Advertisement

Accurate 3D Shape Correspondence by a Local Description Darcyan Principal Curvature Fields

  • Ilhem SbouiEmail author
  • Majdi JribiEmail author
  • Faouzi GhorbelEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 684)

Abstract

In this paper, we propose a novel approach for finding correspondence between three-dimensional shapes undergoing non-rigid transformations. Our proposal is based on the computation of the mean of curvature fields values on a local parametrization constructed around interest points on the surface. This local parametrization corresponds to the Darcyan coordinates system. Thereafter, correspondence is found by measuring the \(L_{2}\) distance between obtained descriptors. We conduct the experimentation on the full objects of the Tosca database which contains a set of 3D objects with non-rigid deformations. The obtained results show the performance of the proposed approach.

Keywords

3D shapes Correspondence Darcyan coordinates system Principal curvatures 

References

  1. 1.
    Bronstein, A.M., Bronstein, M.M.: Regularized partial matching of rigid shapes. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008. LNCS, vol. 5303, pp. 143–154. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-88688-4_11 CrossRefGoogle Scholar
  2. 2.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. Nat. Acad. Sci. U.S.A. 103(5), 1168–1172 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R., Mahmoudi, M., Guillermo, S.: A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching, pp. 612–626 (2009)Google Scholar
  4. 4.
    Cohen, L., Kimmel, R.: Global minimum for active contour models. Int. J. Comput. Vis. 24(1), 57–78 (1997)CrossRefGoogle Scholar
  5. 5.
    Funkhouser, T., Shilane, P.: Partial matching of 3D shapes with priority-driven search. In: Proceedings of the Fourth Eurographics Symposium on Geometry Processing, pp. 131–142 (2006)Google Scholar
  6. 6.
    Gadacha, W., Ghorbel, F.: A stable and accurate multi-reference representation for surfaces of R3: application to 3D faces description. In: IEEE International Conference on Automatic Face and Gesture Recognition (FG 2013), Shanghai, China (2013)Google Scholar
  7. 7.
    Jiang, L., Zhang, X., Zhang, G.: Partial shape matching of 3D models based on the Laplace-Beltrami operator eigen function. J. Multimed. 8(6), 655–661 (2013)CrossRefGoogle Scholar
  8. 8.
    Kim, V.G., Lipman, Y., Funkhouser, T.: Blended intrinsic maps. ACM Trans. Graph. 30(4), 1 (2011)CrossRefGoogle Scholar
  9. 9.
    Kimmel, R., Sethian, J.A.: Computing geodesic paths on manifolds. Proc. Nat. Acad. Sci. U.S.A. 95(15), 8431–8435 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Lähner, Z., Rodolà, E., Schmidt, F.R., Bronstein, M.M., Cremers, D.: Efficient Globally optimal 2D-to-3D deformable shape matching (2016)Google Scholar
  11. 11.
    Meyer, M., Desbrun, M., Schroder, P., Barr, A.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Hege, H.C., Polthier, K. (eds.) Visualization and Mathematics III. Mathematics and Visualization (2002)Google Scholar
  12. 12.
    Hilaga, M., Shinagawa, Y., Kohmura, T., Kunii, T.: Topology matching for fully automatic similarity estimation of 3D shapes. Proc. SIGGRAPH 32(6), 203–212 (2001)Google Scholar
  13. 13.
    Ovsjanikov, M., Mérigot, Q., Mémoli, F., Guibas, L.: One point isometric matching with the heat kernel. In: Eurographics Symposium on Geometry Processing, vol. 29, no. 5, pp. 1555–1564 (2010)Google Scholar
  14. 14.
    Sahillio\(\breve{g}\)lu, Y., Yemez, Y.: Minimum-distortion isometric shape correspondence using EM algorithm. IEEE Trans. Pattern Anal. Mach. Intell. 34(11), 2203–2215 (2012)Google Scholar
  15. 15.
    Sahillio\(\breve{g}\)lu, Y., Yemez, Y.: Partial 3-D correspondence from shape extremities. Comput. Graph. Forum 33(6), 63–76 (2014)Google Scholar
  16. 16.
    Sahillioglu,Y., Yemez, Y.: 3D shape correspondence by isometry-driven greedy optimization. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 453–458 (2010)Google Scholar
  17. 17.
    Thomas, F., Yaron, L.: Mobius Voting For Surface Correspondence. World (2009)Google Scholar
  18. 18.
    Thompson, D.: On Growth and Form. University Press, Cambridge (1917)CrossRefGoogle Scholar
  19. 19.
    Van Kaick, O., Zhang, H., Hamarneh, G.: Bilateral maps for partial matching. Comput. Graph. Forum 32(6), 189–200 (2013)CrossRefGoogle Scholar
  20. 20.
    Van Kaick, O., Zhang, H., Hamarneh, G., Cohen-Or, D.: A survey on shape correspondence. Comput. Graph. Forum xx, 1–23 (2010)Google Scholar
  21. 21.
    Zhang, H., Sheffer, A., Cohen-Or, D., Zhou, Q., Van Kaick, O., Tagliasacchi, A.: Deformation-driven shape correspondence. In: Eurographics Symposium on Geometry Processing, vol. 27, no. 5, pp. 1431–1439 (2008)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.CRISTAL Laboratory, GRIFT Research Group, National School of Computer Sciencesla Manouba, UniversityManoubaTunisia

Personalised recommendations