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# l02 - Face Recognition Using aces E igenf Math A Turkand A...

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Face Recognition Using Eigenfaces Mathew A.Turkand A lexP.Pentland Presenter: Polina Golland

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r l inition P obem Def ac ac Recognize f es vs.non-f es ac Recognize f es ofa particular person vs. ac f es ofother peop le • Do it f ast 0 0 881 2 02/7/5 6.
Basic Idea ac PCAon f e images œ Face images lie in a low dimensional space œ Images ofthe same person are c lose to eachother mages ofdiff erent peop le are f œ I arther away 0 0 881 3 02/7/5 6.

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Recognition ec ac Given a new image, proj t onto f e space f ac œ Ithe residual is too h igh , it‘s not a f e f ec œ Ithe proj tion is c lose to one ofthe —prototypes“, assign it to that c lass œ Otherwise, it‘s a new f e ac 0 0 881 4 02/7/5 6.
Illustr ation ofFace Space 0 0 881 5 02/7/5 6. u 1 u 2 Ω 1 Ω 2 Ω 3 3 4 2 1 Face Space Figure by MIT OCW.

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T aining r nput: M input images in a vec tor f • I orm i ac • Mean f e = M -1 ƒ i • Zero-mean data = - i i • Zero-mean data matrix A = [ 1 M ] 2 … • Covariance matrix C = M -1 ƒ T = AA T i i 0 0 881 6 02/7/5 6.
T aining cont‘d r ac • E igenf es u k are the eigenvec tors of C • Keepa small number ( M ‘) ofeigenf es ac œ In the experiments, M = 16, M ‘ = 7 • Resultingmodel: œ Mean f e ac ac œ M ‘ eigenf es u k ( k = 1,…, M ‘) 0 0 881 7 02/7/5 6.

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