Finsler-Laplace-Beltrami Operators With Application to Shape Analysis
MCML Authors
Simon Weber
* Former Member
Thomas Dagès
Dr.
Thomas Bayes Fellow
Daniel Cremers
Prof. Dr.
Director
Abstract
Simon Weber
* Former Member
Thomas Dagès
Dr.
Thomas Bayes Fellow
Daniel Cremers
Prof. Dr.
Director
Abstract
The Laplace-Beltrami operator (LBO) emerges from studying manifolds equipped with a Riemannian metric. It is often called the swiss army knife of geometry processing as it allows to capture intrinsic shape information and gives rise to heat diffusion, geodesic distances, and a mul-titude of shape descriptors. It also plays a central role in geometric deep learning. In this work, we explore Finsler manifolds as a generalization of Riemannian manifolds. We revisit the Finsler heat equation and derive a Finsler heat kernel and a Finsler-Laplace-Beltrami Operator (FLBO): a novel theoretically justified anisotropic Laplace-Beltrami operator (ALBO). In experimental evaluations we demon-strate that the proposed FLBO is a valuable alternative to the traditional Riemannian-based LBO and ALBOs for spa-tialfiltering and shape correspondence estimation. We hope that the proposed Finsler heat kernel and the FLBO will inspire further exploration of Finsler geometry in the Computer vision community.
inproceedings WDG+24
CVPR 2024
IEEE/CVF Conference on Computer Vision and Pattern Recognition. Seattle, WA, USA, Jun 17-21, 2024.
Authors
S. Weber • T. Dagès • M. Gao • D. CremersLinks
DOIResearch Area
BibTeXKey: WDG+24