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 structure, though very helpful for generating clean definitions, can be ignored by the reader for whom sheaves are unfamiliar.
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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.
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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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
- Algebraic topology
- Euler calculus
- Integral transform
- Persistent homology
Mathematics Subject Classification
- MSC 65R10
- MSC 58C35