Reduksi Dimensi Image dengan Reduksi Dimensi Image dengan Principal Components Principal Components

Analysis (PCA) Analysis (PCA)

Sumber:Sumber:-Trucco & Verri chap. 10 chap. 10-Standford Vision & ModelingStandford Vision & Modeling

Contoh: problem Pattern RecognitionContoh: problem Pattern Recognition

Rotate coordinate system:Rotate coordinate system:

Problem Dimensi tinggi ??Problem Dimensi tinggi ??

PCA (Principal Component Analysis)PCA (Principal Component Analysis)

• Untuk reduksi dimensi data (Dimensional Untuk reduksi dimensi data (Dimensional Reduction) !!!Reduction) !!!

• Ekstraksi struktur data dari dataset high Ekstraksi struktur data dari dataset high dimenson. dimenson.

• Mencari basis signal berdasarkan data Mencari basis signal berdasarkan data statistik objek.statistik objek.

PCAPCA

PCAPCA

Demo dengan Matlab:Demo dengan Matlab:

• Mencari basis signal citra wajah.Mencari basis signal citra wajah.• Image recognition, face recognition.Image recognition, face recognition.

PCAPCA

Reduksi dimensi linear:Reduksi dimensi linear:

High-dimensionalInput Space

Linear Subspace:Linear Subspace:

+=

+ 1.7=

Linear Subspace:Linear Subspace:

Principal Components Analysis:Principal Components Analysis:

xWy ~

N

nT mnys

1

22 )][(

TN

nT xxS )~()~(

1

TTT WWSs 2

m

Contoh:Contoh:

Data:

Kirby, Weisser, Dangelmayer 1993

Contoh:Contoh:

Data:

PCA

New Basis Vectors

Contoh:Contoh:

Data:

PCA

EigenLips

Contoh:Contoh:

Face Recognition dengan Eigenfaces (Turk+Pentland, ):

Contoh:Contoh:

Face Recognition System (Moghaddam+Pentland):

Contoh: Visual CortexContoh: Visual Cortex

Hubel

Contoh: Visual CortexContoh: Visual Cortex

Hubel

Contoh: Receptive FieldsContoh: Receptive Fields

Hubel

Contoh: Receptive FieldsContoh: Receptive Fields

Hancock et al: The principal components of natural images

Contoh: Receptive FieldsContoh: Receptive Fields

Hancock et al: The principal components of natural images

Contoh:Contoh:

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

Contoh:Contoh:

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

Contoh:Contoh:

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

Contoh:Contoh:

3D Morphable Models (Blanz+Vetter)

UlasanUlasan

E(V)V V

Constrain-

Analytically derived:Affine, Twist/Exponential Map

Learned:Linear/non-linearSub-Spaces

S = (p ,…,p )

E(S) Constrain

1 n

Non-Rigid Constrained Spaces

Non-Rigid Constrained Spaces

Nonlinear Manifolds:

Linear Subspaces:

• Small Basis Set

• Principal Components Analysis

Mixture Models

Training Data Mixture of Patches

EM

Manifold Learning

InfluenceFunction

LinearPatch

P1 P2

G1G2

P x Gi x P i x

i

Gi x i----------------------------------------=

Mixture of Projections

Contoh:Contoh:

Eigen Tracking (Black and Jepson)

Contoh:Contoh:

Shape Models for tracking:

Feature/Shape Models secara umum:

Visual Motion Contours:Blake, Isard, Reynard

Feature/Shape Models secara umum:

Visual Motion Contours:Blake, Isard, Reynard

Linear Discriminant Analysis:Linear Discriminant Analysis:

Fisher’s linear discriminant:Fisher’s linear discriminant:

21

))(())(( 1111Cn

Tnn

Cn

TnnW xxxxS T

BS ))(( 1212

wSwWSwJ

WT

BT

KCn

nK

k xN1

)( 121

WSw

Contoh: Eigenfaces vs FisherfacesContoh: Eigenfaces vs Fisherfaces

Glasses or not Glasses ?

Contoh: Eigenfaces vs FisherfacesContoh: Eigenfaces vs Fisherfaces

Input New Axis

Belhumeur, Hespanha, Kriegman 1997

Basis Shape Algorithms lainnya:Basis Shape Algorithms lainnya:

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

Basis Shape Algorithms lainnya:Basis Shape Algorithms lainnya:

• NMF (non-negative matrix factorization, Lee+Seung)• LNMF (local NMF, Li et al)