lecture22 - EECS 442 Computer vision Face Recognition PCA...

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EECS 442 – Computer vision Face Recognition PCA (Eigen-faces) LDA (Fisher-faces) Boosting Segments of this lectures are courtesy of Prof F. Li
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Face Recognition Digital photography
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Face Recognition Digital photography Surveillance
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Face Recognition Digital photography Surveillance Album organization
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Face Recognition Digital photography Surveillance Album organization Person tracking/id.
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Face Recognition Digital photography Surveillance Album organization Person tracking/id. Emotions and expressions
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Face Recognition Digital photography Surveillance Album organization Person tracking/id. Emotions and expressions Security/warfare Tele-conferencing Etc.
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vs. Identification What’s ‘recognition’?
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What’s ‘recognition’? vs. Categorization Identification
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Categorization Identification No localization Yes, there are faces
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Categorization Identification No localization Yes, there is John Lennon
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Categorization Identification No localization Detection or Localizatoin John Lennon
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Categorization Identification No localization Detection or Localizatoin
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What’s ‘recognition’? Categorization Identification No localization Detection or Localizatoin
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Categorization Identification No localization 1. PCA & Eigenfaces 2. LDA & Fisherfaces 3. AdaBoost 4. Constellation model Detection or Localizatoin Face Recognition methods
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Eigenfaces and Fishfaces Principle Component Analysis (PCA) Linear Discriminant Analysis (LDA)
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The Space of Faces An image is a point in a high dimensional space An N x M image is a point in R NM [Thanks to Chuck Dyer, Steve Seitz, Nishino]
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Images in the possible set are highly correlated. So, compress them to a low-dimensional subspace that captures key appearance characteristics of the visual DOFs. Key Idea } x ˆ { = χ USE PCA for estimating the sub-space (dimensionality reduction) Compare two faces by projecting the images into the subspace and measuring the EUCLIDEAN distance between them. EIGENFACES: [Turk and Pentland 91]
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Image space Computes p-dim subspace such that the projection of the data points onto the subspace has the largest variance among all p-dim subspaces. Face space Maximize the scatter of the training images in face space
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x1 x2 1 2 3 4 5 6 x1 x2 1 2 3 4 5 6 X1’ PCA projection USE PCA for estimating the sub-space Computes p-dim subspace such that the projection of the data points onto the subspace has the largest variance among all p-dim subspaces.
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x 1 x 2 1 st principal component 2rd principal component USE PCA for estimating the sub-space
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Orthonormal PCA Mathematical Formulation Define a transformation, W, m-dimensional n-dimensional = Data Scatter matrix T j N 1 j j T ) x x )( x x ( S = = N ... 2 , 1 j x W y j T j = = PCA = eigenvalue decomposition of a data covariance matrix = Transf. data scatter matrix Eigenvectors of S T k W S W ) y y )( y y ( S ~ T T T j N 1 j j T = = =
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Eigenfaces PCA extracts the eigenvectors of S T Gives a set of vectors v 1 , v 2 , v 3 , . ..
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lecture22 - EECS 442 Computer vision Face Recognition PCA...

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