Persistent homology and Euler integral transforms
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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.
KeywordsAlgebraic topology Euler calculus Integral transform Persistent homology
Mathematics Subject ClassificationMSC 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.
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Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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