Mathematical Image Analysis Group, Saarland University

Welcome to the homepage of the lecture

Differential Equations in Image Processing and Computer Vision

Summer Term 2010

Differential Equations in Image Processing and Computer Vision

Two Computer Science Teaching Awards (summer term 2003 and 2006)
One Mathematics Teaching Award (summer term 2009)

Lecturer: Dr. Andrés Bruhn
Office hours: Friday, 14:15 - 15:15.

Coordinator of tutorials: Markus Mainberger

Summer Term 2010

Lectures (4h) with theoretical exercises (2h)
(9 ETCS points)

Lectures: Tuesday, Friday 10-12 am c.t., Building E 1 3, Lecture Hall 001

First lecture: Tuesday, April 13, 2010

Tutorials: 2 hours each week; see below.

NEWS: The certificates are ready and can be fetched in room 111, building E2.4 (Geschaeftszimmer Mathematik, Frau Voss, opening hours for certificates: Mon-Thu 9.00-11.30 am).

Synopsis – Prerequisites – Assignments and Tutorials – Written Exams – Contents – Material for the Programming Assignments – References

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 master thesis in our group.

Prerequisites

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

Assignments and Tutorials

A combination of classroom and homework assignments (including theoretical as well as programming problems) is offered. The classroom assignments are intended to be solved in the tutorials and are not graded. The homework assignments are intended to be solved at home and have usually to be submitted Fridays, at 10.00 am before the lecture. In order to qualify for the exam you must

attend 80% of the tutorials (we do check)
gain 50% of all points from the homework assignments

Working in groups of up to 3 people is permitted, but all persons must be in the same tutorial group. Both classroom as well as homework assignments will be discussed in the tutorials.

If you have questions concerning the assignments or tutorials, please do not hesitate to contact Markus Mainberger. The tutorials are conducted by Pascal Peter and Christian Schmaltz.

Three groups are scheduled Wednesdays and Thursdays:

Group 1 (Christian Schmaltz):
Wed, 10-12 am, Bldg. E1.3, seminar room 015
Group 2 (Pascal Peter):
Thu, 2-4 pm, Bldg. E2.5, seminar room 2 (H04)
Group 3 (Pascal Peter):
Thu, 4-6 pm, Bldg. E2.5, seminar room 2 (H04)

The tutors can be reached via the mail addresses:
dic-g# -- at -- mia.uni-saarland.de
where # has to be replaced by the group number.

You had to register for the lecture and enroll for a tutorial on this web page from Tue, Apr. 13, 2010, 2.00 pm to Fri, Apr. 16, 2010, 4.00 pm. Still you can check in which group you are via web form.

Written Exams

There will be two written exams:

The first written exam has taken place on
Tuesday, July 27, 2010 from 2:00 pm to 5:00 pm,
in Building E 2.5, Lecture Hall I

The second written exam will take place on
Tuesday, October 12, 2010 from 2:00 to 5:00 pm,
in Building E 2.2, AudioMO.

In order to qualify for the exams you must

attend 80% of the tutorials (we do check)
gain 50% of all points from the homework assignments

In case of qualification, you are allowed to take part in both exams. The better grade counts.

Here you can download the admission list.

These are the rules during the exams:

For the exams, you can use the course material (including lecture notes and example solutions from this web page) and hand-written notes, but neither books nor any other printed material.
Pocket calculators are not allowed.
Mobile phones, PDAs, laptops and other electronic devices have to be turned off.
Please keep the student ID card ready for an attendance check during the exam.
Solutions that are written with pencil will not be graded.

The results of the first written exam can be found here, and the corresponding distribution of points and grades here.

Each student who has participated in the first written exam had the opportunity to inspect his/her graded solutions in room 3.06 in Bldg. E1.1 on Friday, August 6th, 2010, from 2:00 pm to 3:30 pm.

The results of the second written exam can be found here, and the corresponding distribution of points and grades here.

Each student who has participated in the second written exam had the opportunity to inspect his/her graded solutions in room 3.06 in Bldg. E1.1 on Monday, October 18th, 2010, from 3:30 pm to 4:30 pm.

Contents

Course material will be made available on this webpage in order to support the classroom teaching and the tutorials, not to replace them. Additional organisational information, examples and explanations that may be relevant for your understanding and the exam are provided in the lectures and tutorials. It is solely your responsibility - not ours - to make sure that you receive this infomation.

The following table shows a preliminary list of topics that will be covered during the semester.

Material for the Programming Assignments

Here you can download the material for the programming assignments:

Date Topic

16/04 H1 - Linear Diffusion, Gaussian Convolution

23/04 H2 - Linear Diffusion

07/05 H4 - Nonlinear Isotropic Diffusion

14/05 H5 - Nonlinear Anisotropic Diffusion

21/05 H6 - Selection of the Stopping Time

28/05 H7 - Diffusion-Reaction Methods

04/06 H8 - Iterated Bilateral Filtering

18/06 H10 - Optic Flow

25/06 H11 - Morphology

02/07 H12 - Curvature-Based Morphology

References

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. Second Edition, Springer, New York, 2006.
T. F. Chan and J. Shen: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia, 2005.
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.