Persistent homology and Euler integral transforms

Abstract

The Euler calculus—an integral calculus based on Euler characteristic as a valuation on constructible functions—is shown to be an incisive tool for answering questions about injectivity and invertibility of recent transforms based on persistent homology for shape characterization.

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Notes

  1. 1.

    This structure, though very helpful for generating clean definitions, can be ignored by the reader for whom sheaves are unfamiliar.

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Acknowledgements

This work supported by the Office of the Assistant Secretary of Defense Research and Engineering through a Vannevar Bush Faculty Fellowship, ONR N00014-16-1-2010.

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Correspondence to Huy Mai.

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Ghrist, R., Levanger, R. & Mai, H. Persistent homology and Euler integral transforms. J Appl. and Comput. Topology 2, 55–60 (2018). https://doi.org/10.1007/s41468-018-0017-1

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Keywords

  • Algebraic topology
  • Euler calculus
  • Integral transform
  • Persistent homology

Mathematics Subject Classification

  • MSC 65R10
  • MSC 58C35