lec17 Face Recognition III

lec17 Face Recognition III - Why is Face Recognition Hard?...

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1 CSE190a Fal 06 Face Recognition: Lighting Biometrics CSE 190-a Lecture 17 Why is Face Recognition Hard? CS252A, Winter 2005 Computer Vision I Fisherfaces: Class specific linear projection P. Belhumeur, J. Hespanha, D. Kriegman, Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection , PAMI, July 1997, pp. 711--720. •An n -pixel image x R n can be projected to a low-dimensional feature space y R m by y = W x where W is an n by m matrix. • Recognition is performed using nearest neighbor in R m . • How do we choose a good W ? CS252A, Winter 2005 Computer Vision I PCA & Fisher’s Linear Discriminant • Between-class scatter • Within-class scatter • Total scatter •W h e r e c is the number of classes μ i is the mean of class χ i –| χ i | is number of samples of χ i. . T i i c i i B S ) )( ( 1 μ χ = = ∑∑ =∈ = c ix T i k i k W i k x S 1 ) )( ( W B c T k k T S S x S i k + = = 1 ) )( ( μ 1 μ 2 μ χ 1 χ 2 CS252A, Winter 2005 Computer Vision I PCA & Fisher’s Linear Discriminant • PCA (Eigenfaces) Maximizes projected total scatter • Fisher’s Linear Discriminant Maximizes ratio of projected between-class to projected within-class scatter W S W W T T W PCA max arg = W S W W S W W W T B T W fld max arg = χ 1 χ 2 PCA FLD CS252A, Winter 2005 Computer Vision I Harvard Face Database 15 o 45 o 30 o 60 60 o • 10 individuals • 66 images per person • Train on 6 images at 15 o • Test on remaining images
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2 CS252A, Winter 2005 Computer Vision I Recognition Results: Lighting Extrapolation 0 5 10 15 20 25 30 35 40 45 0-15 degrees 30 degrees 45 degrees Light Direction Error Rate Correlation Eigenfaces Eigenfaces (w/o 1st 3) Fisherface © Jain, 2004 (2D) Model-based Active Appearance Model • Model Construction (linear) labeled image landmarks shape-free texture © Jain, 2004 Active Appearance Model (AAM) • Shape model • Appearance model • Combined model T n n y x y x s ) , ,..., , ( 1 1 = s s b P s s + = g g b P g g + = T m I I g ) ,..., ( 1 = = = ) ( ) ( g g P s s P W b b W b T g T s s g s s Qc b = PCA © Jain, 2004 AAM • Model fitting – Minimize the objective function (gray level difference between the given image and the stored model – Searching by learning • Annotated model (true model parameters) • Relation: known model displacements observed difference vector • Use multivariate multiple regression to learn the relation and predict the displacement during searching 2 I δ = Δ © Jain, 2004 AAM Initial 3 its 8 its 11 its Converged Original The challenge caused by lighting variability Same Person or Different People
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3 Same Person or Different People Same Person or Different People
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4 Illumination & Image Set Lack of illumination invariants [Chen, Jacobs, Belhumeur 98] Set of images of Lambertian surface w/o shadowing is 3-D linear subspace [Moses 93], [Nayar, Murase 96], [Shashua 97] Empirical evidence that set of images of object is well-approximated by a low- dimensional linear subspace [Hallinan 94], [Epstein, Hallinan, Yuille 95] Illumination cones [Belhumeur, Kriegman 98]
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lec17 Face Recognition III - Why is Face Recognition Hard?...

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