Probabilistic Methods in Image Analysis

Summer term 2016

Probabilistic Methods in Image Analysis

Lecturer: Martin Schmidt

Examiner: Prof. Dr. Joachim Weickert

Summer term 2016

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

Lectures: Wednesday, 14-16 c.t., Building E1.3, Lecture Hall 003
Tutorials: Friday, 14-16 c.t., Building E1.3, Lecture Hall 001

First lecture: Wednesday, April 20, 2016 Building E1.3, Lecture Hall 003
First tutorial: Friday, May 6, 2016, Building E1.3, Lecture Hall 001


NewsPrerequisitesSynopsis Assessments / Exams Course MaterialLiterature


NEWS: The results of the second written exam are now online.

NEWS: Opportunity for exam inspection:
Friday, September 23, Room 4.10, Building E1 7, 10:00 a.m. - 10:30 a.m.

NEWS: The results of the first written exam are now online.

NEWS: Opportunity for exam inspection:
Wednesday, August 10, Room 4.10, Building E1 7, 2:00 p.m. - 3:00 p.m.

Please register in the HISPOS system for this lecture.

This course is suitable for students of mathematics, physics or computer science who completed their undergraduate studies in mathematics. Knowledge of probability 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.

The first written exam took place on
Friday, July 29, 2016 from 14:00 to 16:00,
in Building E1.3, Lecture Halls 001.

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

The second written exam takes place on
Wednesday, September 21, 2016 from 14:00 to 16:00,
in Building E1.3, Lecture Halls 001.

The results of the second written exam can be found here.

The homework assignments are intended to be solved at home and have to be submitted in the lecture break, or earlier. In order to qualify for the exams you must obtain 50% of the possible points on average. In case of qualification, you are allowed to take part in both exams.
The better grade counts, but each exam will count as an attempt individually.

Both exams will be closed book exams. You will have to follow these rules:

  • You are allowed and obliged to bring two things to your desk only: Your student ID card (Studierendenausweis) and a ball-pen that has no function other than writing. Everything else has to be deposited at the walls of the exam hall.
  • In particular, electronic devices (including your cell phone), bags, jackets, briefcases, lecture notes, homework and classroom work solutions, handwritten notes, books, dictionaries, and paper are not allowed at your desk.
  • Please keep your student ID card ready for an attendance check during the exam.
  • Do not use pencils or pens that are erasable with a normal rubber.
  • You are not allowed to take anything with you that contains information about the exam.
    A violation of this rule means failing the course.
  • You must stay until the exam is completely over.

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

Lecture slides

DateTopicLecture
20.4. Organisational Issues Notes
20.4. Images, and Image Degradations Lecture 01
27.4. Elements of Probability Theory I Lecture 02
4.5. Histogram Based Operations on Images I Lecture 03 (Update 1: typo on slide 15)
11.5. Elements of Probability Theory II Lecture 04
18.5. Histogram Based Operations on Images II Lecture 05
25.5. Elements of Probability Theory III Lecture 06
1.6. Estimation in Statistics: Parzen and ML Lecture 07
8.6. Registration by Maximization of Mutual Information Lecture 08
15.6. Elements of Probability Theory IV Lecture 09 (Update 1: several typos)
22.6. Markov Chains in Image Processing Lecture 10
29.6. Minimally Stochastic Approach to Singular Diffusion Equations Lecture 11
6.7. Singular Value Decomposition and Principal Component Analysis Lecture 12
13.7. Markov Random Fields and Texture Lecture 13
20.7. Summary Lecture 14

Homework Assignments

Date Topic Submission Deadline
27.4. Assignment 1 May 4
4.5. Assignment 2 May 11
11.5. Assignment 3 May 18
18.5. Assignment 4 May 25
25.5. Assignment 5 June 1
8.6 Assignment 6 June 15
15.6 Assignment 7 June 22
22.6 Assignment 8 June 29
29.6 Assignment 9 July 6
6.7 Assignment 10 July 13
14.7 Assignment 11 July 21

Relevant references will be provided in the lecture.


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