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Persistent homology of graph-like digital images

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Abstract

In this paper, we introduce persistent homology for graph-like digital images as a new type of computation of digital homology groups. We calculate persistent homology groups of some graph-like digital images. Moreover, we prove some theorems related to a singleton point and \(\kappa \)-connected graph-like digital images. It has been shown that identity and composition axioms are satisfied for digital persistent homology groups. Finally, we give some applications of the new theory to image processing.

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Acknowledgements

We would like to express our gratitude to the anonymous referees for their helpful suggestions and corrections.

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  1. Department of Mathematics, Ege University, 35100, Bornova, Izmir, Turkey

    Ozgur Ege & Ismet Karaca

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  1. Ozgur Ege
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  2. Ismet Karaca
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Correspondence to Ozgur Ege.

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Ege, O., Karaca, I. Persistent homology of graph-like digital images. Annali di Matematica 199, 2167–2179 (2020). https://doi.org/10.1007/s10231-020-00962-x

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