## Abstract for February 15, 2006

###
Martin Welk: Analysis of Space-Discrete Image Filters by Dynamical Systems

Joint work with Joachim Weickert, Gabriele Steidl, Irena Galic, Michael
Breuss

In digital image processing, filters based on partial
differential equations (PDEs) are known as a versatile tool. Among the
most interesting filters of this kind are some that rely on PDEs with
singularities which make them difficult to analyse and implement.
Dynamical systems of ordinary differential equations can be used to model
spatially discretised versions of PDE-based filters. Singularities are often
easier to control, and useful theoretical properties for the discretised
filters can be derived. In some cases, it is even possible to obtain
explicit analytic solutions that lead to novel numerical methods for the
underlying PDEs. The examples discussed in the talk reveal also
interesting relations to image filters defined via wavelets and via local
image statistics.

Postdoc Seminar Homepage