Simplicial Homology Of K-adjacent Digital Image

A digital image analysis is a theoretical basis of digital image processing.In digital topology,a digital space can have topological structures and topological methods prove to be effective in digital image analysis.A digital image can be connected with homology groups,and homology groups are isomorphic invariants,so homology groups become an important tool of a digital image analysis.In this thesis,we consider the digital space and digital images with a K-product topological structure.On this basis,we study a KA-mapping which is more extensive than a topological continuous mapping,and establish a K-adjacency category(KAC).In KAC,firstly,we introduce the concepts of KA-simplex,KA-simplicial complex,KA-simplicial homology group by means of a K-adjacency relation,and prove that KA-simplicial homology groups are isomorphic invariant,but not homotopic type invariant.Secondly,we define a KA-surface,calculate the homology groups of the KA-surface and by examples show differences of homology groups in the category of KAC and DTC.Thirdly,we consider simple operations of digital image and their influence on the calculation of homology groups,discuss some properties of Euler characteristic of K-adjacent digital images.Finally,we also introduce KA-relative homology groups and discuss the exact homology sequence and its applications.