Mathematical Image Analysis Group, Saarland University

Seminar:

Gamma-Convergence

Winter Term 2007 / 2008

Seminar on
Gamma-Convergence held by Dr. Bernhard Burgeth (burgeth@mia.uni-saarland.de)

Winter Term 2007 Seminar (2h)

Important Dates – Description – Administrative details – Requirements – Overview of Topics

Important Dates

First Session: Wednesday, Oktober 31st, 2007, 10:15, Bld. E1.1, room 3.06

Regular meetings during winter term 2007:
Wednesdays, 10:15, Bld. E1.1, room 3.06, starting October 31st, 2007

Please direct all organisatorial requests to B. Burgeth.

Description

Contents: The notion of Gamma-Convergence has been introduced by the Fields Medalist E. Di Giorgi in the seventies. It describes the asymptotic behaviour of families of minimisation problems indexed by some parameter of geometric or constitutive nature. As a natural and very flexible notion of convergence for variational problems it can be applied to discontinuity problems in Computer Visison as well as to the transition from discrete systems to the continuous setting.

The Seminar is mainly based on the chapters of the book by

Andrea Braides, Gamma-Convergence for Beginners
Oxford University Press, Oxford, 2002.

Potential topics are

Definitions and properties of Gamma-convergence
Integral problems
Homogenisation problems
Transition discrete systems to continuous functionals
Segmentation problems
Free-discontinuity problems (Mumford-Shah functional)
Approximation of free-discontinuity problems (Ambrosio Tortorelli approximation)
Discrete systems and free-discontinuity problems (Perona-Malik approximation)

Depending on the interest of the participants more advanced topics from image processing involving Gamma-convergence may be also included.

Prerequisites: The seminar is suitable for graduate students (i.e. advanced Bachelor, Master) of mathematics, physics and computer science with solid mathematical knowledge. Knowledge of basic Functional Analysis and Measure Theory is useful but may also be acquired during the seminar.

Language: Understanding scientific text in English is indispensable. Talks can be delivered in English or German.

Administrative details

Sign-up: If you are interested to participate, please send an e-mail with the subject Gamma Seminar to burgeth@mia.uni-saarland.de before Thursday, July 19th, 2007. Please include your name, student ID (Matrikelnummer), date of birth, study program, and valid e-mail address.
Since the number of talks is limited, we ask for your understanding that participants are considered strictly in the order of incoming e-mails – no exceptions!

Sessions: First meeting takes place Friday, July 20th, 2007, 14:15h, Bld. E1.1, room 3.06. Regular sessions will be weekly during the winter term. Exact schedule to be determined at first meeting.

Requirements for successful participation («Schein»)

Regular attendance: It is expected that you attend all seminar meetings.

Talk: Talk duration approx. 45 min, plus 15 min for discussion. Please do not deviate significantly from this time schedule.
You may give a presentation using a data projector (»beamer«), overhead projector or blackboard, or mix these media appropriately. English is preferred as language of presentation; if you should decide to talk in German anyway, you should use slides in English.

Write-up: The write-up has to be handed in untill the end of the lecture period. It should summarise your talk, in some 3+ pages.
Electronic submission is preferred. File format for electronic submissions is PDF – text processor files (like .doc) are not acceptable. We recommend using LaTeX.
Please adhere to the standards of scientific referencing: Quotations and copied material (such as images) must be clearly marked as such, and a bibliography is required.

Mandatory consultation: Talk preparation has to be presented to your seminar supervisor not later than in the week before the talk is given. It's your responsibility to approach us timely and make your appointment!

Bernhard Burgeth / July 11th, 2007