Describing and Matching 2D Shapes by Their Points of Mutual Symmetry

  • Arjan Kuijper
  • Ole Fogh Olsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3953)


A novel shape descriptor is introduced. It groups pairs of points that share a geometrical property that is based on their mutual symmetry. The descriptor is visualized as a diagonally symmetric diagram with binary valued regions. This diagram is a fingerprint of global symmetry between pairs of points along the shape. The descriptive power of the method is tested on a well-known shape data base containing several classes of shapes and partially occluded shapes. First tests with simple, elementary matching algorithms show good results.


Medial Axis Shape Descriptor Tangency Point Equidistant Point Maximal Circle 
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.
    Blum, H.: Biological shape and visual science (part i). Journal of Theoretical Biology 38, 205–287 (1973)CrossRefGoogle Scholar
  2. 2.
    Kimia, B.: On the role of medial geometry in human vision. Journal of Physiology- Paris 97, 155–190 (2003)CrossRefGoogle Scholar
  3. 3.
    Ogniewicz, R.L., Kübler, O.: Hierarchic voronoi skeletons. Pattern Recognition 28, 343–359 (1995)CrossRefGoogle Scholar
  4. 4.
    Sebastian, T., Kimia, B.B.: Curves vs. skeletons in object recognition. Signal Processing 85, 247–263 (2005)zbMATHCrossRefGoogle Scholar
  5. 5.
    Siddiqi, K., Kimia, B.: A shock grammar for recognition. In: Proceedings CVPR 1996, pp. 507–513 (1996)Google Scholar
  6. 6.
    Sebastian, T., Klein, P., Kimia, B.B.: Recognition of shapes by editing shock graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 550–571 (2004)CrossRefGoogle Scholar
  7. 7.
    Pelillo, M., Siddiqi, K., Zucker, S.: Matching hierarchical structures using association graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 1105–1120 (1999)CrossRefGoogle Scholar
  8. 8.
    Bruce, J.W., Giblin, P.J., Gibson, C.: Symmetry sets. Proceedings of the Royal Society of Edinburgh 101, 163–186 (1985)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Giblin, P.J., Kimia, B.B.: On the local form and transitions of symmetry sets, medial axes, and shocks. International Journal of Computer Vision 54, 143–156 (2003)zbMATHCrossRefGoogle Scholar
  10. 10.
    Blake, A., Taylor, M., Cox, A.: Grasping visual symmetry. In: Proceedings Fourth International Conference on Computer Vision, pp. 724–733 (1993)Google Scholar
  11. 11.
    Blake, A., Taylor, M.: Planning planar grasps of smooth contours. In: Proceedings IEEE International Conference on Robotics and Automation, vol. 2, pp. 834–839 (1993)Google Scholar
  12. 12.
    Kuijper, A., Olsen, O.: On extending symmetry sets for 2D shapes. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 512–520. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Kuijper, A., Olsen, O., Giblin, P., Bille, P., Nielsen, M.: From a 2D shape to a string structure using the symmetry set. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3022, pp. 313–326. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Kuijper, A., Olsen, O.: Transitions of the pre-symmetry set. In: Proceedings of the 17th International Conference on Pattern Recognition, vol. III, pp. 190–193 (2004)Google Scholar
  15. 15.
    Sharvit, D., Chan, J., Tek, H., Kimia, B.: Symmetry-based indexing of image databases. Journal of Visual Communication and Image Representation 9, 366–380 (1998)CrossRefGoogle Scholar
  16. 16.
    Sebastian, T., Klein, P., Kimia, B.B.: Recognition of shapes by editing shock graphs. In: Proceedings of the 8th ICCV, pp. 755–762 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Arjan Kuijper
    • 1
  • Ole Fogh Olsen
    • 2
  1. 1.RICAMLinzAustria
  2. 2.IT-University of CopenhagenDenmark

Personalised recommendations