The construction of simplicial groups in digital images

Journal of inequalities and applications

Simge Ö¹ 

关键词: digital image;    adjacency relation;    simplicial map;    face and degenerate map;    simplicial set;    simplicial group;   

DOI  :  10.1186/1029-242X-2013-143

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY