Scalable and Efficient Functional Map Computations on Dense Meshes
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Date
2023
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We propose a new scalable version of the functional map pipeline that allows to efficiently compute correspondences between potentially very dense meshes. Unlike existing approaches that process dense meshes by relying on ad-hoc mesh simplification, we establish an integrated end-to-end pipeline with theoretical approximation analysis. In particular, our method overcomes the computational burden of both computing the basis, as well the functional and pointwise correspondence computation by approximating the functional spaces and the functional map itself. Errors in the approximations are controlled by theoretical upper bounds assessing the range of applicability of our pipeline.With this construction in hand, we propose a scalable practical algorithm and demonstrate results on dense meshes, which approximate those obtained by standard functional map algorithms at the fraction of the computation time. Moreover, our approach outperforms the standard acceleration procedures by a large margin, leading to accurate results even in challenging cases.
Description
CCS Concepts: Computing methodologies -> Shape analysis; Theory of computation -> Computational geometry
@article{10.1111:cgf.14746,
journal = {Computer Graphics Forum},
title = {{Scalable and Efficient Functional Map Computations on Dense Meshes}},
author = {Magnet, Robin and Ovsjanikov, Maks},
year = {2023},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14746}
}