Title: Subspace Representation for Face Recognition
1Subspace Representation for Face Recognition
Presenters Jian Li and Shaohua Zhou
2Overview
- 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
3Subspace 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
4PCA, 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
5Kernel 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)
6Gallery, 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
7ATT Database
- Pose variation
- 40 classes, 10 images/class, 28 by 23
Set1
Set2 (Mirror of Set1)
8FERET Database
- Facial expression and illumination variation
- 200 classes, 3 images/class, 24 by 21
Set1
Set2
Set3
9Probabilistic 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
10Probabilistic 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
11Probabilistic KPCA (PKPCA)
- Replace PCA by KPCA in the PPCA algorithm
- Estimating e by computing sum of all remaining
PCs.
12ICA
- Independent face
- PCA pre-whitening X1 U X
- Y W X1
- Independent facial expression
- Y W X
13Kernel ICA
- F. Bach and M. I. Jordan 01
- Kernel trick is played when measuring
independence - Canonical correlation -- independence
-
-
14Experimental Setup
- Training
- Ranking the gallery based on the distance or
probability - CMS curve
15Distance Metric
- SAD, SQD, Correlation (mean removed)
16Tweaking Gaussian kernel width
17Eigenfaces Fisherfaces
Eigenfaces
Fisherfaces
18Independent Basis Faces Facial Features
Ind. Faces
Ind. Facial Features
19Performance on pose variation
20Performance on facial expression variation
21Performance on illumination variation
22Comparison of 4 methods
23Comparison of Kernel/Non-kernel methods
24Computational 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