limited programmatically. Fig. 2 presents tracking results with scenarios such as entering, leaving, re-entering, and occluding from the top. Whenever a person appears first in the video, a new person model is built and added to the persons’ list (Fig. 2(a)). In the event of occlusion, the occluded individual is considered to have exited the scene (Fig. 2(b)). During tracking the person, the proposed adaptive tracking system updates the corresponding person model at each frame, and the system keeps the person’s information after the person has exited the scene (Fig. 2(c)). When the person later reenters the video, the system looks for a model in the previously recorded persons’ list (Fig. 2(d)). Then the system tracks and updates the person and the person’s model. The goal of this paper was to track and identify many persons using a video surveillance system which warns of long-term unauthorized behavior and transmits their model-based information between networked cameras. The next phase in our work is to build a networked surveillance system with disjoint cameras and to improve the approach proposed in this paper for wide-area surveillance.

Acknowledgements This work was supported by Korea Research Foundation Grant (KRF-2004-003D00376).

References 1. Aggarwal, J.K., and Cai, Q., Human motion analysis: a review, Computer vision and image understanding, Vol. 73, No. 3, (1997) 428–440 2. Foresti, G., Mahonen, P., and Regazzoni, C.S., Multimedia video-based surveillance systems: requirements, issues and solutions, Dordrecht, The Netherlands: Kluwer (2000) 3. Foresti, G., Mahonen, P., and Regazzoni, C.S., Automatic detection and indexing of videoevent shots for surveillance applications, IEEE transactions on multimedia, Vol. 4, No. 4, (2002) 459-471 4. Garcia, C., and Tziritas, G., Face detection using quantized skin color regions merging and wavelet packet analysis, IEEE transactions on multimedia, Vol. 1, No. 3, (1999) 264-277 5. Gavrila, D., The visual analysis of human movement: a survey. Computer vision and image understanding, Vol. 73, No. 1, (1999) 82–98 6. Lee, K.-M., and Street, W.N., Model-based detection, segmentation, and classification using on-line shape learning, Machine vision and applications, Vol. 13, No. 4, (2003)222-233 7. Lee, K.-M., Elliptical clustering with incremental growth and its application to skin color region segmentation, Journal of korean information science society, Vol. 31, No. 9 (2004) 8. Niu, W., Jiao, L., Han, D., and Wang, Y.-F., Real-time multi-person tracking in video surveillance, Proceedings of the pacific rim multimedia conference (2003) 1144-1148 9. Park, S. and Aggarwal, J.K., Segmentation and tracking of interacting human body parts under occlusion and shadowing, Proceedings of international workshop on motion and video computing (2002) 105-111

A Novel Noise Modeling for Object Detection Using Uncalibrated Difference Image Joungwook Park and Kwan H. Lee Gwangju Institute Science and Technology (GIST), Intelligent Design and Graphics laboratory, Department of Mechatronics, 1 Oryong-dong, Buk-gu, Gwangju, 500-712, Korea {vzo, lee}@kyebek.kjist.ac.kr http://kyebek9.kjist.ac.kr Abstract. In order to extract the region of an object from an image, the difference image method is attractive since it is computationally inexpensive. However, the difference image is not frequently used due to the noise in the difference image. In this paper, we analyze the noise in an uncalibrated difference image and propose a statistical noise calibration method. In the experiment, the proposed method is verified using a real image.

1

Introduction

In image-based modeling, it is important to separate an object that we are interested in from the background. In background removal methods without considering illumination change, color-based and template matching methods are generally used. In a color-based method, we search the object with the known color information of an object. However, there are two drawbacks in the colorbased methods. First drawback is that the color information can be contaminated by environmental changes such as light position and intensity. Second, the colorbased methods require additional computational cost due to a large amount of color transformation and matrix calculations [2–4]. In a template matching method, we find the object based on the template set that has information on the object. However, we should design the template set. The use of a template can improve the performance but it also increases the computational cost [5]. A computationally inexpensive background removal method is therefore needed. One inexpensive background removal method is the difference image method. The difference image gives us information of the changed part in the image. Nevertheless, the difference image has not been frequently used due to the noise occurring from the interaction between the object and the background. Assume that there are two images: one has an object and the other has not. If we compare the backgrounds of both images, the statistical properties of their backgrounds are not the same [1]. The object between camera and background becomes another noise source. As a result, the object degrades the quality of the difference image [6, 7]. Recently, many researchers have been intensively studied the noise modeling considering illumination change [8, 9]. J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1208–1215, 2004. c Springer-Verlag Berlin Heidelberg 2004


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In this paper, however, we focus on the case where an object appears in the image, with a fixed illumination environment and no occurrence of shadows. This affects the change of the background region, but not that of the object region. In section 2, a new noise model is described that verifies the effect introducing an object and improves the quality of difference image generated from uncalibrated images. In section 3, we improve the noise model considering the effect of object appearance. In section 4, we propose the procedure for improving the quality of difference image. In section 5, a numerical example is given for verification of the proposed method. Finally the conclusion is given in section 6.

2

Noise Modeling

Generally the change of noise distribution in the image occurs though images are sequentially taken in the same condition such as no change of foreground, background and illumination. The model of the image taken is defined as follows:

where

Ito ,

n×m

It , Vt ∈ R

It (i, j) = Ito (i, j) + Vt (i, j),

(1)

Vt (i, j) ∼ N (0, σ 2 ),

(2)

, i ∈ [0, n] , j ∈ [0, m], and t ∈ [0, T ].

It : the t-th image with noise Vt : the noise in the image T : the number of image taken

Ito : the original image without noise t ; the t-th image in the sequence i, j : integer indices

To calculate the noise distribution of sequence images, the model of difference image is defined as follows: DIa,b (i, j)
Ia (i, j) − Ib (i, j) = Va (i, j) − Vb (i, j) (∵ Iao = Ibo ),

(3)

where DIa,b is the difference image of Ia , Ib and a, b are integer indices, which satisfy a, b ∈ [0, t] and a =b. DIa,b (i, j) satisfies the Gaussian distribution because of Va (i, j), Vb (i, j) as given in eq. (2). DIa,b (i, j) ∼ N (0, 2σ 2 ) (4) In the case of detection or recognition of object with difference image, generally a threshold value is used to decide whether a pixel is in the region of an object or not. DIa,b (i, j) is replaced by | DIa,b (i, j) | as below.
True |Da,b (i, j)| ≥ Threshold (5) IsObject(i, j) = False |Da,b (i, j)| < Threshold To decide which pixel is noisy, the distribution of | DIa,b (i, j) | is deduced from DIa,b (i, j). The distribution function of DIa,b (i, j) is given by eq.(6) based on eq.(4). The mean of | DIa,b (i, j) | is given by eq.(7).

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P (z) = E(|z|) =

4σ 2 e√ 2 πσ

∞ 0

(6)

−z 2

2 z e√4σπσ

dz

(7)

It should be considered whether all levels of the pixel satisfied the previous assumptions or not. Assume that an image is represented by a gray scale with 8-bit depth. In general, the effect of noise is reduced near the limit level of pixel such as 0 or 255. Therefore the distribution and the noise model in eq.(1) should be changed near the limit level. ⎧ ⎪ (Ito + Vt (i, j) ≤ 0) ⎨0 It (i, j) = Ito (i, j) + Vt (i, j) (0 < Ito (i, j) + Vt (i, j < 255)) ⎪ ⎩ 255 (Ito (i, j) + Vt (i, j) ≥ 255)

(8)

In addition the variance should be defined for the model according to the level of pixel value. Let pt (i, j) define the pixel value at position (i, j) located in t − th image, and sx,k also defines the set of position where pt (i, j) in t − th image is equivalent to any pixel level, x. Then the mean of | DIa,b (i, j) | at each pixel level is represented by EDI (x) and the set of means is M eanDI . pt (i, j) = {x|x ∈ [0, 255]}

(9)

sx,t = {(i, j)|pt (i, j) = x, x ∈ [0, 255], for all(i, j)}

(10)

Fig. 1. Concept of the proposed method

A Novel Noise Modeling for Object Detection T


EDI (x) =

T





k=i l=0,l
=k sx,k

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|DIk,l (sx,k )|

# of Element

M eanDI = {EDI (x)|x ∈ [0, 255], for all x}

(11) (12)

Fig. 1 shows this concept. Assume that there are two images which are sequentially taken in the same condition. One of the images is temporarily named the base image. Firstly, in the base image, we generate sx,k , the set of positions of the pixel for each pixel level and then calculate the mean of the pixel values at the position corresponding to sx,k in difference image. These steps repeat for all levels of pixel. Whole procedure repeats until no more image is considered as the base image.

3

The Effect of Introducing an Object

In the previous section, the noise model is generated in the same condition and is regarded as a kind of random noise. To remove the noise in the difference image, we consider the effect of introducing an object in this section. Assume that the image with only background is named the background image and the image with the background and an object is the object image. In ideal case the region of background in the object image is not changed when an object enters the image unless the shadow or illumination changes. In real case, however, the image is changed by only introducing an object. In this paper we define the difference generated from the effect as situation-dependent noise (SDN). The SDN is generated due to interaction between the object and the background. Fig. 2 shows the effect from introducing an object. Fig. 2 (a) shows that the portion of the emitted light from background goes through the lens and it makes the background image. If an object obstructs the way of the emitted light, some of the light from the background is either fully obstructed or partially obstructed. And some of the light is not obstructed as shown in Fig. 2 (b). When some of the light is partially obstructed, the shape of acquired image is not changed, but the value of each pixel is changed in comparison to that of the pixel in the image taken from only the background. Assume that if the pixel which belongs to the background is able to be seen, the ratio of obstruction is the same for all pixels corresponding to the background. Each pixel value on the region of background in the object image is less than that in the background image. Therefore the effect from introducing an object can be computed from the portion of the difference image, which is regarded as the area corresponding to the portion of background in the object image. To represent the noise model in the object image we assume that we have two images: one is a background image of which M eanDI is known as given eq.(12). The other is a difference image generated from the background image and object image which is taken in the same background. The portion of background in the obj bk (i, j) and the portion of object is DIbk,obj (i, j). When difference image is DIbk,obj

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(a)

(b) Fig. 2. The effect from introducing an object all the object image is taken, Vobj (i, j) is the variance of noise generated in the same bk (i, j) is the variance of noise generated condition as the background image. Vobj from introducing the object. We assume that Iobj (i, j) is given as follows:
o all (i, j) + Vobj (i, j), IsObject(i, j) = True Iobj Iobj (i, j) = , (13) o all bk Ibk (i, j) + Vobj (i, j) + Vobj (i, j), IsObject(i, j) = False all where Vobj (i, j) ∼ N (0, σ 2 ). To distinguish the region of object from difference image, the model of difference image is represented as below. o o all DIobj,bk (i, j) = Iobj (i, j) − Ibk (i, j) + (Vobj (i, j) − Vbk (i, j))

(14)

bk all bk o o (i, j) = (Vobj (i, j) − Vbk (i, j)) + Vobj (i, j) (∵ Iobj (i, j) = Ibk (i, j)) (15) DIobj,bk

4

Procedure of Noise Removal

A simple object detection algorithm is suggested in order to verify the proposed noise model. Once generated the difference image without noise, it is easy to detect the region of the object. Therefore we should first find the noise distribution of difference image with background images. And then difference image is generated from background image and object image. The bounding box is

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created by the mean and the variance of the difference image. The noise distribk bution of the outside of the bounding box(DIbk,obj (i, j)) according to the level of pixel is generated and the noise of the difference image is removed by the noise distribution. The process is performed as follows: a) Computation of noise distribution of difference image from background images b) Computation of noise distribution resulting from introducing an object c) Modification of the difference image using noise distribution d) Creation of a bounding edge using the modified difference image

5

Experimental Results

The size of the image used is 640×480 with 8bit-RGB color. Five background images are taken at one image per second. The experiment is carried out inside of a room. In order to capture images the camera for web chatting is used. Fig. 3(b) is one of background images. Fig. 3(a), (c) show the error maps of the difference image using background images about red and blue color. Fig. 4 illustrates that the noise distribution of the difference image from five background images tends to behave constantly according to each pixel level, except near the limit, 0 or 255. Fig. 5 shows the bounding box of the object, which is generated from the mean and the variance of the difference image. The difference image is generated from background image and object image. The offset is applied to the bounding box in order to entirely exclude the portion of image corresponding to the object bk (i, j)) in Fig. 5 (b). (DIbk,obj Fig. 6 shows that the error is dependent on the level of the pixel value in the background image. It also illustrates that the distribution of noise resulting from introducing an object tends to behave linearly according to the pixel level, except near the limit, 0 or 255.

