Summer Term 2005

Differential Equations in Image Processing and Computer Vision

Dr. Bernhard Burgeth

Lectures (4h) with theoretical and programming exercises (2h)
(9 credit points)

Lectures:
Tuesday 14-16 c.t., Thursday 11-13 c.t., Building 45, Lecture Hall 003
First lecture: Tuesday, April 12, 2005

Exercises:

The registration is closed!

• Thursday 2-4 p.m.
  Theoretical exercises: building 45, room no. 16, Programming exercises: building 27.1, room 009
• Friday 2-4 p.m.
  Theoretical exercises: building 45, room no. 16, Programming exercises: building 27.1, room 009

Theoretical and programming exercises take place in weekly alternation.
The exercises are supervised by Dr. Martin Welk.

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 delivered 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.

Written Exams: Update !

The results of the written exam can be found here , finally!

The participants of the first written exam have the opportunity of inspecting their exam sheets on
Friday, September 16th, between 1:00 and 3:00 p.m., building 27.2, basement, room 26 (opposite ladies' restrooms).
Outside this time, individual inspection is possible upon appointment in the office of Bernhard Burgeth.

The second written exam has taken place on Tuesday, October 4th, 2005 in the afternoon, from 2:00 to 5:00 p.m. in Hörsaal I Mathematik (mathematics lecture hall), building 27.2

The results of the second written exam can be found here !

Contents

No.	Date	Topic	Assignments
1	12/4	Introduction, Overview	–
2	14/4	Linear Diffusion Filtering I: Basic Concepts	T1
3	19/4	Linear Diffusion Filtering II: Numerical Aspects, Limitations, Alternatives	P1
4	21/4	Nonlinear Isotropic Diffusion Filtering I: Modeling and Continuous Theory	–
5	26/4	Nonlinear Isotropic Diffusion Filtering II: Semidiscrete and Discrete Theory	T2
6	28/4	Nonlinear Isotropic Diffusion Filtering III: Efficient Sequential and Parallel Algorithms	–
7	3/5	Nonlinear Anisotropic Diffusion I: Modeling	–
8	10/5	Nonlinear Anisotropic Diffusion II: Theoretical and Discrete Aspects	P2
9	12/5	Diffusion Filtering: Parameter Selection	T3
10	17/5	Variational Methods I: Basic Ideas	T4
11	19/5	Variational Methods II: Discrete Aspects	–
12	24/5	Variational Methods III: TV Denoising, Equivalence Results	P3
13	31/5	Variational Methods IV: Mumford-Shah, Diffusion-Reaction	–
14	2/6	Vector - and Matrix-Valued Images	T5
15	7/6	Image Sequence Analysis I: Global Methods	–
16	9/6	Image Sequence Analysis II: Local Methods	P4
17	14/6	Image Sequence Analysis III: Combined Local-Global Methods	–
18	16/6	Image Sequence Analysis IV: Numerical Methods for the Variational Approaches	P5
19	21/6	Continuous-Scale Morphology I: Basic Ideas, PDE Formulation, Shock Filters	T6
20	23/6	Continuous-Scale Morphology II – Curvature-Based Morphology I	–
21	28/6	Curvature-Based Morphology II: Affine-Invariant Evolution, Extensions, Applications	P6;
22	30/6	Image Segmentation by Active Contour Methods	–
23	5/7	Region Based Image Segmentation	–
24	7/7	Summary and Outlook	–

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. Exercises are supervised by Martin Welk and Natalia Slesareva.

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.