Shock graphs and shape matching

International Journal of Computer Vision

Volumn 35, Issue 1, 1999, Pages 13-32

  Siddiqi, Kaleem ^a   Shokoufandeh, Ali ^b   Dickinson, Sven J ^b   Zucker, Steven W ^c  

^a MCGILL UNIVERSITY   (Canada)

^b RUTGERS UNIVERSITY   (United States)

^c YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; PATTERN MATCHING; POLYNOMIALS; TREES (MATHEMATICS);

SHAPE MATCHING; SHOCK GRAPHS;

COMPUTER VISION;

EID: 0033323113     PISSN: 09205691     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008102926703     Document Type: Article

References (66)

1. Alizadeh, F. 1995. Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optim., 5(1):13-51.
2. Alvarez, L., Lions, P.L., and Morel, J.M. 1992. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal., 29:845-866.
3. Arnold, V. 1991. The Theory of Singularities and Its Applications. Lezioni Fermiane, Piza, Italy.
4. Basri, R., Costa, L., Geiger, D., and Jacobs, D. 1995. Determining the similarity of deformable shapes. In Proc. ICCV Workshop on Physics-Based Modeling in Computer Vision, pp. 135-143.
5. Basri, R. and Ullman, S. 1988. The alignment of objectswith smooth surfaces. In Second International Conference on Computer Vision (Tampa, FL, December 5-8, 1988), Computer Society Press: Washington, DC, pp. 482-488.
6. Blum, H. 1973. Biological shape and visual science. J. Theor. Biol., 38:205-287.
7. Brady, M. and Asada, H. 1984. Smoothed local symmetries and their implementation. International Journal of Robotics Research, 3(3).
8. Brockett, R. and Maragos, P. 1992. Evolution equations for continuous-scale morphology. In Proc. of the IEEE Conference on Acoustics, Speech and Signal Processing, San Francisco, CA.
9. Bulthoff, H.H. and Edelman, S. 1992. Psychophysical support for a two-dimensional view interpolation theory of object recognition. Proc. of the National Academy of Sciences, 89:60-64.
10. Burbeck, C.A. and Pizer, S.M. 1995. Object representation by cores: Identifying and representing primitive spatial regions. Vision Research, 35:1917-1930.
11. Burns, J. and Kitchen, L. 1987. Recognition in 2D images of 3D objects from large model bases using prediction hierarchies. In Proc. International Joint Conference on Artificial Intelligence, Milan, Italy, pp. 763-766.
12. Cootes, T.F., Hill, A., Taylor, C.J., and Haslam, J. 1996. The use of active shape models for locating structures in medical images. In Fourth European Conference on Computer Vision, Cambridge, UK.
13. Dickinson, S., Pentland, A., and Rosenfeld, A. 1992. 3-D shape recovery using distributed aspect matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2):174-198.
14. Edmonds, J. and Matula, D. 1968. An algorithm for subtree identification. SIAM Rev., 10:273-274 (Abstract).
15. Forsyth, D., Mundy, J., Zisserman, A., Coelho, C., Heller, A., and Rothwell, C. 1991. Invariant descriptors for 3d object recognition and pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13:971-992.
16. François, A. and Medioni, G. 1996. Generic shape learning and recognition. In International Workshop on Object Representation in Computer Vision.
17. Fu, K. (Ed.) 1977. Syntactic Pattern Recognition, Applications. Springer-Verlag: New York.
18. Gabow, H.N., Goemans, M.X., and Williamson, D.P. 1993. An efficient approximate algorithm for survivable network design problems. In Proc. of the Third MPS Conference on Integer Programming and Combinatorial Optimization, pp. 57-74.
19. Garey, M. and Johnson, D. 1979. Computer and Intractability: A Guide to the Theory of NP-Completeness. Freeman: San Francisco.
20. Gdalyahu, Y. and Weinshall, D. 1996. Measures for silhouettes resemblance and representative silhouettes of curved objects. In Fourth European Conference on Computer Vision, Cambridge, UK.
21. Gold, S. and Rangarajan, A. 1996. A graduated assignment algorithm for graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(4):377-388.
22. Grenander, U. 1996. Elements of Pattern Theory. Johns Hopkins University Press: New Baltimore.
23. 5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput., 2:225-231.
24. Ikeuchi, K. and Kanade, T. 1988. Automatic generation of object recognition pograms. In Proc. of the IEEE, 76:1016-1035.
25. Kimia, B.B., Tannenbaum, A., and Zucker, S.W. 1995. Shape, shocks, and deformations I: The components of two-dimensional shape and the reaction-diffusion space. International Journal of Computer Vision, 15:189-224.
26. Kobler, J. 1993. The Graph Isomorphism Problem: Its Structural Complexity. Birkhauser: Boston.
27. Koenderink, J.J. and van Doom, A.J. 1979. The internal representation of solidshape with respect to vision. Biol. Cyber., 32:211-216.
28. Kriegman, D.J. and Ponce, J. 1990. On recognizing and positioning curved 3d objects from image contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:1127-1137.
29. Lax, P.D. 1971. Shock waves and entropy. In Contributions to Nonlinear Functional Analysis, E.H. Zarantonello (Ed.), Academic Press: New York, pp. 603-634.
30. Lewis, H. and Papadimitriou, C. 1981. Elements of the Theory of Computation. Prentice-Hall.
31. Leyton, M. 1988. A process grammar for shape. Artificial Intelligence, 34:213-247.
32. Liu, T.-L., Geiger, D., and Kohn, R.V. 1998. Representation and self-similarity of shapes. In Sixth International Conference on Computer Vision.