(a)

(b)

(c)

Fig. 3. The error map of difference image from background images

Fig. 4. The noise distribution of the difference image according to the level of pixel

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(a)

(b)

(c)

Fig. 5. The noise distribution of the difference image according to the level of pixel

Fig. 6. The noise distribution resulting from introducing an object according to the level of pixel value

(a)

(b)

(c)

Fig. 7. The result of using the proposed method

Fig. 7(a) illustrates the difference image without any process. Fig. 7 (b) is the result using the information of the difference image with the threshold of 2σ. Fig. 7 (c) is the result using the proposed method. The result shown in Fig. 7 (c) is more precise and distinguishable than the result shown in Fig. 7 (b).

6

Conclusion

In this paper we proposed a noise reduction method for the difference image. Noise in a difference image is analyzed. Based on noise analysis, we developed the noise estimation process and noise removal algorithm. In the experiment, it is verified by the proposed method that the noise is removed and the loss of

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the object is minimized in the difference image. The property of noise is used to remove the noise and to find the area of the object. The loss of the detected region of an object is minimized by this procedure.

References 1. Papoulis, A.: Probability, Random Variables, and StochasticProcess. 3rd edn. McGraw-Hill, New York (1991) 2. Gonzalez, R. G., Woods, R. E.: Digital Image Processing. Addison Wesley, Massachusetts (1992) 3. Duda, R. O., Hart, P. E., Stork, D. G.: Pattern Classification. 2nd edn. WileyInterscience, New York (2001) 4. Ritter, G. X., Wilson, J. N.: Handbook of Computer Vision Algorithms in Image Algebra. 2nd edn. CRC Press, Boca Raton (2001) 5. Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer (2003) 6. Bruzzone, L., Prieto, D. F.: Automatic Analysis of the Difference Image for Unsupervised Change Detection. IEEE Transactions on Geoscience and Remote Sensing, Vol. 38. Issue 3. IEEE(2000) 1171-1182 7. Khashman, A.: Noise-Dependent Optimal Scale in Edge Detection. Proceedings of the IEEE International Symposium on Industrial Electronics 2002, Vol. 2. IEEE(2002) 467-471 8. Stauffer, C.,Grimson, W.E.L.: Adaptive Background Mixture Models for Real-time Tracking. Computer Vision and Pattern Recognition, Vol. 2. IEEE (1999) 246-252 9. Javed, O., Shafique, K., Shah, M.: A Hierarchical Approach to Robust Background Subtraction using Color and Gradient Information. Workshop on Motion and Video Computing 2002, IEEE(2002) 22-27

Fast and Accurate Half Pixel Motion Estimation Using the Property of Motion Vector MiGyoung Jung and GueeSang Lee∗ Department of Computer Science, Chonnam National University, 300 Youngbong-dong, Buk-gu, Kwangju 500-757, Korea {mgjung, gslee}@chonnam.chonnam.ac.kr

Abstract. To estimate an accuracy motion vector (MV), a two step search is generally used. In the first step, integer pixel points within a search area are examined to find the integer pixel MV. Then, in the second step, 8 half pixel points around the selected integer pixel MV are examined and the best matching point is chosen as the final MV. Many fast integer pixel motion estimation (ME) algorithms can be found by examining less than about 10 search points. However, the half pixel ME requires huge computational complexity. In this paper, We propose a new fast algorithm for half pixel ME that reduces the computational overhead by limiting the number of interpolations of the candidate half pixel points. The proposed method based on the property of MVs and the correlations between integer pixel MVs and half pixel MVs. Experimental results show that the speedup improvement of the proposed algorithm over a full half pixel search (FHPS), horizontal and vertical directions as references (HVDR), chen’s half pixel search algorithm (CHPS-1) and a parabolic prediction-based fast half-pixel search (PPHPS) can be up to 1.4 ∼ 3.9 times on average. Also the image quality improvement can be better up to 0.05(dB)∼ 0.1(dB) compare with CHPS and PPHPS.

1

Introduction

The most popular ME and motion compensation method has been the blockbased motion estimation, which uses a block matching algorithm (BMA) to find the best matched block from a reference frame. ME based on the block matching is adopted in many existing video coding standards such as H.261/H.263 and MPEG-1/2/4. Generally, ME consists of two steps, the integer pixel ME and the half pixel ME. For the first step, the integer pixel ME, many search algorithms such as Diamond Search (DS) [1, 2], New Three Step Search (NTSS) [3], HEXagonBased Search (HEXBS) [4], Motion Vector Field Adaptive Search Technique (MVFAST) [5] and Predictive Motion Vector Field Adaptive Search Technique (PMVFAST) [6] have been proposed to reduce the computational complexity. ∗

corresponding author.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1216–1223, 2004. c Springer-Verlag Berlin Heidelberg 2004 

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Most recent fast methods for the integer pixel ME can be found by examining less than about 10 search points. As a consequence, the computation complexity of half pixel ME becomes comparable to that of integer pixel ME and the development of a fast half pixel ME algorithm becomes important. For the second step, the half pixel ME, FHPS that is a typical method, a half pixel search generally needs to check all 8 half pixels to find the final MV. FHPS requires huge computational complexity. Hence, it becomes more meaningful to reduce the computational complexity of half pixel ME. For these reasons, a few methods such as HDVR [7], CHPS-1 [8] and PPHPS [8] have been developed to accelerate the half pixel ME by proposing the prediction models. As a result, the number of half pixels needed for the half pixel MV can be reduced. In this paper, we propose a new fast algorithm for half pixel ME that reduces the computational overhead by limiting the number of interpolations of the candidate half pixel points. The proposed method based on the property of MVs and the correlations between integer pixel MVs and half pixel MVs. As a result, we reduce the total number of search points used to find the half pixel MV of the current block and improve the ME accuracy. This paper is organized as follows. Section 2 describes the observation of the property of motion vector. The proposed algorithm is described in Section 3. Section 4 reports the simulation results and conclusions are given in Section 5.

2

Observation of the Property of Motion Vector

This section introduces the observation of the property of MV. We propose a new fast and accurate algorithm for half pixel MV based on the property of MV from several commonly used test image sequences. The property of MV is represented in the following subsections. Table 1 and Table 2 documents the MV distribution probabilities within certain distances from the search window center by exploiting the FS algorithm to three commonly used test image sequences, ”Akiyo”, ”Carphone” and ”Table”, based on the SAD matching criterion. 2.1

The Ratio of Integer Pixels and Half Pixels in the Final Motion Vector

Table 1 shows that the ratio of integer pixels and half pixels in the final MV is about 24 to 1 in small motion case and about 2 to 1 in large motion case. In this case, the most of integer pixels for the final MV is the search origin (0,0). And the probability of the MVs located at the horizontal and vertical direction of the search center is about 79% (in small motion case ) ∼ 66% (in large motion case) and the probability of the MVs located at the diagonal direction of the search center is about 21% (in small motion case ) ∼ 34% (in large motion case). Also, the half pixels for the final MV are concentrated in the horizontal and vertical direction instead of the diagonal direction of the search center. In this paper, The proposed algorithm is based on the ratio of integer pixels and half pixels in the final MV and the cross center-biased distribution property of half pixel MVs.

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Table 1. The ratio of integer pixels and half pixels in the final motion vector Akiyo Carphone Table Integer Pixel MV : C(0,0) 95.07% 68.77% 64.01% Half Pixel MV 3.93% 30.22% 34.03% Diagonal Direction Cross Direction 21.03% 78.97% 35.02% 64.98% 33.95% 66.05%

M Vt (dxt, dyt)

M V1 (dx1, dy1)

M Vt : M V0 : MV1: MV2: MV3:

M V2

M V3

(dx2, dy2)

(dx3, dy3)

cur rent block

M V0 (dx0, dy0)

the M V of the same coordinate block in the reference frame the M V of the search origin (0,0) of the current block the M V of left block the M V of above block the M V of above - right block

Fig. 1. Blocks for spatial-temporal correlation information

2.2

Spatial-Temporal Correlation of Motion Vector

Since the time interval between successive frames is very short, there are high temporal correlations between successive frames of a video sequence. In other words, the motion of current block is very similar to that of the same coordinate block in the reference frame in table 2. And also there are high spatial correlations among the blocks in the same frame. The proposed method exploits spatially and temporally correlated MVs depicted in Fig. 1. In Fig. 1, the MV mvt is the block with the same coordinate in the reference frame, the MV mv0 is the search origin (0,0) of the current block, the MV mvc is MV of the current block, and the MVs mv1 , mv2 , and mv3 are MVs of neighboring blocks in the current frame. If the information of spatially and temporally correlated motion vectors is used to decide one among 8 half pixel search points, the half pixel MV will be found with much smaller number of search points. As indicated in Table 3, about 98.75% (in small motion case) ∼ 64.77% (in large motion case) of the MVs are same MV at same coordinates in two successive frames. And about 98.79% (in small motion case) ∼ 48.67% (in large motion case) of the MVs are same MV at neighboring blocks in the current frame. 2.3

The Correlations Between Integer Pixel Motion Vectors and Half Pixel Motion Vectors

The integer pixel positions and the half pixel positions are shown in Fig. 2(a). In Fig. 2(a), assume the integer pixel C in the current frame, which is pointed to by the estimated integer MV from the previous frame, has 8 neighbors of

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Table 2. Spatial-temporal Correlation of Motion Vector

mv1 =mv2 =mv3 =mvc mv1 =mv2 =mv3 =(0.0) Spatial Correlation mv1 =mv2 =mv3 =mvt mv1 =mv2 =mv3 =mvt =(0,0) Temporal Correlation mvt =mvc (The ratio of integer pixels)

-1

D1

-0.5

0

H1

d1

v1

h1

C

d3

+0.5

+1

V1

D3

v2

Akiyo 88.86% (100%) 88.70% (100%) 93.03% (96.90%)

Carphone 41.73% (99.97%) 38.83% (99.98%) 55.74% (75.98%)

D2

d2

h2

H2 A

h

v

d

D4

V2

-0.5 Integer Pixel

0

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d4

C -1

Table 39.97% (99.93%) 39.60% (99.93%) 58.93% (79.64%)

+0.5

D

+1

Half Pixel

h = (A+B)/2 v = (A+C)/2 d= (A+B+C+D)/4

(a) Position of integer pixels and half pixels

(b) Calculation of half pixels

Fig. 2. The position and calculation of half pixel

integer pixels H1 , H2 , V1 , V2 , D1 , D2 , D3 , D4 and 8 neighbors of half pixels h1 , h2 , v1 , v2 , d1 , d2 , d3 , d4 . If the centered integer pixel point (C) is selected as a minimum distance block at the integer pixel search step, then this point and 8 neighbouring interpolated half pixel candidates will be selected at the half pixel search step. The formulas for the half pixel interpolations are shown in Fig. 2(b). The half pixel MV motion estimation is the most computationally intensive part. In Fig. 2(b), Therefore, we propose a new fast algorithm using the correlations between integer pixel MVs and half pixel MVs.

3

The Proposed Algorithm

We propose a new fast algorithm for half pixel accuracy ME that reduces the computational overhead by limiting the number of interpolations of the candidate half pixel points. The proposed algorithm contain two main steps : In the first step, the final integer pixel MV at the integer pixel search step is examined

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to check the final integer pixel MV with the search origin (0,0). If the final integer pixel MV is the search origin (0,0), the MVs mv1 , mv2 , mv3 and mvt in Fig. 1 are examined. Then, in the second step, if the final integer pixel MV is not the search origin (0,0), 3 candidate half pixel points instead of 8 half pixel points around the selected integer pixel MV are examined using the correlations between integer pixel MVs and half pixel MVs. The proposed method is summarized as follows. Step 1. Decide Categories to Which the Current Macroblock Belongs. The final integer pixel MV at the integer pixel search step is examined to check the final integer pixel MV C with the search origin (0,0). If C is the search origin (0,0), the MVs mv1 , mv2 , mv3 and mvt are utilized to divide motion flow into two categories as follows. I. All motion vectors are equal, which is mv1 =mv2 =mv3 =mvt II. Some of motion vectors are not equal Step 2. Decide the Candidate Search Points. Category I: If all motion vectors are equal to the search origin (0,0), which is mv1 =mv2 =mv3 =mvt =(0,0), the the search origin (0,0) is selected as the final MV without the half pixel search step. Category II: Some motion flow of spatial macroblocks are similar to temporal macroblock or not related at all. The SAD0 is the SAD of the search origin (0,0), the SADH1 is the SAD of H1 , the SADH2 is the SAD of H2 , the SADV 1 is the SAD of V1 , the SADV 2 is the SAD of V2 , the SADD1 is the SAD of D1 , the SADD2 is the SAD of D2 , the SADD3 is the SAD of D3 , and the SADD4 is the SAD of D4 are calculated. The lowest SAD among SAD0 , SADH1 , SADH2 , SADV 1 , SADV 2 , SADD1 , SADD2 , SADD3 and SADD4 is calculated. The motion flow is categorized in two cases according to the lowest SAD. Case 1 : The lowest SAD is one among SADH1 , SADH2 , SADV 1 and SADV 2 on horizontal and vertical direction. If the SAD of the integer pixels on horizontal and vertical direction is the lowest SAD, the half pixel point correspond to integer pixel point of the lowest SAD and its neighbouring points are selected as the candidate half pixel points. For example, the integer pixel point of the lowest SAD is H1 , the candidate half pixel points are h1 , d1 and d3 . The lowest SAD among the SAD of C, h1 , d1 and d3 is selected as the finial MV. Case 2 : The lowest SAD is one among SADD1 , SADD2 , SADD3 and SADD4 on diagonal direction. If the SAD of the integer pixels on diagonal direction is the lowest SAD, The half pixel point correspond to integer pixel point of the lowest SAD and its neighbouring points are selected as the candidate half pixel points. For example, the integer pixel point of the lowest SAD is D1 , the candidate half pixel points are d1 , h1 and v1 . The lowest SAD among the SAD of C, d1 , h1 and v1 is selected as the finial MV.

