Differential Equations in Image Processing and Computer Vision
Prof. Joachim Weickert
Summer Term 2006
Lectures (4h) with theoretical and programming exercises (2h)
(9 credit points)
Lectures: Tuesday, Friday 1113 c.t., Building E13, Lecture Hall 1
First lecture: Friday, April 21, 2006
Tutorials: 2 hours each week; see below.
Prerequisites –
Synopsis –
Planned Contents –
Assignments –
References
Equally suited for students of mathematics and computer science.
Requires undergraduate knowledge in mathematics (e.g. ''Mathematik
für Informatiker IIII'') . Knowledge in image processing or differential
equations is useful, but not required. The lectures will be given
in English.
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 PDEbased techniques. In this
course we will get an indepth 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 combination 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
Andres Bruhn and
Dr. Michael Breuss.
Date  Topic

2/5 
P1  Linear diffusion, convolution, finite differences 
23/5 
P2  Nonlinear isotropic diffusion 
6/6 
P3  Nonlinear anisotropic diffusion, diffusionreaction filtering 
20/6 
P4  Inpainting 
4/7 
P5  Optic flow 
18/7 
P6  Morphology, mean curvature motion 
3 groups are scheduled for Tuesday and Wednesday,
the tutorials of group T2 will be held in German.
 Group T1: Tue, 1416, Bldg. E13, room SR 15 (theory) and CIP 105 (programming)
 Group T2: Tue, 1618, Bldg. E13, room SR 15 (theory) and CIP 105 (programming)  in German
 Group W1: Wed, 1416, Bldg. E11, room U 12 (theory) and E13, room CIP 012 (programming)
You could enroll
for a tutorial from Fri, Apr. 21, 2006, 14:00h
to Tue, Apr. 25, 2006, 16:00h.
The first written exam took place on July 26 from 2 to 5 PM
in Building E13, Lecture Hall 002.
The second written exam took place on October 5 from 2 to 5 PM in
Building E2.5 (formerly 27.2), Lecture
Hall I (Math Building)
You can bring your lecture notes and
notes from the tutorials.
You have to pass one exam, and the better grade counts.
The following thresholds were applied in determining the grades:
 grade 1.0 : 55  62 points
 grade 1.3 : 52  54 points
 grade 1.7 : 50  51 points
 grade 2.0 : 47  49 points
 grade 2.3 : 44  46 points
 grade 2.7 : 41  43 points
 grade 3.0 : 38  40 points
 grade 3.3 : 35  37 points
 grade 3.7 : 33  34 points
 grade 4.0 : 30  32 points
 grade 5.0 : 0  29 points
The best results of both exams can be queried via our online query form.
Exam sheets of the second written exam can be inspected
from October 16 to October 17 (monday to tuesday) after a personal
appointment (via mail).
 J. Weickert:
Anisotropic Diffusion in Image Processing.
Teubner, Stuttgart, 1998.
 G. Aubert and P. Kornprobst:
Mathematical Problems in Image Processing: Partial Differential
Equations and the Calculus of Variations.
Springer, New York, 2002.
 F. Cao:
Geometric Curve Evolutions and Image Processing.
Lecture Notes in Mathematics, Vol. 1805, Springer, Berlin, 2003.
 R. Kimmel:
The Numerical Geometry of Images.
Springer, New York, 2004.
 G. Sapiro:
Geometric Partial Differential Equations in Image Analysis.
Cambridge University Press, 2001.
 Articles from journals and conferences.
