Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing
Gerhard Dziuk, Ulrich Reif, Martin Rumpf, Peter Schröder · Oberwolfach Reports · 2005
In different areas of mathematics and computer science significant progress has been achieved with respect to geometric modeling, the processing of detailed surface models and geometric methods in morphological image processing. In contrast to classical tools in approximation theory such as spline curves and surfaces these new approaches rely on methods from the calculus of variations and geometric evolution problems. As examples we would like to mention here: Recently it has become clear that even though the applications areas differ significantly the methodological overlap is enormous. E.g. currently Willmore flow is one of the hot topics in geometric analysis and at the same time it turned out to be an adequate approach for the restoration of destroyed surfaces. Simultaneously the Willmore energy is a fundamental building block in variational methods of morphological image processing. Indeed as for surfaces it can be used for restoration and the disocclusion of images. Furthermore, it enters important fairness criteria in geometry processing and the generation of C^1 smooth surface models. The progress in this new, active and already very successful research field has its roots in originally completely different disciplines of mathematics and computer science. Hence, an exchange of different methodologies and a joining of activities is very promising. This was the intention of the mini workshop. To achieve this goal researchers from completely different areas of mathematics and mathematically oriented computer science were invited to share their point of view and their recent achievements with others. The intention of this mini-workshop was to initiate stronger exchange, to encourage the exploration of synergies and the building of bridges between the different disciplines and the different types of approaches for closely related research fields. In particular we intended to bring together people from Let us unroll one of these synergy fields: The organizers contributed introductory talks into the different fields to stimulate discussion and interaction. In parallel to this mini workshop another mini workshop on fluid interfaces took place. Together with the organizers of the latter workshop we arranged for several joined talks on the common interest field of geometric evolution problems by participants of both workshops. This interplay turned out to be very fruitful and inspiring. One Thursday evening we had a longer evening talk on a new approach for the discretization of fluid motion given by Peter Schröder.