Skip to main content

Deterministic search strategies for relational graph matching

  • Deterministic Methods
  • Conference paper
  • First Online:
Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 1997)

Abstract

This paper describes a comparative study of various deterministic discrete search-strategies for graph-matching. The framework for our study is provided by the Bayesian consistency measure recently reported by Wilson and Hancock [47–49]. We investigate two classes of update process. The first of these aim to exploit discrete gradient ascent methods. We investigate the effect of searching in the direction of both the local and global gradient maximum. An experimental study demonstrates that although more computationally intensive, the global gradient method offers significant performance advantages in terms of accuracy of match. Our second search strategy is based on tabu search. In order to develop this method we introduce memory into the search procedure by defining context dependant search paths. We illustrate that although it is more efficient than the global gradient method, tabu search delivers almost comparable performance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Amit Y. and A. Kong, “Graphical Templates for Model Registration”, IEEE PAMI, 18, pp. 225–236, 1996.

    Google Scholar 

  2. Barrow H.G. and R.M Burstall, “Subgraph Isomorphism, Matching Relational Structures and Maximal Cliques”, Information Processing Letters, 4, pp. 83–84, 1976.

    Google Scholar 

  3. Barrow H.G. and R.J. Popplestone, “Relational Descriptions in Picture Processing”, Machine Intelligence, 6, 1971.

    Google Scholar 

  4. Boyer K. and A. Kak, “Structural Stereopsis for 3D Vision”, IEEE PAMI, 10, pp 144–166, 1988.

    Google Scholar 

  5. Cross A.D.J. and E.R. Hancock, “Relational Matching with Stochastic Optimisation” IEEE International Symposium on Computer Vision, pp. 365–370, 1995.

    Google Scholar 

  6. Cross A.D.J., R.C. Wilson and E.R. Hancock, “Genetic Search for structural matching”, Proceedings ECCV96, LNCS 1064, pp. 514–525, 1996.

    Google Scholar 

  7. Finch A.M., Wilson R.C. and Hancock E.R., “Matching Delaunay Graphs”, to appear in Pattern Recognition, 1996.

    Google Scholar 

  8. Finch A.M., Wilson R.C. and Hancock E.R., “Relational Matching with Mean-Field Annealing”, Proceedings of the 13th International Conferrence on Pattern Recognition, Volume II, pp. 359–363, 1996.

    Google Scholar 

  9. Finch A.M., Wilson R.C. and Hancock E.R., “Softening Discrete Relaxation”, to appear in Neural Information Processing Systems 9, MIT Press 1997.

    Google Scholar 

  10. Flynn P.J. and A.K. Jain, “CAD-Based Vision — from CAD Models to Relational Graphs”, IEEE PAMI, 13, pp 114–132, 1991.

    Google Scholar 

  11. Geman D. and S. Geman, “Stochastic Relaxation, Gibbs Distributions and Bayesian Restoration of Images”, IEEE PAMI, 6, pp 721–741, 1984.

    Google Scholar 

  12. Geiger D. and F. Girosi, “Parallel and Deterministic Algorithms from MRF's: Surface Reconstruction”, IEEE PAMI, 13, pp 401–412, 1991.

    Google Scholar 

  13. Glover F., “Ejection chains, reference structures and alternating path methods for traveling salesman problems”, Discrete Applied Mathematics, 65, pp. 223–253, 1996.

    Google Scholar 

  14. Rolland E., H. Pirkul and F. Glover, “Tabu search for graph partitioning”, Annals of Operations Research, 63, pp. 290–232, 1996.

    Google Scholar 

  15. Glover F., “Genetic algorithms and tabu search — hybrids for optimisation”, Discrete Applied Mathematics, 49, pp. 111–134, 1995.

    Google Scholar 

  16. Glover F., “Tabu search for nonlinear and parametric optimisation (with links to genetic algorithms)”, Discrete Applied Mathematics, 49, pp. 231–255, 1995.

