CSE586/EE554 Computer Vision II
Mathematical Tools for Computer Vision
CSE Department, Penn State University
Instructor: Robert Collins

Spring 2011 Schedule: Tues/Thurs 9:45-11:00AM, 371 Willard

Course Syllabus

Course Introduction
Lecture Notes
Intro to Course (Jan 11)   [slides]   [6 per page]
Review of prob and statistics (Jan 13)   [notes]
Homework Assignments
Homework 1 due Mon, Jan 24
Reference Material
Paper Search/Reading/Writing/Vision Resources
Prob/Stats review chapters [on Angel course site]

Gaussian Mixture Models and Expectation Maximization
Lecture Notes
The Gaussian Distribution (Jan 18,20,25)   [scanned notes]
Intro to Gaussian Mixture Models (Jan28)   [scanned notes]
GMM / EM derivation (Jan28,Feb1)   [slides]   [6 per page]
Homework Assignments
EM programming assignment due Mon, Feb 14
Reference Material
Intro to Gaussian Distribution , Bishop, PRML book
Old and New Matrix Algebra Useful for Statistics, Tom Minka.
Estimating Gaussian Mixture Densities with EM - A Tutorial, Carlo Tomasi.
Mixture Models and EM , Bishop, PRML book
EM Project Ideas
- One straightforward idea for testing your EM implementation is to go back to the programming example from assignment 1 where you were plotting contours of the bivariate histograms for red-green, green-blue and red-blue color channels for images with "interesting" colors. Instead of a histogram representation, how about using EM to fit a mixture of Gaussian distribution to each 2D set of color pixel data (or even to the full 3D R-G-B color distribution). Think about how you might use the histograms you estimated earlier to check the sanity of the mixture of Gaussian distributions you estimate this time (for example, are significant modes found in the same places in both representations).
- From Bishop book: use kmeans or EM to label/compress colors in an image. Try diff values of K. maybe compare k-means and EM results. Bishop's idea text is available here
- From Forsyth and Ponce: a number of ideas, including color/texture segmentation (e.g. blobworld), fitting line segments (maybe compare EM with RANSAC?), motion segmentation, background subtraction (Power and Shoonees paper). See the [Forsyth and Ponce ideas].
- Two other project ideas from the last time I taught this course. One involves motion segmentation (I provide a dataset), one involves experimenting with the Jones and Rehg skin color classifier. [here are the ideas].
- Of course, I encourage you to come up with your own ideas involving data that is relevant to you.

Procrustes Analysis
Lecture Notes
Intro to Procrustes Analysis (Feb 17-23)   [scanned lecture notes]
Shape Models and PCA (Mar 1)   [slides]   [6 per page]
Homework Assignments
Procrustes analysis assignment due Thurs, Mar 17
Bookstein's Schizophrenia Dataset
Reference Material
Solving for 2D similarity using complex numbers
Cootes and Taylor Active Shape Model paper
Fun Reading: The Shape of Madness, Mackenzie, Discover Magazine

Graphical Models
Lecture Notes
Intro to Graphical Models (Mar 22,24)   [slides]   [6 per page]
Hidden Markov Models (Mar 29)   [slides]   [6 per page]
Kalman Filter derivation (Mar 31)   [scanned notes]   These are lecture notes from my tracking course.
Don't freak out when you see a reference to "homework" on the very first page!
Reference Material
PRML Graphical Models Chapter, Bishop, PRML book
HMM Reading: A Tutorial on Hidden Markov Models, Rabiner

Markov Random Fields (Graphical Models II)
Lecture Notes
Brief Intro to MRF   [scanned notes]
movie Dan Huttenlocher   Speeding Up Belief Propagation. There are several options of how to play it. I have verified that both "Stream on RTSP-enabled devices" and the "QuickTime: 10846-10846-QuickTime.mov" link on that page work on my Windows machine (right clicking on the quicktime link lets you download and save the whole movie to watch locally).

Final Programming Project Ideas due Tues, May 3

Sampling and Markov Chain Monte Carlo
Lecture Notes
Intro to Sampling and MCMC (Apr 12,14)   [slides]   [6 per page]
Reference Material
Intro to Monte Carlo Methods, D.J.C.MacKay
An Intro to MCMC for Machine Learning, Andrieu, DeFrietas, Doucet and Jordan
MCMC for Computer Vision, ICCV 2005 Tutorial, Zhu, Dellaert and Tu