Tree structure for contractible regions in ℝ3

International Journal of Computer Vision

Volumn 74, Issue 2, 2007, Pages 103-116

  Damon, James ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

Blum medial axis; Contractible region; Essential and inessential fin curves; Irreducible medial components; Top level and second level (directed) trees; Y network

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; DATA STRUCTURES; TOPOLOGY;

BLUM MEDIAL AXIS; CONTRACTIBLE REGION; IRREDUCIBLE MEDIAL COMPONENTS; SMOOTH MEDIAL SHEETS; Y-NETWORK;

COMPUTER VISION;

EID: 34248396356     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-006-0004-1     Document Type: Article

References (25)

1. Bille, P. 2005. A survey on tree edit distance and related problems. Theor. Comput. Sci., 337(1-3):217-239.
2. Bogaevski, I. 1990. Metamorphoses of singularities of minimum functions and bifucations of shock waves of the Burgers equation with vanishing viscosity. St. Petersburg (Leningrad) Math. J., 1(4):807-823.
3. Bogaevski, I. 2002. Perestroikas of shocks and singularities of minimum functions. Physica D, 173:1-28.
4. Blum, H. and Nagel, R. 1978. Shape description using weighted symmetric axis features. Pattern Recognition, 10:167-180.
5. Damon, J. 2003. Smoothness and Geometry of boundaries associated to skeletal structures I: Sufficient conditions for smoothness. Ann. Inst. Fourier, 53(6):1945-1981.
6. Damon, J. 2005. Determining the Geometry of boundaries of objects from medial data. Int. Jour. Comp. Vision, 63(1):45-64.
7. 3. To appear in Geometry and Topology.
8. Damon, J. Global Geometry of Regions and Boundaries via Skeletal and Medial Integrals. To appear in Comm. Anal. and Geom.
9. Gage, M. 1984. Curve shortening makes convex curves circular. Invent. Math., 76:357-364.
10. Gage, M. and Hamilton, R. 1986. The heat equation shrinking convex plane curves. J. Diff. Geom., 23:69-96.
11. Giblin, P.J. 2000. Symmetry sets and medial axes in two and three dimensions. In The Mathematics of Surfaces, R. Cipolla and Ra. Martin (Eds.), Springer-Verlag, pp. 306-321.
12. Giblin, P.J. and Kimia, B. 2002. Transitions of the 3D medial axis under a one-parameter family of deformations. Proc. ECCV 2002, Lecture Notes in Comput. Sci., 2351:718-734.
13. Goodman, S.E. 2005. Beginning Topology. Brooks Cole Publication, Belmont, CA.
14. Grayson, M. 1987. The heat equation shrinks embedded curves to round points. J. Diff. Geom., 26:285-314.
15. Kimia, B.B., Tannenbaum, A., and Zucker, S. 1990. Toward a computational theory of shape: An overview.In Three. Dimensional Computer Vision, O. Faugeras (Ed.), MIT Press.
16. Mather, J. 1983. Distance from a manifold in Euclidean space. In Proc. Symp. Pure Math., vol. 40, Pt. 2, pp. 199-216.
17. Munkres, J. 2000. Topology, 2nd edn., Prentice Hall Publication, Englewood Cliffs, NJ.
18. Pizer, S. et al. 2003. Deformable M-reps for 3D medical image segmentation. Int. Jour. Comp. Vision, 55(2-3):85-106.
19. Pizer, S. et al. 2003. Multiscale medial loci and their properties. Int. J. Comp. Vision, 55(2-3):155-179.
20. Pizer, S. and Siddiqi, K. (Eds.), Medial Representations: Mathematics, Algorithms, and Applications. Springer-Verlag Series on Computational Imaging and Vision (to appear).
21. Siddiqi, K., Bouix, S., Tannenbaum, A., and Zucker, S. 2002. The Hamilton-Jacobi Skeleton. Int. Jour. Comp. Vision, 48:215-231.
22. Sethian, J. 1996. Level Set Methods. Cambridge University Press.
23. Szekely, G., Naf, M., Brechbuhler, Ch., and Kubler, O. 1994. Calculating 3d Voronoi diagrams of large unrestricted point sets for skeleton generation of complex 3d shapes. Proc. 2nd Int. Workshop on Visual Form, World Scientific Publication, pp. 532-541.
24. Valiente, G. 2002. Algorithms on Trees and Graphs. Springer-Verlag, Berlin.
25. Yomdin, J. 1981. On the local structure of the generic central set. Composit. Math., 43:225-238.