Laplace–Beltrami Operator on Digital Surfaces

Abstract : 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. [5] for triangular meshes to topological border of subsets of 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.
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Submitted on : Saturday, July 28, 2018 - 1:43:27 PM
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Thomas Caissard, David Coeurjolly, Jacques-Olivier Lachaud, Tristan Roussillon. Laplace–Beltrami Operator on Digital Surfaces. Journal of Mathematical Imaging and Vision, Springer Verlag, 2019, 61 (3), pp.359-379. ⟨https://doi.org/10.1007/s10851-018-0839-4⟩. ⟨10.1007/s10851-018-0839-4⟩. ⟨hal-01717849v3⟩

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