8/16/99 Computer Vision and Modeling. 8/16/99 Principal Components with SVD.

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Presentation transcript:

8/16/99 Computer Vision and Modeling

8/16/99 Principal Components with SVD

8/16/99 Linear Dimension Reduction: High-dimensional Input Space

8/16/99 Linear Subspace: += + 1.7=

8/16/99 Linear Subspace:

8/16/99 Principal Components Analysis: m

8/16/99 Examples: Data: Kirby, Weisser, Dangelmayer 1993

8/16/99 Examples: Data: PCA New Basis Vectors

8/16/99 Examples: Data: PCA EigenLips

8/16/99 Examples: Face Recognition with Eigenfaces (Turk+Pentland, ):

8/16/99 Examples: Face Recognition System (Moghaddam+Pentland):

8/16/99 Examples: Visual Cortex Hubel

8/16/99 Examples: Visual Cortex Hubel

8/16/99 Examples: Receptive Fields Hubel

8/16/99 Examples: Receptive Fields Hancock et al: The principal components of natural images

8/16/99 Examples: Receptive Fields Hancock et al: The principal components of natural images

8/16/99 Examples: Active Appearance Models (AAM): (Cootes et al)

8/16/99 Examples: Active Appearance Models (AAM): (Cootes et al)

8/16/99 Examples: Active Appearance Models (AAM): (Cootes et al)

8/16/99 Examples: 3D Morphable Models (Blanz+Vetter)

8/16/99 Examples: 3D Morphable Models (Blanz+Vetter)

8/16/99 Review E(V) VV Constrain - Analytically derived: Affine, Twist/Exponential Map Learned: Linear/non-linear Sub-Spaces

8/16/99 S = (p,…,p ) E(S) Constrain 1n Non-Rigid Constrained Spaces

8/16/99 Non-Rigid Constrained Spaces Nonlinear Manifolds: Linear Subspaces : Small Basis Set Principal Components Analysis Mixture Models

8/16/99 Examples: Eigen Tracking (Black and Jepson)

8/16/99 Examples: Shape Models for tracking:

8/16/99 More generic Feature/Shape Models: Visual Motion Contours: Blake, Isard, Reynard

8/16/99 More generic Feature/Shape Models: Visual Motion Contours: Blake, Isard, Reynard

8/16/99 Linear Discriminant Analysis:

8/16/99 Fisher’s linear discriminant:

8/16/99 Example: Eigenfaces vs Fisherfaces Glasses or not Glasses ?

8/16/99 Example: Eigenfaces vs Fisherfaces Input New Axis Belhumeur, Hespanha, Kriegman 1997

8/16/99 Nonlinear Manifolds Nonlinear Manifolds: Linear Subspaces : Small Basis Set Principal Components Analysis Mixture Models