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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Amit Y. and A. Kong, “Graphical Templates for Model Registration”, IEEE PAMI, 18, pp. 225–236, 1996.
Barrow H.G. and R.M Burstall, “Subgraph Isomorphism, Matching Relational Structures and Maximal Cliques”, Information Processing Letters, 4, pp. 83–84, 1976.
Barrow H.G. and R.J. Popplestone, “Relational Descriptions in Picture Processing”, Machine Intelligence, 6, 1971.
Boyer K. and A. Kak, “Structural Stereopsis for 3D Vision”, IEEE PAMI, 10, pp 144–166, 1988.
Cross A.D.J. and E.R. Hancock, “Relational Matching with Stochastic Optimisation” IEEE International Symposium on Computer Vision, pp. 365–370, 1995.
Cross A.D.J., R.C. Wilson and E.R. Hancock, “Genetic Search for structural matching”, Proceedings ECCV96, LNCS 1064, pp. 514–525, 1996.
Finch A.M., Wilson R.C. and Hancock E.R., “Matching Delaunay Graphs”, to appear in Pattern Recognition, 1996.
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.
Finch A.M., Wilson R.C. and Hancock E.R., “Softening Discrete Relaxation”, to appear in Neural Information Processing Systems 9, MIT Press 1997.
Flynn P.J. and A.K. Jain, “CAD-Based Vision — from CAD Models to Relational Graphs”, IEEE PAMI, 13, pp 114–132, 1991.
Geman D. and S. Geman, “Stochastic Relaxation, Gibbs Distributions and Bayesian Restoration of Images”, IEEE PAMI, 6, pp 721–741, 1984.
Geiger D. and F. Girosi, “Parallel and Deterministic Algorithms from MRF's: Surface Reconstruction”, IEEE PAMI, 13, pp 401–412, 1991.
Glover F., “Ejection chains, reference structures and alternating path methods for traveling salesman problems”, Discrete Applied Mathematics, 65, pp. 223–253, 1996.
Rolland E., H. Pirkul and F. Glover, “Tabu search for graph partitioning”, Annals of Operations Research, 63, pp. 290–232, 1996.
Glover F., “Genetic algorithms and tabu search — hybrids for optimisation”, Discrete Applied Mathematics, 49, pp. 111–134, 1995.
Glover F., “Tabu search for nonlinear and parametric optimisation (with links to genetic algorithms)”, Discrete Applied Mathematics, 49, pp. 231–255, 1995.
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.
Gold S. and A. Rangarajan, “A Graduated Assignment Algorithm for Graph Matching”, IEEE PAMI, 18, pp. 377–388, 1996.
Hancock E.R. and J. Kittler, “Discrete Relaxation,” Pattern Recognition, 23, pp. 711–733, 1990.
Haralick R.M. and J. Kartus, “Arrangements, Homomorphisms and Discrete Relaxation”, IEEE SMC, 8, pp. 600–612, 1978.
Haralick R.M. and L.G. Shapiro, “The consistent labelling problem-part I”, IEEE PAMI, 1, pp. 173–184, 1979.
Haralick R.M. and L.G. Shapiro, “The consistent labelling problem-part II”, IEEE PAMI, 2, pp. 193–203, 1980.
Haralick R.M. and G. Elliott, “Increasing Tree Search Efficiency for Constraint Satisfaction Problems” Artificial Intelligence, 14, pp. 263–313, 1980.
Harary F., “Graph Theory”, Addison Wesley, Reading, MA, 1969.
Henderson T.C., “Discrete Relaxation Techniques”, Oxford University Press, 1990.
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.
Horaud R. and T. Skordas, “Stereo Correspondence through Feature Grouping and Maximal Cliques”, IEEE PAMI, 11, pp. 1168–1180, 1989.
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.
Hummel R.A. and S. W. Zucker, “On the foundations of relaxation processes”, IEEE PAMI, 5, pp. 267–287, 1983.
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.
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.
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.
Li S.Z., “Matching Invariant to Translations, Rotations and Scale Changes”, Pattern Recognition, 25, pp. 583–594, 1992.
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.
Mjolsness E., G. Gindi and P. Anandan, “Optimisation in model matching and perceptual organisation”, Neural Computation, 1, pp. 218–219, 1989.
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.
Nilsson N.J., “Problem solving Methods in Artificial Intelligence”, McGraw-Hill, New York, 1971.
Sanfeliu A. and Fu K.S., “A Distance Measure Between Attributed Relational Graphs for Pattern Recognition”, IEEE SMC, 13, pp 353–362, 1983.
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.
Shapiro L.G. and R.M. Haralick, “Structural Description and Inexact Matching”, IEEE PAMI, 3, pp 504–519, 1981.
Shapiro L.G. and R.M. Haralick, “A Metric for Comparing Relational Descriptions”, IEEE PAMI, 7, pp 90–94, 1985.
Simic P., “Constrained nets for graph matching and other quadratic assignment problems”, Neural Computation, 3, pp. 268–281, 1991.
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.
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.
Ullman J.R., “Associating parts of patterns”, Information and Control, 9, pp. 583–601, 1966.
Ullman J.R., “An algorithm for subgraph isomorphism”, Journal of the ACM, 23, 31–42, 1976.
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.
Wilson R.C, A.N. Evans and E.R Hancock, “Relational Matching by Discrete Relaxation”, Image and Vision Computing, 13, pp. 411–422, 1995.
Wilson R.C. and E.R. Hancock, “A Bayesian Compatibility Model for Graph Matching”, Pattern Recognition Letters, 17, pp. 263–276, 1996.
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.
Yuille A., “Generalised Deformable Models, Statistical Physics and Matching Problems”, Neural Computation, 2, pp. 1–24, 1990.
Yuille A.L. and Kosowsky J.J., “Statistical Physics Algorithms that Converge”, Nueral Computation, 6, pp 341–356, 1994.
Author information
Authors and Affiliations
Editor information
Rights 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