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Modèle de reconstruction d'une surface échantillonnée par un méthode de ligne de niveau, et applications

Abstract : Over the last years, surface reconstruction from sampled data remains an important and active area of research. The challenge is then to handle a wide range of geometries and topologies. The aim of this work is to find a regular surface (typically C2 continuous), denoted by Gamma, fitting at best a given set of point V, i.e. such that the Euclidian distance d(x,Gamma ) is minimal for all x in V. We formulate the problem using a partial differential equation which characterizes the evolution of a surface Gamma(t). This PDE relies on an attraction term, which involves the distance to the data set, and on a surface tension term which preserves the regularity of Gamma(t) during its evolution. We show that the problem is well-posed, its solution exists and is unique. This PDE is numerically formulated using the level set method, and it is solved using specific numerical schemes (with an approximation of the first and second order space derivatives in each node of the mesh), adapted anisotropic triangulations (in order to improve the numerical approximation of the manifold). From the analytical point of view, we show that the schemes are consistent and L2 stable. Some application examples are presented to illustrate the efficiency of our approach.
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https://tel.archives-ouvertes.fr/tel-00443640
Contributor : Alexandra Claisse <>
Submitted on : Thursday, December 31, 2009 - 6:23:32 PM
Last modification on : Thursday, December 10, 2020 - 10:52:44 AM
Long-term archiving on: : Thursday, October 18, 2012 - 11:40:58 AM

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  • HAL Id : tel-00443640, version 1

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Alexandra Claisse. Modèle de reconstruction d'une surface échantillonnée par un méthode de ligne de niveau, et applications. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2009. Français. ⟨tel-00443640⟩

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