Mersenne banner
no. 1
Robust Shape Reconstruction and Optimal Transportation
Pierre Alliez1; Simon Giraudot1; David Cohen-Steiner1
1 Inria Sophia Antipolis - Mediterranée 2004 route des Lucioles 06902 Sophia Antipolis FRANCE
Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 79-88.

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.

Published online:
DOI: 10.5802/acirm.57
Classification: 51XX
Keywords: shape reconstruction, optimal transportation, noise robustness, outlier robustness
Pierre Alliez 1; Simon Giraudot 1; David Cohen-Steiner 1

1 Inria Sophia Antipolis - Mediterranée 2004 route des Lucioles 06902 Sophia Antipolis FRANCE 
@article{ACIRM_2013__3_1_79_0,
     author = {Pierre Alliez and Simon Giraudot and David Cohen-Steiner},
     title = {Robust {Shape} {Reconstruction}  and {Optimal} {Transportation}},
     journal = {Actes des rencontres du CIRM},
     pages = {79--88},
     publisher = {CIRM},
     volume = {3},
     number = {1},
     year = {2013},
     doi = {10.5802/acirm.57},
     zbl = {06938605},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.57/}
}
TY  - JOUR
AU  - Pierre Alliez
AU  - Simon Giraudot
AU  - David Cohen-Steiner
TI  - Robust Shape Reconstruction  and Optimal Transportation
JO  - Actes des rencontres du CIRM
PY  - 2013
SP  - 79
EP  - 88
VL  - 3
IS  - 1
PB  - CIRM
UR  - https://acirm.centre-mersenne.org/articles/10.5802/acirm.57/
DO  - 10.5802/acirm.57
LA  - en
ID  - ACIRM_2013__3_1_79_0
ER  - 
%0 Journal Article
%A Pierre Alliez
%A Simon Giraudot
%A David Cohen-Steiner
%T Robust Shape Reconstruction  and Optimal Transportation
%J Actes des rencontres du CIRM
%D 2013
%P 79-88
%V 3
%N 1
%I CIRM
%U https://acirm.centre-mersenne.org/articles/10.5802/acirm.57/
%R 10.5802/acirm.57
%G en
%F ACIRM_2013__3_1_79_0
Pierre Alliez; Simon Giraudot; David Cohen-Steiner. Robust Shape Reconstruction  and Optimal Transportation. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 79-88. doi : 10.5802/acirm.57. https://acirm.centre-mersenne.org/articles/10.5802/acirm.57/

[1] Haim Avron; Andrei Sharf; Chen Greif; Daniel Cohen-Or ℓ 1 -Sparse reconstruction of sharp point set surfaces, ACM Trans. on Graphics, Volume 29 (2010) no. 5, pp. 1-12 | DOI

[2] Haim Avron; Andrei Sharf; Chen Greif; Daniel Cohen-Or L1-Sparse reconstruction of sharp point set surfaces, ACM Transactions on Graphics, Volume 29 (2010), p. 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 (J.D. Boissonnat; M. Teillaud, eds.), Springer-Verlag, Math. and Visualization, 2006, pp. 231-276 | DOI | Zbl

[5] Frédéric Chazal; David Cohen-Steiner; Quentin Mérigot Geometric Inference for Probability Measures, Journal on Foundations of Computational Mathematics, Volume 11 (2011), pp. 733-751 | DOI | MR | Zbl

[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, Volume 30 (2011) no. 5, pp. 1593-1602 (Special issue for EUROGRAPHICS Symposium on Geometry Processing) | DOI

[7] Tamal K. Dey Curve and Surface Reconstruction: Algorithms with Mathematical Analysis, Cambridge Monographs on Applied and Computational Mathematics, 2006 | Zbl

[8] S. Fleishman; D. Cohen-Or; C.T. Silva Robust moving least-squares fitting with sharp features, ACM SIGGRAPH 2005 Papers (2005), 552 pages | DOI

[9] Simon Giraudot; David Cohen-Steiner; Pierre Alliez Noise-Adaptive Shape Reconstruction from Raw Point Sets, Computer Graphics Forum, Volume 32 (2013) no. 5, pp. 229-238 http://diglib.eg.org/EG/CGF/volume32/issue5/v32i5pp229-238.pdf | DOI

[10] Leo Grady Random Walks for Image Segmentation, Pattern Analysis and Machine Intelligence, IEEE Transactions on, Volume 28 (2006) no. 11, pp. 1768-1783 | DOI

[11] Michael Kazhdan; M. Bolitho; Hugues Hoppe Poisson Surface Reconstruction, Symposium on Geometry Processing (2006), pp. 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), pp. 11-21

[13] Yaron Lipman; Ingrid Daubechies Surface Comparison with Mass Transportation (2010) (ArXiv preprint 0912.3488)

[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, Volume 29 (2010) no. 5, pp. 1733-1741 (Proceedings of EUROGRAPHICS Symposium on Geometry Processing) | DOI

[15] Yuqing Song Boundary fitting for 2D curve reconstruction, The Visual Computer, Volume 26 (2010), pp. 187-204 | DOI

[16] S. Sotoodeh Outlier detection in laser scanner point clouds, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume 36 (2006) no. 5, pp. 297-302

[17] C. Villani Topics in Optimal Transportation, American Mathematical Society, 2010

Cited by Sources: