Subspace Analysis for Face Recognition

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Subspace Analysis for Face Recognition
Subspace Representation for
Face Recognition
Presenters:
Jian Li and Shaohua Zhou
Overview
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4 different subspace representations
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2 options
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PCA, PPCA, LDA, and ICA
Kernel v.s. Non-Kernel
2 databases with 3 different variations
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Pose, Facial expression, and Illumination
Subspace representations
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Training data X (d,n)
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Subspace decomposition matrix W (d,m)
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X = [x1, x2, …, xn]
W = [w1, w2, …, wm]
Representation Y (m,n)
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Y = W’ * X
PCA, PPCA, LDA and ICA
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PCA, in an unsupervised manner, minimizes
the representation error ||X – Y||.
LDA, in a supervised manner, minimizes the
within-class distance while maximizing the
between-class distance.
ICA, in an unsupervised manner, maximizes
the independence between Y ’s.
Probabilistic PCA, coming late …
Kernel or Non-Kernel
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Often somewhere reduces to some
forms related to dot product
Kernel trick
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Replacing dot product by kernel function
Mapping the original data space into a
high-dimensional feature space
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K(x,y) = <f(x) , f(y)>
Gaussian kernel: exp(- 0.5 |x – y|^2/sigma^2)
Gallery, Probe, Pre-processing
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Training dataset
Testing dataset
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Gallery: Reference images in testing
Probe: Probe images in testing
Pre-processing
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Down-sampling
Zero-mean-unit-variance
x = { x - mean(x) } / var(x)
Crop face region only
AT&T Database
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Pose variation
40 classes, 10 images/class, 28 by 23
Set1
Set2
(Mirror
of Set1)
FERET Database
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Facial expression and illumination
variation
200 classes, 3 images/class, 24 by 21
Set1
Set2
Set3
Probabilistic PCA (PPCA) -- I
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PCA only extracts PCs thereby losing
probabilistic flavor
PPCA add this by interpreting the
reconstruction error as confidence level
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y=u+W*x+e
Different choices of e
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Factor analysis,
PPCA (Tipping and Bishop ’99)
PCA
Probabilistic PCA (PPCA) -- II
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Assume e has covariance matrix, pho*I
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R = U * D * U’
W = Um * (Dm – pho*I) ^(1/2)
Pho = mean of the remaining eigenvalues
Implemented algorithm
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B. Moghaddam ’01
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W = Um * (Dm) ^(1/2)
- 2log P(y) = sum (Pci^2/Di) + e^2 / pho + const
Construct inter-person space
Probabilistic KPCA (PKPCA)
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Replace PCA by KPCA in the PPCA
algorithm
Estimating e by computing sum of all
remaining PC’s.
ICA
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Independent face
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PCA pre-whitening: X1 = U’ * X
Y = W * X1
Independent facial expression
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Y = W * X’
Kernel ICA
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F. Bach and M. I. Jordan ‘01
‘Kernel trick’ is played when measuring
independence
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Canonical correlation -- independence
 ( x1 , x2 )  max corr (1 ' x1 ,  2 ' x2 ) 
1 , 2

1 ' C12 2
1 ' C111 2 ' C22 2
cov(1 ' x1 ,  2 ' x2 )
var(1 ' x1 ) var( 2 ' x2 )
Experimental Setup
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Training
Ranking the gallery based on the
distance or probability
CMS curve
Distance Metric
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SAD, SQD, Correlation (mean removed)
Tweaking Gaussian kernel
width
Eigenfaces & Fisherfaces
Eigenfaces
Fisherfaces
Independent Basis Faces &
Facial Features
Ind. Faces
Ind. Facial
Features
Performance on pose variation
Performance on facial
expression variation
Performance on illumination
variation
Comparison of 4 methods
0.8
0.7
0.6
0.5
Pose
Expression
Illumination
Average
0.4
0.3
0.2
0.1
0
PCA
PPCA
FDA
ICA*
Comparison of Kernel/Nonkernel methods
0.7
0.6
0.5
Pose
Expression
Illumination
Average
0.4
0.3
0.2
0.1
0
Non-Kernel
Kernel
Computational load
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Training time:
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PCA < LDA < PPCA < ICA
KPCA < KLDA < PKPCA << KICA
Testing time:
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PCA = LDA = ICA < PPCA
KPCA = KLDA = KICA < PKPCA

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