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 R m given by stacking columns A = [v 1 v 2 v 3 v 4,…..,v n ] ϵ R mxn A test image y = A i x i, assuming no occlusion where y = test image of the i th object

If ρ is the fraction of pixels occluded, y = y 0 + e = Ax 0 + e Problem statement: Given A 1, A 2, A 3,…., A k & y by sampling an image from the i th class & perturbing the values of ρ of its pixels arbitrarily, find the correct class.

Algorithm n training samples partitioned into k classes B = [A 1 A 1 ….A n I], normalize to have unit l 2 norm. ẃ 1 = arg min ||w|| 1 S.T Bw = y w Residuals r i (y) = ||y – Aδ i (ẋ 1 ) – ê 1 ||2 for i = 1,2,….k. Output = arg min i r i (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

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