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Articulation-Invariant Representation of Non-planar Shapes

  • Raghuraman Gopalan
  • Pavan Turaga
  • Rama Chellappa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)

Abstract

Given a set of points corresponding to a 2D projection of a non-planar shape, we would like to obtain a representation invariant to articulations (under no self-occlusions). It is a challenging problem since we need to account for the changes in 2D shape due to 3D articulations, viewpoint variations, as well as the varying effects of imaging process on different regions of the shape due to its non-planarity. By modeling an articulating shape as a combination of approximate convex parts connected by non-convex junctions, we propose to preserve distances between a pair of points by (i) estimating the parts of the shape through approximate convex decomposition, by introducing a robust measure of convexity and (ii) performing part-wise affine normalization by assuming a weak perspective camera model, and then relating the points using the inner distance which is insensitive to planar articulations. We demonstrate the effectiveness of our representation on a dataset with non-planar articulations, and on standard shape retrieval datasets like MPEG-7.

References

  1. 1.
    Zhang, J., Collins, R., Liu, Y.: Representation and Matching of Articulated Shapes. In: CVPR, pp. 342–349 (2004)Google Scholar
  2. 2.
    Ling, H., Jacobs, D.: Shape classification using the inner-distance. IEEE TPAMI 29, 286–299 (2007)Google Scholar
  3. 3.
    Bronstein, A.M., Bronstein, M.M., Bruckstein, A.M., Kimmel, R.: Matching two-dimensional articulated shapes using generalized multidimensional scaling. In: AMDO, pp. 48–57 (2006)Google Scholar
  4. 4.
    Mateus, D., Horaud, R.P., Knossow, D., Cuzzolin, F., Boyer, E.: Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration. In: CVPR, pp. 1–8 (2008)Google Scholar
  5. 5.
    Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of Shapes by Editing Their Shock Graphs. IEEE TPAMI 26, 550–571 (2004)Google Scholar
  6. 6.
    Felzenszwalb, P.F., Schwartz, J.D.: Hierarchical matching of deformable shapes. In: CVPR, pp. 1–8 (2007)Google Scholar
  7. 7.
    Schoenemann, T., Cremers, D.: Matching non-rigidly deformable shapes across images: A globally optimal solution. In: CVPR, pp. 1–6 (2008)Google Scholar
  8. 8.
    Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. IEEE TPAMI 25, 1285–1295 (2003)Google Scholar
  9. 9.
    Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Eurographics Symposium on Geometry Processing, pp. 225–233 (2007)Google Scholar
  10. 10.
    Latecki, L.J., Lakämper, R., Eckhardt, T.: Shape descriptors for non-rigid shapes with a single closed contour. In: CVPR, pp. 424–429 (2000)Google Scholar
  11. 11.
    Veltkamp, R.C., Hagedoorn, M.: State of the Art in Shape Matching. In: Principles of Visual Information Retrieval, pp. 87–119 (2001)Google Scholar
  12. 12.
    Yang, X., Köknar-Tezel, S., Latecki, L.J.: Locally constrained diffusion process on locally densified distance spaces with applications to shape retrieval. In: CVPR, pp. 357–364 (2009)Google Scholar
  13. 13.
    Wang, J., Chan, K.L.: Shape evolution for rigid and nonrigid shape registration and recovery. In: CVPR, pp. 164–171 (2009)Google Scholar
  14. 14.
    Bronstein, A.M., Bronstein, M.M., Bruckstein, A.M., Kimmel, R.: Partial similarity of objects, or how to compare a centaur to a horse. IJCV 84, 163–183 (2009)CrossRefGoogle Scholar
  15. 15.
    Hoffman, D.D., Richards, W.: Parts of recognition. Cognition 18, 65–96 (1984)CrossRefGoogle Scholar
  16. 16.
    Lingas, A.: The power of non-rectilinear holes. In: Colloquim on Automata, Languages and Programming, pp. 369–383 (1982)Google Scholar
  17. 17.
    Lien, J.M., Amato, N.M.: Approximate convex decomposition of polygons. In: Computational Geometry: Theory and Applications, vol. 35, pp. 100–123 (2006)Google Scholar
  18. 18.
    Rosin, P.L.: Shape partitioning by convexity. IEEE Transactions on Systems, Man, and Cybernetics, Part A 30, 202–210 (2000)CrossRefGoogle Scholar
  19. 19.
    Zunic, J., Rosin, P.L.: A new convexity measure for polygons. IEEE TPAMI 26, 923–934 (2004)Google Scholar
  20. 20.
    Rahtu, E., Salo, M., Heikkila, J.: A new convexity measure based on a probabilistic interpretation of images. IEEE TPAMI 28, 1501–1512 (2006)Google Scholar
  21. 21.
    Shapiro, L.G., Haralick, R.M.: Decomposition of two-dimensional shapes by graph-theoretic clustering. IEEE TPAMI 1, 10–20 (1979)Google Scholar
  22. 22.
    Walker, L.L., Malik, J.: Can convexity explain how humans segment objects into parts? Journal of Vision 3, 503 (2003)CrossRefGoogle Scholar
  23. 23.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE TPAMI 22, 888–905 (2000)Google Scholar
  24. 24.
    Schwarz, C., Teich, J., Vainshtein, A., Welzl, E., Evans, B.L.: Minimal enclosing parallelogram with application. In: Symposium on Computational Geometry, pp. 434–435 (1995)Google Scholar
  25. 25.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE TPAMI 24, 509–522 (2002)Google Scholar
  26. 26.
    Yang, X., Bai, X., Latecki, L.J., Tu, Z.: Improving shape retrieval by learning graph transduction. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part IV. LNCS, vol. 5305, pp. 788–801. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  27. 27.
    Tu, Z., Yuille, A.L.: Shape matching and recognition-using generative models and informative features. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3023, pp. 195–209. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Raghuraman Gopalan
    • 1
  • Pavan Turaga
    • 1
  • Rama Chellappa
    • 1
  1. 1.Dept. of ECEUniversity of MarylandCollege ParkUSA

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