A sampling theory for compact sets in Euclidean space

Proceedings of the Annual Symposium on Computational Geometry

Volumn 2006, Issue , 2006, Pages 319-326

  Chazal, Frédéric ^a   Cohen Steiner, David ^b   Lieutier, André ^c  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b INRIA   (France)

^c DASSAULT SYSTÈMES   (France)

Author keywords

Distance function; Sampling; Surface and manifold reconstruction

Indexed keywords

COMPUTATIONAL GEOMETRY; FUNCTIONS; INTERPOLATION; SET THEORY; TOPOLOGY;

DISTANCE FUNCTION; SURFACE AND MANIFOLD RECONSTRUCTION;

SAMPLING;

EID: 33748084033     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1137856.1137904     Document Type: Conference Paper

References (30)

1. N. Amenta, S. Choi, T. Dey and N. Leekha A simple algorithm for homeomorphic Surface Reconstruction. International Journal of Computational Geometry and Applications Vol.12, No. 1,2(2002) pp.125-141
2. N. Amenta and M. Bern Surface Reconstruction by Voronoi Filtering Discrete and Computational Geometry, no 22 pp.481-504(1999)
3. J.D. Boissonnat and S. Oudot, Provably Good Sampling and Meshing of Lipschitz Surfaces, submitted.
4. R. Chaine, A Geometric Convection Approach of 3-D Reconstruction In 1st Symposium on Geometry Processing, pp. 218-229, 2003
5. F. Chazal, A. Lieutier, The λ-medial axis In Graphical Models (GMOD),vol. 67 (4) pp. 304-331, 2005
6. F. Chazal, A. Lieutier, Weak feature size and persistent homology: computing homology of solids in ℝ from noisy data samples 21st Symposium on Computational geometry (2005) pp. 255-262
7. F. Chazal, A. Lieutier, Weak feature size and persistent homology: computing homology of solids in ℝ from noisy data samples preprint of the Institut Mathématiques de Bourgogne. Available at http://math.ubourgogne. fr/topologie/chazal/publications.htm
8. F. Chazal, A. Lieutier, Topology guaranteeing manifold reconstruction using distance function to noisy data to appear in proc. SoCG'06. Available at http://math.u-bourgogne.fr/topologie/chazal/publications.htm
9. F. Chazal, R. Soufflet, Stability and finiteness properties of medial axis and skeleton, Journal of Dynamical and Control Systems, vol.10, No. 2, pp. 149-170, 2004.
10. J. Cheeger, Critical Points of Distance Functions and Applications to Geometry, Geometric Topology: recent developments,Montecatini Terme, 1990, Springer Lecture Notes, 1504 (1991), 1-38.
11. F.H. Clarke, Optimization and NonSmooth Analysis, Wiley-Interscience, New-York, 1983.
12. F.H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247-262.
13. D. Cohen-Steiner, H. Edelsbrunner and J. Harer, Stability of Persistence Diagrams, Proc. 21th ACM Sympos. Comput. Geom. (2005), 263-271.
14. T. K. Dey, J Giesen, E.A. Ramos and B. Sadri, Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction. 21st symposium on Computational geometry (2005), pp 218-227.
15. T. K. Dey and S. Goswami, Provable surface reconstruction from noisy samples, Proc. 20th ACM Sympos. Comput, Geom. (2004), 330-339.
16. T. K. Dey and R. Wenger, Reconstructing Curves with Sharp Corners, Proc. 16th ACM Sympos. Comput. Geom. (2000), 233-241.
17. H. Edelsbrunner. Surface reconstruction by wrapping finite point sets in space, in Ricky Pollack and Eli Goodman Festschrift ed. B. Aronov, S. Basu, J. Pach and M. Sharir.Springer-Verlag, 379-404
18. H. Edelsbrunner, E. P. Mücke. Three-dimensional alpha shapes, ACM Trans. Graphics 13 (1994), 43-72.
19. H. Federer, Curvature measures, Trans. Amer. Math. Soc. Vol. 93, p 418 (1959).
20. M. Foskey, M. C. Lin and D. Manocha, Efficient computation of a simplified medial axis, ACM Symposium on Solid Modeling and Applications 2003, pp 96-107.
21. J.H.G. Fu, Tubular Neighborhoods in Euclidean Spaces, Duke Math. Jornal, Vol. 52, No. 4 (1995).
22. J. Giesen and M. John, The Flow Complex: A Data Structure for Geometric Modeling. Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), (2003) 285-294.
23. K. Grove, Critical Point Theory for Distance Functions, Proc. of Symp. in Pure Mathematics, Vol. 54 (1993), Part 3.
24. K. Grove, K. Shiohama, A generalized sphere theorem, Ann. of Math., vol 106, 1977, pp 201-211.
25. A. Lieutier, Any open bounded subset of ℝ has the same homotopy type as its medial axis, Computer-Aided Design, 36(2004) 1029-1046, Elsevier.
26. B. Mederos,N. Amenta,L. Velho and L.H. de Figueiredo Surface Reconstruction from Noisy Point Clouds Proc, of Geometry Processing 2005,(Eurographics/ ACM SIGGRAPH) pp.53-62
27. P. Niyogi, S. Smale and S. Weinberger, Finding the Homology of Submanifolds with High Confidence from Random samples, preprint available at http://www.tti-c.org/smale.papers.html
28. V. Robins, J.D. Meiss and L. Bradley, Computing Connectedness: Disconnectedness and Discreteness, Physica D 139:276-300, 2000.
29. J. Ruppert, A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation, Journal of Algorithms 18(3):548:585, 1995.
30. J.L. Starck, V.J. Martínez, D.L. Donoho, O. Levi, P. Querre and E. Saar, Analysis of the Spatial Distribution of Galaxies by Multiscale Methods, arXiv:astro-ph/0406425 v1 18 Jun 04.