Laplace-Beltrami operator on Digital Curves


Many problems in image analysis, digital processing and shape optimization are expressed as variational prob- lems 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.

      address = {Grenoble, France},
      author = {Caissard, Thomas and Coeurjolly, David and Roussillon, Tristan and Lachaud, Jacques-Olivier},
      booktitle = {JFIG},
      hal_id = {hal-01497255},
      keywords = {laplacians ; heat equation ; convolution ; digital
      month = {November},
      pdf = {},
      title = {Laplace-Beltrami operator on Digital Curves},
      url = {},
      year = {2016}