33. Malladi, R., Sethian, J.A., and Vemuri, B.C. 1995. Shape modeling with front propagation: A level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(2):158-175.
34. Matheron, G. 1988. Examples of topological properties of skeletons. In Image Analysis and Mathematical Morpholpogy, Part II: Theoretical Advances, J. Serra (Ed.), Academic Press, pp. 217-238.
35. Mjolsness, E., Gindi, G., and Anandan, P. 1989. Optimization in model matching and perceptual organization. Neural Computation, 1:218-229.
36. Mokhtarian, F. 1997. Silhouette-based occluded object recognition through curvature scale space. Machine Vision and Applications, 10(3):87-97.
37. Mokhtarian, F. and Mackworth, A. 1992. A theory of multiscale, curvature-based shape representation for planar curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(8):789-805.
38. Moons, T., Pauwels, E., Gool, L.V., and Oosterlinck, A. 1995. Foundations of semi-differential invariance. International Journal of Computer Vision, 14(1):25-47.
39. Murase, H. and Nayar, S. 1995. Visual learning and recognition of 3-D objects from appearance. International Journal of Computer Vision, 14:5-24.
40. Ogniewicz, R.L. and Kübler, O. 1995. Hierarchic voronoi skeletons. Pattern Recognition, 28:343-359.
41. Osher, S.J. and Sethian, J.A. 1988. Fronts propagation with curvature dependent speed: Algorithms based on hamilton-jacobi formulations. Journal of Computational Physics, 79:12-49.
42. Overton, M.L. and Womersley, R.S. 1993. Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices. Math. Programming, 62(2):321-357.
43. Pauwels, E., Moons, T., Gool, L.J.V., Kempenaers, P., and Oosterlinck, A. 1995. Recognition of planar shapes under affine distortion. International Journal of Computer Vision, 14(1): 49-65.
44. Pelillo, M., Siddiqi, K., and Zucker, S.W. 1998. Matching hierarchical structures using association graphs. In Fifth European Conference on Computer Vision, vol. 2, Freiburg, Germany, pp. 3-16.
45. Pizer, S.M., Fritsch, D.S., YushKevich, P.A., Johnson, V.E., and Chaney, E.L. 1999. Segmentation, registration and measurement of shape variation via image object shape. IEEE Transactions on Medical Imaging, Special Issue on Model-Based Analysis of Medical Images. (to appear)
46. Pizer, S.M., Oliver, W.R., and Bloomberg, S.H. 1987. Hierarchical shape description via the multiresolution symmetric axis transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9(4):505-511.
47. Pope, A. and Lowe, D. 1993. Learning object recognition models from images. In Proc. IEEE International Conference on Computer Vision, Berlin, pp. 296-301.
48. Reyner, S.W. 1977. An analysis of a good algorithm for the subtree problem. SIAM J. Comput., 6:730-732.
49. Richards, W. and Hoffman, D.D. 1985. Codon constraints on closed 2d shapes. CVGIP, 31(2):265-281.
50. Rom, H. and Medioni, G. 1993. Hierarchical decomposition and axial shape description. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(10):973-981.
51. Rosch, E., Mervis, C.B., Gray, W.D., Johnson, D.M., and Boyes-Braem, P. 1976. Basic objects in natural categories. Cognitive Psychology, 8:382-439.
52. Rosenfeld, A. 1979. Picture Languages: Formal Models for Picture Recognition. Academic Press: New York.
53. Sapiro, G. and Tannenbaum, A. 1993. Affine invariant scale-space. International Journal of Computer Vision, 10:25-44.
54. Sclaroff, S. 1997. Deformable prototypes for encoding shape categories in image databases. Pattern Recognition, 30(4).
55. Sclaroff, S. and Pentland, A. 1995. Modal matching for correspondence and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(6):545-561.
56. Serra, J. 1982. Image Analysis and Mathematical Morphology. Academic Press.
57. Sharvit, D., Chan, J., Tek, H., and Kimia, B.B. 1998. Symmetry-based indexing of image databases. In IEEE Workshop on Content- Based Access of Image and Video Libraries.
58. Siddiqi, K. and Kimia, B.B. 1995. A shock grammar for recognition. Technical Report LEMS 143, LEMS, Brown University.
59. Siddiqi, K., Lauzière, Y.B., Tannenbaum, A., and Zucker, S.W. 1998a. Area and length-minimizing flows for shape segmentation. IEEE Transactions on Image Processing, 7(3):433-443.
60. Siddiqi, K., Tannenbaum, A., and Zucker, S.W. 1998b. Hyperbolic "smoothing" of shapes. In Sixth International Conferenceon Computer Vision.
61. Tari, Z.S.G., Shah, J., and Pien, H. 1997. Extraction of shape skeletons from grayscale images. Computer Vision and Image Understanding, 66:133-146.
62. Tek, H., Stoll, P., and Kimia, B. 1997. Shocks from images Propagation of orientation elements. In International Conference on Computer Vision and Pattern Recognition, IEEE Computer Society Press, pp. 839-845.
63. Turk, M. and Pentland, A. 1991. Eigenfaces for recognition. Journal of Cognitive Neuroscience, 3(1):71-86.
64. Ullman, S. 1995. The visual analysis of shape and form. In The Cognitive Neurosciences, M.S. Gazzaniga (Ed.), MIT Press: Cambridge, MA, pp. 339-350.
65. Ullman, S. and Basri, R. 1991. Recognition by linear combinations of models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(10):992-1006.
66. Zhu, S. and Yuille, A.L. 1996. Forms: A flexible object recognition and modelling system. International Journal of Computer Vision, 20(3):187-212.