An Improved Coordinate System for Point Correspondences of 2D Articulated Shapes

  • Adrian Ion
  • Yll Haxhimusa
  • Walter G. Kropatsch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


To find corresponding points in different poses of the same articulated shape, a non rigid coordinate system is used. Each pixel of each shape is identified by a pair of distinct coordinates. The coordinates are used to address corresponding points. This paper proposes a solution to a discretization problem identified in a previous approach. The polar like coordinate system is computed in a space where the problem cannot occur, followed by mapping the computed coordinates to pixels.


eccentricity transform discrete shape coordinate system 


  1. 1.
    Pizlo, Z.: Shape: Its Unique Place in Visual Perception, 2nd edn. Springer, Heidelberg (2002)Google Scholar
  2. 2.
    Rosenfeld, A.: A note on ’geometric transforms’ of digital sets. Pattern Recognition Letters 1(4), 223–225 (1983)CrossRefzbMATHGoogle Scholar
  3. 3.
    Borgefors, G.: Digital distance transforms in 2D, 3D, and 4D. In: Handbook of Pattern Recognition & Computer Vision, 3rd edn. World Scientific, Singapore (2005)Google Scholar
  4. 4.
    Gorelick, L., Galun, M., Sharon, E., Basri, R., Brandt, A.: Shape representation and classification using the poisson equation. In: IEEE CVPR, pp. 61–67 (2004)Google Scholar
  5. 5.
    Aouada, D., Dreisigmeyer, D.W., Krim, H.: Geometric modeling of rigid and non-rigid 3d shapes using the global geodesic function. In: NORDIA workshop in conjunction with IEEE CVPR, Anchorage, Alaska, USA. IEEE, Los Alamitos (2008)Google Scholar
  6. 6.
    Ion, A., Kropatsch, W.G., Andres, E.: Euclidean eccentricity transform by discrete arc paving. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol. 4992, pp. 213–224. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Felzenszwalb, P.F.: Representation and detection of deformable shapes. In: CVPR (2003)Google Scholar
  8. 8.
    Felzenszwalb, P.F., Schwartz, J.D.: Hierarchical matching of deformable shapes. In: CVPR (2007)Google Scholar
  9. 9.
    Ozcanli, O.C., Kimia, B.B.: Generic object recognition via shock patch fragments. In: BMVC 2007, Warwick Print, pp. 1030–1039 (2007)Google Scholar
  10. 10.
    Ling, H., Jacobs, D.W.: Shape classification using the inner-distance. IEEE TPAMI 29(2), 286–299 (2007)CrossRefGoogle Scholar
  11. 11.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE TPAMI 24(4), 509–522 (2002)CrossRefGoogle Scholar
  12. 12.
    Siddiqi, K., Shokoufandeh, A., Dickinson, S., Zucker, S.W.: Shock graphs and shape matching. International Journal of Computer Vision 30, 1–24 (1999)Google Scholar
  13. 13.
    Crum, W.R., Hartkens, T., Hill, D.L.: Non-rigid image registration: theory and practice. The British Journal of Radiology 77 Spec. No. 2 (2004)Google Scholar
  14. 14.
    Brechbuhler, C., Gerig, G., Kubler, O.: Parametrization of closed surfaces for 3-D shape-description. CVIU 61(2), 154–170 (1995)Google Scholar
  15. 15.
    Kambhamettu, C., Goldgof, D.B.: Curvature-based approach to point correspondence recovery in conformal nonrigid motion. Computer Vision, Graphics and Image Processing: Image Understanding 60(1), 26–43 (1994)CrossRefGoogle Scholar
  16. 16.
    Ion, A., Haxhimusa, Y., Kropatsch, W.G., López Mármol, S.B.: A coordinate system for articulated 2d shape point correspondences. In: Proceedings of 19th International Conference on Pattern Recognition (ICPR), IAPR. IEEE, Los Alamitos (2008)Google Scholar
  17. 17.
    Weisstein, E.W.: CRC Concise Encyclopedia of Mathematics, 2nd edn. Chapman & Hall/CRC, Boca Raton (2002)Google Scholar
  18. 18.
    Kropatsch, W.G., Ion, A., Haxhimusa, Y., Flanitzer, T.: The eccentricity transform (of a digital shape). In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 437–448. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing their shock graphs. IEEE TPAMI 26(5), 550–571 (2004)CrossRefGoogle Scholar
  20. 20.
    Ion, A.: The Eccentricity Transform of n-Dimensional Shapes with and without Boundary. PhD thesis, Vienna Univ. of Technology, Faculty of Informatics (2009)Google Scholar
  21. 21.
    Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3d surface construction algorithm. In: Stone, M.C. (ed.) Proceedings of the 14st Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1987, pp. 163–169. ACM, New York (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Adrian Ion
    • 1
  • Yll Haxhimusa
    • 1
  • Walter G. Kropatsch
    • 1
  1. 1.Pattern Recognition and Image Processing Group, Faculty of InformaticsVienna University of TechnologyAustria

Personalised recommendations