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Simulation Result

In this section, we show the experiment results for the proposed algorithm. We compared FHPS, HVDR, CHPS-1 and PPHPS with the proposed method in both image quality and search speed. Nine QCIF test sequences are used for the experiment: Akiyo, Carphone, Claire, Foreman, Mother and Daughter, Salesman, Table, Stefan and Suzie. The mean square error (MSE) distortion function is used as the block distortion measure (BDM). The quality of the predicted image is measured by the peak signal to noise ratio (PSNR), which is defined by 
M  N 1 2 MSE = [x(m, n) − x ˆ(m, n)] (1) M N m=1 n=1 PSNR = 10 log10

2552 MSE

(2)

In Eq. (1), x(m, n) denotes the original image and x ˆ(m, n) denotes the reconstructed image. From Table 3 and 4, we can see that the proposed method is better than FHPS, HVDR, CHPS-1 and PPHPS in terms of the computational complexity (as measured by the average number of search points per motion vector) and is better than CHPS-1 and PPHPS in terms of PSNR of the predicted image. In terms of PSNR, the proposed method is about 0.06 (dB) better than HVDR in stationary sequences such as Table and about 0.05(dB)∼ 0.1(dB) compare with CHPS-1 and PPHPS in Table 3. In terms of the average number of search points per MV, experiments in Table 4 show that the speedup improvement of the proposed algorithm over FHPS, HVDR, CHPS-1 and PPHPS can be up to 1.4 ∼ 3.9 times on average. As a result, we can estimate MV fast and accurately. Table 3. Average PSNR of the test image sequence Integer-pel ME method Half-pel Method Akiyo Carphone Claire Foreman M&D Salesman Table Stefan Suzie Average

FHSM 35.374 32.213 35.694 31.020 32.482 33.706 32.909 28.095 34.276 32.863

Full Search HVDR CHPS-1 PPHPS Proposed 35.227 35.319 35.046 35.104 32.161 32.181 32.172 32.181 35.619 35.655 35.466 35.513 30.940 30.952 30.880 30.942 32.398 32.420 32.317 32.320 33.611 33.662 33.514 33.665 32.843 32.863 32.716 32.902 28.054 28.063 27.934 28.069 34.209 34.262 34.140 34.247 32.785 32.820 32.687 32.771

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Table 4. Average number of search points per half pixel motion vector estimation Integer-pel ME method Full Search Half-pel Method FHSM HVDR CHPS-1 PPHPS Proposed Akiyo 8 5 4 3 1.10 Carphone 8 5 4 3 2.44 Claire 8 5 4 3 1.32 Foreman 8 5 4 3 2.71 M&D 8 5 4 3 1.72 Salesman 8 5 4 3 1.29 Table 8 5 4 3 2.47 Stefan 8 5 4 3 2.71 Suzie 8 5 4 3 2.48 Average 8 5 4 3 2.03

5

Conclusion

In this paper, we propose a new fast algorithm for half pixel accuracy ME that reduces the computational overhead by limiting the number of interpolations of the candidate half pixel points. The proposed method makes an accurate estimate of the half pixel MV using the property of MV and the correlations between integer pixel MVs and half pixel MVs. As a result, we reduce the total number of search points used to find the half pixel MV of the current block and improve the ME accuracy.

Acknowledgement This work was supported by grant No.R05-2003-000-11345-0 from the basic Research Program of the Korea Science & Engineering Foundation.

References 1. Tham, J.Y., Ranganath, S., Kassim, A.A.: A Novel Unrestricted Center-Biased Diamond Search Algorithm for Block Motion Estimation. IEEE Transactions on Circuits and Systems for Video Technology. 8(4) (1998) 369–375 2. Shan, Z., Kai-kuang, M.: A New Diamond Search Algorithm for Fast block Matching Motion Estimation.IEEE Transactions on Image Processing. 9(2) (2000) 287–290 3. Renxiang, L., Bing, Z., Liou, M.L.: A New Three Step Search Algorithm for Block Motion Estimation. IEEE Transactions on Circuits and Systems for Video Technology. 4(4) (1994) 438–442 4. Zhu, C., Lin, X., Chau, L.P.: Hexagon based Search Pattern for Fast Block Motion Estimation. IEEE Transactions on Circuits and Systems for Video Technology. 12(5) (2002) 349–355 5. Ma, K.K., Hosur, P.I.: Report on Performance of Fast Motion using Motion Vector Field Adaptive Search Technique. ISO/IEC/JTC1/SC29/WG11.M5453 (1999)

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6. Tourapis, A.M., Au, O.C., Liou, M.L.: Optimization Model Version 1.0, ISO/IEC JTC1/SC29/WG11 M5866 (2000). 7. K.H., Lee, J.H., Choi, B.K., Lee and D.G., Kim: Fast Two-step Half-Pixel Accuracy Motion Vector Prediction. Electronics Letters, 36, (2000) 625–627 8. C., Du and Y., He: A Comparative Study of Motion Estimation for Low Bit Rate Video Coding. VCIP2000, 4067(3), (2000) 1239–1249

An Efficient Half Pixel Motion Estimation Algorithm Based on Spatial Correlations HyoSun Yoon1 , GueeSang Lee1,∗ , and YoonJeong Shin2 1

2

Department of Computer Science, Chonnam National University, 300 Youngbong-dong, Buk-gu, Kwangju 500-757, Korea [email protected], [email protected] Department of Computer Science Engineering, Gwangju University, 592-1 Jinwol-dong Namgu, Gwnagju 503-703, Korea [email protected]

Abstract. Motion estimation is an important part of video encoding systems, because it can significantly affect the output quality and the compression ratio. Motion estimation which consists of integer pixel motion estimation and half pixel motion estimation is very computationally intensive part. To reduce the computational complexity, many methods have been proposed in both integer pixel motion estimation and half pixel motion estimation. For integer pixel motion estimation, some fast methods could reduce their computational complexity significantly. There remains, however, room for improvement in the performance of current methods for half pixel motion estimation. In this paper, an efficient half pixel motion estimation algorithm based on spatial correlations is proposed to reduce the computational complexity. According to spatially correlated information, the proposed method decides whether half pixel motion estimation is performed or not for the current block. Experimental results show that the proposed method outperforms most of current methods in computation complexity by reducing the number of search points with little degradation in image quality. When compared to full half pixel search method, the proposed algorithm achieves the search point reduction up to 96% with only 0.01 ∼ 0.1 (dB) degradation of image quality.

1

Introduction

Recently, great interest has been devoted to the study of different approaches in video compressions. The high correlation between successive frames of a video sequence makes it possible to achieve high coding efficiency by reducing the temporal redundancy. Motion estimation (ME) and motion compensation techniques are an important part of video encoding systems, since it could significantly affect the compression ratio and the output quality. But, ME is very computational intensive part. ∗

corresponding author.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1224–1231, 2004. c Springer-Verlag Berlin Heidelberg 2004 

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Generally, ME is made of two parts, integer pixel motion estimation and half pixel motion estimation. For the first part, integer pixel motion estimation, many search algorithms such as Diamond Search (DS) [1, 2], Three Step Search (TSS) [3], New Three Step Search (NTSS) [4], Four Step Search (FSS) [5], Two Step Search (2SS) [6], Two-dimensional logarithmic search algorithm [7], HEXagon-Based Search (HEXBS) [8], Motion Vector Field Adaptive Search Technique (MVFAST) [9] and Predictive MVFAST (PMVFAST) [10] have been proposed to reduce the computational complexity. Some fast integer pixel motion estimation algorithms among these algorithms can find an integer pixel Motion Vector (MV) by examining less than 10 search points. For the second part, half pixel motion estimation, Full Half pixel Search Method (FHSM) that is a typical method, examines eight half pixel points around the integer motion vector to determine a half pixel motion vector. This method takes nearly half of the total computations in the ME that uses fast algorithms for integer pixel motion estimation. Therefore, it becomes more important to reduce the computational complexity of half pixel motion estimation. For these reasons, Horizontal and Vertical Direction as Reference (HVDR) [11], the Parabolic Prediction-based, Fast Half Pixel Search algorithm (PPHPS) [12], Chen’s Fast Half Pixel Search algorithm (CHPS)[13] and the methods [14–16] have been proposed to reduce the computational complexity of half pixel motion estimation. Since these algorithms do not have any information on the motion of the current block, they always perform half pixel motion estimation to find a half pixel motion vector. In this paper, we propose an efficient half pixel motion estimation algorithm based on spatial correlations among integer and half pixel motion vectors to reduces more computational complexity. According to spatially correlated information, the proposed method decides whether half pixel motion estimation is performed or not for the current block. Experimental results show that the proposed method reduces the computational complexity significantly when compared to that of FHSM with a little degradation of image quality. This paper is organized as follows. Section 2 describes the previous works. The proposed method is described in Section 3. Section 4 reports the simulation results and conclusions are given in Section 5.

2

The Previous Works

In Motion Estimation and Compensation, half pixel motion estimation is used to reduce the prediction error between the original image and the predicted image. FHSM that is a typical method, examines eight half pixel points around the integer motion vector ’C’ illustrated in Fig. 1. The cost function values of eight half pixel points are calculated to find the best matching point. Finally, the half pixel motion vector is obtained by comparing the cost function value of the best matching point with that of the point ’C’. This method takes nearly half of the total computations in the ME. Therefore, it becomes more important to reduce the computational complexity of half pixel motion estimation. For these reasons, some fast half pixel motion estimation algorithms have been proposed.

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In HVDR which is one of fast half pixel motion estimation algorithms, 2 neighboring half pixel points in vertical direction and 2 neighboring half pixel points in horizontal direction around the integer motion vector ’C’ illustrated in Fig. 1. are examined to decide the best matching point in each direction. Then, a diagonal point between these two best matching points is also examined. The point having the minimum cost function value among these 5 points and the point ’C’ is decided as a half pixel motion vector. In HVDR, only 5 half pixel points are checked to find a half pixel motion vector.

Sub_area_1

A

Sub_area_2

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2

3

4

C

5

6

7

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C

D

E

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Sub_area_4

INTEGER MV INTEGER PIXEL HALF PIXEL

Fig. 1. The Position of integer pixels, half pixels and Subareas

CHPS examines 4 horizontal and vertical half pixel points ’2’,’4’,’5’,’7’ shown Fig. 1. The best matching point is decided as a half pixel motion vector by comparing the cost function values of these 4 half pixel points and the point ’C’. In CHPH, only 4 half pixel points are checked to find a half pixel motion vector. PPHPS predicts the possible optimal half pixel point by using the cost function values of 5 integer pixel points ’A’,’B’,’C’,’D’,’E’ shown Fig. 1. The cost function values of the optimal half pixel point and its nearest points are calculated to find the best matching point. The point of the minimum cost function value is decided as a final half pixel MV by comparing the cost function value of this best matching point with that of the point ’C’. In PPHPS, only 3 half pixel points are checked to find a half pixel motion vector.

