Towards Efficient Time Stepping for Numerical Shape Correspondence
Alexander Köhler Michael Breuß
The computation of correspondences between shapes is a principal task in
shape analysis. To this end, methods based on partial differential equations
(PDEs) have been established, encompassing e.g. the classic heat kernel
signature as well as numerical solution schemes for geometric PDEs. In this
work we focus on the latter approach.
  We consider here several time stepping schemes. The goal of this
investigation is to assess, if one may identify a useful property of methods
for time integration for the shape analysis context. Thereby we investigate the
dependence on time step size, since the class of implicit schemes that are
useful candidates in this context should ideally yield an invariant behaviour
with respect to this parameter.
  To this end we study integration of heat and wave equation on a manifold. In
order to facilitate this study, we propose an efficient, unified model order
reduction framework for these models. We show that specific $l_0$ stable
schemes are favourable for numerical shape analysis. We give an experimental
evaluation of the methods at hand of classical TOSCA data sets.