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)