Cohomology theory for digital images

EGE Ö., Karaca I.

Romanian Journal of Information Science and Technology, cilt.16, sa.1, ss.10-28, 2013 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2013
  • Dergi Adı: Romanian Journal of Information Science and Technology
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.10-28
  • Anahtar Kelimeler: Digital image, digital simplicial cohomology group, Universal Coefficient Theorem, Kunneth formula, cup product
  • Manisa Celal Bayar Üniversitesi Adresli: Hayır

Özet

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.