The construction of simplicial groups in digital images

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ÖZTUNÇ S., Bildik N., MUTLU A.

Journal of Inequalities and Applications, cilt.2013, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2013
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1186/1029-242x-2013-143
  • Dergi Adı: Journal of Inequalities and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: digital image, adjacency relation, simplicial map, face and degenerate map, simplicial set, simplicial group
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this paper, we recall some definitions and properties from digital topology, and we consider the simplices and simplicial complexes in digital images due to adjacency relations. Then we define the simplicial set and conclude that the simplicial identities are satisfied in digital images. Finally, we construct the group structure in digital images and define the simplicial groups in digital images. Consequently, we calculate the digital homology group of two-dimensional digital simplicial group. MSC: 55N35, 68R10, 68U10, 18G30. © 2013 Öztunç et al.; licensee Springer.