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.

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