Summer Term 2004
Lectures (4h) with theoretical and programming exercises (2h)
(9 credit points)
Lectures:
Monday 14-16 c.t., Building 45, Lecture Hall 3;
Thursday 14-16 c.t., Building 45, Lecture Hall 2
First lecture: Monday, April 26, 2004
Exercises:
(please register – to register, send an e-mail to
Martin Welk)
Theoretic and programming exercises are held in weekly alternation.
The exercises are supervised by
Dr. Bernhard Burgeth.
In the first week (April 27/28), a mathematical introduction was given, comprising multidimensional differential calculus and basic facts about differential equations.
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.
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.
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 Bernhard Burgeth and Mostafa Khabouze.
No. | Topic | Tutorials | Problem sheet | Program and image files |
---|---|---|---|---|
P1 | Linear Diffusion Filtering | 4–5/5 | Lecture 3 (3/5) | Download tar file |
P2 | Isotropic Nonlinear Diffusion | 18–19/5 | Lecture 7 (17/5) | Download tar file |
P3 | Anisotropic Nonlinear Diffusion | 25–26/5 | Lecture 8 (24/5) | Download tar file |
P4 | Diffusion--Reaction Filtering | 15–16/6 | Lecture 12 (14/6) | Download tar file |
P5 | Variational Optic Flow Computation | 29–30/6 | Lecture 16 (28/6) | Download tar file |
P6 | Classical and Curvature-Based Morphology | 13–14/7 | Lecture 20 (12/7) | Download tar file |
No. | Topic(s) | Tutorials | Problem sheet | Deadline |
---|---|---|---|---|
T1 | Linear diffusion, convolution, finite differences | 11–12/5 | Lecture 2 (29/4) | 6/5 |
T2 | Isotropic nonlinear diffusion, numerical schemes | 1–2/6 | Lecture 7 (17/5) | 27/5 |
T3 | Anisotropic diffusion, stopping criteria | 8–9/6 | Lecture 9 (27/5) | 3/6 |
T4 | Euler-Lagrange equations; diffusion-reaction discretisations | 22–23/6 | Lecture 11 (7/6) | 17/6 |
T5 | Energy functionals; wavelet shrinkage; optic flow | 6–7/7 | Lecture 15 (24/6) | 1/7 |
T6 | Half-quadratic regularisation, iterative solvers, morphology | 20–21/7 | Lecture 19 (8/7) | 15/7 |
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.