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Graph Partition for Matching

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Graph Based Representations in Pattern Recognition (GbRPR 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2726))

Abstract

Although inexact graph-matching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework or cast in a way which is amenable to parallel computation. In this paper we demonstrate how the Fiedler-vector can be used to partition graphs for the purposes of decomposition. We show how the resulting subgraphs can be matched using a variety of algorithms. We demonstrate the utility of the resulting graph-matching method on both real work and synthetic data. Here it proves to provide results which are comparable with a number of state-of-the-art graph matching algorithms.

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References

  1. Luc Brun and Walter G. Kropatsch. Irregular pyramids with combinatorial maps. SSPR/SPR, 1451:256–265, 2000.

    Google Scholar 

  2. F.R.K. Chung. Spectral Graph Theory. CBMS series 92. American Mathmatical Society Ed., 1997.

    Google Scholar 

  3. J. Diaz, J. Petit, and M. Serna. A survey on graph layout problems. Technical report LSI-00-61-R, Universitat Politècnica de Catalunya, Departament de Llenguatges i Sistemes Informàtics, 2000.

    Google Scholar 

  4. A.M. Finch, R.C. Wilson, and E.R. Hancock. An energy function and continuous edit process for graph matching. Neural Computation, 10(7):1873–1894, 1998.

    Article  Google Scholar 

  5. S. Gold and A. Rangarajan. A graduated assignment algorithm for graph matching. IEEE PAMI, 18(4):377–388, 1996.

    Google Scholar 

  6. W.H. Haemers. Interlacing eigenvalues and graphs. Linear Algebra and its Applications, (226–228):593–616, 1995.

    Article  MathSciNet  Google Scholar 

  7. B.W. Kernighan and S. Lin. An efficient heuristic procedure for partitioning graphs. The Bell System Technical Journal, pages 291–307, 1970.

    Google Scholar 

  8. B. Luo, A. D. Cross, and E. R. Hancock. Corner detection via topographic analysis of vector potential. Proceedings of the 9 th British Machine Vision Conference, 1998.

    Google Scholar 

  9. B. Luo, R.C. Wilson, and E.R. Hancock. Spectral embedding of graphs. 2002 Winter Workshop on Computer Vision.

    Google Scholar 

  10. Bin Luo and Edwin R. Hancock. Structural graph matching using the em algorithm and singular value decomposition. IEEE PAMI, 23(10):1120–1136, 2001.

    Google Scholar 

  11. B.T. Messmer and H. Bunke. A new algorithm for error-tolerant subgraph isomorphism detection. IEEE PAMI, 20:493–504, 1998.

    Google Scholar 

  12. B. Mohar. Some applications of laplace eigenvalues of graphs. Graph Symmetry: Algebraic Methods and Applications, 497 NATO ASI Series C:227–275, 1997.

    Google Scholar 

  13. Richard Myers, Richard C. Wilson, and Edwin R. Hancock. Bayesian graph edit distance. IEEE PAMI, 22(6):628–635, 2000.

    Google Scholar 

  14. Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. IEEE PAMI, 22(8):888–905, 2000.

    Google Scholar 

  15. A. Shokoufandeh, S.J. Dickinson, K. Siddiqi, and S.W. Zucker. Indexing using a spectral encoding of topological structure. In Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition, pages 491–497, 1999.

    Google Scholar 

  16. S. Umeyama. An eigendecomposition approach to weighted graph matching problems. IEEE PAMI, 10:695–703, 1988.

    MATH  Google Scholar 

  17. Richard C. Wilson and Edwin R. Hancock. Structural matching by discrete relaxation. IEEE PAMI, 19(6):634–648, 1997.

    Google Scholar 

  18. R.J. Wilson and John J. Watkins. Graphs: an introductory approach: a first course in discrete mathematics. Wiley international edition. New York, etc., Wiley, 1990.

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Qiu, H., Hancock, E.R. (2003). Graph Partition for Matching. In: Hancock, E., Vento, M. (eds) Graph Based Representations in Pattern Recognition. GbRPR 2003. Lecture Notes in Computer Science, vol 2726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45028-9_16

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  • DOI: https://doi.org/10.1007/3-540-45028-9_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40452-1

  • Online ISBN: 978-3-540-45028-3

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