Digital Hurewicz theorem and digital homology theory

Abstract

In this paper, we develop homology groups for digital images based on cubical singular homology theory fortopological spaces. Using this homology, we obtain two main results that make this homology different from alreadyexisting homologies of digital images. We prove digital analog of Hurewicz theorem for digital cubical singular homology.We also show that the homology functors developed in this paper satisfy properties that resemble the Eilenberg–Steenrodaxioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digitalhomology theory.