Matching hierarchical structures using association graphs

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 21, Issue 11, 1999, Pages 1105-1119

  Pelillo, Marcello ^a   Siddiqi, Kaleem ^a   Zucker, Steven W ^a  

^a CA' FOSCARI UNIVERSITY OF VENICE   (Italy)

Author keywords

Association graphs; Maximal cliques; Maximal subtree isomorphisms; Replicator dynamical systems; Shape recognition; Shock trees

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER VISION; MATHEMATICAL MODELS; OPTIMIZATION; QUADRATIC PROGRAMMING; TREES (MATHEMATICS);

ASSOCIATION GRAPHS; MOTZKIN-STRAUS THEOREM;

PATTERN MATCHING;

EID: 0033220897     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.809105     Document Type: Article

References (66)

1. A.P. Ambler, H.G. Barrow, CM. Brown, RM. BurstalJ, and RJ. Popplestone, "A Versatile Computer-Controlled Assembly System," Proc. Int'l Joint Conf. Artificial Intelligence, pp. 298-307, Stanford, Calif., 1973.
2. D.H. Ballard and C.M. Brown, Computer Vision. Englewood Cliffs, N.J.: Prentice Hall, 1982.
3. H.G. Barrow and R.M. Burstall, "Subgraph Isomorphism, Matching Relational Structures, and Maximal Cliques/' Information Processing Letters, vol. 4, no. 4, pp. 83-84, 1976.
4. M. Bartoli, M Pelillo, K. Siddiqi, and S.W. Zucker, "Attributed Tree Homomorphism Using Association Graphs," Technical Report CS-99-12, Dipartimento di Informatica, Università Ca' Foseari di Venezia, 1999.
5. L.E. Baum and J.A. Eagon, "An Inequality with Applications to Statistical Estimation for Probabilistic Functions of Markov Processes and to a Model for Ecology," Bulletin Am. Math. Soc., vol. 73, pp. 360-363, 1967.
6. R.C. Boues and R.A. Cain, "Recognizing and Locating Partially Visible Objects: The Locus-Feature-Focus Method," Int'l}. Robotics Research, vol. 1, no. 3, pp. 57-82, 1982.
7. I.M. Bomze, "Evolution Towards the Maximum Clique," /, Global Optimization, vol. 10, pp. 143-164,1997.
8. I.M. Bomze, "On Standard Quadratic Optimization Probîems," J. Global Optimization, vol. 13, pp. 369-387, 1998.
9. I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo, "The Maximum Clique Problem," Handbook of Combinatorial Optimization, D.-Z. Du and P.M. Pardalos, eds., vol. 4. Boston, Mass.: Kluwer Academic, 1999.
10. LM, Bomze, M. Pelilîo, and K. Giacomini, "Evolutionary Approach to the Maximum Clique Problem: Empirical Evidence on a Larger Scale," Developments in Global Optimization, I.M. Bomze, T. Csendes, R. Horst, and P.M. Pardalos, eds., pp. 95-108, Dordrecht, The Netherlands: Kluwer, 1997.
11. I.M. Bomze, M. Pelillo, and V. Stix, "Approximating the Maximum Weight Clique Using Replicator Dynamics," Technical Report CS-99-13, Dipartimento di Informatica, Université Ça' Foseari di Venezia, 1999.
12. K. Brockettand P. Maragos, "Evolution Equations for ContinuousScale Morphology," Proc. IEEE Conf. Acoustics, Speech, and Signa! Processing, San Francisco, Mar. 1992.
13. J.F. Crow and M. Kimura, An Introduction to Population Genetics Theory. New York: Harper & Row, 1970.
14. R. Durbin and D. Willshaw, "An Analog Approach to the Travelling Salesman Problem Using an Elastic Net Method," Nature, vol. 326, pp. 689-691, 1987.
15. R.A. Fisher, The Geneticnl Theory of Nnturnl Selection. London: Oxford Univ. Press, 1930.
16. V. Fu and P.W. Anderson, "Application of Statistical Mechanics to NP-Complete Problems in Combinatorial Optimization," J. Physics A, vol. 19, pp. 1,605-1,620, 1986.
17. M.R. Garey and D. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness. San Francisco: Freeman, 1979.
18. L.E. Gibbons, D.W. Hearn, and P.M. Pardalos, "A Continuous Based Heuristic for the Maximum Clique Problem/' Cliques, Coloring, and Satisfiability-Second DIMACS Implementation Challenge, D.S. Johnson and M. Trick, eds., pp. 103-124, 1996.
