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Subspace Representation for Face Recognition

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Subspace Representation for Face Recognition Presenters: Jian Li and Shaohua Zhou Overview 4 different subspace representations PCA, PPCA, LDA, and ICA 2 options ... – PowerPoint PPT presentation

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Title: Subspace Representation for Face Recognition


1
Subspace Representation for Face Recognition
Presenters Jian Li and Shaohua Zhou
2
Overview
  • 4 different subspace representations
  • PCA, PPCA, LDA, and ICA
  • 2 options
  • Kernel v.s. Non-Kernel
  • 2 databases with 3 different variations
  • Pose, Facial expression, and Illumination

3
Subspace representations
  • Training data X (d,n)
  • X x1, x2, , xn
  • Subspace decomposition matrix W (d,m)
  • W w1, w2, , wm
  • Representation Y (m,n)
  • Y W X

4
PCA, PPCA, LDA and ICA
  • 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

5
Kernel or Non-Kernel
  • Often somewhere reduces to some forms related to
    dot product
  • Kernel trick
  • Replacing dot product by kernel function
  • Mapping the original data space into a
    high-dimensional feature space
  • K(x,y) ltf(x) , f(y)gt
  • Gaussian kernel exp(- 0.5 x y2/sigma2)

6
Gallery, Probe, Pre-processing
  • Training dataset
  • Testing dataset
  • Gallery Reference images in testing
  • Probe Probe images in testing
  • Pre-processing
  • Down-sampling
  • Zero-mean-unit-variance
  • x x - mean(x) / var(x)
  • Crop face region only

7
ATT Database
  • Pose variation
  • 40 classes, 10 images/class, 28 by 23

Set1
Set2 (Mirror of Set1)
8
FERET Database
  • Facial expression and illumination variation
  • 200 classes, 3 images/class, 24 by 21

Set1
Set2
Set3
9
Probabilistic PCA (PPCA) -- I
  • PCA only extracts PCs thereby losing
    probabilistic flavor
  • PPCA add this by interpreting the reconstruction
    error as confidence level
  • y u W x e
  • Different choices of e
  • Factor analysis,
  • PPCA (Tipping and Bishop 99)
  • PCA

10
Probabilistic PCA (PPCA) -- II
  • Assume e has covariance matrix, phoI
  • R U D U
  • W Um (Dm phoI) (1/2)
  • Pho mean of the remaining eigenvalues
  • Implemented algorithm
  • B. Moghaddam 01
  • W Um (Dm) (1/2)
  • - 2log P(y) sum (Pci2/Di) e2 / pho
    const
  • Construct inter-person space

11
Probabilistic KPCA (PKPCA)
  • Replace PCA by KPCA in the PPCA algorithm
  • Estimating e by computing sum of all remaining
    PCs.

12
ICA
  • Independent face
  • PCA pre-whitening X1 U X
  • Y W X1
  • Independent facial expression
  • Y W X

13
Kernel ICA
  • F. Bach and M. I. Jordan 01
  • Kernel trick is played when measuring
    independence
  • Canonical correlation -- independence

14
Experimental Setup
  • Training
  • Ranking the gallery based on the distance or
    probability
  • CMS curve

15
Distance Metric
  • SAD, SQD, Correlation (mean removed)

16
Tweaking Gaussian kernel width
17
Eigenfaces Fisherfaces
Eigenfaces
Fisherfaces
18
Independent Basis Faces Facial Features
Ind. Faces
Ind. Facial Features
19
Performance on pose variation
20
Performance on facial expression variation
21
Performance on illumination variation
22
Comparison of 4 methods
23
Comparison of Kernel/Non-kernel methods
24
Computational load
  • Training time
  • PCA lt LDA lt PPCA lt ICA
  • KPCA lt KLDA lt PKPCA ltlt KICA
  • Testing time
  • PCA LDA ICA lt PPCA
  • KPCA KLDA KICA lt PKPCA
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