3

The Proposed Method

In order to reduce the computational complexity of half pixel motion estimation, the proposed method exploits spatial correlations among integer and half pixel

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MV1_Integer (dx1,dy1) MV1_Half (dxh1,dyh1) MV2_Integer (dx2,dy2) MV2_Half (dxh2,dyh2)

MVC_Integer (dxc,dyc) Current Block

MV1_Integer (dx1,dy1) : integer pixel MV of above block MV2_Integer (dx2,dy2) : integer pixel MV of left block MVC_Integer (dxc,dyc) : integer pixel MV of current blcok MV1_Half (dxh1,dyh1) : half pixel MV of above block MV2_Half (dxh2,dyh2) : half pixel MV of left block

Fig. 2. Blocks for Spatial Correlation Information

motion vectors to decide whether half pixel motion estimation is performed or not for the current block. In other words, the proposed method exploits spatially correlated motion vectors depicted in Fig. 2. to decide whether the half pixel motion estimation is performed or not for the current block. In case half pixel motion estimation is performed, the proposed method predicts the possible subarea by using the cost function values of integer pixel points. According to the position of the possible subarea, three half pixel points in its possible subarea are examined to find a half pixel motion vector. In this paper, we proposed Yoon’s Fast Half Pixel Search algorithm (YFHPS) as a search pattern for half pixel motion estimation. At first, YFHPS decides the best horizontal matching point between 2 horizontal integer pixel points ’A’, ’B’ depicted in Fig. 1. and the best vertical matching point between 2 vertical integer pixel points ’D’, ’E’ depicted in Fig. 1. And then, the possible subarea is selected by using the best horizontal and vertical matching points. According to the position of the possible subarea, three half pixel points in its possible subarea are examined. Finally, the point having the minimum cost function value among these three half pixel points and the point ’C’ that is pointed by the integer MV shown Fig. 1. is decided as a half pixel motion vector. For example, assumes that ’A’ and ’D’ are the best horizontal and vertical matching points respectively. The Sub area 1 between these two best matching points is selected as the possible subarea. The half pixel points ’1’, ’2’, ’4’ in Sub area 1 are examined. The point having the minimum cost function value among these three half pixel points and the point’C’ is decided as a half pixel motion vector. The block diagram of the proposed method appears in Fig. 3. The proposed method is summarized as follows. Step 1. If MVC Integer (dxc,dyc), the integer pixel MV of the current block shown in Fig. 2., is equal to (0,0), go to Step 2. Otherwise, go to Step 3. Step 2. I. If MV1 Integer (dx1, dy1) which is the integer pixel MV of the above block shown in Fig. 2., and MV2 Integer (dx2, dy2) which is the

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True

False

MVC_Integer == (0,0) ?

MV1_Integer ==(0,0) MV2_Integer == (0,0)

False

False

True

MV1_Half ==(0,0) MV2_Half == (0,0)

MV1_Integer ==MVC_Integer MV2_Integer == MVC_Integer

True False MV1_Half ==MV2_Half False

True

True

MVC_Half ==(0,0)

MVC_Half ==MV1_Half

YFHPS

Fig. 3. The Block Diagram of the proposed method

integer pixel MV of the left block shown in Fig. 2., are equal to (0,0), go to II. Otherwise, go to III. II. If MV1 Half (dxh1, dyh1) which is the half pixel MV of the above block shown in Fig. 2., and MV2 Half (dxh2, dyh2) which is the half pixel MV of the left block shown in Fig. 2., are equal to (0,0), (0,0) is decided as the half pixel MV of the current block. In other words, half pixel motion estimation is not performed for the current block. Otherwise, go to III. III. YFHPS is performed to find a half pixel motion vector. Step 3. I. If MV1 Integer (dx1, dy1) and MV2 Integer (dx2, dy2) are equal to MVC Integer (dxc, dyc), go to II. Otherwise, go to III. II. If MV1 Half (dxh1, dyh1) is equal to MV2 Half (dxh2, dyh2), (dxh2, dyh2) is decided as the half pixel MV of the current block. In other words, half pixel motion estimation is not performed. Otherwise, go to III. III. YFHPS is performed to find a half pixel motion vector.

4

Simulation Result

In this section, we show experimental results for the proposed method. The proposed method has been evaluated in the H.263 encoder. Ten QCIF test sequences are used for the experiment: Akiyo, Carphone, Claire, Foreman, Mother and Daughter, News, Salesman, Silent, Stefan and Suzie. The mean square error (MSE) distortion function is used as the block distortion measure (BDM). The quality of the predicted image is measured by the peak signal to noise ratio (PSNR), which is defined by

An Efficient Half Pixel Motion Estimation Algorithm


MSE =

1 MN

 M  N

[x(m, n) − x ˆ(m, n)]

2

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(1)

m=1 n=1

2552 (2) MSE In Eq. (1), x(m, n) denotes the original image and x ˆ(m, n) denotes the motion compensated prediction image. For integer pixel motion estimation, Full Search algorithm is adopted. For half pixel motion estimation, we compared FHSM, HVDR, CHPS, PPHPS and YFHPS to the proposed method in both of image quality and search speed. The simulation results in Table 1 and 2 show that the search speed of the proposed method is faster than the other methods (FHSM, HVDR, CHPS, PPHPS and YFHPS) while its PSNR is similar to them except PSNR = 10 log10

Table 1. Average PSNR for half pixel motion estimation algorithms Integer-pel ME method Half-pel ME method Akiyo Carphone Claire Foreman M&D News Salesman Silent Stefan Suzie

FHSM 34.5 30.88 35.05 29.54 31.54 30.59 32.7 31.81 23.89 32.19

HVDR 34.41 30.85 35.02 29.52 31.50 30.49 32.64 31.80 23.85 32.17

Full search CHPS PPHPS 34.46 34.43 30.86 30.88 35.03 35.05 29.50 29.51 31.54 31.52 30.54 30.57 32.67 32.70 31.76 31.79 23.86 23.87 32.15 32.19

YFHPS Proposed 34.5 34.40 30.88 30.87 35.05 35.04 29.51 29.48 31.54 31.46 30.57 30.51 32.70 32.63 31.80 31.71 23.87 23.82 32.19 32.18

Table 2. The Number of Search points per half pixel MV

Akiyo Carphone Claire Foreman M &D News Salesman Silent Stefan Suzie Average

FHSM HVDR CHPS PPHPS YFHPS Proposed 8 5 4 3 3 0.29 8 5 4 3 3 2.1 8 5 4 3 3 1.01 8 5 4 3 3 2.5 8 5 4 3 3 1 8 5 4 3 3 0.76 8 5 4 3 3 0.48 8 5 4 3 3 0.97 8 5 4 3 3 2.09 8 5 4 3 3 2.08 8 5 4 3 3 1.3

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for FHSM. In other words, the proposed method can achieves the search point reduction up to 96% with only 0.01 ∼ 0.1 (dB) degradation of image quality When compared to FHSM.

5

Conclusion

Based on spatial correlations among integer pixel MVs and half pixel MVs, an efficient method for half pixel motion estimation is proposed in this paper. According to spatially correlated information, the proposed method decides whether half pixel motion estimation is performed or not for the current block. As a result, the proposed method reduce the computational complexity significantly. Experimental results show that the speedup improvement of the proposed method over FHSM can be up to 4 ∼ 25 times faster with a little degradation of the image quality.

Acknowledgement This Study was financially supported by special research fund of Chonnam National University in 2004.

References 1. Tham, J.Y., Ranganath, S., Kassim, A.A.: A Novel Unrestricted Center-Biased Diamond Search Algorithm for Block Motion Estimation. IEEE Transactions on Circuits and Systems for Video Technology. 8(4) (1998) 369–375 2. Shan, Z., Kai-kuang, M.: A New Diamond Search Algorithm for Fast block Matching Motion Estimation. IEEE Transactions on Image Processing. 9(2) (2000) 287– 290 3. Koga, T., Iinuma, K., Hirano, Y., Iijim, Y., Ishiguro, T.: Motion compensated interframe coding for video conference. In Proc. NTC81. (1981) C9.6.1–9.6.5 4. Renxiang, L., Bing, Z., Liou, M.L.: A New Three Step Search Algorithm for Block Motion Estimation. IEEE Transactions on Circuits and Systems for Video Technology. 4(4) (1994) 438–442 5. Lai-Man, P., Wing-Chung, M.: A Novel Four-Step Search Algorithm for Fast Block Motion Estimation. IEEE Transactions on Circuits and Systems for Video Technology. 6(3) (1996) 313–317 6. Yuk-Ying, C., Neil, W.B.: Fast search block-matching motion estimation algorithm using FPGA. Visual Communication and Image Processing 2000. Proc. SPIE. 4067 (2000) 913–922 7. Jain, J., Jain, A.: Displacement measurement and its application in interframe image coding. IEEE Transactions on Communications. COM-29 (1981) 1799– 1808 8. Zhu, C., Lin, X., Chau, L.P.: Hexagon based Search Pattern for Fast Block Motion Estimation. IEEE Transactions on Circuits and Systems for Video Technology. 12(5) (2002) 349–355

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9. Ma, K.K., Hosur, P.I.: Report on Performance of Fast Motion using Motion Vector Field Adaptive Search Technique. ISO/IEC/JTC1/SC29/WG11.M5453 (1999) 10. Tourapis, A.M., Liou, M.L.: Fast Block Matching Motion Estimation using Predictive Motion Vector Field Adaptive Search Technique. ISO/IEC/JTC1/SC29/WG11.M5866 (2000) 11. Lee, K.H.,Choi, J.H.,Lee, B.K., Kim. D.G.: Fast two step half pixel accuracy motion vector prediction. Electronics Letters 36(7)(2000) 625–627 12. Cheng, D., Yun, H., Junli, Z.: A Parabolic Prediction-Based, Fast Half Pixel Search Algorithm for Very Low Bit-Rate Moving Picture Coding. IEEE Transactions on Circuits and Systems for Video Technology. 13(6) (2003) 514–518 13. Cheng, D., Yun, H.: A Comparative Study of Motion Estimation for Low Bit Rate Video Coding. SPIE 4067(3)(2000) 1239–1249 14. Sender, Y., Yano, M.: A Simplified Motion Estimation using an approximation for the MPEG-2 real time encoder. ICASSP’95,(1995) 2273–2276 15. Choi, W.I., Jeon, B.W.: Fast Motion Estimation with Modified diamond search for variable motion block sizes. ICIP 2003. (2003) 371–374 16. Li, X., Gonzles, C.: A locally Quadratic Model of the Motion Estimation Error Criterion Function and Its Application to Subpixel Interpolations. IEEE Transactions on Circuits and Systems for Video Technology. 6(1) (1996) 118–122

Multi-step Subdivision Algorithm for Chaikin Curves Ling Wu, Jun-Hai Yong, You-Wei Zhang, and Li Zhang School of Software, Tsinghua University, Beijing 100084, P. R. China [email protected]

Abstract. A Chaikin curve is a subdivision curve. Subdivision begins from an initial control polygonal curve. For each subdivision step, all corners of the polygonal curve are cut off, and a new polygonal curve is thus produced as the input of the next subdivision step. In the limit of subdivision, a Chaikin curve is created. In this paper, a multi-step subdivision algorithm for generating Chaikin curves is proposed. For an arbitrary positive integer k, the algorithm builds the resultant polygonal curve of the kth subdivision step directly from the initial polygonal curve. Examples show that the new algorithm speeds up curve generation in several times. Keywords: Subdivision scheme; Chaikin curve; Corner cutting.

1

Introduction

Research on subdivision schemes for generating curves and surfaces is popular in graphical modeling [1–3, et al.], animation [4, et al.] and CAD/CAM [5, 6, et al.] because of their stability in numerical computation and simplicity in coding. In 1974, Chaikin [2] proposed the first subdivision scheme for generating subdivision curves. Since then, more and more subdivision schemes come up including the Catmull-Clark subdivision method [1], the 4-point interpolatory √ subdivision scheme [7], and the 3 subdivision algorithm [8]. All the subdivision schemes in the literature to date start from an initial control polygon (i.e., a polygonal curve) or control mesh, denoted by L0 , and refine the control polygon or mesh step by step. At each step, the subdivision scheme is performed on the control polygon or mesh Lk once, and results in a new control polygon or mesh Lk+1 , which is the input for the next subdivision step. Here, Lk , where k = 0, 1, 2, · · ·, represents the resultant control polygon or mesh of the kth subdivision step. Thus, with any existing subdivision scheme, Lk must be calculated before Lk+1 is generated. In this paper, a multi-step subdivision algorithm is proposed to build Lk directly from L0 for the Chaikin subdivision scheme. It offers at least the following two advantages: J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1232–1238, 2004. c Springer-Verlag Berlin Heidelberg 2004


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(1) with the same initial control polygon L0 , the polygonal curve Lk built with the multi-step subdivision algorithm in this paper is exactly the same as the result of the Chaikin subdivision scheme after the kth subdivision step, and (2) it is not necessary to calculate Li , for all i = 1, 2, · · · , (k − 1), before generating Lk . Thus, the new algorithm saves the memory space at least for storing the subdivision results of the previous subdivision steps, and experience shows that the new generation method is several times faster than the original Chaikin scheme for producing Lk . The remaining part of the paper is organized as follows. Section 2 briefly introduces the Chaikin subdivision scheme, which is from Reference [2]. Section 3 provides the multi-step subdivision algorithm for Chaikin curves. Some examples are given in Section 4. The last section addresses some concluding remarks of the paper.

