In this talk, I will discuss ongoing work in my junior research group, which
is concerned with statistical techniques in geometry processing. The main
focus of our current work is in the area of geometric correspondence
problems. This means, we are trying to identify geometric shapes as being
(maybe partially) identical up to some transformation and possible noise. In
particular, I will describe shape matching algorithms for rigid, deformable
and animated data as well as symmetry detection algorithms that find partial
matches within one and the same geometric object. It will turn out that all
of these problems can be handled within a similar statistical framework but
different algorithms are necessary to solve the resulting optimization
problems. In addition to recent research results, I will also discuss
general, long term research goals and motivate the choice of the research
area.