CVPR 2007 Tutorial on Generalized Principal Component Analysis (GPCA)
Description
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
  1. Introduction to Generalized Principal Component Analysis (slides)
  2. Basic GPCA Theory and Algorithms (slides)
    • Review of Principal Component Analysis (PCA)
    • Introductory Cases: Line, Plane and Hyperplane Segmentation
    • Segmentation with Known Number of Subspaces
    • Segmentation with Unknown Number of Subspaces
  3. Advanced Statistical and Algebraic Methods for GPCA (slides)
    • Model Selection for Subspace Arrangements
    • Robust Sampling Techniques for Subspace Segmentation
    • Voting Techniques for Subspace Segmentation
  4. Applications to Motion and Video Segmentation (slides)
    • 2-D and 3-D Motion Segmentation
    • Temporal Video Segmentation
    • Segmentation of Dynamic Textures
  5. Applications to Image Representation and Segmentation (slides)
    • Multi-Scale Hybrid Linear Models for Sparse Image Representation
    • Hybrid Linear Models for Image Segmentation