Face recognition via
sparse representation
Breakdown
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Problem
Classical techniques
New method based on sparsity
Results
Classical Techniques
• Eigenfaces
• Uses PCA for feature extraction
• Problems faced
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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 ||2
X
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.
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