Persistent homology and Euler integral transforms

  • Robert Ghrist
  • Rachel Levanger
  • Huy MaiEmail author


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.


Algebraic topology Euler calculus Integral transform Persistent homology 

Mathematics Subject Classification

MSC 65R10 MSC 58C35 



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.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Departments of Mathematics and Electrical and Systems EngineeringUniversity of Pennsylvania, David Rittenhouse Lab.PhiladelphiaUSA
  2. 2.Department of Electrical and Systems EngineeringUniversity of PennsylvaniaPhiladelphiaUSA
  3. 3.Department of MathematicsUniversity of Pennsylvania, David Rittenhouse Lab.PhiladelphiaUSA

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