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

Julie Digne 1, 2 David Cohen-Steiner 2 Pierre Alliez 3 Fernando de Goes 4 Mathieu Desbrun 4
1 GeoMod - Modélisation Géométrique, Géométrie Algorithmique, Fractales
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
3 TITANE - Geometric Modeling of 3D Environments
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We introduce a robust and feature-capturing surface reconstruction and simpli cation method that turns an input point set into a low triangle-count simplicial complex. Our approach starts with a (possibly non-manifold) simplicial complex ltered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simpli ed based on an error metric that measures, through optimal transport, the distance between the input points and the current simplicial complex|both seen as mass distributions. Our approach is shown to exhibit both robustness to noise and outliers, as well as preservation of sharp features and boundaries. Our new feature-sensitive metric between point sets and triangle meshes can also be used as a post-processing tool that, from the smooth output of a reconstruction method, recovers sharp features and boundaries present in the initial point set.
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Julie Digne, David Cohen-Steiner, Pierre Alliez, Fernando de Goes, Mathieu Desbrun. Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets. Journal of Mathematical Imaging and Vision, Springer Verlag, 2013, pp.1-14. ⟨10.1007/s10851-013-0414-y⟩. ⟨hal-00827623⟩



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