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 |