Saarland University | Mathematical Image Analysis Group | Teaching

Differential geometric aspects of image processing

Lectures, winter term 2003/2004

Dr. Martin Welk (Geb. 27.1, R. 410, Tel. 0681-302-64383)

The course is concerned with modern methods of digital image processing which rely on the differential geometry of curves and surfaces. This includes methods of image enhancement (like smoothing procedures) as well as feature extraction and segmentation (like locating contures using active contour models).

The lecture aims at combining theoretical foundation directly with a variety of applications from the above-mentioned fields; the range of topics extends up to recent research problems.

An introduction to the relevant concepts and results from differential geometry will be included in the course.

The lecture is designed for advanced students of mathematics as well as of computer science. Previous knowledge in either digital image processing or differential geometry is helpful but not required.

Time: Monday 14–16 (2–4 p.m.) starting Oct. 27, 2003
Location: Seminar room no. 5 (bld. 27.1)

Participants of the course can download the transparencies here (access password-protected):
Overview Overview
Chapter 1 Introduction
Chapter 2 Mathematical Background from Topology and Differential Geometry
Topological foundation, manifolds
Curves in Euclidean Space, 1
Curves in Euclidean Space, 2 + Surfaces in Euclidean Space, 1
Surfaces in Euclidean Space, 2 + Affine invariant curve theory
Chapter 3 Curve evolution
Introduction, basic examples (morphology, curvature motion)
Morphology and curvature motion (cont.); geodesic active contours
Geodesic active regions; self-snakes; tensor-valued level set methods
Modifications of geodesic active regions and contours; variants of curvature motion
Modifications of geodesic active contours, continued
Chapter 4 Surface evolution and minimal surface models
Chapter 5 Diffusion in Euclidean space
Chapter 6 Diffusion of non-scalar data on Euclidean manifolds
Chapter 7 Geometric diffusion of surface data
Chapter 8 Diffusion on manifolds

Martin Welk / September 25, 2003–February 19, 2004 / back to MIA home.
The author is not responsible for the content of external pages.
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