Advertisement

Retrieving Articulated 3-D Models Using Medial Surfaces and Their Graph Spectra

  • Juan Zhang
  • Kaleem Siddiqi
  • Diego Macrini
  • Ali Shokoufandeh
  • Sven Dickinson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)

Abstract

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation and deformation of parts. We demonstrate the use of this representation for both indexing and matching 3-D object models. Our formulation uses the geometric information associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. We present comparative results against the techniques of shape distributions [17] and harmonic spheres [12] on a database of 320 models representing 13 object classes. The results demonstrate that medial surface based graph matching significantly outperforms these techniques for objects with articulating parts.

Keywords

3-D model matching indexing medial surfaces graph spectra 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alt, H., Aichholzer, O., Rote, G.: Matching Shapes With a Reference Point. In: Proceedings of the Tenth Annual Symposiusm on Computational Geometry, pp. 85–92 (1994)Google Scholar
  2. 2.
    Amenta, N., Choi, S., Kolluri, R.: The Power Crust, Unions of Balls, and the Medial Axis Transform. Computational Geometry: Theory and Applications 19(2), 127–153 (2001)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Ankerst, M., Kastenmüller, G., Kriegel, H., Seidl, T.: 3-D Shape Histograms for Similarity Search and Classification in Spatial Databases. In: Advances in Spatial Databases, 6th International Symposium, vol. 18, pp. 700–711 (1999)Google Scholar
  4. 4.
    Biederman, I.: Recognition–By–Components: A Theory of Human Image Understanding. Psychological Review 94(2), 115–147 (1987)CrossRefGoogle Scholar
  5. 5.
    Binford, T.O.: Visual Perception by Computer. In: IEEE Conference on Systems and Control (December 1971)Google Scholar
  6. 6.
    Blum, H.: Biological Shape and Visual Science. Journal of Theoretical Biology 38, 205–287 (1973)CrossRefGoogle Scholar
  7. 7.
    Elad, M., Tal, A., Ar, S.: Content Based Retrieval of VRML Objects- An Iterative and Interactive Approach. In: 6th Europgraphics Workshop on Multimedia, Manchester, UK, pp. 107–118 (2001)Google Scholar
  8. 8.
    Giblin, P.J., Kimia, B.B.: A formal Classification of 3D Medial Axis Points and Their Local Geometry. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2), 238–251 (2004)CrossRefGoogle Scholar
  9. 9.
    Hamza, A.B., Krim, H.: Geodesic Object Representation and Recognition. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 378–387. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Hilaga, M., Shinagawa, Y., Kohmura, T., Kunii, T.L.: Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes. In: Proceedings of ACM SIGGRAPH, pp. 203–212 (2001)Google Scholar
  11. 11.
    Kazhdan, M., Chazelle, B., Dobkin, D., Funkhouser, T., Rusinkiewicz, S.: A Reflective Symmetry Descriptor for 3-D Models. Algorithmica 38(1), 201–225 (2003)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors. In: Symposium on Geometry Processing (June 2003)Google Scholar
  13. 13.
    Leymarie, F.F., Kimia, B.B.: Computation of the Shock Scaffold for Unorganized Point Clouds in 3D. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Madison, Wisconsin, pp. 821–827 (2003)Google Scholar
  14. 14.
    Macrini, D.: Indexing and Matching for View-Based 3-D Object Recognition Using Shock Graphs. PhD thesis, University of Toronto (2003)Google Scholar
  15. 15.
    Malandain, G., Bertrand, G., Ayache, N.: Topological Segmentation of Discrete Surfaces. International Journal of Computer Vision 10(2), 183–197 (1993)CrossRefGoogle Scholar
  16. 16.
    Marr, D., Nishihara, K.H.: Representation and Recognition of the Spatial Organization of Three Dimensional Structure. Proceedings of the Royal Society of London, B 200, 269–294 (1978)CrossRefGoogle Scholar
  17. 17.
    Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape Distributions. ACM Transactions on Graphics 21(4), 807–832 (2002)CrossRefGoogle Scholar
  18. 18.
    Pellilo, M., Siddiqi, K., Zucker, S.W.: Matching Hierarchical Structures Using Association Graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(11), 1105–1120 (1999)CrossRefGoogle Scholar
  19. 19.
    Pentland, A.: Perceptual organization and the representation of natural form. Artificial Intelligence 28, 293–331 (1986)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Reyner, S.W.: An Analysis of a Good Algorithm for the Subtree Problem. SIAM J. Comput. 6, 730–732 (1977)zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Rosch, E.: Principles of Categorization. In: Cognition and Categorization. L. Erlbaum Associates, Mahwah (1978)Google Scholar
  22. 22.
    Sebastian, T., Klein, P., Kimia, B.: Recognition of shapes by editing their shock graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 551–571 (2004)CrossRefGoogle Scholar
  23. 23.
    Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton Shape Benchmark. In: Shape Modeling International, Genova, Italy (June 2004)Google Scholar
  24. 24.
    Shinagawa, Y., Kunii, T.L., Kergosien, Y.L.: Surface Coding Based on Morse Theory. IEEE Transactions on Computer Graphics and Applications 11(5), 66–78 (1991)CrossRefGoogle Scholar
  25. 25.
    Shokoufandeh, A., Dickinson, S.J., Siddiqi, K., Zucker, S.W.: Indexing Using a Spectral Encoding of Topological Structure. In: IEEE Conference on Computer Vision and Pattern Recognition, Fort Collins, CO, June 1999, pp. 491–497 (1999)Google Scholar
  26. 26.
    Shokoufandeh, A., Macrini, D., Dickinson, S., Siddiqi, K., Zucker, S.: Indexing Hierarchical Structures Using Graph Spectra. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(7) (2005)Google Scholar
  27. 27.
    Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.W.: Hamilton-Jacobi Skeletons. International Journal of Computer Vision 48(3), 215–231 (2002)CrossRefzbMATHGoogle Scholar
  28. 28.
    Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock Graphs and Shape Matching. International Journal of Computer Vision 35(1), 13–32 (1999)CrossRefGoogle Scholar
  29. 29.
    Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton Based Shape Matching and Retrieval. In: International Conference on Shape Modeling International and Applications, Seoul, Korea, May 2003, pp. 130–142 (2003)Google Scholar
  30. 30.
    Vranic, D., Saupe, D.: 3-D Model Retrieval With Spherical Harmonics and Moments. In: Radig, B., Florczyk, S. (eds.) DAGM 2001. LNCS, vol. 2191, pp. 392–397. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Juan Zhang
    • 1
  • Kaleem Siddiqi
    • 1
  • Diego Macrini
    • 2
  • Ali Shokoufandeh
    • 3
  • Sven Dickinson
    • 2
  1. 1.School of Computer Science & Centre for Intelligent MachinesMcGill University 
  2. 2.Department of Computer ScienceUniversity of Toronto 
  3. 3.Department of Computer ScienceDrexel University 

Personalised recommendations