Reduksi Dimensi Image dengan Principal Components...

1

ReduksiReduksi DimensiDimensi Image Image dengandenganPrincipal Components Principal Components

Analysis (PCA) Analysis (PCA)

SumberSumber::

-Trucco & Verri chap. 10chap. 10

--StandfordStandford Vision & ModelingVision & Modeling

ContohContoh: problem Pattern Recognition: problem Pattern Recognition

2

Rotate coordinate system:Rotate coordinate system:

Problem Problem DimensiDimensi tinggitinggi ????

3

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

•• UntukUntuk reduksireduksi dimensidimensi data (Dimensional data (Dimensional Reduction) !!!Reduction) !!!

•• EkstraksiEkstraksi strukturstruktur data data daridari dataset high dataset high dimensondimenson. .

•• MencariMencari basis signal basis signal berdasarkanberdasarkan data data statistikstatistikobjekobjek..

PCAPCA

4

PCAPCA

Demo Demo dengandengan MatlabMatlab::

•• MencariMencari basis signal basis signal citracitra wajahwajah..

•• Image recognition, face recognition.Image recognition, face recognition.

5

PCAPCA

ReduksiReduksi dimensidimensi linear:linear:

High-dimensionalInput Space

6

Linear Subspace:Linear Subspace:

+=

+ 1.7=

Linear Subspace:Linear Subspace:

7

Principal Components Analysis:Principal Components Analysis:

xWy ~=

∑=

−=N

nT mnys

1

22 )][(

TN

nT xxS )~()~(

1

µµ −−= ∑=

TTT WWSs =2

m

ContohContoh::

Data:

Kirby, Weisser, Dangelmayer 1993

8

ContohContoh::

Data:

PCA

New Basis Vectors

ContohContoh::

Data:

PCA

EigenLips

9

ContohContoh::

Face Recognition dengan Eigenfaces (Turk+Pentland, ):

ContohContoh::

Face Recognition System (Moghaddam+Pentland):

10

ContohContoh: Visual Cortex: Visual Cortex

Hubel

ContohContoh: Visual Cortex: Visual Cortex

Hubel

11

ContohContoh: Receptive Fields: Receptive Fields

Hubel


Hancock et al: The principal components of natural images

12


Hancock et al: The principal components of natural images

ContohContoh::

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

13

ContohContoh::


ContohContoh::


14

ContohContoh::

3D Morphable Models (Blanz+Vetter)

UlasanUlasan

E(V)V V

Constrain-

Analytically derived:Affine, Twist/Exponential Map

Learned:Linear/non-linear

Sub-Spaces

15

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

16

Training Data Mixture of Patches

EM

Manifold Learning

��

��

��

��

��

��

��

��

��

��

�

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

��

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

InfluenceFunction

LinearPatch

P1 P2

�

��

G1G2

P x( )

Gi x( ) Pi x( )⋅i

∑

Gi x( )i

∑----------------------------------------=

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

Mixture of Projections

17

ContohContoh::

Eigen Tracking (Black and Jepson)

ContohContoh::

Shape Models for tracking:

18

Feature/Shape Models secara umum:

Visual Motion Contours:Blake, Isard, Reynard

Feature/Shape Models secara umum:

Visual Motion Contours:Blake, Isard, Reynard

19

Linear Linear DiscriminantDiscriminant Analysis:Analysis:

Fisher’s linear Fisher’s linear discriminantdiscriminant::

∑∑∈∈

−−+−−=21

))(())(( 1111Cn

Tnn

Cn

TnnW xxxxS µµµµT

BS ))(( 1212 µµµµ −−=

wSw

WSwJ

WT

BT

=

∑∈

=KCn

nK

k xN

1µ

)( 121 µµ −∝ −

WSw

20

ContohContoh: : EigenfacesEigenfaces vsvs FisherfacesFisherfaces

Glasses or not Glasses ?

ContohContoh: : EigenfacesEigenfaces vsvs FisherfacesFisherfaces

Input New Axis

Belhumeur, Hespanha, Kriegman 1997

21

Basis Shape Algorithms Basis Shape Algorithms lainnyalainnya::

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

Basis Shape Algorithms Basis Shape Algorithms lainnyalainnya::

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

Reduksi Dimensi Image dengan Principal Components...

Documents

Transcript of Reduksi Dimensi Image dengan Principal Components...