Saarland University |
Mathematical Image Analysis Group |
Teaching

Summer Term 2003

# Differential Equations in Image Processing and Computer Vision

Lectures (4h) with theoretical and programming exercises (2h)

(9 credit points)

The **written exam** took place on July 28. The results are
displayed on floor 4, building 27.2, and can also be retrieved
here.
Opportunity for inspection of the graded exam sheets is given
on August 21, from 4 p.m., in building 27.2, room 26 (basement,
next to Mr. Hoffmann's flat).

Lectures: Tuesday, Friday 11-13 c.t., Building 45, Lecture Hall 3

First lecture: Friday, April 25, 2003

Exercises (please register!):

- Tuesday 4-6 p.m. (group A)

Theoretic exercises: lecture hall H07 (so-called *Zeichensaal*),
basement of building 27.2;

Programming exercises: room 012, building 45
- Wednesday 2-4 p.m. (group B)

Theoretic exercises: room U12, building 36.1

Programming exercises: room 012, building 45

Theoretic and programming exercises are held in weekly alternation.

## Prerequisites

Equally suited for students of mathematics and computer science.
Requires undergraduate knowledge in mathematics (e.g. ''Mathematik
für Informatiker I,II'') . Knowledge in image processing or differential
equations is useful, but not required. The lectures will be given
in English if requested.

## Synopsis

Many modern techniques in image processing and computer vision make
use of methods based on partial differential equations (PDEs) and
variational calculus. Moreover, many classical methods may be
reinterpreted as approximations of PDE-based techniques. In this
course we will get an in-depth insight into these methods.
For each of these techniques, we will discuss the basic ideas
as well as theoretical and algorithmic aspects. Examples from
the fields of medical imaging and computer aided quality control
illustrate the various application possibilities.
Since this class guides its participants to many
research topics in our group, its attendance is required for
everyone who wishes to pursue a diploma or master thesis in our
group.

## Contents

## Assignments

A balance of theoretical and programming assignments will be
offered. Previous experiences have shown that they are very helpful
for understanding the methods that are presented in the lectures.
The exercises are supervised by
Martin Welk and Dmitry Ovrutskiy.

## Files for the Programming Assignments

## References

- J. Weickert:
Anisotropic Diffusion in Image Processing.
Teubner, Stuttgart, 1998.
- G. Sapiro:
Geometric Partial Differential Equations in Image Analysis.
Cambridge University Press, 2001.
- G. Aubert and P. Kornprobst:
Mathematical Problems in Image Processing: Partial Differential
Equations and the Calculus of Variations.
Springer, New York, 2002.
- Articles from journals and conferences.

Joachim Weickert /
July 31, 2003 /
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