Laplace--Beltrami Operator on Digital Surfaces


This article presents a novel discretization of the Laplace–Beltrami operator on digital surfaces.We adapt an existing convolution technique proposed by Belkin et al. for triangular meshes to topological border of subsets of $\mathbb{Z}^n$. The core of the method relies on first-order estimation of measures associated with our discrete elements (such as length, area etc.). We show strong consistency (i.e. pointwise convergence) of the operator and compare it against various other discretizations.

Journal of Mathematical Imaging and Vision, 61(3): 359-379, 2019
Jacques-Olivier Lachaud
Jacques-Olivier Lachaud
Professor of Computer Science

My research interests include digital geometry, geometry processing, image analysis, variational models and discrete calculus.