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

Digne, Julie and Cohen-Steiner, David and Alliez, Pierre and de Goes, Fernando and Desbrun, Mathieu (2014) Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets. Journal of Mathematical Imaging and Vision, 48 (2). pp. 369-382. ISSN 0924-9907. doi:10.1007/s10851-013-0414-y.

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We introduce a robust and feature-capturing surface reconstruction and simplification method that turns an input point set into a low triangle-count simplicial complex. Our approach starts with a (possibly non-manifold) simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified 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.

Item Type:Article
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URLURL TypeDescription
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2013 Springer Science+Business Media New York. Published online: 24 January 2013. This work was funded by the European Research Council (ERC Starting Grant “Robust Geometry Processing”, Grant agreement 257474). We also thank the National Science Foundation for partial support through the CCF grant 1011944.
Funding AgencyGrant Number
European Research Council (ERC) Starting Grant "Robust Geometry Processing"257474
NSF CCF1011944
Subject Keywords:Optimal transportation; Wasserstein distance; Linear programming; Surface reconstruction; Shape simplification; Feature recovery
Issue or Number:2
Record Number:CaltechAUTHORS:20140213-143249205
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43819
Deposited By: Tony Diaz
Deposited On:21 Feb 2014 21:26
Last Modified:10 Nov 2021 16:43

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