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Mathematical Morphology in Image Processing

Summer term 2007

Mathematical Morphology in Image Processing

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

Summer term 2007

Lectures (2h) with theoretical and programming assignments (1h); 5 ECTS points

Lectures: Thursday, 11-13 c.t., Building E13, Lecture Hall 003

First lecture: Thursday 19th, 2007

Tutorials: 2 hours every second week; see below.

NEWS: Certificates available now in room 111, bldg. E2 4 (Mathematics)

TutorialsPrerequisitesTypes of LecturesTutorialsWritten ExamContentsMaterial for the Programming AssignmentsLiterature

This course is suitable for students of mathematics or computer science. It counts either as a theoretical course in computer science or as an applied mathematics course. It is based on mathematical knowledge from the first three semesters. For the programming assignments, some elementary knowledge of C is required. The lectures are given in English.

Mathematical Morphology is a discipline with a 40-year history in image processing. Its techniques have been applied successfully to a variety of image processing tasks that, roughly speaking, involve shape information of image objects. The lectures is divided into three parts: The first part is devoted to the basic concepts and operations of classical discrete morphology for scalar images which rely on the notion of infimum and supremum, and give rise to the so-called dilation and erosion.
Continuous non-flat morphology is the subject of the second part of the lectures. Remarkably one can establish partial differential equations (PDEs) that mimic the processes of dilation and erosion. We will discuss these nonlinear evolution equations, especially some sophisticated modern algorithms for their numerical solution. Other PDEs help to explore the connection between morphological operations and curve evolution of object boundaries.
Part three provides access to very recent research results: We will see how morphological operations, both the ordering and the PDE-based setting, can be transfered to matrix-valued images. This data type makes its appearance in diffusion tensor magnetic resonance imaging (DT-MRI) but also in image processing itself, namely in the form of structure tensor concepts.

The tutorials include programming and theoretical assignments. The programming assignments give an intuition about the way how morphological image processing algorithms work, while the theoretical assignments provide additional mathematical insights. The tutorials are conducted by the lecturer.

Update: Thursday, 14-16,
Building E2 5, HS 3 (theory)
Building E1 3, CIP 103 (programming)

A list with the student id numbers of all students qualified for the exams can be found at the information board next to the entrance of our work group. In case of qualification, you are allowed to take part in both exams. Only the better grade counts.
There are several rules during the exams:

  • For the exams, you can use the course material (including lecture notes and example solutions from this web page) and hand-written tutorial notes, but no books.
  • A non-programmable pocket calculator is required.
  • Mobile phones, PDAs, laptops and other electronic devices have to be turned off.
  • Please keep the student ID card ready for an attendance check during the exam.

The first written exam took place on Monday, July 30, 2007, from 2 PM to 3:30 PM in lecture hall 001, building E1 4.

Course material will be made available on this webpage in order to support the classroom teaching and the tutorials, not to replace them. Additional organisational informations, examples and explanations that may be relevant for your understanding and the exam are provided in the lectures and tutorials.

Date Topic
19.04. Introduction and Basics
26.04. Dilation, Erosion, and Beyond
10.05. Opening, Closing and Applications
10.05. Morphological Reconstructions
24.05. Geodesic Distances
14.06. Morphological Filters
14.06. Morphological Segmentation
21.06. Morphological Segmentation II and Classification
21.06. Morphology and Convolution
21.06. Continuous Scale Morphology I (Assignments)
05.07. Continuous Scale Morphology II
05.07. Discrete Morphology for Matrix Fields
12.07. PDE-Based Morphology for Matrix Fields
19.07. Non-Flat Morphology and Slope Transform
19.07. Logarithmic Connection: LST and Morphology

21.06. Programming Assignment: Basic morphological operations

There is no specific book for this class, but some of the morphological image processing topics are treated in one of the following books:

  • J.P. Soille: Morphological Image Analysis. Springer, Berlin, 2003.
  • F. Cao: Geometric Curve Evolution and Image Processing. LNM 1805, Springer, Berlin, 2003.

These books can be found in the computer science library.
If you are looking for a specific reference, check out Keith Price's Annotated Computer Vision Bibliography. Numerous citations and online articles can be extracted from the CiteSeer webpage.

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