2

Chaikin Subdivision Scheme

This section briefly introduces the subdivision scheme proposed by Chaikin in Reference [2]. Let Lk = {P0,k , P1,k , · · · , Pnk ,k } , where k = 0, 1, 2, · · ·, be the resultant control polygon of the kth subdivision step with P0,k , P1,k , · · · , Pnk ,k being the control points of Lk . The Chaikin subdivision scheme is a recursive procedure.

Pi−1,k−1

Pi,k−1P2i+1,k Pi+1,k−1 P2i,k P2i+2,k P2i−1,k P2i−2,k P2i+3,k Pi+2,k−1

Fig. 1. Subdivision step k: Lk−1 (dashed) is subdivided, and result in Lk (solid)

When k = 0, L0 = {P0,0 , P1,0 , · · · , Pn0 ,0 } is the given initial polygonal curve. Figure 1 illustrates how the kth subdivision step of the Chaikin scheme is carried out. At this step, Lk−1 is subdivided, and result in Lk . For each line segment between Pi,k−1 and Pi+1,k−1 , where i = 0, 1, · · · , (nk−1 − 1), of the polygonal curve Lk−1 , the two points at ratios of 14 and 34 between the endpoints Pi,k−1 and Pi+1,k−1 are taken as P2i,k and P2i+1,k in the polygonal curve Lk . Thus, all points in Lk are obtained. Connect those points, and Lk is produced. As shown in Figure 1, a visual relationship between Lk−1 and Lk is that each corner Pi,k−1 of the polygonal curve Lk−1 is cut by the line segment between P2i−1,k and P2i,k of the polygonal curve Lk . Therefore, the Chaikin subdivision scheme is considered as a corner-cutting scheme as well.

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Multi-step Subdivision Algorithm

This section gives explicit formulae and an algorithm for calculating Lk from L0 directly. The idea of the Chaikin subdivision scheme is corner cutting. All corners of the polygonal curve are cut recursively. Thus, as the subdivision steps increase, the resulting polygonal curves become ever smoother. In the limit, a smooth curve is produced. Analyzing the corners of the initial polygonal curve, we find that the points P2k (i−1)+j,k , where j = 1, 2, · · · , 2k , of the polygonal curve Lk depend only on Pi−1,0 , Pi,0 and Pi+1,0 , as shown in Figure 2. Thus, by mathematical induction, we obtain the theorem below. Pi,0

P2k i+1,k Pi+1,0

· · · P2k i,k P2k i+2,k P2k (i−1)+2,k ··· P2k (i−1)+1,k P2k (i−1),k

P2k (i+1),k P2k (i+1)+1,k

Pi−1,0

Pi+2,0

Fig. 2. Multi-step subdivision: Lk (solid) is calculated from L0 (dashed) directly

Theorem 1. All points in Lk (k = 1, 2, · · ·) can be calculated directly from points in L0 by ⎧ = (2−1 + 2−(k+1) )P0,0 + (2−1 − 2−(k+1) )P1,0 , ⎨ P0,k Pk = F (j, k)Pi−1,0 + G(j, k)Pi,0 + H(j, k)Pi+1,0 , (1) ⎩ 2 (i−1)+j,k P2k n0 −2k +1,k = (2−1 − 2−(k+1) )Pn0 −1,0 + (2−1 + 2−(k+1) )Pn0 ,0 , where i = 1, 2, · · · , n0 − 1, j = 1, 2, · · · , 2k , and ⎧ ⎨ F (j, k) = 2−1 − 2−(k+1) − (j − 1)(2−k − j2−2k−1 ), G(j, k) = 2−1 + 2−(k+1) + (j − 1)(2−k − j2−2k ), ⎩ H(j, k) = (j − 1)j2−2k−1 .

(2)

Proof. Here, the mathematical induction method is used. When k = 1, we have ⎧ ⎧ ⎨ F (2, 1) = 0, ⎨ F (1, 1) = 14 , G(2, 1) = 34 , G(1, 1) = 34 , and ⎩ ⎩ H(2, 1) = 14 . H(1, 1) = 0, Thus, from the conclusion in Theorem 1, we obtain  P2i,1 = 34 Pi,0 + 14 Pi+1,0 , P2i+1,1 = 14 Pi,0 + 34 Pi+1,0 ,

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for all i = 0, 1, · · · , n0 − 1. The above equations match the Chaikin subdivision scheme very well. Therefore, Theorem 1 is true when k = 1. Now assume that Theorem 1 is true when k = m, where m = 1, 2, · · ·. The following will prove that Theorem 1 holds for the case k = m + 1. According to the Chaikin subdivision scheme, we have ⎧ P0,m+1 = 34 P0,m + 14 P1,m , ⎪ ⎪ ⎨ P (m+1) = 1P m

3 j−1 j+1 4 2 (i−1)+ 2 ,m + 4 P2m (i−1)+ 2 ,m , 3 1 P (m+1) (i−1)+j,m+1 = 4 P2m (i−1)+ j ,m + 4 P2m (i−1)+ j +1,m , ⎪ ⎪ 2 2 ⎩ 2 P2(m+1) n0 −2(m+1) +1,m+1 = 14 P2m n0 −2m ,m + 34 P2m n0 −2m +1,m , 2

(i−1)+j,m+1

when j is odd, when j is even,

where i = 1, 2, · · · , n0 − 1, and j = 1, 2, · · · , 2m+1 . In the above equations, substitute all points in Lm with the expressions which contain only points in L0 according to the assumption for the case k = m, and we demonstrate that Theorem 1 is valid for the case k = m + 1. Thus, Theorem 1 is proved.   From Equations (1) and (2), we have that the coefficients F (j, k), G(j, k) and H(j, k) do not depend on indices i while P2k (i−1)+j,k are calculated. Therefore, F (j, k), G(j, k) and H(j, k) can be precomputed and stored in arrays with size 2k to accelerate the calculation. Thus, we obtain the algorithm as follows for generating Lk from L0 directly. Algorithm 1. Computing Lk from L0 directly. Input. L0 = {P0,0 , P1,0 , · · · , Pn0 ,0 } . Output. Lk = {P0,k , P1,k , · · · , Pnk ,k } . (1) Calculate F (j, k), G(j, k) and H(j, k), for all j = 1, 2, · · · , 2k , according to Equations (2), and store the results in three arrays; (2) Compute P0,k and P2k n0 −2k +1,k with Equations (1); (3) For i = 1 to n0 − 1, do For j = 1 to 2k , do Calculate P2k (i−1)+j,k with Equations (1); (4) End of the algorithm.

4

Examples

Some examples are provided to illustrate the algorithm proposed in this paper. The first example is shown in Figure 3. The initial polygonal curve as shown in Figure 3(a) is         1 2 3 4 L0 = , , , . 1 2 2 1

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(a)

(b)

(c)

(d)

Fig. 3. Example 1: (a) L0 ; (b) L1 ; (c) L2 ; (c) L3

WithTheorem . The for  1, we obtain  L3 directly  from L0  points obtained   1.4375 1.5625 1.6875 1.8125 1.9375 2.0625 L3 are , , , , , , 1.4375 1.5625 1.6719 1.7656 1.8438 1.9063               2.1875 2.3125 2.4375 2.5625 2.6875 2.8125 2.9375 , , , , , , , 1.9531 1.9844 2.0000 2.0000 1.9844 1.9531 1.9063           3.0625 3.1875 3.3125 3.4375 3.5625 , , , and , respectively. The 1.8438 1.7656 1.6719 1.5625 1.4375 results are the same as those produced by the method provided in Reference [2]. However, the method in Reference [2] has to calculate L1 and L2 before L3 is computed.

(a)

(b)

Fig. 4. Chaikin curves: (a) Example 2; (b) Example 3

Table 1. Performance results of the new algorithm and the method in [2] Example 3

Example 2 k (nk + 1) tC (ms) tM (ms) 2 34 4 130 6 514 8 2050 10 8194 12 32770

111 379 780 1320 2023 2976

75 161 244 331 433 568

tC (ms) tm (ms)

1.48 2.35 3.20 3.99 4.67 5.24

k (nk + 1) tC (ms) tM (ms) 2 194 4 770 6 3074 8 12290 10 49154 12 196610

128 398 811 1387 2324 4385

76 150 228 312 453 822

tC (ms) tm (ms)

1.68 2.65 3.56 4.45 5.13 5.33

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Examples 2 and 3 are used to illustrate the efficiency of the new algorithm proposed in this paper. The numbers of control points in the initial polygonal curves of Example 2 (see Figure 4(a)) and Example 3 (see Figure 4(b)) are 10 and 50, respectively. Table 1 gives the time cost of the multi-step subdivision algorithm compared with that of the method in Reference [2] for those two examples. In the table, tC represents for the time cost used by the method in Reference [2] for generating the resultant polygonal curve Lk , and tM for the time cost by the new algorithm. All the data are calculated on a laptop personal computer with Celeron 1.7GHz CPU and 256M memory. The programming language is Java with JBuilder environment. As shown in the table, the new algorithm is several times faster than the method in Reference [2].

5

Conclusions

A new algorithm for calculating the resultant polygonal curve of the kth subdivision step for a Chaikin curve is proposed in this paper. It obtains results directly from the input polygonal curve, while the method in Reference [2] has to calculate all resultant polygonal curves from the first subdivision step to the kth subdivision step. Thus, the new algorithm has better space and time complexity than the method in Reference [2]. Examples shows that the new algorithm is several times faster than the method in Reference [2].

Acknowledgements The research was supported by Chinese 863 Program (2003AA4Z3110) and 973 Program (2002CB312106). The second author was supported by a project sponsored by SRF for ROCS, SEM (041501004), and a Foundation for the Author of National Excellent Doctoral Dissertation of P. R. China (200342).

References 1. Catmull, E. and Clark, J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design 10 (1978) 350–355 2. Chaikin, G.: An algorithm for high-speed curve generation. Computer Graphics and Image Processing 3 (1974) 346–349 3. Riesenfeld, R.F.: On Chaikin’s algorithm. Computer Graphics and Image Processing 4 (1975) 304–310 4. Zorin, D., Schr¨ oder, P., and Sweldens, W.: Interactive multiresolution mesh editing. In: Proceedings of SIGGRAPH. (1997) 259–268 5. Litke, N., Levin, A., and Schr¨ oder, P.: Trimming for subdivision surfaces. Computer Aided Geometric Design 18 (2001) 463–481

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6. Stam, J.: Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values. In: Proceedings of SIGGRAPH. (1998) 395–404 7. Dyn, N., Levin, D., and Gregory, J.A.: A 4-point interpolatory subdivision scheme for curve design. √ Computer Aided Geometric Design 4 (1987) 257–268 8. Kobbelt, L.: 3 subdivision. In: Proceedings of SIGGRAPH. (2000) 103–112

Imaging Electromagnetic Field Using SMP Image 1

2

Wei Guo , Jianyun Chai , and Zesheng Tang 1

1

Department of Computer Science & Technology, Tsinghua University, Beijing, China [email protected], [email protected] 2 Department of Electrical Engineering, Tsinghua University, Beijing, China [email protected]

Abstract. This paper proposes a novel texture based method for visualization of electromagnetic fields. According to the characteristics of electric eddy current fields, a scalar potential is constructed to express the field on the surfaces. Then the potential is used in deducing an extension form of the Sinusoidal function Modulated Potential (SMP) image of general surface eddy current fields. The SMP Image can display the distribution of both the direction and amplitude of the field. The paper also presents a new algorithm based on hardware accelerated texture mapping. The algorithm could render the SMP image in real time and can be further used in dynamic visualization of time-varying electromagnetic field. The rendered dynamic images can reflect the variation of the field with space and time simultaneously. The only requirements for the method are that the vector field is distributed on surface and that its divergent is free, which makes the method suitable for visualization of general divergentfree vector field distributed on surface.

1 Introduction Visualization of vector fields with computer graphics is very important in interpreting the structure of the field. Texture based visualization methods, such Line Integral Convolution (LIC) [1], produce a representation of the field at much higher resolution compared with the traditional flux line or hedgehog based method. These methods can display much more details of field. But the large computations needed in these methods make them inappropriate in real time applications such as visualization of time-varying field. Fast LIC (FLIC) [2] method greatly improves the rendering speed of LIC images, but it’s still not fast enough for real time applications. Another problem with these methods is that amplitude information of the underlying field is missed in the final image [3]. LIC based methods have also been extended in imaging of vector field defined on 3D surfaces and in dynamic imaging of time-varying fields [4, 5, 6]. But they still suffer from the problems of missing of amplitude information and relatively low frame rate. Sinusoidal function Modulated Potential (SMP) map is a new method for imaging of planar magnetic fields [7]. The method is based on the existence of a scalar magnetic potential. Modulating this potential with a periodic function and mapping the J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1239–1246, 2004. © Springer-Verlag Berlin Heidelberg 2004

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modulated potential onto grayscale pixels, the method renders soft and continuous images of the flux tubes of the magnetic field. Both the amplitude and direction information of the field can be shown. In this paper, taking eddy current field as an example, we extend the SMP map method for imaging of electromagnetic field distributed on general surfaces. A scalar potential is constructed for eddy current field on conductor surface and the concept of SMP map is extended to the field on the surface. Then a new algorithm based on texture mapping for rendering SMP image on surfaces is presented. The use of texture mapping accelerates the rendering speed of the algorithm greatly. Finally, the application of this method in dynamic rendering of time-vary field is presented with several examples.

2 SMP Map of Eddy Current Field on Surface 2.1 Potential Function of Eddy Current Field on Surface Eddy currents are induced in a conductor if the conductor is placed in a time-varying magnetic field. Since there is no eddy current flowing into or out of the surface of the conductor, the current density vector consists of only two tangent components at any point P on the conductor surface, i.e.,

G J = J s sˆ + Jττˆ [8]. According to Maxwell

equations, the current density vector is always divergent free, namely

G ∂J ∂J ∂J ∂J ∂J ∇⋅J = s + τ + n = s + τ = 0 ∂s ∂τ ∂n ∂s ∂τ

(1)

If we construct a thin uniform shell near the conductor surface, and let all compo-

G

nents of current density J along any normal line of the surface have the same value with those at the surface point (see Figure 1), then we get the relations ∂J s / ∂n = ∂Jτ / ∂n = ∂J n / ∂n = 0 in the shell. With this construction we can define an adjoint vector

G G G J ' in the shell as J ' = nˆ × J = − Jτ sˆ + J sτˆ . It is obvious

G J ' is zero in the shell, G ∂ Js ∂ Jτ ∂J ∂J (2) ∇× J' = − sˆ − τˆ + ( s + τ ) nˆ = 0 ∂n ∂n ∂s ∂τ G Therefore, the adjoint vector J ' can be expressed by the gradient of a scalar potential Φ as G ∂Φ ∂Φ τˆ J ' = ∇Φ = sˆ + (3) ∂s ∂τG And Φ can be calculated by the integral of J ' as

that the curl of

Imaging Electromagnetic Field Using SMP Image

G G G G Φ = ∫ J '⋅ dl = ∫ (nˆ × J ) ⋅ dl L

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(4)

L

where L is an arbitrary path started from a reference point on the conductor surface, and

G ∂Φ / ∂s = − Jτ , ∂Φ / ∂τ = J s . Since the curl of the adjoint vector J ' is zero,

Φ will be only dependent on the distribution of the eddy current and the selection of the reference point. From the construction of the thin shell, we know that the scalar potential can only be defined on the conductor surface for the original eddy current field.

Fig. 1. Construct the thin shell for the definition of the scalar potential

G Φ is the adjoint vector J ' , the contour of Φ is perpenG G G dicular to J ' . Thus from J ' = nˆ × J we can say that the direction of the contour of G Φ is coincide with the direction of J . Another important fact about the potential Φ is that for any two points P and Q Since the gradient of

on the conductor surface, the difference of their potential represents the flux of eddy current flowing through the path PQ. That is

G G G Q G Q Φ Q − Φ P = ∫ J ' ⋅ dl = ∫ ( nˆ × J ) ⋅ dl P P G Q G Q G Q G ˆ ) = ∫ ( J ⋅ uˆ ) dl =ψ = ∫ J ⋅ ( dl × nˆ ) = ∫ J ⋅ (udl P

P

(5)

P

G G G where uˆ = dl × nˆ / || dl || , dl =|| dl || . uˆ is a unit vector along the conductor surface and is perpendicular to nˆ .

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2.2 SMP Map of Eddy Current Field In the case of planar magnetic field, potential map is generated by mapping potential into grayscale [7]. If the mapping function is periodic function, the generated potential map can display the direction and amplitude information of the filed with an image of flux tubes. With the definition of the potential function on the conductor surface, the concept of potential map can be extended to eddy current fields. The mapping from potential to grayscale is similar. With different selections for the mapping function, the generated potential maps show different images of the original field. If we choose sinusoidal function as the mapping function g( Φ ), the generated potential map is called Sinusoidal function Modulated Potential (SMP) map. The definition of such mapping function is

g (Φ ) = g av + g m sin(ωΦ + ϕ 0 )

(6)

where gav and gm represent the average grayscale and the amplitude of the grayscale respectively; ω =2π/ Φ 0, with Φ 0 being the period of the mapping function; ϕ0 represents the initial angle. Similar to the planar magnetic filed potential map in [7], the eddy current potential map can show the image of the eddy current flux tube on the conductor surface intuitively. Figure 2 shows two SMP images of the eddy current distributed on the surface of a conductor sphere viewed from two different directions. The conductor sphere is placed in a uniform alternating magnetic field. The eddy current field on the conductor surface is also an alternating field. The image in Figure 2 is just the image of the field at a specific moment. From Eq. (5), the flux in each tube is always equal to the period Φ 0 of mapping function. Thus the field is strong if the width of the flux tube is small, and vice versa.

3 Texture Mapping Accelerated Rendering Algorithm Source data used in visualization is usually obtained from numerical methods such as Finite Element Method (FEM). The surface is represented using polygonal meshes. The representation of the surface with polygonal meshes makes OpenGL a very suitable tool to render it into 2D image. 3.1 Rendering Algorithm The texture mapping functionality of OpenGL can be utilized to do the potential interpolation and modulation automatically. The algorithm is briefly described as follows: i. Compute the potentials of the field on vertices as stated in the previous section; ii. Given the periodic modulating function g( Φ ) with period Φ 0, generate a 1D texture with T ( s ) = g ( s ⋅ Φ 0 ), s ∈ [0,1] and set the wrapping mode in OpenGL texture mapping as “REPEAT”.

Imaging Electromagnetic Field Using SMP Image

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iii. Set the 1D texture coordinate for each vertex P as Φ P/ Φ 0, submit the texture coordinates and positions of the vertices to OpenGL to render the image. The procedure of the potential interpolation and modulation by 1D texture mapping are as follows. First, the interpolation of texture coordinate in each polygon of the meshes is used to automatically interpolate the potentials. Secondly, the “REPEAT” mode of texture mapping means that the texture mapping function T(s) defined on coordinate s in interval [0, 1] is equivalent to a periodical function defined on the whole real axis with period 1.0. Thus, the final texture mapping function becomes

Fig. 2. The eddy current SMP images on the surface of a conductor sphere. A yellow light source with specular highlight effect is used to enhance the visual effect

T ( s ) = g ( s ⋅ Φ 0 ), s ∈ (−∞, +∞) Finally, taking texel is

Φ P/ Φ 0 as the texture coordinate for vertex P, the corresponding

T (Φ P / Φ 0 ) = g (Φ P / Φ 0 ⋅ Φ 0 ) = g ( Φ P ) where

(7)

(8)

g (Φ P ) is just the modulated potential. Figure 3 shows the process of modula-

tion using texture mapping. The pattern inside the red box in Figure 3(a) is the 1D texture data (2D image is used to show the pattern clearly). The flux tube marked as blue in Figure 3(b) is generated from one period of the 1D texture data which is also marked as blue. Since texture mapping is supported by almost all graphics hardware, the algorithm is easy to implement and can render the SMP image in real time.

4 Dynamic Images of Time-Varying Field Using a PC with ATI RADEON™ 7500 graphics card, the images such as in Fig. 2 can be rendered within 20ms. The total number of vertices on the conductor surface

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W. Guo, J. Chai, and Z. Tang

is over 16,000 and the total number of facets is over 32,000. Thus the algorithm is believed very suitable for visualization of time-varying eddy current field. The images in Figure 4 show a set of images of the eddy current field at different time. From the images, we can see clearly the variation of the field with time t in addition to the distribution of the field in space in each frame. For example, the amplitudes of the field are decreasing gradually from Figure 4(a) to (c), since the total number of flux tubes becomes smaller and smaller, while the flux in each tube remains unchanged (namely the period Φ 0 of the modulating function). In Figure 4(c), the field almost vanishes. From the animation of these image sequences, one can also observe the variation speed of the field from the changing rate of the number of the flux tubes.

Fig. 3. Utilize texture mapping to automatically modulate the potential

Fig. 4. Dynamic SMP image of eddy current field

The hardware accelerated algorithm can also be applied to planar field visualization. Figure 5 shows a set of images of the time-varying planar magnetic field excited by a pair of current filaments with opposite flow directions. Figure 6 shows a set of images of the time-varying field excited by 3 pairs of current filament with a 1200 phase difference between each other (three-phase windings).

Imaging Electromagnetic Field Using SMP Image

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Fig. 5. Dynamic SMP image of planar magnetic field excited by a pair of current filaments

Fig. 6. Dynamic SMP image of planar magnetic field excited by 3-phase windings

(a)

(b)

(c)

Fig. 7. Dynamic SMP image of eddy current field excited by a traveling magnetic field

The images in Figure 7 show the eddy current field excited by a traveling magnetic field. Two perpendicular uniform alternating magnetic fields in space with a o phase difference of 90 in time are used as the source fields. From the images, we find that the total number of flux tubes doesn’t vary a lot with time; but the pattern of the eddy current moves with time following the traveling excited magnetic field.

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5 Conclusions Taking eddy current field as an example, SMP method is extended for imaging of electromagnetic field distributed on general surfaces. A new algorithm is also presented for the rendering of the SMP images on surfaces. 1D texture mapping is utilized to do the modulation of the potential automatically. This makes it possible for the SMP image to be rendered in real time and possible for dynamic imaging of timevarying fields. In the rendered dynamic images, the distribution of the flux tubes in each frame reflects the distribution of the direction and amplitude of the field in space, while the changing of the numbers and the patterns of the flux tubes between successive frames gives an intuitive image of the variation of the field with time. In the deducing of the scalar potential of eddy current field, the only requirements are that the eddy current field is distributed on the surface and its divergent is free. So SMP method can be generalized for imaging of other divergent-free vector fields distributed on surfaces.

References 1. Cabral, B., Leedom, L.: Imaging vector fields using line integral convolution”. Proceedings of the ACM SIGGRAPH '93 Conference on Computer Graphics. (1993) 263-270 2. Stalling, D., Hege, H.C.: Fast and Resolution Independent Line Integral Convolution. Proceedings of the ACM SIGGRAPH ’95 Conference on Computer Graphics. (1995) 249-256 3. Tang, Z.: Visualization of Three Dimensional Data Field. Tsinghua University Press, Beijing (1999, in Chinese). 4. Battke, H., Stalling, D., Hege, H.C.: Fast Line Integral Convolution for Arbitrary Surfaces in 3D. Visualization and Mathematics, Springer-Verlag, Heidelberg New York (1997) 181195 5. Shen, H., Kao, D.: A New Line Integral Convolution Algorithm for Visualizing TimeVarying Flow Fields. IEEE Transaction on Visualization and Computer Graphics. (1998) 98-108 6. Sundquist, A.: Dynamic Line Integral Convolution for Visualizing Streamline Evolution. IEEE Transaction on Visualization and Computer Graphics. (2003) 273-282 7. Zhao, Y., Chai, J.: Imaging planar magnetic vector field via SMP. Journal of Tsinghua Univ, 2002, 42(9): 1200-1203. (in Chinese). 8. Smythe, W.R.: Static and Dynamic Electricity. 2nd edn. McGraw-Hill Book Company, Inc., New York (1950)

Support Vector Machine Approach for Partner Selection of Virtual Enterprises* Jie Wang1,2, Weijun Zhong1, and Jun Zhang2 1

School of Economics & Management, Southeast University, Nanjing, Jiangsu 210096, China 2 Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA [email protected], [email protected]

Abstract. With the rapidly increasing competitiveness in global market, dynamic alliances and virtual enterprises are becoming essential components of the economy in order to meet the market requirements for quality, responsiveness, and customer satisfaction. Partner selection is a key stage in the formation of a successful virtual enterprise. The process can be considered as a multi-class classification problem. In this paper, The Support Vector Machine (SVM) technique is proposed to perform automated ranking of potential partners. Experimental results indicate that desirable outcome can be obtained by using the SVM method in partner selections. In comparison with other methods in the literatures, the SVM-based method is advantageous in terms of generalization performance and the fitness accuracy with a limited number of training datasets.

1 Introduction An important activity in the formation of a virtual enterprise (VE) is the selection of partners. How to select appropriate partners to form a team is a key problem for successful operation and management of VEs. This problem has attracted much attention recently [1, 2]. Partner selection is an unstructured and multi-criterion decision problem. Qualitative analysis methods are commonly used in many research works [3]. However, quantitative analysis methods for partner selection are still a challenge. Existing quantitative methods in the related literatures can be classified into several categories: mathematical programming models, weighting models, genetic algorithms, dynamic clustering, neural network and fuzzy sets. Talluri and Baker [4] proposed a two-phase mathematical programming approach for partner selection by designing a VE, in which the factors of cost, time and distance were considered. The weighting model includes the linear scoring model and analytic hierarchy process (AHP). The linear scoring model assigns weights and scores arbitrarily. In the AHP model, the *

This work was supported by grant No. 70171025 of National Science Foundation of China and grant No. 02KJB630001 of Research Project Grant of JiangSu, China.

