Shape Decomposition and Shape Similarity Measure

  • Longin Jan Latecki
  • Rolf Lakämper
Conference paper
Part of the Informatik aktuell book series (INFORMAT)


We propose a simple and natural rule for decomposition of 2D objects into parts of visual form. The hierarchical convexity rule states that visual parts axe enclosed by maximal convex boundary arcs (with respect to the object) at various levels of curve evolution. The proposed rule is based on a novel curve evolution method by digital linearization in which a significant visual part will become a convex part at some level of the evolution. The hierarchical convexity rule determines not only parts of boundary curves but directly the visual parts of objects, and the evolution hierarchy induces a hierarchical structure of the obtained visual parts.

Further, we derive a shape similarity measure based on the decomposition into visual parts and apply it to shape matching of object contours in an image database. The experimental results justify that our shape matching procedure is stable and robust with respect to noise deformations and gives an intuitive shape correspondence.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Beusmans, D. D. Hoffman, and B. M. Bennett. Description of solid shape and its inference from occluding contours. Journal of the Optical Society of America A. 4, 1155–1167, 1987.MathSciNetGoogle Scholar
  2. 2.
    H. Freeman. Shape description via the use of critical points. Pattern Recognition 10, 159–166, 1978.zbMATHCrossRefGoogle Scholar
  3. 3.
    I. Debled-Rennesson and J.-P. Reveilles. A Linear Algorithm for Segmentation of Digital Curves. Intl. J. Pattern Recognition and A19, 635–662, 1995.Google Scholar
  4. 4.
    D. D. Hoffman and W. A. Richards. Parts of Recognition. Cognition 18, 65–96, 1984.CrossRefGoogle Scholar
  5. 5.
    D. D. Hoffman and M. Singh. Salience of visual parts. Cognition 63, 29–78, 1997.CrossRefGoogle Scholar
  6. 6.
    B. B. Kimia, A. R. Tannenbaum, and S. W. Zucker. Shapes, shocks, and deformations, I: The components of shape and the reaction-diffusion space. Int. J. of Computer Vision 15 (3), 189–224, 1995.CrossRefGoogle Scholar
  7. 7.
    R. Lakamper and F. Seytter. Manipulation objektbasiert codierter Bilder als Anwendungsbeipspiel neuer Videostandards. Proc. DAGM Mustererkennung, Braun-schweig, 427–434, Springer 1997.Google Scholar
  8. 8.
    L. J. Latecki and A. Rosenfeld. Supportedness and Supportedness: Differentialless Geometry of Plane Curves. Pattern Recognition 31, 607–622, 1998.CrossRefGoogle Scholar
  9. 9.
    L. J. Latecki and R. Lakämper. Discrete Approach to Curve Evolution. Proc. DAGM Mustererkennung, Stuttgart 1998.Google Scholar
  10. 10.
    L. J. Latecki and R. Lakamper. Scholar
  11. 11.
    E. J. Pauwels, P. Fiddelaers, and F. Mindru. Fully Unsupervised clustering using center-surround receptive fields with applications to colour-segmentation. Proc. of 7th Int. Conf. on Computer Analysis of Images and Patterns, Kiel, 17–24, 1997.Google Scholar
  12. 12.
    K. Siddiqi and B. B. Kimia. Parts of Visual Form: Computational Aspects. IEEE Trans. PAMI 17, 239–251, 1995.CrossRefGoogle Scholar
  13. 13.
    K. Siddiqi, K. Tresness, and B. B. Kimia. Parts of Visual Form: Ecological and Psychophysical Aspects. Proc. IAPR’s Int. Workshop on Visual Form, Capri, 1994.Google Scholar
  14. 14.
    N. Ueda and S. Suzuki. Learning Visual Models from Shape Contours Using Multi- scale Convex/Concave Structure Matching. IEEE Trans. PAMI 15, 337–352, 1993.CrossRefGoogle Scholar
  15. 15.
    Y. Uesaka. A New Fourier Description applicable to open curves. Trans, on IECE Japan A J67-A, 166–173, 1984 (in Japanese).Google Scholar
  16. 16.
    C. T. Zahn and R. Z. Roskies. Fourier Descriptors for Plane Closed Curves. IEEE Trans, on Computers 21, 269–281, 1972.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Longin Jan Latecki
    • 1
  • Rolf Lakämper
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HamburgGermany

Personalised recommendations