Date:	Tue, March 3, 2009
Time:	17:15
Place:	West Hall 8

Abstract: The talk discusses nonlinear anisotropic geometric diffusion models for the processing of images and image-sequences. The methods only depend on the morphology of the images (=shapes in the images) and thus are invariant under monotone transformations of the gray values. In particular the evolution is steered by the principal curvatures and the principal directions of curvature of the iso-surfaces of the images. This is done by diffusion tensors which weight the eigenvalues of the second fundamental form (=the shape operator) in directions of the eigenvectors.

This model results in an evolution which -- in contrast to the mean curvature motion -- is capable of retaining important geometric features such as corners and edges of the level-sets. Thinking of the mean curvature motion as the geometric equivalent to the Euclidean heat-equation, the presented model can be seen as the geometric equivalent to the anisotropic diffusion by Weickert. Various examples illustrate this analogy.

The regularizations can be seen as compact operations on the corresponding image spaces. In fact, using a fixed point argument the compactness of the regularizations can be used to show the existence of viscosity solutions for the anisotropic and nonlinear level-set method.