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Issue ESAIM: PROC
Volume 27, 2009
CANUM 2008
Page(s) 254 - 271
DOI 10.1051/proc/2009031
Published online 25 June 2009

ESAIM: Proc., 2009, Vol. 27, pp. 254-271
DOI: 10.1051/proc/2009031

Level set driven smooth curve approximation from unorganized or noisy point set

A. Claisse1 and P. Frey1, 2

1  UPMC Univ Paris 06, UMR 7598, Laboratoire J.-L. Lions, F-75005 Paris, France.
2  Universidad de Chile, UMI 2807, Centro de Modelamiento Matemático, Santiago, Chile.

claisse@ann.jussieu.fr
frey@ann.jussieu.fr

Published online: 25 June 2009

Abstract
In this paper, we propose a curve construction method for a non uniform point data set based on a minimal curve approximation model. Numerically, the level set method is used for curve reconstruction. We represent the shape of the curve through its distance function and formulate curve reconstruction as a constrained minimization problem. We solve the minimization problem on a highly anisotropic triangulation to improve the accuracy of the numerical scheme. This method can handle complex geometries and deal with arbitrary topologies as well as with noisy data sets. Several numerical examples are provided to show the efficiency of the proposed approach.


Résumé
Dans ce papier, on propose un modèle de courbe d'approximation minimale pour construire une courbe à partir d'un nuage de points. Numériquement, la reconstruction de la courbe s'appuie sur une formulation de type ligne de niveau. On représente la forme de la courbe par sa fonction distance aux points et on exprime ce problème comme un problème de minimisation. Ce dernier est résolu sur une triangulation anisotrope qui permet d'améliorer la précision du schéma numérique. Cette méthode permet de traiter des géométries complexes et des topologies quelconques ainsi que des données bruitées. Des exemples de reconstruction sont proposés pour montrer l'éfficacité de cette approche.



© EDP Sciences, ESAIM 2009


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