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

Model Order Reduction for Efficient Descriptor-Based Shape Analysis