Face recognition via sparse representation

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

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

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

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

Problem• A w x h image is identified as a vector v ϵ Rm

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

• 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.

• ẋ2 = arg min || y – Ax ||2X

• 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.

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 mini ri(y).

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

RESULTS

1. Random pixel corruption

2. Random block occlusion

Recognition despite disguise

THANK YOU