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Probabilistic Methods in Image Analysis

Winter term 2008/09

Probabilistic Methods in Image Analysis

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

Winter term 2008/09

Lectures (3h) with exercises and assignments (1h); 6 ECTS points

Lectures / tutorials:
Tuesday, 12-14 c.t., Friday, 8-10 c.t. Building E13, Lecture Hall 001

First lecture: Tuesday, October 21st, 2008

Last Reminder

As indicated in personal e-mail messages sent out on March 26th the

2nd oral exam will take place on Tuesday, April 7th, 2009.

Please respond to the e-mail by Thursday, April 2nd .
Only the registered participants will receive an e-mail with a detailed schedule!

Prerequisites – Synopsis – Tutorials – Exams – Course Material – Literature

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

Probabilistic techniques are employed quite successfully in the processing and analysis of images, however, they also play a vital role in pattern classification, data mining and learning theory.
In this course we will discuss

• basic notions from probability theory and statistics as well as from image processing


• histogram based image analysis and enhancement methods


• the probabilistic background of the Karhunen-Loeve expansion used for data compression, for example


• independent component analysis and applications


• the notion of entropy in image registration


• and, if time permits, we will give an introduction to the basic ideas of Markov random fields and simulated annealing.

On Fridays, 9:15 -- 10:00
The tutorials include assignments that provide important additional mathematical insights. The tutorials are conducted by the lecturer.

There will be an opportunity for an oral exam at the end of the lecture period, Friday, February 13th, and a second oral exam at the end of the semester. Active participation in the in the exercises is expected in order to be admitted to the exams.
The better grade of the two exams counts.
Further details will follow.

Participants of the course can download the course material (access is password-protected).

Lecture slides

Date	Topic	Lecture
21.10.	Organisational Issues	Notes
21.10.	Images, and Image Degradations	Lecture 01
24.10.	Elements of Probability Theory I	Lecture 02
28.10.	Elements of Probability Theory II	Lecture 03
04.11.	Elements of Probability Theory III	Lecture 04
14.11.	Elements of Probability Theory IV	Lecture 05
18.11.	Elements of Probability Theory V	Lecture 06
21.11.	Elements of Probability Theory VI	Lecture 07
5.12.	Histogram Based Operations on Images I	Lecture 08
9.12.	Histogram Based Operations on Images II	Lecture 09
16.12.	Histogram Based Operations on Images III	Lecture 10
13.01.	Parzen Windows and ML	Lecture 11
20.01.	Registration by Maximization of Mutual Information	Lecture 12
27.01.	Minimally Stochastic Approach to Diffusion Equations	Lecture 13
03.02.	PCA, POD, KLT via SVD	Lecture 14

Assignments

Date	Topic
31.10.	Assignment 1
07.11.	Assignment 2
05.12.	Assignment 3
12.12.	Assignment 4

Relevant references will be provided in the lecture.

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