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Introduction to Integral Equations in Visual Computing

Summer term 2008

Introduction to Integral Equations in Visual Computing

Lecturer: Dr. Bernhard Burgeth
Office Hours: Tuesday: 15:00-16:00.

Summer term 2008

Lectures (2h) with exercises and assignments (2h); 6 ECTS points

Lectures: Thursday, 10-12 c.t., Building E13, Lecture Hall 001

First lecture: Thursday, April 17th, 2008

Tutorials: Monday, 16-18 c.t., Building E13, Seminar Room 014, see below

First tutorial: Monday, April 21st, 2008

Breaking News:
Results of the written exam are available on a list attached to the black board at the entrance of the floor of the MIA group in building E1 1.
Each participant has been informed about his individual results by e-mail.

Opportunity for exam inspection:
Tuesday, August 19th, 14:00 - 15:00, Room 3.06, Bld. E1 1

Opportunity for oral exam: First Info!

Prerequisites – Synopsis – Tutorials – Exams – Material for Assignments – Literature

This course is suitable for students of mathematics , physics or computer science who completed their undergraduate studies in mathematics. Knowledge of functional analysis or image processing is helpful but not required. The lectures will be given in English. Hence passive knowledge of English is necessary. The lectures are given in English.

Integral equations are an important tool to model evolution processes from physics, engineering, and biology. As the name already indicates an integral equation involves integrals of an unknown function u one wishes to solve for.
In the lectures we will concentrate on linear Fredholm and Volterra integral equations of the second type. After theoretical considerations concerning existence and uniqueness of solutions we will discuss numerical aspects of these equations.
Usually the treatment of equations of the first type is more involved. Hence we convey in this introductory course only the basic facts about this type of equations. Among the numerous applications of integral equations we restrict ourselves to two fields:

• integro-differential equations in image processing, and
• computer tomography, a medical image acquisition technique.

After Appointment.
The tutorials include assignments that provide important additional mathematical insights. The tutorials are conducted by the lecturer.

The first exam has taken place in the lecture hall 001, bldg. E1 4 on July 17th, 2008 from 10:15 to 11:45.

Each student qualified to participate in the first exam will have an opportunity for an oral exam at September 30th, 2008.
The better grade counts.
Further details will follow.

Participants of the course can download the assignments.

Homework:

Date	Topic
25.04.	Assignment H1
08.05.	Assignment H2
23.05.	Assignment H3
05.06.	Assignment H4
12.06.	Assignment H5

Classroom assignments:

Date	Topic
28.04.	Assignment C1
05.05.	Assignment C2
05.06.	Assignment C3
16.06.	Assignment C4
23.06.	Assignment C5
07.07.	Assignment C6

Images and drawings supplementing chapter 6 of the lecture are available here

There are numerous books on Integral Equations. We will not follow a specific one, but most topics are treated in one of the following samples:

• Heinz Engl: Integralgleichungen, Springer, Wien, 1997.
• W. Hackbusch: Integralgleichungen, Theorie und Numerik, Teubner, Stuttgart, 1989.
• R. Kress: Linear Integral Equations, Springer-Verlag, Berlin, 1989.

These and further books can be found in the computer science library.

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