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CVPR 2007 Tutorial on Generalized Principal Component Analysis (GPCA)

Over the past two decades, we have seen tremendous advances on the simultaneous segmentation and estimation of a collection of models from sample data points, without knowing which points correspond to which model. Most existing segmentation methods treat this problem as "chicken-and-egg", and iterate between model estimation and data segmentation.

This course will show that for a wide variety of data segmentation problems (e.g. mixtures of subspaces), the "chicken-and-egg" dilemma can be tackled using an algebraic geometric technique called Generalized Principal Component Analysis (GPCA). This technique is a natural extension of classical PCA from one to multiple subspaces.

The course will also include several applications of GPCA to computer vision problems such as image/video segmentation, 3-D motion segmentation, and dynamic texture segmentation.

List of topics

I Introduction to Generalized Principal Component Analysis (slides)

II Basic GPCA Theory and Algorithms (slides)

  1. Review of Principal Component Analysis (PCA)
  2. Introductory Cases: Line, Plane and Hyperplane Segmentation
  3. Segmentation with Known Number of Subspaces
  4. Segmentation with Unknown Number of Subspaces

III Advanced Statistical and Algebraic Methods for GPCA (slides)

  1. Model Selection for Subspace Arrangements
  2. Robust Sampling Techniques for Subspace Segmentation
  3. Voting Techniques for Subspace Segmentation

IV Applications to Motion and Video Segmentation (slides)

  1. 2-D and 3-D Motion Segmentation
  2. Temporal Video Segmentation
  3. Segmentation of Dynamic Textures

V Applications to Image Representation and Segmentation (slides)

  1. Multi-Scale Hybrid Linear Models for Sparse Image Representation
  2. Hybrid Linear Models for Image Segmentation
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