    Google Scholar 

  17. Gold S., A. Rangarajan and E. Mjolsness, “Learning with pre-knowledge: Clustering with point and graph-matching distance measures”, Neural Computation, 8, pp. 787–804, 1996.

    Google Scholar 

  18. Gold S. and A. Rangarajan, “A Graduated Assignment Algorithm for Graph Matching”, IEEE PAMI, 18, pp. 377–388, 1996.

    Google Scholar 

  19. Hancock E.R. and J. Kittler, “Discrete Relaxation,” Pattern Recognition, 23, pp. 711–733, 1990.

    Article  Google Scholar 

  20. Haralick R.M. and J. Kartus, “Arrangements, Homomorphisms and Discrete Relaxation”, IEEE SMC, 8, pp. 600–612, 1978.

    Google Scholar 

  21. Haralick R.M. and L.G. Shapiro, “The consistent labelling problem-part I”, IEEE PAMI, 1, pp. 173–184, 1979.

    Google Scholar 

  22. Haralick R.M. and L.G. Shapiro, “The consistent labelling problem-part II”, IEEE PAMI, 2, pp. 193–203, 1980.

    Google Scholar 

  23. Haralick R.M. and G. Elliott, “Increasing Tree Search Efficiency for Constraint Satisfaction Problems” Artificial Intelligence, 14, pp. 263–313, 1980.

    Article  Google Scholar 

  24. Harary F., “Graph Theory”, Addison Wesley, Reading, MA, 1969.

    Google Scholar 

  25. Henderson T.C., “Discrete Relaxation Techniques”, Oxford University Press, 1990.

    Google Scholar 

  26. Horaud R., F.Veilon and T.Skordas, “Finding Geometric and Relational Structures in an Image”, Proceedings of the First European Conference on Computer Vision, pp 374–384, 1990.

    Google Scholar 

  27. Horaud R. and T. Skordas, “Stereo Correspondence through Feature Grouping and Maximal Cliques”, IEEE PAMI, 11, pp. 1168–1180, 1989.

    Google Scholar 

  28. Herault L., R. Horaud, F. Veillon and J-J. Niez, “Symbolic Image Matching by Simulated Annealing”, Proceedings of First British Machine Vision Conference, pp. 319–324, 1990.

    Google Scholar 

  29. Hummel R.A. and S. W. Zucker, “On the foundations of relaxation processes”, IEEE PAMI, 5, pp. 267–287, 1983.

    Google Scholar 

  30. Kittler J., W.J. Christmas and M.Petrou, “Probabilistic Relaxation for Matching Problems in Machine Vision”, Proceedings of the Fourth International Conference on Computer Vision, pp. 666–674, 1993.

    Google Scholar 

  31. Kosowsky J.J. and Yuille A.L., “The Invisible Hand Algorithm: Solving the Assignment Problem with Statistical Physics”, Neural Networks, 7, pp 477–490, 1994.

    Article  Google Scholar 

  32. Lades M., J.C. Vorbruggen, J. Buhmann, J. Lange, C. von der Malsburg, R.P. Wurtz and W. Konen, “Distortion Invariant Object Recognition in the Dynamic Link Architecture”, IEEE Transactions on Computers, 42, pp. 300–311, 1992.

    Article  Google Scholar 

  33. Li S.Z., “Matching Invariant to Translations, Rotations and Scale Changes”, Pattern Recognition, 25, pp. 583–594, 1992.

    Article  MathSciNet  Google Scholar 

  34. Messmer B.T. and Bunke H., “Efficient Error-tolerant Subgraph Isomorphism Detection”, Shape, Structure and Pattern Recognition, Edited by D. Dori and A. Bruchstein, pp. 231–240, 1995.

    Google Scholar 

  35. Mjolsness E., G. Gindi and P. Anandan, “Optimisation in model matching and perceptual organisation”, Neural Computation, 1, pp. 218–219, 1989.

