Laplace-Beltrami operator on Digital Curves

Abstract : Many problems in image analysis, digital processing and shape optimization are expressed as variational problems and involve the discritization of laplacians. Indeed, PDEs containing Laplace-Beltrami operator arise in surface fairing, mesh smoothing, mesh parametrization, remeshing, feature extraction, shape matching, etc. The discretization of the laplace-Beltrami operator has been widely studied, but essentially in the plane or on triangu-lated meshes. In this paper, we propose a digital Laplace-Beltrami operator, which is based on the heat equation described by [BSW08] and adapted to 2D digital curves. We give elements for proving its theoretical convergence and present an experimental evaluation that confirms its convergence property.
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Thomas Caissard, David Coeurjolly, Tristan Roussillon, Jacques-Olivier Lachaud. Laplace-Beltrami operator on Digital Curves. JFIG, Nov 2016, Grenoble, France. ⟨hal-01497255⟩

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