Laplace-Beltrami operator on Digital Curves

National audienceMany 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