In this paper we investigate how to construct a shape space for sets of shock trees. To do this we construct a super-tree to span the union of the set of shock trees. We learn this super-tree and the correspondences of the node in the sample trees using a maximizing likelihood approach. We show that the likelihood is maximized by the set of correspondences that minimizes the sum of the tree edit distance between pair of trees, subject to edge consistency constraints. Each node of the super-tree corresponds to a dimension of the pattern space. Individual such trees are mapped to vectors in this pattern space.


Multiple Path Shock Tree Shape Space Edit Operation Pattern Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    H. G. Barrow and R. M. Burstall, Subgraph isomorphism, matching relational structures and maximal cliques, Inf. Proc. Letter, Vol. 4, pp. 83, 84, 1976.zbMATHCrossRefGoogle Scholar
  2. 2.
    H. Bunke and A. Kandel, Mean and maximum common subgraph of two graphs, Pattern Recognition Letters, Vol. 21, pp. 163–168, 2000.CrossRefGoogle Scholar
  3. 3.
    T. F. Cootes, C. J. Taylor, and D. H. Cooper, Active shape models-their training and application, CVIU, Vol. 61, pp. 38–59, 1995.Google Scholar
  4. 4.
    T. Heap and D. Hogg, Wormholes in shape space: tracking through discontinuous changes in shape, ICCV, pp. 344–349, 1998.Google Scholar
  5. 5.
    T. Sebastian, P. Klein, and B. Kimia, Recognition of shapes by editing shock graphs, in ICCV, Vol. I, pp. 755–762, 2001.Google Scholar
  6. 6.
    B. Luo, et al., Clustering shock trees, in CVPR, Vol 1, pp. 912–919, 2001.Google Scholar
  7. 7.
    M. Pelillo, K. Siddiqi, and S. W. Zucker, Matching hierarchical structures using association graphs, PAMI, Vol. 21, pp. 1105–1120, 1999.Google Scholar
  8. 8.
    S. Sclaroff and A. P. Pentland, Modal matching for correspondence and recognition, PAMI, Vol. 17, pp. 545–661, 1995.Google Scholar
  9. 9.
    K. Siddiqi et al., Shock graphs and shape matching, Int. J. of Comp. Vision, Vol. 35, pp. 13–32, 1999.CrossRefGoogle Scholar
  10. 10.
    A. Torsello and E. R. Hancock, Efficiently computing weighted tree edit distance using relaxation labeling, in EMMCVPR, LNCS 2134, pp. 438–453, 2001Google Scholar
  11. 11.
    K. Zhang, R. Statman, and D. Shasha, On the editing distance between unorderes labeled trees, Inf. Proc. Letters, Vol. 42, pp. 133–139, 1992.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Andrea Torsello
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkHeslingtonUK

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