Persistent homology and Euler integral transforms


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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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).

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

Mathematics Subject Classification

  • MSC 65R10
  • MSC 58C35