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Journal Articles Journal of Mathematical Imaging and Vision Year : 2019

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. [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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Dates and versions

hal-01717849 , version 1 (26-02-2018)
hal-01717849 , version 2 (10-03-2018)
hal-01717849 , version 3 (28-07-2018)



Thomas Caissard, David Coeurjolly, Jacques-Olivier Lachaud, Tristan Roussillon. Laplace–Beltrami Operator on Digital Surfaces. Journal of Mathematical Imaging and Vision, 2019, 61 (3), pp.359-379. ⟨10.1007/s10851-018-0839-4⟩. ⟨hal-01717849v3⟩
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