Advanced Variational Methods
in Image Processing and Computer Vision

Summer Term 2016

Advanced Variational Methods in
Image Processing and Computer Vision

Dr. Peter Ochs

Summer Term 2016
Lecture (2h) with exercises (2h)
6 credit points

Lecture: Thursday 12-14 c.t., Building E1.3, Lecture Hall 001
First lecture: Thursday, April 21, 2016.

Tutorial: Monday 16-18 c.t., Building E1.3, Seminar Room 014
First tutorial: Monday, May 02, 2015.


25/07/2016: Schedule for the second on 20/10/2016 is online.
25/07/2016: Schedule for the first exam on 28/07/2016 is online.
14/07/2016: Note the registration deadline (22/07/2016) for the first oral exam.
10/05/2016: First part of lecture notes uploaded.
15/03/2016: Website is online.

Many problems in image processing, computer vision, and machine learning can be formulated as a variational model. Variational models allow for a clean formulation of the problem without hidden features. Moreover, usually they are amenable to efficient optimization techniques. Although we will also consider how to efficiently optimize the models, the focus of this lecture is the modelling of the problems. Modelling and optimization must be considered together. A perfect model that cannot be solved is as bad as a too simple model that can be solved without any computation. Key for the modelling with variational models is the trade-off between accuracy in modelling and the solvability.
In this lecture, we will discuss regularization techniques for inverse problems, meet the so-called Euler-Lagrange equations that reveal a relationship to partial differential equations, introduce variational models for denoising, segmentation, 3D reconstruction, etc..

Prerequisites: Basic mathematics (such as Mathematik für Informatiker I-III, or calculus and linear algebra). Knowledge in image processing and computer vision is helpful, but not required. Understanding English is necessary.

The tutorials include practical and theoretical classroom assignments. Attendance of the tutorials is not mandatory, but highly recommended.

In order to register for the Lecture, write an e-mail to Peter Ochs. The subject line must begin with the tag [AVIC16]. Please use the following template for the e-mail:

First name: [myFirstName]
Last name: [myLastName]
Date of birth: [dd.mm.yyyy]
Student ID number: [...]
Course of study: [Bachelor/Master/...]
Subject: [Computer science/Mathematics/...]

Note that the e-mail address from which you send this information will be used to provide you with urgent information concerning the lecture.

This registration is for internal purposes at our chair only and completely independent of any System like LSF/Hispos. They require a separate registration.

First exam: 28. July 2016
Second exam: 20. October 2016

  • You can attend both exams.
  • Each exam counts as one try.
  • Second exam can be taken to improve the grade.

Registration for the second exam:

  • eMail to Peter Ochs what date/exam you would like to take
    (Deadline: 14. October 2016
    Subject: [AVIC16] exams
    (I will arrange the time slots and let you know.)

Time schedule for the second exam: (20. October 2016)

Time slot Name
13.30 – 14.00 Damaris Gatzsche
14.00 – 14.30 Carlos Fernandez de Tejada Quemada

Participants of the course can download the lecture materials here after the lecture (access is password-protected). However, be aware that these slides are only provided to support the classroom teaching, not to replace it. Additional organisational information, such as examples and explanations that may be helpful or necessary to understand the content of the course (and thus relevant for the exam), will be provided in the lectures. It is solely your responsibility - not ours - to make sure that you receive this infomation.

The topics given here are preliminary and might change.

Date. Title
21/04 Introduction
28/04 Tikhonov regularization
(contains exercise 1)
12/05 Basic variational calculus
(contains exercise 2)
19/05 The need for total variation
02/06 Total variation and ROF model
(contains exercise 3)
09/06 Binary segmentation
(contains exercise 4, testimages: [1], [2])
16/06 Primal-dual hybrid gradient algorithm
(contains exercise 5)
23/06 Relaxations of the minimal partition problem
(contains exercise 6)
30/06 Extensions of the minimal partition problem
07/07 Mumford-Shah model
(contains exercise 7)
14/07 Convex relaxation approaches
21/07 Summary

Lecture Notes.

References will be given during the lecture.

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