Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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)
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)
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)
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)
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)
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)
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)
Lipman, Y., Rustamov, R., Funkhouser, T.: Biharmonic distance. ACM Trans. Graph. 29(3), 27:1–27:11 (2010)
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)
Ovsjanikov, M., Merigot, Q., Memoli, F., Guibas, L.: One point isometric matching with the heat kernel. Comput. Graph. Forum 29(5), 1555–1564 (2010)
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)
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)
Starck, J., Hilton, A.: Surface capture for performance based animation. IEEE Comput. Graph. Appl. 27(3), 21–31 (2007)
Tari, S.: Hierarchical shape decomposition via level sets. In: ISMM, pp. 215–225. Springer, Berlin (2009)
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 The Author(s) and the Association for Women in Mathematics
About this chapter
Cite this chapter
Genctav, A., Tari, S. (2018). Adaptive Deflation Stopped by Barrier Structure for Equating Shape Topologies Under Topological Noise. In: Genctav, A., et al. Research in Shape Analysis. Association for Women in Mathematics Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-77066-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-77066-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77065-9
Online ISBN: 978-3-319-77066-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)