Perturbation robust representations of topological persistence diagrams

Anirudh Som, Kowshik Thopalli, Karthikeyan Natesan Ramamurthy, Vinay Venkataraman, Ankita Shukla, Pavan Turaga

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in non-linear dynamical modeling. The increasing success of these methods is attributed to the complementary information that topology provides, as well as availability of tools for computing topological summaries such as persistence diagrams. However, persistence diagrams are multi-sets of points and hence it is not straightforward to fuse them with features used for contemporary machine learning tools like deep-nets. In this paper we present theoretically well-grounded approaches to develop novel perturbation robust topological representations, with the long-term view of making them amenable to fusion with contemporary learning architectures. We term the proposed representation as Perturbed Topological Signatures, which live on a Grassmann manifold and hence can be efficiently used in machine learning pipelines. We explore the use of the proposed descriptor on three applications: 3D shape analysis, view-invariant activity analysis, and non-linear dynamical modeling. We show favorable results in both high-level recognition performance and time-complexity when compared to other baseline methods.

Original languageEnglish (US)
Title of host publicationComputer Vision – ECCV 2018 - 15th European Conference, 2018, Proceedings
EditorsVittorio Ferrari, Cristian Sminchisescu, Martial Hebert, Yair Weiss
PublisherSpringer Verlag
Pages638-659
Number of pages22
ISBN (Print)9783030012335
DOIs
StatePublished - Jan 1 2018
Event15th European Conference on Computer Vision, ECCV 2018 - Munich, Germany
Duration: Sep 8 2018Sep 14 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11211 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th European Conference on Computer Vision, ECCV 2018
CountryGermany
CityMunich
Period9/8/189/14/18

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Keywords

  • Grassmann manifold
  • Invariance learning
  • Persistence diagrams
  • Perturbed topological signature
  • Topological data analysis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Som, A., Thopalli, K., Ramamurthy, K. N., Venkataraman, V., Shukla, A., & Turaga, P. (2018). Perturbation robust representations of topological persistence diagrams. In V. Ferrari, C. Sminchisescu, M. Hebert, & Y. Weiss (Eds.), Computer Vision – ECCV 2018 - 15th European Conference, 2018, Proceedings (pp. 638-659). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11211 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-01234-2_38