Finsler-Laplace-Beltrami Operators with Application to Shape Analysis

arXiv:2404.03999v1 Announce Type: new
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 multitude 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 …

abstract analysis application arxiv cs.cv diffusion geometry heat information intrinsic operators processing studying type