    Google Scholar 

  36. Motzkin T.S. and E.G. Straus, “Maxima for graphs and a new proof of a theorem of Turan”, Canadian Journal of Mathematics, 17, pp. 533–540, 1965.

    Google Scholar 

  37. Nilsson N.J., “Problem solving Methods in Artificial Intelligence”, McGraw-Hill, New York, 1971.

    Google Scholar 

  38. Sanfeliu A. and Fu K.S., “A Distance Measure Between Attributed Relational Graphs for Pattern Recognition”, IEEE SMC, 13, pp 353–362, 1983.

    Google Scholar 

  39. Sarker S. and K.L. Boyer, “Perceptual Organisation in Computer Vision: A Review and Proposal for a Classificatory Structure”, IEEE SMC, 23, pp 382–399, 1993.

    Google Scholar 

  40. Shapiro L.G. and R.M. Haralick, “Structural Description and Inexact Matching”, IEEE PAMI, 3, pp 504–519, 1981.

    Google Scholar 

  41. Shapiro L.G. and R.M. Haralick, “A Metric for Comparing Relational Descriptions”, IEEE PAMI, 7, pp 90–94, 1985.

    Google Scholar 

  42. Simic P., “Constrained nets for graph matching and other quadratic assignment problems”, Neural Computation, 3, pp. 268–281, 1991.

    Google Scholar 

  43. Suganathan P.N., E.K. Teoh and D.P. Mital, “Pattern Recognition by Graph Matching using Potts MFT Networks”, Pattern Recognition, 28, pp. 997–1009, 1995.

    Article  Google Scholar 

  44. Tang Y.C. and C.S.G. Lee, “A Geometric Feature Relation Graph Formalism for Consistent Sensor Fusion”, IEEE SMC, 22, pp 115–129, 1992.

    Google Scholar 

  45. Ullman J.R., “Associating parts of patterns”, Information and Control, 9, pp. 583–601, 1966.

    Google Scholar 

  46. Ullman J.R., “An algorithm for subgraph isomorphism”, Journal of the ACM, 23, 31–42, 1976.

    Article  Google Scholar 

  47. Wilson R.C. and E.R Hancock, “Graph Matching by Discrete Relaxation”, Pattern Recognition in Practice IV: Multiple Paradigms, Comparative Studies and Hybrid Systems, North Holland pp. 165–177, 1994.

    Google Scholar 

  48. Wilson R.C, A.N. Evans and E.R Hancock, “Relational Matching by Discrete Relaxation”, Image and Vision Computing, 13, pp. 411–422, 1995.

    Article  Google Scholar 

  49. Wilson R.C. and E.R. Hancock, “A Bayesian Compatibility Model for Graph Matching”, Pattern Recognition Letters, 17, pp. 263–276, 1996.

    Article  Google Scholar 

  50. Yang D. and J. Kittler, “MFT-Based Discrete Relaxation for Matching High-Order Relational Structures”, Proceedings 12th International Conference on Pattern Recognition, pp. 219–223, 1994.

    Google Scholar 

  51. Yuille A., “Generalised Deformable Models, Statistical Physics and Matching Problems”, Neural Computation, 2, pp. 1–24, 1990.

    Google Scholar 

  52. Yuille A.L. and Kosowsky J.J., “Statistical Physics Algorithms that Converge”, Nueral Computation, 6, pp 341–356, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marcello Pelillo Edwin R. Hancock

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Williams, M.L., Wilson, R.C., Hancock, E.R. (1997). Deterministic search strategies for relational graph matching. In: Pelillo, M., Hancock, E.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 1997. Lecture Notes in Computer Science, vol 1223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62909-2_85

Download citation

  • DOI: https://doi.org/10.1007/3-540-62909-2_85

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62909-2

  • Online ISBN: 978-3-540-69042-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics