Annali Di Matematica Pura Ed Applicata, cilt.199, ss.1-14, 2020 (SCI Expanded İndekslerine Giren Dergi)
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.