Weighted Graph-Matching Using Modal Clusters

  • Marco Carcassoni
  • Edwin R. Hancock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2124)


This paper describes a new eigendecomposition method for weighted graph-matching. Although elegant by means of its matrix representation, the eigendecomposition method is proved notoriously susceptible to differences in the size of the graphs under consideration. In this paper we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. We place the weighted graph matching problem in a probabilistic setting in which the correspondences between pairwise clusters can be used to constrain the individual correspondences. By assigning nodes to pairwise relational clusters, we compute within-cluster and between-cluster adjacency matrices. The modal co-efficients for these adjacency matrices are used to compute cluster correspondence and cluster-conditional correspondence probabilities. A sensitivity study on synthetic point-sets reveals that the method is considerably more robust than the conventional method to clutter or point-set contamination.


pattern recognition eigendecomposition method weighted graph matching 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chung, F.R.K.: Spectral Graph Theory. CBMS series 92. AMS Ed. (1997)Google Scholar
  2. 2.
    Carcassoni, M., Hancock, E.R.: Point Pattern Matching with Robust Spectral Correspondence. CVPR (2000)Google Scholar
  3. 3.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum-likelihood from incomplete data via the EM algorithm. J. Royal Statistical Soc. Ser. B (methodological) 39 (1977) 1–38zbMATHMathSciNetGoogle Scholar
  4. 4.
    Horaud, R., Sossa, H.: Polyhedral Object Recognition by Indexing. Pattern Recognition 28 (1995) 1855–1870CrossRefGoogle Scholar
  5. 5.
    Inoue, K., Urahama, K.: Sequential fuzzy cluster extraction by a graph spectral method. Pattern Recognition Letters, 20 (1999) 699–705CrossRefGoogle Scholar
  6. 6.
    Mokhtarian, F., Suomela, R.: Robust Image Corner Detection Through Curvature Scale Space. IEEE PAMI, 20 (December 1998) 1376–1381Google Scholar
  7. 7.
    Perona, P., Freeman, W.: A Factorisation Approach to Grouping. ECCV 98, Vol 1 (1998) 655–670CrossRefGoogle Scholar
  8. 8.
    Scott, G.L., Longuet-Higgins, H.C.: An algorithm for associating the features of 2 images. In: Proceedings of the Royal Society of London Series B (Biological) 244 (1991) 21–26CrossRefGoogle Scholar
  9. 9.
    Sengupta, K., Boyer, K.L.: Modelbase partitioning using property matrix spectra. Computer Vision and Image Understanding, 70 (1998) 177–196zbMATHCrossRefGoogle Scholar
  10. 10.
    Shokoufandeh, A., Dickinson, S.J., Siddiqi, K., Zucker, S.W.: Indexing using a spectral encoding of topological structure. In: Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition (1999) 491–497Google Scholar
  11. 11.
    Shapiro, L.S., Brady, J.M.: Feature-based correspondence-an eigenvector approach. Image and Vision Computing, 10 (1992) 283–288CrossRefGoogle Scholar
  12. 12.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. In: Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition (1997)Google Scholar
  13. 13.
    Umeyama, S.: An eigen decomposition approach to weighted graph matching problems. IEEE PAMI 10 (1988) 695–703zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marco Carcassoni
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkYorkUK

Personalised recommendations