Persistent homology of graph-like digital images
Articles > Article · 2020
Authors: Özgür EGE, İsmet KARACA
Annali di Matematica Pura ed Applicata (1923 -), Journal Indexed in SCI Expanded, International, WoS, 2020, vol 199, pp 2167-2179
DOI: 10.1007/s10231-020-00962-x
Summary
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.