J. Zhang, J.-H. He, and Y. Fu (Eds.): CIS 2004, LNCS 3314, pp. 1247–1253, 2004. © Springer-Verlag Berlin Heidelberg 2004

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priorities are converted into the ratings with regard to each criterion using pairwise comparisons and the consistency ratio [5]. Clustering technology can also be used in the partner selection process, which is based on the rule that multiple potential partners can be classified into one class if no significant difference on evaluation criteria exists in these partners. While artificial neural network (ANN) approach seems to be the best one available that efficiently combines qualitative and quantitative analysis to ensure the objective of selection processes, the prerequisite for the ANN approach is a large number of training data and the method may easily lead to local optimum. This paper proposes a new approach to partner selection process by utilizing the Support Vector Machine technique. Based on well developed machine learning theory, Support Vector Machine (SVM) is a supervised learning technique that has received much attention for superior performances in various applications, such as pattern recognition, regression estimation, time series predication and text classfication. To employ SVM for distinguishing more than two classes, several approaches have been introduced [7]. In this paper, we focus on how to use binary SVM technique in the multiclass problem of partner selection.

2 Design of SVM-Based Partner Selection System Basically partner selection is a process that produces partner rank in the order of overall scores of their performance according to a certain criterion system. Let us consider a pool of potential partners containing k independent organizations, and a criterion system containing d sub-criteria. Define xi to be a feature vector of length d for the i-th potential partner.

xi = ( xi1 , xi 2 ,..., xij ,..., xid ) , ( i=1,..., k; j=1,..., d ) where xij is the value of the j-th criterion for the i-th potential partner. 2.1 Selection Criterion System Partners are selected based on their skills and resources to fulfill the requirements of the VE [4]. The selection process is based on multiple variables such as organizational fit, technological capabilities, relationship development, quality, price, and speed [6]. A three-layer selection criterion is developed as shown in Fig.1. The hierarchical structure includes goal, criteria and sub-criteria. The hierarchy can easily be extended to more detailed levels by breaking down the criteria into sub-criteria. Some sub-criteria are determined by five rating levels: outstanding, above average, average, below average and unsatisfactory. Since the SVM method requires that each data be represented as a vector of real numbers, such sub-criteria should be converted into numerical data simply by using 5 to represent the best level and 1 for the lowest level.

Support Vector Machine Approach for Partner Selection of Virtual Enterprises Goal

Criteria

1249

Sub-criteria

Quality

C1: Pass rate in quality control C2: Total quality management C3: Quality system certification C4: Remedy for quality problems

Cost

C5: Product Price C6: Delivery cost

Time

C7: Due date

Partner Rank

C8: Attitude

Service

C9: Maintenance quality C10:Cooperation and information exchange Financial status

C11: Balance ratio C12: Investment / revenue

Compatibility

C13: Enterprise culture C14: Management compatibility C15: Information format

Environment

C16: Geographical limitation C17: Political environment C18: Law restriction C19: Economy environment C20: Organization credit standing

Fig. 1. The three-layer criterion structure for supplier partner selection

2.2 Binary Support Vector Machine SVM is basically a binary classifier. For a two-class classification problem, given a set G of training data (xi,yj), for i=1,2,…,n, i.e., the input vectors x i ∈ \ d with corresponding labels yi ∈ {1, −1} , here +1 and –1 indicate two classes, SVM seeks the solution of the following optimization problem:

min w , b ,ξ

s.t.

l 1 T ω ω + C ∑ ξi 2 i =1

yi (ω T φ ( xi ) + b) ≥ 1 − ξi

ξi ≥ 0,

i = 1,..., n

where C is a parameter to be chosen by the user. A larger C corresponds to assigning a larger penalty to errors. ξi is slack variables when the training data is not linearly separable in the feature space. The decision function is

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J. Wang, W. Zhong, and J. Zhang

n

f ( x) = ( wi x) + b = ∑ α i yi ( xi i x) + b i =1

2.3 Key Problems of Design

Using the idea of SVM, the class number is equal to the number of potential partners. We need to find a classifier with the decision function, f(x) such that y = f(x), where y is the class label for x. K is a variable determined by the actual number of training data. Obviously the SVM method cannot be applied directly. The following three problems need to be solved when applying the SVM method to the selection process: 1. decompose the ranking problem into classification problems, 2. construct multi-class classification SVM from the binary SVM, 3. transform results of classification into numerical values.

3 System Implementation 3.1 One-to-One Comparison of Potential Partners

Given two partners denoted by i and j, with the feature vectors xi and xj of dimension d, their ranks are represented by F(xi) and F(xj) respectively. We define the vector of cij of dimension 2d by combining xi and xj

cij = ( xi1 , x j1 ,..., xim , x jm ,..., xid , x jd ) (i,j =1,..., k; i≠j, m=1,...,d) Let yij be the class label, according to the overall score of the partners i and j, we have ⎧+1, ⎪ yij = ⎨ 0, ⎪ −1, ⎩

F ( xi ) > F ( x j ) F ( xi ) = F ( x j )

i, j = 1,..., k and j ≠ i

F ( xi ) < F ( x j )

Therefore the class number for two partners is 3, which does not change with the total number of training samples. The original training sets represented by (xi , yj) is transformed into the format of (cij , yij). In this case, the SVM approach can be applied to classify cij to determine the relative performance of any pair of partners. 3.2 Multi-class Classification SVM

Through the format variation of (cij , yij), the selection process can be initiated by a three-class classification process. The one-against-one method is used to construct all the possible classifiers where each one is generated between two classes chosen out of the k classes from the training data [8]. The decision function for the class pair pq is defined by fpq(x). Since fpq(x)=–fqp(x), there exist k(k–1)/2 different classifiers for a k-class problem. The “max wins” algo-

Support Vector Machine Approach for Partner Selection of Virtual Enterprises

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rithm is used for class identification of the one-against-one method. In the “max wins” algorithm each classifier casts one vote for its preferred class, and the final result is the class with the most votes. k

the class of X = arg max p

∑

sign( f pq ( x))

q ≠ p , q =1

When more than one class have the same number of votes, each point in the unclassifiable region is assigned to the closest class using the real valued decision functions as: k

the class of X = arg max p

∑

f pq ( x)

q ≠ p , q =1

Based on the above one-against-one algorithm, we developed three binary classifiers between every two classes. 3.3 Transformation of Classification Results

In order to compute the final rank of the partners, we have to decide how to transform the results of classification into the final rank of partners. The idea of Round Robin are utilized here in which each partner is compared with every other partners in the same test dataset. Let n be the total number of the test datasets, xi be the feature vector of the i-th partner, then cij is constructed by combining xi with every other xj ( j = 1,…,n and j≠i). Using 3-class SVM in Section 3.2, the n-1 class labels yij are calculated for each cij. Define

⎧ 2, yij = 1, ⎪ g i ( x j ) = ⎨ 1, yij = 0, i, j = 1,..., n and j ≠ i ⎪ 0, y = −1, ij ⎩ where gi(xj) is the score of the i-th partner with respect to the j-th partner. And define n

f ' ( xi ) = ∑ gi ( x j )

i = 1,..., n

j =1 j ≠i

where f ' ( xi ) is the final score of the i-th partner. Therefore, the order of potential partners in the test dataset can be determined according to the absolute value of each f ' ( xi ) in either ascending or descending order.

4 Experimental Analysis Using the ideas discussed in Section 3, a partner selection system based on the multiclass SVM method was implemented. We point out that in the multiclass SVM method, the kernel function and the parameter adjustment are very important. We used a polynomial function.

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K ( x, xi ) = [( x ⋅ xi ) + 1] q We ran experiments with different kernel parameters and measured accuracy and CPU time for the training time. Table 2 indicates that the values of q and C have direct effect on the accuracy and training time of the system. Table 1. Accuracies and trainning times for kernel parameter q and penalty coefficient C Kernel Function

Kernel Parameters

Polynomial function K ( x , x ) = [( x ⋅ x ) + 1] i

i

q

Accuracy(%)

Training time(second)

q=2, C=0.1 q=2, C=0.2 q=2, C=0.3

96.6 96.6 97.1

31 24 24

q=3, C=0.1

98.1

22

q=3, C=0.2 q=3, C=0.3

98.1 98.1

20 19

q=4, C=0.1

97.5

24

q=4, q=4, q=5, q=5,

C=0.2 C=0.3 C=0.1 C=0.2

97.6 97.6 97.1 97.1

22 22 31 25

q=5, q=8, q=8, q=8,

C=0.3 C=0.1 C=0.2 C=0.3

97.1 96.1 96.1 95.6

23 56 56 43

5 Conclusion By transforming the ranking of partners into multiple binary classification problems, we proposed and implemented a new approach to the solution of partner selection of virtual enterprise. Results of our experiments indicate that in comparison with other methods reported in the literatures, the SVM-based method presented in the paper is advantageous in terms of achieving certain fitness accuracy with a limited number of training datasets. More works need to be done in the selection of the kernel function and parameters. Determining the best kernel parameters would be an interesting topic for future research. Furthermore, the comparison of the SVM-based system with those based on other methods such as PCA and Fisher are desirable in order to demonstrate that better accuracy can be obtained by the adoption of SVM in the ranking system.

References 1. Subramai, M., Walden, E.: Economic Returns to Firms from Business-to-Business Electronic Commerce Initiatives: An Empirical Examination. In Proc. 21st Int’l Conf. Information Systems (2000) 229-241

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2. Davulcu, H., Kifer, M., et al: Modeling and Analysis of Interactions in Virtual Enterprises. In Proceedings of Ninth International Workshop on Research Issues on Data Engineering (1999) 3. Maloni, M.J., Benton, W.C.: Supply Chain Partnerships: Opportunities for Operations Research. European Journal of Operational Research 101 (1997) 419-429 4. Talluri, S., Baker, R.C.: Quantitative Framework for designing efficient business process alliances. In: Proceedings of 1996 International Conference on Engineering and Technology Management (1996) 656-661 5. Lee, E.K., et al.: Supplier Selection and Management System Considering Relationships in Supply Chain Management. IEEE Transactions on Engineering Management, vol. 48. (2001) 307-318 6. Sarkis, J., Sundarraj, P.: Evolution of Brokering; Paradigms in E-Commerce Enabled Manufacturing. Int. J. Production Economics, vol. 75. (2002) 21-31 7. Platt, J., Cristianini, N., and Shawe-Taylor. J.: Large Margin DAGs for Multiclass Classification. In Advances in Neural Information Processing Systems 12 (NIPS Conference, Denver, CO, 1999) (2000) 547–553 8. David, M.J., Robert, P.W.: Using Two-Class Classifiers for Multiclass Classification. www.ph.tn.tudelft.nl/People/ bob/papers/icpr_02_mclass.pdf

Author Index

Achalakul, Tiranee 38 Ahn, Hyunchul 922 Amodio, Pierluigi 1 Azuaje, Francisco 556 Bae, Misook 940 Bae, Yongeun 219 Baik, Ran 245 Baik, Sung Wook 245, 910 Bala, Jerzy 910 Bedregal, Benjam´ın Ren´e Callejas 928 Black, Norman 556 Black, Norman D 498 Bogen, Daniel K. 916 Cao, Chunhong 324, 449 Cao, Jiannong 77 Cao, Zhenfu 1034 Chai, Zhenchuan 1034 Chan, Keith C.C. 77 Chan, Tony F. 718 Chen, Bao-Xing 19 Chen, Guihai 1041 Chen, Guo-liang 213 Chen, Jiaxun 995 Chen, Jiu Jun 806 Chen, Wang 32 Chen, Tiejun 330 Chen, Zhide 888 Cheng, Daizhan 768 Cho, Dong-Sub 812 Cho, Jae-Hyun 613 Cho, June-Sik 589 Cho, Sehyeong 407 Cho, Wanhyun 639 Choi, Byung-Jae 148, 582 Choi, Jong-Hwa 238 Choi, Soo-Mi 504 Choi, Yoo-Joo 504 Cho, Yongyoon 752 Choy, Yoon-Chul 873 Chu, Wanming 51 Chung, Llyong 219 Chung, Tae-Sun 252 Cui, Xia 44