19. L.E. Gibbons, D.W. Hearn, P.M. Pardalos, and M.V. Ramana, "Continuous Characterizations of the Maximum Clique Problem," Math. Operations Research, vol. 22, pp. 754-768, 1997.
20. S. Gold and A. Rangarajan, "A Graduated Assignment Algorithm for Graph Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 4, pp. 377-388, Apr. 1996
21. M. Grotschel, L. Lovâsz, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization. Berlin: Springer-Verlag, 1988.
22. |22] F. Harary, Graph Theory. Reading, Mass.: Addison-Wesley, 1969,
23. J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems. Cambridge, U.K.; Cambridge Univ. Press, 1988/
24. ].}. Hopfield and D.W. Tank, "Neural Computation of Decisions in Optimization Problems," Biological Cybernetics, vol. 52, pp. 141-
25. R. Horaud and T. Skordas, "Stereo Correspondence through Feature Grouping and Maximal Cliques," IEEE Trans, Pattern Analysis and Machine Intelligence, vol. 11, no. 11, pp. 1,168-1,180, Nov. 1989.
26. A. Jagota, "Approximating the Maximum Clique with a Hopfield Network," IEEE Trans. Neural Networks, vol. 6, pp. 724-735,1995.
27. B.B. Kimia, A. Tannenbaum, and S.W. Zucker, "Toward a Computational Theory of Shape: An Overview," Lecture Notes in Computer Science, vol. 427, pp. 402-407, 1990.
28. B.B. Kimia, A. Tannenbaum, and S.W. Zucker, "Shape, Shocks, and Deformations I: The Components of Two-Dimensional Shape and the Reaction-Diffusion Space," Int' J.Computer Vision, vol. 15, pp. 189-224, 1995.
29. JJ. Kosowsky and A.L. Yuille, "The Invisible Hand Algorithm: Solving the Assignment Problem with Statistical Physics," Neural Networks, vol. 7, pp. 477-490, 1994.
30. P.D. Lax, "Shock Waves and Entropy," Contributions to Nonlinear functional Analysis, E.H. Zarantonello, éd., pp. 603-634, New York: Academic Press, 1971.
31. J,T. Li, K. Zhang, K. Jeong, and D. Shasha, "A System for Approximate Tree Matching," IEEE Trans, Knowledge and Data Eng., vol. 6, pp. 559-571, 1994.
32. T.L. Liu, D. Geiger, and R.V. Kohn, "Representation and SelfSimilarity of Shapes," Proc. Int'l Conf. Computer Vision, pp. 1,1291,135, Bombay, 1998.
33. V, Losert and E. Akin, "Dynamics of Games and Genes: Discrete versus Continuous Time," J. Math. Biology, vol. 17, pp. 241-251, 1983.
34. S.Y. Lu, "A Tree-Matching Algorithm Based on Node Splitting and Merging," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 249-256, 1984.
35. Y. Lyubich, G.D. Maistrowskii, and Y.G. Ol'khovskii, "SelectionInduced Convergence to Equilibrium in a Single-Locus Autosomal Population," Problems of Information Transmission, vol. 16, pp. 66-75,1980.
36. D. Marr and K.H. Nishihara, "Representation and Recognition of the Spatial Organization of Three-Dimensional Shapes," Proc. Royal Sac, London B, vol. 200, pp. 269-294, 1978.
37. D.W. Manila, "An Algorithm for Subtree Identification," SIAM Review, vol. 10, pp. 273-274, 1968.
38. D. Miller and S.W. Zucker, "Efficient Simplex-Like Methods for Equilibria of Nonsymmetric Analog Networks," Neural Computation, vol. 4, no. 2, pp. 167-190, 1992.
39. D. Miller and S.W. Zucker, "Computing with Self-Excitatory Cliques: A Model and an Application to Hyperacuity-Scale Computation in Visual Cortex," Neural Computation, vol. 11, no. 1, pp. 21-66, 1999.
40. T.S. Motzkin and E.G. Straus, "Maxima for Graphs and a New Proof of a Theorem of Turân," Canadian }. Math., vol. 17, pp. 533540,1965.
41. M. Neff, R. Byrd, and O. Rizk, "Creating and Querying Hierarchical Lexical Databases," Proc, Conf. Applied Natural Language Processes, pp. 84-93, 1988.
