Transitions of the 3D medial axis under a one-parameter family of deformations

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 31, Issue 5, 2009, Pages 900-918

  Giblin, Peter J ^a   Kimia, Benjamin B ^b   Pollitt, Anthony J ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

^b Brown University   (United States)

Author keywords

Medial axis; Shape; Singularity; Skeleton; Transition

Indexed keywords

MEDIAL AXIS; SHAPE; SINGULARITY; SKELETON; TRANSITION;

COMPUTER VISION; DEFORMATION; THREE DIMENSIONAL; TWO DIMENSIONAL;

OBJECT RECOGNITION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; IMAGE ENHANCEMENT; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 64849115461     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2008.120     Document Type: Article

References (32)

1. V.I. Arnold, V.V. Goryunov, O. Lyashko, and V.A. Vasil'ev, Singularity Theory II, vol. 39. Springer-Verlag, 1993.
2. I.A. Bogaevsky, "Metamorphoses of Singularities of Minimum Functions, and Bifurcations of Shock Waves of the Burgers Equation with Vanishing Viscosity," St. Petersburg (Leningrad) Math. J., vol. 1, pp. 807-823, 1990.
3. I.A. Bogaevsky, "Perestroikas of Shocks and Singularities of Minimum Functions," Physica D, vol. 173, pp. 1-28, 2002.
4. J.W. Bruce and P.J. Giblin, "Growth, Motion and 1-Parameter Families of Symmetry Sets," Proc. Royal Soc. Edinburgh, vol. 104A, pp. 179-204, 1986.
5. J.W. Bruce and P.J. Giblin, Curves and Singularities, second ed. Cambridge Univ. Press, 1992.
6. J.W. Bruce, P.J. Giblin, and F. Tari, "Ridges, Crests and Sub-Parabolic Lines of Evolving Surfaces," Int'l J. Computer Vision, vol. 18, no. 3, pp. 195-210, June 1996.
7. M.-C. Chang and B.B. Kimia, "Regularizing 3D Medial Axis Using Medial Scaffold Transforms," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2008.
8. M.-C. Chang, F.F. Leymarie, and B.B. Kimia, "3D Shape Registration Using Regularized Medial Scaffolds," Proc. 3D Data Processing, Visualization, and Transmission, pp. 987-994, Sept. 2004.
9. J. Damon, "Determining the Geometry of Boundaries of Objects from Medial Data," Int'l J. Computer Vision, vol. 63, no. 1, pp. 45-64, 2005.
10. 3," Int'l J. Computer Vision, vol. 74, no. 2, pp. 103-116, 2007.
11. P.J. Giblin and B.B. Kimia, "On the Local Form of Symmetry Sets, and Medial Axes, and Shocks in 3D," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 566-573, June 2000.
12. P.J. Giblin and B.B. Kimia, "Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations," Proc. Seventh European Conf. Computer Vision, pp. 718-724, 2002.
13. P.J. Giblin and B.B. Kimia, "On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks," Int'l J. Computer Vision vol. 54, nos. 1-3, pp. 143-157, Aug. 2003.
14. P.J. Giblin and B.B. Kimia, "A Formal Classification of 3D Medial Axis Points and Their Local Geometry," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 2, pp. 238-251, Feb. 2004.
15. P.L. Hallinan, G.G. Gordon, A.L. Yuille, P.J. Giblin, and D. Mumford, Two and Three Dimensional Patterns of the Face. A.K. Peters, 1999.
16. M.S. Johannes, T.B. Sebastian, H. Tek, and B.B. Kimia, "Perceptual Organization as Object Recognition Divided by Two," Proc. Third Workshop Perceptual Organization in Computer Vision, pp. 41-46, 2001.
17. P. Klein, T. Sebastian, and B. Kimia, "Shape Matching Using Edit-Distance: An Implementation," Proc. 12th Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 781-790, Jan. 2001.
18. P. Klein, S. Tirthapura, D. Sharvit, and B. Kimia, "A Tree-Edit Distance Algorithm for Comparing Simple, Closed Shapes," Proc. 10th Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 696-704, Jan. 2000.
19. L. Lam, S.-W. Lee, and C.Y. Suen, "Thinning Methodologies - A Comprehensive Survey," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 9, pp. 869-885, Sept. 1992.
20. F.F. Leymarie, "3D Shape Representation via Shock Flows," PhD thesis, Division of Eng., Brown Univ., May 2003.
21. F.F. Leymarie, P.J. Giblin, and B.B. Kimia, "Towards Surface Regularization via Medial Axis Transitions," Proc. 17th Int'l Conf. Pattern Recognition, vol. 3, pp. 123-126, Aug. 2004.
22. F.F. Leymarie and B.B. Kimia, "From the Infinitely Large to the Infinitely Small: Applications of Medial Symmetry Representations of Shape," Medial Representations: Math., Algorithms and Applications K. Siddiqi and S. Pizer, eds., Kluwer Academic, 2008.
23. R.L. Ogniewicz and O. Kubler, "Hierarchic Voronoi Skeletons," Pattern Recognition, vol. 28, no. 3, pp. 343-359, 1995.
24. A.J. Pollitt, "Euclidean and Affine Symmetry Sets and Medial Axes," PhD thesis, Univ. of Liverpool, http://www.liv.ac.uk/~pjgiblin/, 2004.
25. T. Sebastian, P. Klein, and B. Kimia, "Recognition of Shapes by Editing Their Shock Graphs," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 5, pp. 551-571, May 2004.
26. D. Shaked and A.M. Bruckstein, "Pruning Medial Axes," Computer Vision and Image Understanding, vol. 69, no. 2, pp. 156-169, 1998.
27. A. Tamrakar and B.B. Kimia, "Medial Visual Fragments as an Intermediate Image Representation for Segmentation and Perceptual Grouping," Proc. CVPR Workshop Perceptual Organization in Computer Vision, p. 47, 2004.
28. S. Tari and J. Shah, "Extraction of Shape Skeletons from Grayscale Images," Computer Vision Image Understanding, vol. 66, no. 2, pp. 133-146, 1997.
29. H. Tek and B.B. Kimia, "Boundary Smoothing via Symmetry Transforms," J. Math. Imaging and Vision, vol. 14, no. 3, pp. 211-223, May 2001.
30. N. Trinh and B.B. Kimia, "A Symmetry-Based Generative Model for Shape," Proc. 11th IEEE Int'l Conf. Computer Vision, Oct. 2007.
31. P.J. Giblin and B.B. Kimia, "Local Form and Transitions of the Medical Axis," Medical Representations: Math, Algorithms, and Applications K. Siddiqi and S. Pizer, eds., Kluwer Academic, 2008.
32. M.C. Chang, "The Medical Scaffold for 3D Shape Modeling and Recognition," PhD thesis, Division of Eng., Brown Univ., Sept. 2008.