Stability and finiteness properties of medial axis and skeleton

Journal of Dynamical and Control Systems

Volumn 10, Issue 2, 2004, Pages 149-170

  Chazal, F ^a   Soufflet, R ^b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Medial axis; Shape modelling; Stability problems; Subanalytic sets

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; SET THEORY;

MEDIAL AXIS; SHAPE MODELLING; STABILITY PROBLEMS; SUBANALYTIC SETS;

COMPUTATIONAL GEOMETRY;

EID: 3943094700     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JODS.0000024119.38784.ff     Document Type: Article

References (32)

1. D. Attali and J.-D. Boissonnat, Complexity of the Delaunay triangulation of points on polyhedral surfaces. Proc. 7th ACM Symp. on Solid Model. Appl. (2002).
2. D. Attali and J.-D. Boissonnat, Approximation of the medial axis. Technical Report ECG-TR-124103-01, INRIA Sophia-Antipolis (2002).
3. D. Attali, J.-D. Boissonnat, and A. Lieutier, Complexity of the Delaunay triangulation of points on surfaces: The smooth case. In: 19th Annual ACM Symp. on Comput. Geometry.
4. J. August, K. Siddiki, and S. W. Zucker, Ligature instabilities and the perseptual organization of shape. Computer Vision and Image Understanding 76 (1999), No. 3, 231-243.
5. R. Benedetti, J. J. Risler, Real algebraic and semi-algebraic sets. Actualités Mathématiques, Hermann, Paris (1990).
6. E. Bierstone and P. Milman, The local geometry of analytic mappings. Univ. di Pisa, ETS Editrice Pisa (1988).
7. E. Bierstone and P. Milman, Semianalytic and subanalytic sets. Publ. Math. IHES 67 (1988), 5-42.
8. W. Blaschke, Kreis und Kugel. Leipzig (1916).
9. H. Blum, A transformation for extracting new descriptors of shape. In: W. Wathen-Dunn (ed.), Models for the perception of speech and visual form, MIT Press (1967), 362-380..
10. J. Bochnak, M. Coste, and F. Roy, Géométrie algébrique réelle. Springer-Verlag (1986).
11. T.Bonnesen and W. Fenchel, Theory of convex bodies. BCS Associates, Moscow-Idaho USA (1987).
12. M. Berger and B. Gostiaux, Géométrie différentielle: variétés, courbes et surfaces. Presses Universitaires de France (1987).
13. H. I. Choi, S. W. Choi, and H. P. Moon, Mathematical theory of medial axis transform. Pac. J. Math. 181 (1997), No. 1.
14. S. W. Choi and H.-P. Seidel, Linear one-sided stability of MAT for weakly injective 3D domain. Proc. 7th ACM Symp. on Solid Model. Appl. (2002), 344-355.
15. M. Coste, An introduction to semialgebraic geometry. Istituti editoriali e poligrafici internazionali, Pisa (1998).
16. T. Culver, J. Keyser, and D. Manocha, Accurate computation of the medial axis of a polyhedron. Proc. ACM Symp. on Solid Model. Appl. (1999), 179-190.
17. G. Comte, Y. Yomdin, Tame topology with application to smooth analysis. Preprint 653, Univ. de Nice Sophia Antipolis (2002).
18. L. van den Dries, Tame topology and o-minimal structures. London Math. Soc. Lect. Notes Ser. 248, Cambridge Univ. Press (1998).
19. J. Erickson, Uniform samples of generic surfaces have nice Delaunay triangulations. (In press).
20. A. M. Gabrielov, Projections of semi-analytic sets. Funct. Anal. Appl. 2 (1968), 282-291.
21. S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry. Springer-Verlag (1993).
22. M. W. Hirsch, Differential topology. Springer-Verlag (1976).
23. K. Leichtweiss, Convexity and differential geometry. In: Handbook of convex geometry, P. M. Gruber and J. M. Wills (eds.), North-Holland (1993).
24. K. Kurdyka, S. Lojasievicz, and M. Zurro, Distinguish stratifications as a tool in semi-analytic geometry. Manuscr. Math. 86 (1995), 81-102.
25. A. Lieutier, Medial axis homotopy. Rapport de recherche LMC/IMAG (2002).
26. S. Lojasiewicz, Ensembles semi-analytiques. Preprint IHES (1965).
27. S. Lojasiewicz, Sur la géométrie semi- et sous-analytique. Ann. Inst. Fourier 43 (1993), No. 5.
28. J. W. Milnor, Morse theory. Princeton Univ. Press, Princeton, NJ (1963).
29. U. Montanari, A method for obtaining skeletons using a quasi-Euclidean distance. J. ACM 15 (1968), No. 4, 600-624.
30. M. Tamm, Subanalytic sets in the calculus of variation. Acta Math. 146 (1981), 167-199.
31. A. Weinstein, The cut locus and conjugate locus of a Riemannian manifold. Ann. Math. (2) 87 (1968), 29-41.
32. Y. Yomdin, Metric properties of semialgebraic sets and mappings and their applications in smooth analysis. In: Géométrie réelle, systèmes différentiels et théorie de