Finsler-Laplace-Beltrami Operators With Application to Shape Analysis
MCML Authors
Thomas Dagès
Dr.
Thomas Bayes Fellow
Daniel Cremers
Prof. Dr.
Director
Abstract
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