Persistence-Based Pooling for Shape Pose Recognition

  • Thomas BonisEmail author
  • Maks Ovsjanikov
  • Steve Oudot
  • Frédéric Chazal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9667)


In this paper, we propose a novel pooling approach for shape classification and recognition using the bag-of-words pipeline, based on topological persistence, a recent tool from Topological Data Analysis. Our technique extends the standard max-pooling, which summarizes the distribution of a visual feature with a single number, thereby losing any notion of spatiality. Instead, we propose to use topological persistence, and the derived persistence diagrams, to provide significantly more informative and spatially sensitive characterizations of the feature functions, which can lead to better recognition performance. Unfortunately, despite their conceptual appeal, persistence diagrams are difficult to handle, since they are not naturally represented as vectors in Euclidean space and even the standard metric, the bottleneck distance is not easy to compute. Furthermore, classical distances between diagrams, such as the bottleneck and Wasserstein distances, do not allow to build positive definite kernels that can be used for learning. To handle this issue, we provide a novel way to transform persistence diagrams into vectors, in which comparisons are trivial. Finally, we demonstrate the performance of our construction on the Non-Rigid 3D Human Models SHREC 2014 dataset, where we show that topological pooling can provide significant improvements over the standard pooling methods for the shape pose recognition within the bag-of-words pipeline.


Shape recognition Bag-of-words Topological Data Analysis 



This work was supported by ANR project TopData ANR-13-BS01-0008. First author was supported by the French Délégation Générale de l’Armement (DGA). Second author was supported by Marie-Curie CIG-334283-HRGP, a CNRS chaire dexcellence, a chaire Jean Marjoulet from Ecole Polytechnique, and a Faculty Award from Google Inc.


  1. 1.
    Bronstein, A.M., Bronstein, M.M., Guibas, L.J., Ovsjanikov, M.: Shape google: Geometric words and expressions for invariant shape retrieval. ACM Trans. Graph. 30, 1–20 (2011)CrossRefGoogle Scholar
  2. 2.
    Masci, J., Boscaini, D., Bronstein, M.M., Vandergheynst, P.: Shapenet: Convolutional neural networks on non-euclidean manifolds.
  3. 3.
    Fei-Fei, L., Pietro, P.: A bayesian hierarchical model for learning natural scene categories. In: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005), CVPR 2005, vol. 2, pp. 524–531. IEEE Computer Society, Washington, DC (2005).
  4. 4.
    Yang, J., Yu, K., Gong, Y., Huang, T.: Linear spatial pyramid matching using sparse coding for image classification. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2009)Google Scholar
  5. 5.
    Boureau, Y.-L., Bach, F., LeCun, Y., Ponce, J.: Learning mid-level features for recognition. In: Proceedings of CVPR (2010)Google Scholar
  6. 6.
    Liu, L., Wang, L., Liu, X.: In defense of soft-assignment coding. In: ICCV 2011, pp. 2486–2493 (2011)Google Scholar
  7. 7.
    Lazebnik, S., Schmid, C., Ponce, J.: Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In: Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2006, vol. 2, pp. 2169–2178 (2006)Google Scholar
  8. 8.
    López-Sastre, R.J., García-Fuertes, A., Redondo-Cabrera, C., Acevedo-Rodríguez, F.J., Maldonado-Bascón, S.: Evaluating 3D spatial pyramids for classifying 3D shapes. Comput. Graph. 37, 473–483 (2013)CrossRefGoogle Scholar
  9. 9.
    Li, C., Hamza, A.B.: Intrinsic spatial pyramid matching for deformable 3D shape retrieval. IJMIR 2, 261–271 (2013)Google Scholar
  10. 10.
    Verri, A., Uras, C., Frosini, P., Ferri, M.: On the use of size functions for shape analysis. Biol. Cybern. 70, 99–107 (1993)CrossRefzbMATHGoogle Scholar
  11. 11.
    Edelsbrunner, H., Harer, J.: Computational Topology - An Introduction. American Mathematical Society, New York (2010)zbMATHGoogle Scholar
  12. 12.
    Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete Comput. Geom. 33, 249–274 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. In: Proceedings of 21st ACM Symposium Computer Geometry, pp. 263–271 (2005)Google Scholar
  14. 14.
    Chazal, F., Cohen-Steiner, D., Guibas, L.J., Glisse, M., Oudot, S.Y.: Proximity of persistence modules, their diagrams. In: Proceedings of 25th ACM Symposium Computer Geometry (2009)Google Scholar
  15. 15.
    Chazal, F., de Silva, V., Glisse, M., Oudot, S.: The structure and stability of persistence modules (2012).
  16. 16.
    Li, C., Ovsjanikov, M., Chazal, F.: Persistence-based structural recognition. In: CVPR, pp. 2003–2010 (2014)Google Scholar
  17. 17.
    Reininghaus, J., Huber, S., Bauer, U., Kwitt, R.: A stable multi-scale kernel for topological machine learning. In: CVPR (2015)Google Scholar
  18. 18.
    Bubenik, P.: Statistical topology using persistence landscapes. JMLR 16, 77–102 (2015)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Sun, J., Ovsjanikov, M., Guibas, L.: A concise, provably informative multi-scale signature based on heat diffusion. In: Proceedings of the Symposium on Geometry Processing, SGP 2009, pp. 1383–1392 (2009)Google Scholar
  20. 20.
    Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Proceedings of CVPR (2010)Google Scholar
  21. 21.
    Bay, H., Ess, A., Tuytelaars, T., Van Gool, L.: Speeded-up robust features (SURF). Comput. Vis. Image Underst. 110, 346–359 (2008)CrossRefGoogle Scholar
  22. 22.
    Salton, G., McGill, M.J.: Introduction to Modern Information Retrieval. McGraw-Hill Inc., New York (1986)zbMATHGoogle Scholar
  23. 23.
    Wang, J., Yang, J., Yu, K., Lv, F., Huang, T., Gong, Y.: Locality-constrained linear coding for image classification. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2010)Google Scholar
  24. 24.
    Perronnin, F., Sánchez, J., Mensink, T.: Improving the fisher kernel for large-scale image classification. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part IV. LNCS, vol. 6314, pp. 143–156. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Zhou, X., Yu, K., Zhang, T., Huang, T.S.: Image classification using super-vector coding of local image descriptors. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part V. LNCS, vol. 6315, pp. 141–154. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  26. 26.
    Chazal, F., Guibas, L.J., Oudot, S.Y., Skraba, P.: Persistence-based clustering in riemannian manifolds. J. ACM 60, 41 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Pickup, D., et al.: SHREC 2014 track: Shape retrieval of non-rigid 3D human models, EG 3DOR 2014 (2014)Google Scholar
  28. 28.
    Kalogerakis, E., Hertzmann, A., Singh, K.: Learning 3D mesh segmentation and labeling. ACM Trans. Graph. 29, 102 (2010)CrossRefGoogle Scholar
  29. 29.
    Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. J. Mach. Learn. Res. 11, 19–60 (2010)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Besl, P.J., McKay, N.D.: A method for registration of 3-d shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14, 239–256 (1992)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Thomas Bonis
    • 1
    Email author
  • Maks Ovsjanikov
    • 2
  • Steve Oudot
    • 1
  • Frédéric Chazal
    • 1
  1. 1.DataShape TeamInria SaclayPalaiseauFrance
  2. 2.Laboratoire d’Informatique de l’Ecole PolytechniquePalaiseauFrance

Personalised recommendations