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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)

Abstract

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.

Keywords

Shape recognition Bag-of-words Topological Data Analysis 

Notes

Acknowledgements

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.

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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

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