Stability and computation of topological invariants of solids in ℝn

Discrete and Computational Geometry

Volumn 37, Issue 4, 2007, Pages 601-617

  Chazal, Frederic ^a   Lieutier, Andre ^b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b DASSAULT SYSTÈMES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247581847     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-007-1309-8     Document Type: Article

References (27)

1. N. Amenta and M. Bern, Surface reconstruction by Voronoi filtering, Disciete Comput. Geom. 22 (1999), 481-504.
2. N. Amenta, S. Choi, T. Dey and N. Leekha, A simple algorithm for homeomoiphic surface reconstruction, Internat. J. Comput. Geom. Appl. 12(1,2) (2002), 125-141.
3. M. Berger, Geometry I, Universitext Series, Springer-Verlag, Berlin, 1998.
4. F. Cazals and J.D. Boissonnat, Smooth surface reconstruction via natural neighbour interpolation of distance functions, Proc. Sixteenth ACM Symp. Computational Geometry, 2000, pp. 223-232.
5. F. Chazal and D. Cohen-Steiner, A condition for isotopic approximation, Proc. ACM Symp. Solid Modeling and Applications, 2004, pp. 390-404.
6. F. Chazal and A. Lieutier, Stability and homotopy of a subset of the medial axis (extended abstract), Proc. ACM Symp. Solid Modeling and Applications, 2004, pp. 243-248.
7. F. Chazal and A. Lieutier, The λ-medial axis, Graphical Models, 67(4) (2005), 304-331.
8. F. Chazal and R. Soufflet, Stability and finiteness properties of medial axis and skeleton, J. Dynam. Control Systems 10(2) (2004), 149-170.
9. J. Cheeger, Critical Points of Distance Functions and Applications to Geometry, in Geometric Topology: Recent Developments, Montecatini Terme, Springer Lecture Notes, 1504, Springer, Berlin, 1991, pp. 1-38.
10. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
11. F.H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247-262.
12. D. Cohen-Steiner, H. Edelsbrunner and J. Harer, Stability of persistence diagrams, Proc. 21st Annual ACM Symp. Computational Geometry, 2005, pp. 263-271.
13. T. K. Dey, J. Giesen and M. John, Alpha-shapes and flow shapes are homotopy equivalent, Proc. 35rd Annual ACM Symp. Theory of Computing (STOC), 2003, pp. 493-502.
14. T. K. Dey and S. Goswami, Provable surface reconstruction from noisy samples, Proc. 20th ACM Symp. Computational Geometry, 2004, pp. 330-339.
15. H. Edelsbrunner, D. Letscher and A. Zomorodian, Topological persistence and simplifications, Discrete Comput. Geom. 28 (2002), 511-533.
16. H. Edelsbrunner and E. P. Mucke, Three-dimensional alpha shapes, ACM Trans. Graphics 13 (1994), 43-72.
17. H. Federer, Curvature measure, Trans. Amer. Math. Soc. 93 (1959), 418-491.
18. J.H.G. Fu, Tubular neighborhoods in Euclidean spaces, Duke. Math. J. 52(4) (1995), pp. 1025-1046.
19. W. Fulton, Algebraic Topology, A First Course, Graduate Texts in Mathematics, Springer-Verlag, New York, 1997.
20. M. Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), pp. 179-195.
21. K. Grove, Critical point theory for distance functions, Proc. of Symposia in Pure Mathematics, Vol. 54, American Mathematical Society, Providence, RI, 1993.
22. K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math. 106 (1977), 201-211.
23. n has the same homotopy type as its medial axis, J. Comput.AidedDesign 36 (2004), 1029-1046.
24. W. Massey, Algebraic Topology: An Introduction. Harbrace College Mathematics Series, Harcourt, Brace and World, Orlando, FL, 1967.
25. J.R. Munkres, Elements of Algebraic Topology. Addison-Wesley Publishing Company, 1984.
26. E.H.Spanier. Algebraic Topology McGraw-Hill Series in Higher Mathematics, McGraw-Hill, New York, 1966.
27. A.J. Zomorodian Computing and comprehending topology: persistence and hierarchical morse complexes, Thesis, University of Illinois at Urbana-Champaign, 2001.