**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**

I Introduction to Generalized Principal Component Analysis
(slides)

II 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

III Advanced Statistical and Algebraic Methods for GPCA
(slides)

- Model Selection for Subspace Arrangements
- Robust Sampling Techniques for Subspace Segmentation
- Voting Techniques for Subspace Segmentation

IV Applications to Motion and Video Segmentation
(slides)

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

V Applications to Image Representation and Segmentation
(slides)

- Multi-Scale Hybrid Linear Models for Sparse Image Representation
- Hybrid Linear Models for Image Segmentation