2019/02/28 by Samira Sahar Jamil, Danish Ali, Ali Danish · 3 citations
Computer Science · Mathematics · #Algebra over a field #Axiom #CW complex #Cellular homology #Cohomology #Digital Image Processing Techniques #Discrete mathematics #Functor #Geometry #Homology (biology) #Homotopy #Mathematics #Mayer–Vietoris sequence #Medical Image Segmentation Techniques #Morse homology #Pure mathematics #Relative homology #Singular homology #Topological and Geometric Data Analysis #math.AT #msc:55N35 #msc:68R10 #msc:68U05 #msc:68U10
paper · pdf · doi:10.3906/mat-2002-52
published in TURKISH JOURNAL OF MATHEMATICS 44(3), 739-759 (Scientific and Technological Research Council of Turkey (TUBITAK))
arxiv created 2019/06/18 · openalex publication_date 2020/03/17 · arxiv updated 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.