Cohomology theory for digital images

EGE Ö., Karaca I.

Romanian Journal of Information Science and Technology, vol.16, no.1, pp.10-28, 2013 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2013
  • Journal Name: Romanian Journal of Information Science and Technology
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.10-28
  • Keywords: Digital image, digital simplicial cohomology group, Universal Coefficient Theorem, Kunneth formula, cup product
  • Manisa Celal Bayar University Affiliated: No

Abstract

In this paper we propose a mathematical framework that can be used for dening cohomology of digital images. We state the Eilenberg-Steenrod axioms and the Universal Coefficient Theorem for this cohomology theory. We show that the Künneth formula doesn't hold. A cup product is dened and its main properties are proved.