Face recognition via sparse representation

1. Face recognition via sparse representation

2. Breakdown • Problem • Classical techniques • New method based on sparsity • Results

3. Classical Techniques • Eigenfaces • Uses PCA for feature extraction • Problems faced • Extremely intensive • Poor results when there’s no frontal view • Poor results with bad lighting • Poor results with noise

4. Classical Techniques • Support Vector Machines • PCA for feature extraction • Radial Basis function • One versus all classifier • Problems faced • Extremely intensive • Poor results with bad lighting • Sensitive to noise

5. Via sparse representation • Redundancy • As the number of image pixels is far greater than the number of subjects that have generated the images • Robustness from sparsity • Identity of the test image • Nature of occlusion

6. Problem • A w x h image is identified as a vector v ϵRm given by stacking columns • A = [v1 v2 v3 v4,…..,vn] ϵ R mxn • A test image y = Aixi, assuming no occlusion where y = test image of the ith object

7. If ρ is the fraction of pixels occluded, • y = y0 + e = Ax0 + e Problem statement: Given A1, A2, A3,…., Ak & y by sampling an image from the ith class & perturbing the values of ρ of its pixels arbitrarily, find the correct class.

8. ẋ2= arg min || y – Ax ||2 X • Error is non-Gaussian so this can give a lot of erroneous results • Exploit sparsity of residue: • X0= arg min || y – Ax ||0 X • l1 is same as l0, sometimes.

9. Algorithm • n training samples partitioned into k classes • B = [A1 A1….An I], normalize to have unit l2 norm. • ẃ1 = arg min ||w||1 S.T Bw = y w • Residuals ri(y) = ||y – Aδi(ẋ1) – ê1||2 for i = 1,2,….k. • Output = arg miniri(y).

10. Dataset • Extended Yale B dataset • 38 subjects • 717 images for training and 453 for testing

11. RESULTS

12. 1. Random pixel corruption

13. 2. Random block occlusion

14. Recognition despite disguise

15. THANK YOU