Prof. Dr. Martin Rumpf (Universität Bonn) Variational Time Discretization of Geodesic Calculus in Shape Space
Thursday, 16.05.2013 16:30 im Raum M5
The talk will introduce a time discrete geometric calculus on the space of shapes with
applications in geometry processing and computer vision. The discretization is based
on a suitable local approximation of the squared distance, which can be efficiently computed.
The approach covers shape morphing and the robust distance evaluation between
shapes based on the computation of discrete geodesic paths, shape extrapolation
via a discrete exponential map, and natural transfer of geometric details along shape
paths using discrete parallel transport. Furthermore, it can be used for the statistical
analysis of time indexed shape data in terms of discrete geodesic regression.
The talk will describe how concepts from Riemannian manifold theory are combined
with application dependent models of physical dissipation. Furthermore, a rigorous
consistency and convergence analysis will be outlined. Applications will be presented
in the shape space of viscous fluidic objects and the space of viscous thin shells.