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.
@inproceedings{caissard16JFIG,
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
surfaces},
month = {November},
pdf = {https://hal.archives-ouvertes.fr/hal-01497255/file/jfig2016_submission.pdf},
title = {Laplace-Beltrami operator on Digital Curves},
url = {https://hal.archives-ouvertes.fr/hal-01497255},
year = {2016}
}