Shock-Based Indexing into Large Shape Databases

  • Thomas B. Sebastian
  • Philip N. Klein
  • Benjamin B. Kimia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2352)


This paper examines issues arising in applying a previously developed edit-distance shock graph matching technique to indexing into large shape databases. This approach compares the shock graph topology and attributes to produce a similarity metric, and results in 100% recognition rate in querying a database of approximately 200 shapes. However, indexing into a significantly larger database is faced with both the lack of a suitable database, and more significantly with the expense related to computing the metric. We have thus (i) gathered shapes from a variety of sources to create a database of over 1000 shapes from forty categories as a stage towards developing an approach for indexing into a much larger database; (ii) developed a coarse-scale approximate similarly measure which relies on the shock graph topology and a very coarse sampling of link attributes. We show that this is a good first-order approximation of the similarly metric and is two orders of magnitude more efficient to compute. An interesting outcome of using this efficient but approximate similarity measure is that the approximation naturally demands a notion of categories to give high precision; (iii) developed an exemplar-based indexing scheme which discards a large number of non-matching shapes solely based on distance to exemplars, coarse scale representatives of each category. The use of a coarse-scale matching measure in conjunction with a coarse-scale sampling of the database leads to a significant reduction in the computational effort without discarding correct matches, thus paving the way for indexing into databases of tens of thousands of shapes.


Similarity metric object recognition shape matching shape retrieval categorization exemplars 


