  In order to investigate correspondences between 3D shapes, many methods rely
on a feature descriptor which is invariant under almost isometric
transformations. An interesting class of models for such descriptors relies on
partial differential equations (PDEs) based on the Laplace-Beltrami operator
for constructing intrinsic shape signatures. In order to conduct the
construction, not only a variety of PDEs but also several ways to solve them
have been considered in previous works. In particular, spectral methods have
been used derived from the series expansion of analytic solutions of the PDEs,
and alternatively numerical integration schemes have been proposed. In this
paper we show how to define a computational framework by model order reduction
(MOR) that yields efficient PDE integration and much more accurate shape
signatures as in previous works. Within the construction of our framework we
introduce some technical novelties that contribute to these advances, and in
doing this we present some improvements for virtually all considered methods.
As part of the main contributions, we show for the first time an extensive and
detailed comparison between the spectral and integration techniques, which is
possible by the advances documented in this paper. We also propose here to
employ soft correspondences in the context of the MOR methods which turns out
to be highly beneficial with this approach.
