Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets

Julie Digne; David Cohen-Steiner; Pierre Alliez; Mathieu Desbrun; Fernando De Goes

hal-00706712, version 1

Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets

Julie Digne ¹, David Cohen-Steiner ¹, Pierre Alliez ¹, Mathieu Desbrun ², Fernando De Goes ²

N° RR-7991 (2012)

Résumé : We propose a robust, feature-preserving surface reconstruction algorithm which turns a point set with noise and outliers into a low triangle-count simplicial complex. Our approach starts with a simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on the optimal cost to transport the point set to the simplicial complex, both seen as measures (or mass distributions). Our optimal transport formulation allows the recovery of sharp features even in the presence of a large amount of outliers and/or noise in the input set.

1 : GEOMETRICA (INRIA Sophia Antipolis / INRIA Saclay - Ile de France)
INRIA
2 : Computer Science Department (CS CALTECH)
California Institute of Technology

hal-00706712, version 1
http://hal.inria.fr/hal-00706712
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Contributeur : Julie Digne <>
Soumis le : Lundi 11 Juin 2012, 14:02:11
Dernière modification le : Lundi 11 Juin 2012, 16:26:09

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%F hal-00706712, version 1
%0 Report
%U http://hal.inria.fr/hal-00706712
%2 INFO:INFO_IA;INFO:INFO_CG
%T Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets
%A Digne, Julie
%A Cohen-Steiner, David
%A Alliez, Pierre
%A Desbrun, Mathieu
%A De Goes, Fernando
%+ GEOMETRICA - INRIA Sophia Antipolis / INRIA Saclay - Ile de France , Computer Science Department - CS CALTECH
%X We propose a robust, feature-preserving surface reconstruction algorithm which turns a point set with noise and outliers into a low triangle-count simplicial complex. Our approach starts with a simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on the optimal cost to transport the point set to the simplicial complex, both seen as measures (or mass distributions). Our optimal transport formulation allows the recovery of sharp features even in the presence of a large amount of outliers and/or noise in the input set.
%2 Nous proposons une méthode robuste de reconstruction de surface qui préserve les bords et les arêtes vives. Cette méthode part d'un nuage de points bruités et contenant des points aberrants pour reconstruire un complexe simplicial parcimonieux. Notre approche débute par la construction d'un complexe simplicial par filtrage d'une triangulation de Delaunay des points initiaux. Cette approximation initiale est ensuite itérativement simplifiée en se basant sur le coût de transport entre le nuage de points et le complexe simplicial, ceux-ci étant vus comme des distributions de masse. Cette formulation basée sur le transport optimal entre les deux distributions permet de retrouver les arêtes vives même en présence de nombreux points aberrants ou de bruit dans le nuage de points initial.
%G Anglais
%2 Rapport de recherche
%P 23
%8 2012-06-11
%K Optimal transportation, Wasserstein distance, Linear programming, Surface recon- struction, Shape simplification, Feature recovery.
%Z RR-7991
%2 85772

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