Digital Hurewicz theorem and digital homology theory

Abstract

In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we obtain two main results that make this homology different from already existing 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-Steenrod axioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digital homology theory.