  1. 1.
    A. Lanitis, C.J. Taylor, and T.F. Cootes. Automatic interpretation and coding of face images using flexible models. PAMI, 19(7):743–756, 1997.Google Scholar
  2. 2.
    R. Basri. Recognition by prototypes. IJCV, 19(2): 147–167, August 1996.Google Scholar
  3. 3.
    R. Basri, L. Costa, D. Geiger, and D. Jacobs. Determining the similarity of deformable shapes. Vision Research, 38:2365–2385, 1998.CrossRefGoogle Scholar
  4. 4.
    S. Belongie, J. Malik, and J. Puzicha. Matching shapes. ICCV, pages 454–461, 2001.Google Scholar
  5. 5.
    J. L. Bentley and J. H. Friedman. Data structures for range searching. ACM Computing Surveys, 11(4):397–409, 1979.CrossRefGoogle Scholar
  6. 6.
    S. Berchtold, D. A. Keim, and H.-P. Kriegel. The X-tree: An index structure for high-dimensional data. VLDB, pages 28–39, 1996.Google Scholar
  7. 7.
    L. Bergman and V. Castelli, editors. Image Databases, Search and Retrieval of Digital Imagery. John Wiley and Sons, 2002.Google Scholar
  8. 8.
    I. Biederman and G. Ju. Surface versus edge-based determinants of visual recognition. Cognitive Psychology, 20:38–64, 1988.CrossRefGoogle Scholar
  9. 9.
    S. Brin. Near neighbor search in large metric spaces. VLDB, pages 574–584, 1995.Google Scholar
  10. 10.
    E. Chavez, G. Navarro, R. Baeza-Yates, and J. L. Marroquín. Searching in metric spaces. ACM Computing Surveys, 33(3):273–321, 2001.CrossRefGoogle Scholar
  11. 11.
    C. Faloutsos, R. Barber, M. Flickner, J. Hafner, W. Niblack, D. Petrkovic, and W. Equitz. Efficient and effective querying by image content. J. Intelligent Information Systems, 3:231–262, 1994.CrossRefGoogle Scholar
  12. 12.
    Y. Gdalyahu and D. Weinshall. Flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes. PAMI, 21(12):1312–1328, 1999.Google Scholar
  13. 13.
    P. J. Giblin and B. B. Kimia. On the local form and transitions of symmetry sets, and medial axes, and shocks in 2D. ICCV, pages 385–391, 1999.Google Scholar
  14. 14.
    W. I. Groski and R. Mehrota. Index-based object recognition in pictorial data management. CVGIP, 52:416–436, 1990.Google Scholar
  15. 15.
    P. Klein, T. Sebastian, and B. Kimia. Shape matching using edit-distance: an implementation. SODA, pages 781–790, 2001.Google Scholar
  16. 16.
    P. Klein, S. Tirthapura, D. Sharvit, and B. Kimia. A tree-edit distance algorithm for comparing simple, closed shapes. SODA, pages 696–704, 2000.Google Scholar
  17. 17.
    C. Lin and R. Chellappa. Classification of partial 2-D shapes using Fourier descriptors. PAMI, 9(5):686–690, 1987.Google Scholar
  18. 18.
    T. Liu and D. Geiger. Approximate tree matching and shape similarity. ICCV, pages 456–462, 1999.Google Scholar
  19. 19.
    E. Milios and E. Petrakis. Shape retrieval based on dynamic programming. IEEE Trans. Image Processing, 9(1):141–146, 2000.CrossRefGoogle Scholar
  20. 20.
    G. Mori, S. Belongie, and J. Malik. Shape contexts enable efficient retrieval of similar shapes. CVPR, pages I: 723–730, 2001.Google Scholar
  21. 21.
    M. Pelillo, K. Siddiqi, and S. Zucker. Matching hierarchical structures using association graphs. PAMI, 21(11):1105–1120, 1999.Google Scholar
  22. 22.
    E. Rivlin and I. Weiss. Local invariants for recognition. PAMI, 17(3):226–238, 1995.Google Scholar
  23. 23.
    H. Samet. The quadtree and related hierarchical data structures. ACM Computing Surveys, 16(2):187–260, 1984.CrossRefMathSciNetGoogle Scholar
  24. 24.
    T. B. Sebastian, P. N. Klein, and B. B. Kimia. Alignment-based recognition of shape outlines. IWVF, pages 606–618, 2001. Springer.Google Scholar
  25. 25.
    T. B. Sebastian, P. N. Klein, and B. B. Kimia. Recognition of shapes by editing shock graphs. ICCV, pages 755–762, 2001.Google Scholar
  26. 26.
    D. Sharvit, J. Chan, H. Tek, and B. B. Kimia. Symmetry-based indexing of image databases. JVCIR, 9(4):366–380, 1998.CrossRefGoogle Scholar
  27. 27.
    R. N. Shepard. Toward a universal law of generalization for psychological science. Science, pages 1317–1323, 1987.Google Scholar
  28. 28.
    K. Siddiqi, A. Shokoufandeh, S. Dickinson, and S. Zucker. Shock graphs and shape matching. IJCV, 35(1):13–32, November 1999.Google Scholar
  29. 29.
    M. J. Tarr and H. H. Bulthoff, editors. Object Recognition in Man, Monkey, and Machine. MIT Press/Elsevier, 1999.Google Scholar
  30. 30.
    A. Torsello and E. R. Hancock. Computing approximate tree edit-distance using relaxation labelling. Worksop on Graph-based Representations in Pattern Recognition, pages 125–136, 2001.Google Scholar
  31. 31.
    J. Uhlmann. Satisfying general proximity/similarity queries with metric trees. Information Processing Letters, 40:175–179, 1991.zbMATHCrossRefGoogle Scholar
  32. 32.
    P. Yianilos. Data structures and algorithms for nearest neighbor search in general metric spaces. SODA, pages 311–321, 1993.Google Scholar
  33. 33.
    L. Younes. Computable elastic distance between shapes. SIAM J. Appl. Math., 58:565–586, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    S. C. Zhu and A. L. Yuille. FORMS: A flexible object recognition and modeling system. IJCV, 20(3):187–212, 1996.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Thomas B. Sebastian
    • 1
  • Philip N. Klein
    • 2
  • Benjamin B. Kimia
    • 1
  1. 1.Division of EngineeringBrown UniversityProvidenceUSA
  2. 2.Department of Computer ScienceBrown UniversityProvidenceUSA

Personalised recommendations