Simplicial Cohomology Of K-topological Adjacency Digital Image

The basis of digital image processing is the digital image analysis.The topological method is important for digital image analysis.One of the basic problems in digital image analysis is to determine whether images are isomorphic,so isomorphic invariants become an effective tool for digital image analysis.The K-product topological structure could be given on the n-dimensional digital space to establish the K-topological adjacency category(KAC).In this category,the K-topological adjacency relationship between pixels of digital images has been established,and the concepts of KA-simplex and KA-simplicial complex associated with digital im-ages has been given.On this basis,the concepts of KA-simplicial cohomology group and cohomology ring of digital images are introduced.It is proved that KA-simplicial cohomology groups and cohomology rings are KA-isomorphic invariants of digital images,but are not homotopic invariants.In the K-topological adjacency category,the concept of KA-relative cohomology group is also introduced,and the coincidence sequences and excision theorem of KA-simplicial cohomology group are proved.The sequences and ex-cision theorem provide an important tool for the calculation of KA-simplicial cohomology groups.We compare the similarities and differences between KA-simplicial cohomology group and the digital k-cohomology group,and also calculate the KA-simplicial cohomol-ogy groups of digital images with typical structures,such as KA-simple closed curves.