Dai, Jing 1027 Dai, Weizhong 304 Dai, Xiaoling 782 de Ara´ ujo, Frederiko Stenio 928 Deng, Zhong-Shan 437 Ding, Peng 1008 Ding, Yihong 672 Doh, Kyu B. 819 Dong, Liju 1079 Dong, Lingjiao 330 Dong, Shoubin 353 Dong, Xiaoju 336 Du, Tao 825 Du, Xiao-yong 1047 Du, Ye 692 Ejaz, Ahmed 685 Enhong, Chen 962 Eom, Young Ik 853 Ermis, Murat 837 Fei, Minrui 330 Feng, Boqin 847 Feng, Deng-Guo 1054 Feng, Dongqing 330 Fu, Cheng 455 Fu, Heng 443 Fu, Yuxi 336, 477, 879 Gao, Ji 806 Gao, Jing 523 Giannoutakis, Konstantinos M. 111 Gong, Lie-Hang 1127 Gravvanis, George A. 111 Grundy, John 782 Gu, Lixu 678 Gu, Wei 93 Gu, Wen 154 Gu, Yonggen 879 Guo, Qing 698 Guo, Ruiqiang 471 Gwun, Ou-Bong 516, 1134 Han, Han, Han, Han,

Ingoo 922 JungHyun 916, 1161 Lixin 1041 Yiqiu 969

1256

Author Index

Han, Zongfen 136 Hasan, M.K. 57 Huazhong Shu 550 He, Ji-Huan 465, 652, 659 He, Kejing 353 He, Lin 477 He, Wenzhang 379 He, Xiaofei 775 He, Xingshi 425 Heo, Won 238 Hiew, Fu San 200 Ho, Kei Shiu 954 Hong, Chuleui 188, 194 Hong, Sugwon 252 Hongqing Zhu 550 Horie, Ken 745 Hou, Meimei 391 Hu, He 1047 Hu, Jun 806 Hu, Laizhao 665, 1020 Hu, Min 672 Hu, Yunxia 7 Huang, Wei 794 Huang, Xiaoqin 1061 Hughes, John G. 498 Huo, Hua 847 Hwang, Buhyun 940 Hwang, Byung-Kon 860 Ibrahim, Zuwairie 71 Iliopoulos, Costas S. 698 Jang, Hyuk Soo 252 Jang, Tae-won 258 Je, Sung-Kwan 613 Jeong, Chang-Sung 1141 Jeong, Ok-Ran 812 Jianyun, Chai 1239 Jian, Zhou 550 Jiao, Licheng 1175 Jin, Hai 136 Jin, Weidong 665, 1020 Jung, MiGyoung 1216 Jung, Moon-Ju 1161 Kang, Min-goo 258 Kang, Sin-Jae 800 Karaa, Samir 124 Kenneth, Revett 685

Khalid, Marzuki 71 Kim, Dong Seong 895 Kim, Dong-oh 258 Kim, Eui-Jeong 595 Kim, Euntai 538 Kim, Eunyoung 916 Kim, Gu Su 853 Kim, HyungJun 207 Kim, Jae-gon 853 Kim, Jae-Kyung 873 Kim, Jeong-Sik 504 Kim, Jong-Wan 800, 860 Kim, Jung-Ja 631 Kim, Kwang Baek 1121 Kim, Kwang-Baek 613, 762 Kim, Kyeongwha 819 Kim, Kyoung-jae 922 Kim, Kyoungjung 538 Kim, Kyungsoo 431 Kim, Myoung-Hee 504 Kim, Pyung Soo 1106 Kim, Sangkyun 739, 788 Kim, Seung-Man 1187 Kim, Seung-Wan 1134 Kim, Sin-Jae 860 Kim, Sun Kyung 231 Kim, Tae Hee 231 Kim, Tae-Hyung 298 Kim, Wonil 188, 194 Kim, Yeongjoon 188, 194 Kim, Yong-Guk 274, 516, 1134 Kim, Yoon Hyuk 413, 431 Kim, Young-Ho 631 Kim, Young-Ju 762 Koay, Kah Hoe 200 Kong, Fansheng 1014 Koo, Han-Suh 1141 Kown, Oh-Kyu 130 Kukkonen, Saku 399 Kurzynski, Marek W. 831 Kwon, Taekyoung 274 Kyung, Kyu Min 538 Lai, Wei 1168 Lam, Wai 969 Lampinen, Jouni 399 Lan, Kwok Cheung 954 Lan, Zhiling 280 Lavrenteva, Olga 93 Le, Jiajin 471, 989

Author Index Lee, Chung Ki 252 Lee, DongWoo 182 Lee, GueeSang 1216, 1224 Lee, Kwan H. 1187, 1208 Lee, Kyoung-Mi 1201 Lee, Moonkey 266 Lee, Ou-seb 258 Lee, Sae-Bom 800 Lee, SangJun 903 Lee, SeongHoon 182 Lee, SuKyoung 142, 160 Lee, Yongbum 576 Leem, Choon Seong 739, 788 Leong, Hong Va 954 Li, Beibei 989 Li, Guoqiang 477, 879 Li, Huaqing 1067 Li, Minglu 510 Li, Qingfeng 419 Li, Wenhui 324, 449 Li, Xue 705, 711 Li, Yaming 51 Li, Yawei 280 Li, Yunfa 136 Li, Zhenquan 118 Liao, Bei Shui 806 Liao, Jun 85 Liao, Lin 77 Lim, Kwa-seop 258 Lim, Soon-Bum 873 Limin, Luo 550 Lin, Chen 1061 Liu, Bihong 1014 Liu, Bing 166 Liu, Dezhi 530 Liu, Huafeng 562 Liu, Hui 172 Liu, Jiang B. 768 Liu, Jinde 85 Liu, Jing 437 Liu, Junhong 399 Liu, Xiaoxiao 570 Liu, Xu-Zheng 44 Liu, Yong 346 Liu, Yu 425 Liu, Yu-Shen 1093 Liu, Yuhua 105 Liu, Zhiqiang 1008 Lixiong, Li 310 Long, Keping 365

Lu, Bao-Liang 867 Lu, Jia 7 Lu, Jian 286 Lu, Ke 775 Lu, Liuming 995 L¨ u, Xin 1054 Luk, Robert Wing Pong 954 Luo, Jianhua 32, 645 Ma, Tieju 794 Mantere, Timo 1148 Mao, Jingzhong 105 Matsuhisa, Takashi 745, 1114 McClean, Stephen 498 Mitsuhashi, Kohei 982 Minrui, Fei 310 Miura, Takao 947, 982 Moon, Jongbae 752 Na, Jong Whoa 934 Nakamori, Yoshiteru 794 Nam, In-Gil 800 Natwichai, Juggapong 705 Ng, Michael K. 718 Nguyen, Ha-Nam 895 Nir, Avinoam 93 No, Jaechun 225 Noh, Seung-Moo 589 Oh, Am-Suk 762 Oh, Young-Cheol 860 Ohn, Jungho 819 Ohn, Syng-Yup 895 Ojha, Piyushc 498 Ono, Osamu 71 Othman, M. 57 Pan, Yunhe 346 Pandya, Abhijit S. 1121 Pang, Yonggang 692 Park, Byung-In 130 Park, Chang-Woo 538 Park, Dong Sun 492 Park, Hyun Suk 607 Park, Jong Sou 895 Park, Jong-Won 589, 595 Park, Jonghyun 639 Park, Joungwook 1208 Park, Mignon 538

1257

1258

Author Index

Park, Soonyoung 639 Park, Sung Soon 225 Park, Won Man 413 Peng, Shietung 51 Peng, Yu 292, 1195 Ping, Xijian 672 Poon, Ting-C 819 Qi, Fei-hu 316 Qi, Feihu 359, 601, 1067 Qi, Zhengwei 455 Qin, Zheng 425 Ramamurthy, Byrar 725 Ramos, Karla Darlene Nempomuceno 928 Razdan, Anshuman 530 Ren, Qingsheng 359 Rhee, Daewoong 910 Ryu, Yeonseung 252 Sahingoz, Ozgur Koray 837 Sang, Nong 570 Sarochawikasit, Rajchawit 38 Seol, Young Joo 607 Seong, Won 589, 595 Sgura, Ivonne 1 Shan, Tan 1175 Shaw, Chris 498 Shen, Dinggang 732 Shen, Yun-Qiu 99 Sheng, Huanye 1008 Shi, Bai-Le 1027 Shi, Lianshuan 443 Shi, Pengcheng 562 Shi, Yonghong 601 Shin, Byeong-Seok 619, 625 Shin, Dongil 238 Shin, Dongkyoo 238 Shin, Jin Wook 492 Shin, YoonJeong 1224 Shioya, Isamu 947, 982 Shu, Wang 962 Silva, Ivan Saraiva 928 Sohn, Won-Sung 873 Song, Bin 213 Song, Binglin 353 Song, Dawei 711 Song, Guoxiang 379

Song, Hyoung-kyu 258 Song, Ju-Whan 516, 1134 Song, Peiming 645 Sonh, Seung-il 258 Su, Hua 1072 Sulaiman, J. 57 Sun, Jia-Guang 44, 292, 1093, 1127, 1155, 1195 Sun, Zhonghua 544 Tang, Qiling 570 Thanneru, Umadevi 768 Tian, Guang 316 Tsai, Du-Yih 576 Tsuboi, Yusei 71 Uejima, Hiroshi 947 Ulengin, Fusun 837 Wan, Chunru 166 Wang, Bin 25, 1155 Wang, Fu Lee 975 Wang, Guojun 77 Wang, Haiying 556 Wang, Huiqiang 692 Wang, Jianxue 825 Wang, Jie 1247 Wang, Lipo 154, 166 Wang, Meng 1002 Wang, Paul P. 582 Wang, Shaoyu 1067 Wang, Shouyang 794 Wang, Xifan 825 Wang, Yonggang 1002, 1181 Wang, Zhaoan 419 Wang, Zheng-Fei 1027 Wei, Guo 1239 Wei, Wang 1027 Wei, Xiaopeng 460 Weng, Wenjie 570 Wiyarat, Thitirat 38 Won, Yonggwan 631 Wu, Aidi 379 Wu, Edmond H. 718 Wu, Ling 1232 Wu, Minna 136 Wu, Yue 465 Wu, Zhaohui 346 Xia, Ling 391

Author Index Xiao, Wen-Jun 19 Xiaobing Zhou 310 Xie, Chao 136 Xie, Dexuan 64 Xie, Li 1041 Xie, Linsen 645 Xu, Congfu 346 Xu, Jianfeng 678 Xu, Qing 1181 Xu, Zenglin 425 Yan, Dong-Ming 292 Yan, Xin 711 Yang, Gab Seok 492 Yang, Geng 13 Yang, Hoonmo 266 Yang, Jianguo 419 Yang, Jie 1002, 1181 Yang, Ju Cheng 492 Yang, Peng 105 Yang, Ruigang 1100 Yang, Xiaobing 1014 Yang, Xiaolong 365 Ye, Rui-song 286 Yi, Wan 449 Yip, Andy M. 718 Yong, Jun-Hai 44, 292, 1072, 1093, 1127, 1155, 1195, 1232 Yong, Jun-Hai Yong 1086 Yoo, Seog-Hwan 148 Yoo, Seong Hwan 582 Yoo, Seong-Joon 607 Yoo, Taeseung D. 916 Yoon, HyoSun 1224 Yoon, Hyung Sik 1161 You, Jinyuan 106, 455 You, Young-hwan 258 Youn, Chunkyun 219 Ypma, Tjalling J. 99 Yu, Donggang 1168 Yu, Ge 1079 Yu, Jian-Yong 465 Yu, Pi-Qiang 1093

Yu, Shengsheng 105 Yu, Shoujian 471 Zeng, Jiazhi 775 Zeng, Jin 359 Zesheng, Tang 1239 Zhan, Yiqiang 732 Zhang, Gexiang 665, 1020 Zhang, Hui 292, 698, 1093, 1195 Zhang, Juan 486 Zhang, Jun 523, 1247 Zhang, Lei 510 Zhang, Li 1232 Zhang, Ling 353 Zhang, Min 365, 477 Zhang, Qiang 460 Zhang, Xianggang 85 Zhang, Xiangrong 1175 Zhang, Xiao-Xin 1127 Zhang, You-Wei 1232 Zhang, Zhizhou 477 Zhao, Hai 867 Zhao, Jing 32, 645 Zhao, Yongqiang 510 Zhao, Yu-Mei 465 Zheng, Guo-Qin 1086, 1127 Zheng, Huiru 498, 544 Zheng, Zhonglong 1002 Zhong, Farong 371 Zhong, Weijun 1247 Zhou, Dongsheng 460 Zhou, Feng-feng 213 Zhou, Quan 13 Zhou, Yue 1181 Zhu, Cheng 1008 Zhu, Guojin 995 Zhu, Hong 888 Zhu, Teng 304 Zhu, Yong-Kang 1086 Zou, Shengrong 385 Zou, Yu-ru 286 Zou, Xukai 725

1259