Reduksi Dimensi Image dengan Principal Components Analysis (PCA)

Reduksi Dimensi Image dengan Principal Components Analysis (PCA) Sumber: -Trucco & Verri chap. 10 -Standford Vision & Modeling

Contoh: problem Pattern Recognition

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Rotate coordinate system:

Problem Dimensi tinggi ??

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PCA (Principal Component Analysis) • Untuk reduksi dimensi data (Dimensional Reduction) !!! • Ekstraksi struktur data dari dataset high dimenson. • Mencari basis signal berdasarkan data statistik objek.

PCA

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PCA

Demo dengan Matlab: • Mencari basis signal citra wajah. • Image recognition, face recognition.

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PCA

Reduksi dimensi linear:

High-dimensional Input Space

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Linear Subspace:

=

+ =

+ 1.7

Linear Subspace:

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Principal Components Analysis:

N

sT2 = ∑ ( y[n ] − m ) 2 n =1

y = W~ x

N

ST = ∑ ( ~ x − µ )( ~ x − µ )T

m

n =1

sT2 = WSTW T

Contoh:

Data:

Kirby, Weisser, Dangelmayer 1993

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Contoh:

New Basis Vectors

Data: PCA

Contoh:

Data:

EigenLips PCA

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Contoh: Face Recognition dengan Eigenfaces (Turk+Pentland, ):

Contoh:

Face Recognition System (Moghaddam+Pentland):

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Contoh: Visual Cortex

Hubel

Contoh: Visual Cortex

Hubel

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Contoh: Receptive Fields

Hubel

Contoh: Receptive Fields

Hancock et al: The principal components of natural images

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Contoh: Receptive Fields

Hancock et al: The principal components of natural images

Contoh: Active Appearance Models (AAM): (Cootes et al)

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Contoh: Active Appearance Models (AAM): (Cootes et al)

Contoh: Active Appearance Models (AAM): (Cootes et al)

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Contoh: 3D Morphable Models (Blanz+Vetter)

Ulasan

Constrain

-

E(V)

V

V

Analytically derived:

Learned:

Affine, Twist/Exponential Map

Linear/non-linear Sub-Spaces

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Non-Rigid Constrained Spaces

Constrain

E(S)

S = (p1 ,…,p ) n

Non-Rigid Constrained Spaces Linear Subspaces: • Small Basis Set • Principal Components Analysis

Nonlinear Manifolds:

Mixture Models

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Manifold Learning

EM

Mixture of Patches

Training Data

Mixture of Projections G2

G1

P1

Influence Function

P2 Linear Patch ∑ Gi( x) ⋅ Pi (x) i

P (x ) = --------------------------------------∑ Gi (x) i

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Contoh: Eigen Tracking (Black and Jepson)

Contoh: Shape Models for tracking:

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Feature/Shape Models secara umum: Visual Motion Contours: Blake, Isard, Reynard

Feature/Shape Models secara umum: Visual Motion Contours: Blake, Isard, Reynard

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Linear Discriminant Analysis:

Fisher’s linear discriminant:

µk =

1 NK

∑x

n∈C K

n

S B = ( µ 2 − µ1 )( µ 2 − µ1 )T

wT S BW J= T w SW w

SW =

∑ (x

n∈C1

n

− µ1 )( xn − µ1 )T +

∑ (x

n∈C 2

n

− µ1 )( xn − µ1 )T

w ∝ SW−1 ( µ 2 − µ1 )

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Contoh: Eigenfaces vs Fisherfaces

Glasses or not Glasses ?

Contoh: Eigenfaces vs Fisherfaces

Input

New Axis

Belhumeur, Hespanha, Kriegman 1997

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Basis Shape Algorithms lainnya: • ICA (Independent Components Analysis, Bell+Sejnowski) • Maximize Entropy (or spread of output distribution):

Basis Shape Algorithms lainnya: • NMF (non-negative matrix factorization, Lee+Seung) • LNMF (local NMF, Li et al)

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