Adaptive Deflation Stopped by Barrier Structure for Equating Shape Topologies Under Topological Noise

  • Asli Genctav
  • Sibel Tari
Part of the Association for Women in Mathematics Series book series (AWMS, volume 12)


Using level sets of a pair of transformations, we adaptively bring two shapes to be matched to a comparable topology prior to a correspondence search. One of the transformations readily provides a central structure for each shape. We utilize the central structure as a reference volume for scale normalization. By adaptively dilating the central structure with the help of the second transformation, we construct what we refer to as the barrier structure. The barrier structure is used to automatically stop topology equating adaptive deflations. Illustrative experiments using different datasets demonstrate that our approach provides robust solutions for the topological noise caused by localized touches or spurious links that connect different shape parts.



The work is funded by TUBITAK under grant 112E208. We thank Adrian Hilton for sharing the flashkick sequence [13] and i3DPost Multi-View Human Action datasets [7].


  1. 1.
    Ahmed, N., Theobalt, C., Rossl, C., Thrun, S., Seidel, H.P.: Dense correspondence finding for parametrization-free animation reconstruction from video. In: Proceedings of Computer Vision and Pattern Recognition (CVPR) (2008)Google Scholar
  2. 2.
    Bronstein, A., Bronstein, M., Kimmel, R., Mahmoudi, M., Sapiro, G.: A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. Int. J. Comput. Vis. 89(2), 266–286 (2010)Google Scholar
  3. 3.
    Bronstein, A., Bronstein, M., Castellani, U., Falcidieno, B., Fusiello, A., Godil, A., Guibas, L., Kokkinos, I., Lian, Z., Ovsjanikov, M., Patane, G., Spagnuolo, M., Toldo, R.: SHREC 2010: robust large-scale shape retrieval benchmark. In: Proceedings of Eurographics Workshop on 3D Object Retrieval (2010)Google Scholar
  4. 4.
    Bronstein, A., Bronstein, M., Castellani, U., Dubrovina, A., Guibas, L., Horaud, R., Kimmel, R., Knossow, D., Von Lavante, E., Mateus, D., Ovsjanikov, M., Sharma, A.: SHREC 2010: robust correspondence benchmark. In: Proceedings of Eurographics Workshop on 3D Object Retrieval (2010)Google Scholar
  5. 5.
    Genctav, M., Genctav, A., Tari, S.: NonLocal via local–nonlinear via linear: a new part-coding distance field via screened Poisson Equation. J. Math. Imaging Vis. 55(2), 242–252 (2016)Google Scholar
  6. 6.
    Genctav, A., Sahillioglu, Y., Tari, S.: 3D shape correspondence under topological noise. In: 24th Signal Processing and Communication Application Conference (SIU), pp. 401–404 (2016) (Preprint in English arXiv:1705.00274)Google Scholar
  7. 7.
    Gkalelis, N., Kim, H., Hilton, A., Nikolaidis, N., Pitas, I.: The i3DPost multi-view and 3D human action/interaction. In: Proceedings of CVMP, pp. 159–168 (2009)Google Scholar
  8. 8.
    Lipman, Y., Rustamov, R., Funkhouser, T.: Biharmonic distance. ACM Trans. Graph. 29(3), 27:1–27:11 (2010)Google Scholar
  9. 9.
    Mateus, D., Horaud, R., Knossow, D., Cuzzolin, F., Boyer, E.: Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration. In: Proceedings of Computer Vision and Pattern Recognition (CVPR) (2008)Google Scholar
  10. 10.
    Ovsjanikov, M., Merigot, Q., Memoli, F., Guibas, L.: One point isometric matching with the heat kernel. Comput. Graph. Forum 29(5), 1555–1564 (2010)Google Scholar
  11. 11.
    Sharma, A., Horaud, R.: Shape matching based on diffusion embedding and on mutual isometric consistency. In: Proceedings of Computer Vision and Pattern Recognition Workshops (2010)Google Scholar
  12. 12.
    Sharma, A., Horaud, R., Cech, J., Boyer, E.: Topologically-robust 3D shape matching based on diffusion geometry and seed growing. In: Proceedings of Computer Vision and Pattern Recognition (CVPR), pp. 2481–2488 (2011)Google Scholar
  13. 13.
    Starck, J., Hilton, A.: Surface capture for performance based animation. IEEE Comput. Graph. Appl. 27(3), 21–31 (2007)Google Scholar
  14. 14.
    Tari, S.: Hierarchical shape decomposition via level sets. In: ISMM, pp. 215–225. Springer, Berlin (2009)Google Scholar
  15. 15.
    Tari, S.: Extracting parts of 2D shapes using local and global interactions simultaneously. In: Chen, C.H. (ed.) Handbook of Pattern Recognition and Computer Vision, 4th edn., pp. 283–303. World Scientific, Hackensack, NJ (2009)Google Scholar
  16. 16.
    Tari, S., Shah, J., Pien, H.: A computationally efficient shape analysis via level sets. In: IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (1996)Google Scholar
  17. 17.
    Vlasic, D., Baran, I., Matusik, W., Popovic, J.: Articulated mesh animation from multi-view silhouettes. ACM Trans. Graph. 27(3), 97:1–97:9 (2008)Google Scholar

Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  1. 1.Department of Computer EngineeringMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations