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Error-tolerant graph matching: A formal framework and algorithms

  • H. Bunke
Invited Talks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1451)

Abstract

This paper first reviews some theoretical results in error-tolerant graph matching that were obtained recently. The results include a new metric for error-tolerant graph matching based on maximum common subgraph, a relation between maximum common subgraph and graph edit distance, and the existence of classes of cost functions for error-tolerant graph matching. Then some new optimal algorithms for error-tolerant graph matching are discussed. Under specific conditions, the new algorithms may be significantly more efficient than traditional methods.

Keywords

structural pattern recognition graphs graph matching error-tolerant matching edit distance maximum common subgraph cost function 

References

  1. [1]
    J.R. Ullman. An algorithm for subgraph isomorphism. Journal of the Association for Computing Machinery, 23(1):31–42, 1976.Google Scholar
  2. [2]
    G. Levi. A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9, pages 341–354, 1972.Google Scholar
  3. [3]
    H. Bunke. Structural and syntactic pattern recognition. in C.H. Chen, L.F. Pau, P. Wang, Handbook of Pattern Recognition and Computer Vision, World Scientific Publ. Co., Singapore, 1993, 163–209.Google Scholar
  4. [4]
    H. Bunke and B. Messmer. Recent advances in graph matching. Int. Journal of Pattern Recognition and Art. Intell., Vol. 11, No. 1, 1997 169–203.CrossRefGoogle Scholar
  5. [5]
    H. Walischewski. Automatic knowledge acquisition for spatial document interpretation. Proc. 4th ICDAR, Ulm, 1997, 243–247.Google Scholar
  6. [6]
    K.R. Shearer. Indexing and retrieval of video using spatial reasoning techniques. PhD thesis, Curtin University of Technology, Perth, Australia, 1998.Google Scholar
  7. [7]
    K. Shearer, H. Bunke, S. Ventakesh and D. Kieronska. Efficient graph matching for video indexing. Accepted for publication in Computing, Springer Verlag, 1998.Google Scholar
  8. [8]
    L. P. Cordella, P. Foggia, C. Sansone and M. Vento. Subgraph transformations for the inexact matching of attributed relational graphs. Accepted for publication in Computing, Springer Verlag, 1998.Google Scholar
  9. [9]
    T. Lourens. A biologically plausible model for corner-based object recognition from color images. PhD thesis, University of Groningen, The Netherlands, 1998.Google Scholar
  10. [10]
    H. Bunke. Error correcting graph matching: On the influence of the underlying cost function. Submitted for publication.Google Scholar
  11. [11]
    H. Bunke and K. Shearer. A graph distance metric based on maximal common subgraph. Accepted for publication in Pattern Recognition Letters.Google Scholar
  12. [12]
    H. Bunke. On a relation between graph edit distance and maximum common subgraph. Pattern Recognition Letters,18, 1997, 689–694.CrossRefGoogle Scholar
  13. [13]
    R.A. Wagner and M.J. Fischer. The string-to-string correction problem. Journal of the Association for Computing Machinery, 21(1):168–173, 1974.Google Scholar
  14. [14]
    S. Rice, H. Bunke and T. Nartker. Classes of cost functions for string matching. Algorithmica, Vol. 18 No. 2, 271–280, 1997.Google Scholar
  15. [15]
    N.J. Nilsson. Principles of Artificial Intelligence. Tioga, Palo Alto, 1980.Google Scholar
  16. [16]
    W.H. Tsai and K.S Fu. Error-correcting isomorphisms of attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics, 9:757–768, 1979.Google Scholar
  17. [17]
    L.G. Shapiro and R.M. Haralick. Structural descriptions and inexact matching. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI, 3:504–519, 1981.Google Scholar
  18. [18]
    A. Sanfeliu and K.S. Fu. A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics, 13:353–363, 1983.Google Scholar
  19. [19]
    M.A. Eshera and K.S. Fu. A graph distance measure for image analysis. IEEE Transactions on Systems, Man, and Cybernetics, 14(3):398–408, May 1984.Google Scholar
  20. [20]
    E. K. Wong.Three-dimensional object recognition by attributed graphs.In H. Bunke and A. Sanfeliu, editors, Syntactic and Structural Pattern Recognition-Theory and Applications, pages 381–414. World Scientific, 1990.Google Scholar
  21. [21]
    R. Wilson, E. Hancock. Graph matching by discrete relaxation. In E.S. Gelsema and L.N. Kanal, editors, Pattern Recognition in Practice IV: Multiple Paradigms, Comparative Studies and Hybrid Systems, pages 165–176. North-Holland, 1994.Google Scholar
  22. [22]
    W.J. Christmas, J. Kittler, and M. Petrou. Structural matching in computer vision using probabilistic relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI, 17(8):749–764, 1995.CrossRefGoogle Scholar
  23. [23]
    J. Feng, M. Laumy, and M. Dhome. Inexact matching using neural networks. In E.S. Gelsema and L.N. Kanal, editors, Pattern Recognition in Practice IV: Multiple Paradigms, Comparative Studies and Hybrid Systems, pages 177–184. North-Holland, 1994.Google Scholar
  24. [24]
    L. Xu and E. Oja. Improved simulated annealing, Boltzmann machine, and attributed graph matching. In L. Almeida, editor, Lecture Notes in Computer Science 412, pages 151–161. Springer Verlag, 1990.Google Scholar
  25. [25]
    A. Cross, R. Wilson, E. Hancock. Genetic search for structural matching. In B. Buxton, R. Cipolla (eds.): Computer Vision — FCCV '96, Lecture Notes in Comp. Science 1064, Springer Verlag, 1996, 514–525.Google Scholar
  26. [26]
    Y.-K. Wang, K.-C Fan, J.-T Horng. Genetic-based search for error-correcting graph isomorphism. IEEE Trans. on Systems, Man and Cybernetics, Vol. 27, May,1997, 588–597.Google Scholar
  27. [27]
    I. Wang, K. Zhang, G. Chirn. The approximate graph matching problem. Proc. 12th ICPR, Jerusalem 1994, 284–288.Google Scholar
  28. [28]
    J. Mc Gregor. Backtrack search algorithms and the maximal common subgraph problem. Software-Practice and Experience, Vol. 12, 1982, 23–34.Google Scholar
  29. [29]
    A. Shonkry, M. Aboutabl. Neural network approach for solving the maximal common subgraph problem. IEEE Trans. on Systems, Man and Cybernetics, Vol. 26, 1996, 785–790.Google Scholar
  30. [30]
    B. T. Messmer. Efficient graph matching algorithms for preprocessed model graphs. PhD thesis, University of Bern, Switzerland, 1995.Google Scholar
  31. [31]
    B. Messmer and H. Bunke. A new algorithm for error tolerant aubgraph isomorphism. Accepted for publication in IEEE Trans. PAMI.Google Scholar
  32. [32]
    B. T. Messmer and H. Bunke. Error-correcting graph isomorphism using decision trees. To appear in Int. Journal of Pattern Recognition and Art. Intelligence.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • H. Bunke
    • 1
  1. 1.Department of Computer ScienceUniversity of BernBernSwitzerland

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