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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Luc Brun and Walter G. Kropatsch. Irregular pyramids with combinatorial maps. SSPR/SPR, 1451:256–265, 2000.
F.R.K. Chung. Spectral Graph Theory. CBMS series 92. American Mathmatical Society Ed., 1997.
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 Informà tics, 2000.
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.
S. Gold and A. Rangarajan. A graduated assignment algorithm for graph matching. IEEE PAMI, 18(4):377–388, 1996.
W.H. Haemers. Interlacing eigenvalues and graphs. Linear Algebra and its Applications, (226–228):593–616, 1995.
B.W. Kernighan and S. Lin. An efficient heuristic procedure for partitioning graphs. The Bell System Technical Journal, pages 291–307, 1970.
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.
B. Luo, R.C. Wilson, and E.R. Hancock. Spectral embedding of graphs. 2002 Winter Workshop on Computer Vision.
Bin Luo and Edwin R. Hancock. Structural graph matching using the em algorithm and singular value decomposition. IEEE PAMI, 23(10):1120–1136, 2001.
B.T. Messmer and H. Bunke. A new algorithm for error-tolerant subgraph isomorphism detection. IEEE PAMI, 20:493–504, 1998.
B. Mohar. Some applications of laplace eigenvalues of graphs. Graph Symmetry: Algebraic Methods and Applications, 497 NATO ASI Series C:227–275, 1997.
Richard Myers, Richard C. Wilson, and Edwin R. Hancock. Bayesian graph edit distance. IEEE PAMI, 22(6):628–635, 2000.
Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. IEEE PAMI, 22(8):888–905, 2000.
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.
S. Umeyama. An eigendecomposition approach to weighted graph matching problems. IEEE PAMI, 10:695–703, 1988.
Richard C. Wilson and Edwin R. Hancock. Structural matching by discrete relaxation. IEEE PAMI, 19(6):634–648, 1997.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-45028-9_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40452-1
Online ISBN: 978-3-540-45028-3
eBook Packages: Springer Book Archive