Matching Two-Dimensional Articulated Shapes Using Generalized Multidimensional Scaling

  • Alexander M. Bronstein
  • Michael M. Bronstein
  • Alfred M. Bruckstein
  • Ron Kimmel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4069)


We present a theoretical and computational framework for matching of two-dimensional articulated shapes. Assuming that articulations can be modeled as near-isometries, we show an axiomatic construction of an articulation-invariant distance between shapes, formulated as a generalized multidimensional scaling (GMDS) problem and solved efficiently. Some numerical results demonstrating the accuracy of our method are presented.


Geodesic Distance Partial Match Planar Shape Intrinsic Geometry Partial Probe 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Geiger, D., Basri, R., Costa, L., Jacobs, D.: Determining the similarity of deformable shapes. Vision Research 38, 2365–2385 (1998)CrossRefGoogle Scholar
  2. 2.
    Gdalyahu, Y., Weinshall, D.: Flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes. IEEE Trans. PAMI 21, 1312–1328 (1999)Google Scholar
  3. 3.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape context. IEEE Trans. PAMI 24, 509–522 (2002)Google Scholar
  4. 4.
    Zhang, J., Collins, R., Liu, Y.: Representation and matching of articulated shapes. In: Proc. CVPR, vol. 2, pp. 342–349 (June 2004)Google Scholar
  5. 5.
    Ling, H., Jacobs, D.: Using the inner-distance for classification of articulated shapes. In: Proc. CVPR (2005)Google Scholar
  6. 6.
    Elad, A., Kimmel, R.: Bending invariant representations for surfaces. In: Proc. CVPR, pp. 168–174 (2001)Google Scholar
  7. 7.
    Gromov, M.: Structures métriques pour les variétés riemanniennes. Number 1 in Textes Mathématiques (1981)Google Scholar
  8. 8.
    Mémoli, F., Sapiro, G.: A theoretical and computational framework for isometry invariant recognition of point cloud data. In: Foundations of Computational Mathematics (to appear, 2005)Google Scholar
  9. 9.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Efficient computation of isometry-invariant distances between surfaces. Technical report, Dept. of Computer Science, Technion, Israel (submitted, 2005)Google Scholar
  10. 10.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. National Academy of Sciences 103(5), 1168–1172 (2006)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Jacobs, D., Weinshall, D., Gdalyahu, Y.: Class representation and image retrieval with non-metric distances. IEEE Trans. PAMI 22, 583–600 (2000)Google Scholar
  12. 12.
    Sethian, J.A.: A review of the theory, algorithms, and applications of level set method for propagating surfaces. Acta numerica, 309–395 (1996)Google Scholar
  13. 13.
    Kimmel, R., Sethian, J.A.: Computing geodesic on manifolds. Proc. US National Academy of Science 95, 8431–8435 (1998)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Borg, I., Groenen, P.: Modern multidimensional scaling - theory and applications. Springer, Heidelberg (1997)MATHGoogle Scholar
  15. 15.
    Bertsekas, D.: Nonlinear programming, 2nd edn. Atlanta Scientific (1999)Google Scholar
  16. 16.
    Bronstein, M.M., Bronstein, A.M., Kimmel, R., Yavneh, I.: Multigrid multidimensional scaling. Numerical Linear Algebra with Applications (NLAA) 13, 149–171 (2006)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alexander M. Bronstein
    • 1
  • Michael M. Bronstein
    • 1
  • Alfred M. Bruckstein
    • 1
  • Ron Kimmel
    • 1
  1. 1.Department of Computer ScienceTechnion – Israel Institute of TechnologyHaifaIsrael

Personalised recommendations