42. H. Ogawa, "Labeled Point Pattern Matching by Delaunay Triangulation and Maximal Cliques," Pattern Recognition, vol. 19, pp. 35-40, 1986.
43. M. Ohlsson, C. Peterson, and B. Soderberg, "Neural Networks for Optimization Problems with Inequality Constraints: The Knapsack Problem," Neural Computation, vol. 5, pp, 331-339, 1993.
44. P.M. Pardalos, "Continuous Approaches to Discrete Optimization Problems," Nonlinear Optimization and Applications, G.D. Pillo and F. Giannessi, eds., pp, 313-328. Plenum Press, 1996.
45. P.M. Pardalos and A.T. Phillips, "A Global Optimization Approach for Solving the Maximum Clique Problem/' htt'l j. Computer Math., vol. 33, pp. 209-216, 1990.
46. M, Pelillo, "Relaxation Labeling Networks for the Maximum Clique Problem," J. Artificial Neural Networks, vol. 2, pp. 313-328, 1995.
47. M, Pelillo, "The Dynamics of Nonlinear Relaxation Labeling Processes," J. Math. Imaging and Vision, vol. 7, pp. 309-323, 1997.
48. M. Pelillo, "A Unifying Framework for Relational Structure Matching," Proc. Int'l Conf. Pattern Recognition, pp. 1,316-1,319, Brisbane, Australia, 1998.
49. M. Pelillo, "Replicator Equations, Maximal Cliques, and Graph Isomorphism," Neural Computation, vol. 11, no. 8, 1999.
50. M. Pelillo and A. Jagota, "Feasible and Infeasible Maxima in a Quadratic Program for Maximum Clique," ]. Artificial Neural Networks, vol. 2, pp. 411-420, 1995.
51. F. Pla and J.A. Marchant, "Matching Feature Points in Image Sequences through a Region-Based Method," Computer Vision and Image Understanding, vol. 66, no. 3, pp. 271-285,1997.
52. B. Radig, "Image Sequence Analysis Using Relational Structures," Pattern Récognition, vol. 17, pp. 161-167,1984.
53. A, Rangarajan and E. Mjolsness, "A Lagrangian Relaxation Network for Graph Matching," IEEE Trans. Neural Networks, vol. 7, no. 6, pp. 1,365-1,381, 1996.
54. S.W. Reyner, "An Analysis of a Good Algorithm for the Subtree Problem," SIAM ]. Computing, vol. 6, pp. 730-732, 1977.
55. H. Rom and G. Medioni, "Hierarchical Decomposition and Axial Shape Description," IEEE Trttns. Pattern Analysis and Machine Intelligence, vol. 15, no. 10, pp. 973-981, Oct. 1993.
56. A. Rosenfeld, R.A. Hummel, and S.W. Zucker, "Scene Labeling by Relaxation Operations," IEEE Trans. Systems, Man, and Cybernetics, vol. 6, pp. 420-433,1976.
57. H, Samet, Design and Analysis of Spatial Data Structures. Reading, Mass.: Addison-Wesley, 1990.
58. B.A. Shapiro and K. Zhang, "Comparing Multiple RNA Secondary Structures Using Tree Comparisons," Computer Applications Bioscience, vol. 6, pp. 309-318, 1990.
59. D. Shasha, J.T.L, Wang, K. Zhang, and F.Y, Shih, "Exact and Approximate Algorithms for Unordered Tree Matching," IEEE Trans. Systems, Man, and Cybernetics, vol. 24, pp. 668-678, 1994.
60. K. Siddiqi and B.B. Kimia, "A Shock Grammar for Recognition," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 507513, 1996.
61. K. Siddiqi, B.B. Kimia, A. Tannenbaum, and S.W. Zucker, "Shapes, Shocks and Wiggles," Image and Vision Computing, vol. 17, nos. 5-6, pp. 365-373,1999.
62. K. Siddiqi, A. Shokoufandeh, SJ, Dickinson, and S.W. Zucker, "Shock Graphs and Shape Matching," Int'l }. Computer Vision, to appear 1999.
63. J.W. Weibull, Evolutionary Game Theory. Cambridge, Mass.: MIT Press, 1995.
64. H.S, Wilf, "Spectral Bounds for the Clique and Independence Numbers of Graphs," J. Combinatorial Theory, Series B, vol. 40, pp. 113-117, 1986.
65. B. Yang, W.E, Snyder, and G.L. Bilbro, "Matching Oversegmented 3D Images Using Association Graphs," Image and Vision Computing, vol. 7, pp. 135-143, 1989.
66. S. Zhu and A.L. Yuille, "FORMS: A Flexible Object Recognition and Modeling System," Int'l ]. Computer Vision, vol. 20, no. 3, pp. 187-212, 1996.