Math 285J, Section 1, Fall 2001

Seminar Applied Mathematics

Variational Methods & PDE's for Image Analysis and Curve Evolution

Lecture Meeting Time: MWF 1.00PM - 1.50PM
Lecture Location: MS 5217.
Instructor: Luminita A. Vese
Office: MS 7354
Office hours: M.W.F. 2-3pm
E-mail: lvese@math.ucla.edu
Class Web page: http://www.math.ucla.edu/~lvese/285j.1.01f

Virtual Office Hours

Course Description: PS   PDF

Plan & References: The lectures will not follow one particular textbook. The topics presented can be found in research papers or recent books. The plan of the lecture and the main papers and books to be used in the presentation are: PS   PDF

Sample Codes: The best choice for image processing calculations is C++. However, for easy routines, such as reading an image and adding noise, Matlab is a good choice to help you to begin to work with images.
Matlab code to add uniform noise to an image and to compute the SNR (signal-to-noise-ratio): NoiseSNR1.m for a synthetic image   NoiseSNR2.m for a real image that you can find here Lena.bmp.gz

Assignments & Projects:
- All enrolled students will have to solve problems and to do numerical implementations of the methods discussed in class (work in group or teams of two or three students is also welcome).
- The assignments will be balanced between "pencil and paper" problems and numerical implementations.
- However, function of your own background and of your own interests, you can work more on one type of assignments, and less on the other type.
- If you have questions, please come and discuss with me your case and your specific interests.
- Students interested in working on a new research project, proposed by the instructor and with the instructor's advise and help, can do so. Then, the research project can substitute all the assignments.

Problems Set 1 in PS   Problems Set 1 in PDF
Please note that for problem #4 (with the convexity), the assumptions may not be so clear. What I wanted was, assuming that f(| |) is convex, and K is linear, then the functional is also convex (for example, f(| |) is convex if f is convex and increasing, and this is the case in our general assumptions).

Numerical Assignments
Numerical Assignments (in PS)   Numerical Assignments (in PDF)