Journal of Mathematical Imaging and Vision

, Volume 48, Issue 2, pp 369–382 | Cite as

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

  • Julie Digne
  • David Cohen-Steiner
  • Pierre Alliez
  • Fernando de Goes
  • Mathieu Desbrun


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.


Optimal transportation Wasserstein distance Linear programming Surface reconstruction Shape simplification Feature recovery 



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.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Julie Digne
    • 1
  • David Cohen-Steiner
    • 1
  • Pierre Alliez
    • 1
  • Fernando de Goes
    • 2
  • Mathieu Desbrun
    • 2
  1. 1.Inria Sophia Antipolis—MéditerranéeLe Chesnay CedexFrance
  2. 2.California Institute of TechnologyPasadenaUSA

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