Singular Homology Group Of Digital Image Based On K-adjacency Relation

Digital image analysis is the theoretical basis of digital image processing,and a topological method is important in digital image analysis.The basic idea is to analyze the digital image by establishing a topological adjacency relation between pixels.The digital topology exactly stems from the needs of digital image processing and digital image analysis.Based on the K-product topology on the digital space Zn,we introduce KA-singular simplex,KA-singular homology group and relative homology group of a digital image in the K-adjacency category KAC.Then we calculate KA-singular homology groups of some digital images,and discuss basic properties of KA-singular homology group.It is proved that the KA-singular homology group is a KA-isomorphic invariant,but it is not a homotopic invariant in the K-adjacency category KAC.At the same time,the KA-singular homology group in the category KAC is compared with the digital singular homology group in the category KDTC.Finally,we show that Mayer-Vietoris pair’s exact homology sequence,the space pair’s exact homology sequence,and the excision theorem in KAC.