09-Biometrics-Lecture-9-Part1-2008-11-17

09-Biometrics-Lecture-9-Part1-2008-11-17 - Master SC...

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1 Biometrics http://scgwww.epfl.ch/courses Master SC – Information and Communication Security Dr. Andrzej Drygajlo Speech Processing and Biometrics Group Signal Processing Institute Ecole Polytechnique Fédérale de Lausanne (EPFL) Center for Interdisciplinary Studies in Information Security (ISIS)
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2 Face Recognition Face detection Face tracking Face recognition (appearance-based) Local features ± DCT-based methods Global features (holistic approach) ± Principal Component Analysis (PCA) ± Linear Discriminant Analysis (LDA) Performance evaluation Advantages and disadvantages
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3 PCA A face image defines a point in the high-dimensional image space Different face images share a number of similarities with each other D They can be described by a relatively low-dimensional subspace D They can be projected into an appropriately chosen subspace of eigenfaces and classification can be performed by similarity computation (distance) 1 x 2 x ,1 PCA x ,2 PCA x
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4 PCA Suppose data consists of M faces with D feature values 1) Place data in D x M matrix x 2) Mean-center the data Compute D -dimensional μ (mean). x 0 = x - μ 3) Compute D x D covariance matrix ( c = x 0 x 0 T ) 4) Compute eigenvectors and eigenvalues of covariance matrix 5) Choose K largest eigenvalues ( K << D ). 6) Form a D x K matrix W with K columns of eigenvectors. 7) The new coordinates x PCA of data (in PCA space) consists of projecting data into K -dimensional subspace by x PCA = W T ( x μ ) = ... ... ... ... ij x x M faces D features
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5 “Eigenfaces” = 0.4 + 0.2 + ... + 0.6 Perfect reconstruction with all eigenfaces = 0.4 + 0.2 Reasonable reconstruction with just a few eigenfaces
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6 PCA Database Samples
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7 PCA Average Major (principal) Minor
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8 PCA
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9 Eigenfaces Shortcomings: Eigenfaces do not distinguish between shape and appearance PCA does not use class information: PCA projections are optimal for reconstruction from a low dimensional basis, they may not be optimal from a discrimination standpoint: “Much of the variation from one image to the next is due to illumination changes.” [Moses, Adini, Ullman] Problems with eigenfaces: Different illumination Different head pose Different alignment Different facial expression
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10 Face Recognition Face detection Face tracking Face recognition (appearance-based) Local features ± DCT-based methods Global features (holistic approach) ± Principal Component Analysis (PCA) ± Linear Discriminant Analysis (LDA) Performance evaluation Advantages and disadvantages
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11 LDA
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12 Face ID: Fisherfaces 1 x 2 x LDA PCA LDA seeks directions that are efficient for discrimination between the data LDA maximizes the between-class scatter LDA minimizes the within-class scatter Class A Class B
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13 Fisherfaces, the algorithm The database 2 1 2 N b b b ⎛⎞ ⎜⎟ = ⎝⎠ M 2 1 2 N c c c = M 2 1 2 N d d d = M 2 1 2 N e e e = M 2 1 2 N a a a = M 2 1 2 N f f f = M 2 1 2 N g g g = M 2 1 2 N h h h = M
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14 Fisherfaces, the algorithm
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09-Biometrics-Lecture-9-Part1-2008-11-17 - Master SC...

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