Robust Shape Reconstruction and Optimal Transportation

Pierre Alliez[1]; Simon Giraudot[1]; David Cohen-Steiner[1]

  • [1] Inria Sophia Antipolis - Mediterranée 2004 route des Lucioles 06902 Sophia Antipolis FRANCE

Actes des rencontres du CIRM (2013)

  • Volume: 3, Issue: 1, page 79-88
  • ISSN: 2105-0597

Abstract

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We describe a framework for robust shape reconstruction from raw point sets, based on optimal transportation between measures, where the input point sets are seen as distribution of masses. In addition to robustness to defect-laden point sets, hampered with noise and outliers, our approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries.

How to cite

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Alliez, Pierre, Giraudot, Simon, and Cohen-Steiner, David. "Robust Shape Reconstruction and Optimal Transportation." Actes des rencontres du CIRM 3.1 (2013): 79-88. <http://eudml.org/doc/275314>.

@article{Alliez2013,
abstract = {We describe a framework for robust shape reconstruction from raw point sets, based on optimal transportation between measures, where the input point sets are seen as distribution of masses. In addition to robustness to defect-laden point sets, hampered with noise and outliers, our approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries.},
affiliation = {Inria Sophia Antipolis - Mediterranée 2004 route des Lucioles 06902 Sophia Antipolis FRANCE; Inria Sophia Antipolis - Mediterranée 2004 route des Lucioles 06902 Sophia Antipolis FRANCE; Inria Sophia Antipolis - Mediterranée 2004 route des Lucioles 06902 Sophia Antipolis FRANCE},
author = {Alliez, Pierre, Giraudot, Simon, Cohen-Steiner, David},
journal = {Actes des rencontres du CIRM},
keywords = {shape reconstruction; optimal transportation; noise robustness; outlier robustness},
language = {eng},
month = {11},
number = {1},
pages = {79-88},
publisher = {CIRM},
title = {Robust Shape Reconstruction and Optimal Transportation},
url = {http://eudml.org/doc/275314},
volume = {3},
year = {2013},
}

TY - JOUR
AU - Alliez, Pierre
AU - Giraudot, Simon
AU - Cohen-Steiner, David
TI - Robust Shape Reconstruction and Optimal Transportation
JO - Actes des rencontres du CIRM
DA - 2013/11//
PB - CIRM
VL - 3
IS - 1
SP - 79
EP - 88
AB - We describe a framework for robust shape reconstruction from raw point sets, based on optimal transportation between measures, where the input point sets are seen as distribution of masses. In addition to robustness to defect-laden point sets, hampered with noise and outliers, our approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries.
LA - eng
KW - shape reconstruction; optimal transportation; noise robustness; outlier robustness
UR - http://eudml.org/doc/275314
ER -

References

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  1. Haim Avron, Andrei Sharf, Chen Greif, Daniel Cohen-Or, ℓ 1 -Sparse reconstruction of sharp point set surfaces, ACM Trans. on Graphics 29 (2010), 1-12 
  2. Haim Avron, Andrei Sharf, Chen Greif, Daniel Cohen-Or, L1-Sparse reconstruction of sharp point set surfaces, ACM Transactions on Graphics 29 (2010), 135:1-135:12 
  3. Nicolas Bonneel, Michiel van de Panne, Sylvain Paris, Wolfgang Heidrich, Displacement Interpolation Using Lagrangian Mass Transport, ACM Transactions on Graphics (SIGGRAPH Asia Proceedings) (2011) 
  4. Frédéric Cazals, Joachim Giesen, Delaunay Triangulation Based Surface Reconstruction, Effective Computational Geometry for Curves and Surfaces (2006), 231-276, BoissonnatJ.D.J.D. Zbl1116.65022
  5. Frédéric Chazal, David Cohen-Steiner, Quentin Mérigot, Geometric Inference for Probability Measures, Journal on Foundations of Computational Mathematics 11 (2011), 733-751 Zbl1230.62074MR2859954
  6. Fernando de Goes, David Cohen-Steiner, Pierre Alliez, Mathieu Desbrun, An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes, Computer Graphics Forum 30 (2011), 1593-1602 
  7. Tamal K. Dey, Curve and Surface Reconstruction: Algorithms with Mathematical Analysis, (2006), Cambridge Monographs on Applied and Computational Mathematics Zbl1213.65028MR2267420
  8. S. Fleishman, D. Cohen-Or, C.T. Silva, Robust moving least-squares fitting with sharp features, ACM SIGGRAPH 2005 Papers (2005) 
  9. Simon Giraudot, David Cohen-Steiner, Pierre Alliez, Noise-Adaptive Shape Reconstruction from Raw Point Sets, Computer Graphics Forum 32 (2013), 229-238 
  10. Leo Grady, Random Walks for Image Segmentation, Pattern Analysis and Machine Intelligence, IEEE Transactions on 28 (2006), 1768-1783 
  11. Michael Kazhdan, M. Bolitho, Hugues Hoppe, Poisson Surface Reconstruction, Symposium on Geometry Processing (2006), 61-70 
  12. Ravikrishna Kolluri, Jonathan Shewchuk, James O’Brien, Spectral Surface Reconstruction from Noisy Point Clouds, Proceedings of EUROGRAPHICS Symposium on Geometry Processing (2004), 11-21 
  13. Yaron Lipman, Ingrid Daubechies, Surface Comparison with Mass Transportation, (2010) 
  14. Patrick Mullen, Fernando De Goes, Mathieu Desbrun, David Cohen-Steiner, Pierre Alliez, Signing the Unsigned: Robust Surface Reconstruction from Raw Pointsets, Computer Graphics Forum 29 (2010), 1733-1741 
  15. Yuqing Song, Boundary fitting for 2D curve reconstruction, The Visual Computer 26 (2010), 187-204 
  16. S. Sotoodeh, Outlier detection in laser scanner point clouds, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 36 (2006), 297-302 
  17. C. Villani, Topics in Optimal Transportation, (2010), American Mathematical Society Zbl1106.90001MR1964483

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