# Seminar Level set methods

Di, 14-16, 5701.EG.026 (IMETUM-Hörsaal im Medizintechnikgebäude) Prof. O. Junge Level set methods are numerical techniques for tracking geometric objects which change their shape. The underlying powerful idea is to represent the \(n-1\)-dimensional boundary of an \(n\)-dimensional object under consideration as the zero level set of a scalar function \(\varphi\) on \(\mathbb{R}^n\) which additionally depends on time. Solving an associated partial differential (evolution) equation for \(\varphi\) (a Hamilton-Jacobi equation) numerically, one implicitely obtains the evolution of the object in terms of the zero level set. These methods have been developed in the 1980s and have since then been applied in numerous applications like fluid dynamics, image processing, computational geometry and materials science.### Talks

- 26.11.10, Chapter 3, Motion in an Externally Generated Velocity Field,
**David Frey** - 9.11.10, Chapter 4, Motion Involving Mean Curvature,
**Patricia Rachinger** - 16.11.10, Chapter 5, Hamilton-Jacobi Equations,
**Thomas Schmelz** - 23.11.10, Chapter 6, Motion in the Normal Direction,
**Christian Reckelkamm** - 7.12.10, Chapter 7, Constructing Signed Distance Functions,
**Christoph Meier** - 21.12.10, Chapter 11, Snakes, Active Contours, and Segmentation,
**Michael Strobel** - 11.1.10, Chapter 12, Image Restoration,
**Benjamin Steber** - 18.1.11, Chapter 13, Reconstruction of Surfaces from Unorganized Data Points,
**Richard Stotz** - 25.1.11, Chapter 14, Hyperbolic Conservation Laws and Compressible Flow,
**Yongming Luo**

### Links

Level set toolbox^{}von Ian Mitchell (University of British Columbia)

### References:

- Osher, Stanley J.; Fedkiw, Ronald P.: Level Set Methods and Dynamic Implicit Surfaces, Springer-Verlag, 2002.
- Sethian, James A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, 1999.
- Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Com- put. Phys. 79: 12–49, 1988.