## 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) __