A Novel Canonical Form for the Registration of Non Rigid 3D Shapes

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9257)

Abstract

In this paper, we address the problem of non rigid 3D shapes registration. We propose to construct a canonical form for the 3D objects corresponding to the same shape with different non rigid inelastic deformations. It consists on replacing the geodesic distances computed from three reference points of the original surface by the Euclidean ones calculated from three points of the novel canonical form. Therefore, the problem of non rigid registration is transformed to a rigid matching between canonical forms. The effectiveness of such method for the recognition and the retrieval processes is evaluated by the experimentation on the TOSCA database objects in the mean of the Hausdorff Shape distance.

Keywords

Registration Non rigid Inelastic 3D Surface Canonical form Matching Geodesic Euclidean Reference points Hausdorff shape distance 
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References

  1. 1.
    Schwartz, E.L., Shaw, A., Wolfson, E.: A numerical solution to the generalized map- maker’s problem: flattening nonconvex polyhedral surfaces. J. IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI) 11, 1005–1008 (1989)CrossRefGoogle Scholar
  2. 2.
    Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. J. IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI) 25, 1285–1295 (2003)CrossRefGoogle Scholar
  3. 3.
    Memoli, F., Sapiro, G.: A theoretical and computational framework for isometry invariant recognition of point cloud data. J. Foundations of Computational Mathematics 5, 313–346 (2005)MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Effcient computation of isometry-invariant distances between surfaces. J. SIAM Scientific Computing 28, 1812–1836 (2006)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. In: National Academy of Science (PNAS), pp. 1168–1172 (2006)Google Scholar
  6. 6.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Rock, paper, and scissors: extrinsic vs. intrinsic similarity of non-rigid shapes. In: Int. Conf. Computer Vision (ICCV), Rio de Janeiro, pp. 1–6 (2007)Google Scholar
  7. 7.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Topology-invariant similarity of nonrigid shapes. J. Int’l J. Computer Vision (IJCV) 81, 281–301 (2008)CrossRefGoogle Scholar
  8. 8.
    Besl, P.J., McKay, N.D.: A method for registration of 3D shapes. J. IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI) 14, 239–256 (1992)CrossRefGoogle Scholar
  9. 9.
    Chen, Y., Medioni, G.: Rock, paper, and scissors: object modeling by registration of multiple range images. In: Conf. Robotics and Automation (2007)Google Scholar
  10. 10.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R., Mahmoudi, M., Sapiro, G.: A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching. J. Int’l J. Computer Vision (IJCV) 89, 266–286 (2010)CrossRefGoogle Scholar
  11. 11.
    Duchenne, O., Bach, F., Kweon, I., Ponce, J.: A tensor-based algorithm for high-order graph matching. J. IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI) 33, 2383–2395 (2011)CrossRefGoogle Scholar
  12. 12.
    Torresani, L., Kolmogorov, V., Rother, C.: Feature correspondence via graph matching: models and global optimization. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 596–609. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  13. 13.
    Zeng, Y., Wang, C., Wang, Y., Gu, X., Samaras, D., Paragios, N.: Dense non-rigid surface registration using high-order graph matching. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), San Francisco, pp. 13–18 (2010)Google Scholar
  14. 14.
    Jain, V., Zhang, H.: A spectral approach to shape-based retrieval of articulated 3D models. J. Computer-Aided Design 39, 398–407 (2007)CrossRefGoogle Scholar
  15. 15.
    Rustamov, R.M.: Laplace-beltrami eigenfunctions for deformation invariant shape representation. In: Eurographics Symposium on Geometry (2007)Google Scholar
  16. 16.
    Tierny, J., Vandeborre, J.P., Daoudi, M.: Partial 3D Shape Retrieval by Reeb Pattern Unfolding. J. Computer Graphics Forum 28, 41–55 (2009)CrossRefGoogle Scholar
  17. 17.
    Ghorbel, F.: A unitary formulation for invariant image description: application to image coding. J. Annals of Telecommunication 53, 242–260 (1998)Google Scholar
  18. 18.
    Ghorbel, F.: Invariants for shapes and movement. Eleven cases from 1D to 4D and from euclidean to projectives (French version), Arts-pi edn., Tunisia (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.CRISTAL Laboratory, GRIFT Research Group, Ecole Nationale des Sciences de l’Informatique (ENSI)La Manouba UniversityLa ManoubaTunisia

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