Digital Topology and the Application to GIS

Digital topology is mainly to study the topological properties of discrete geometric objects,which are obtained by digitizing continuous objects.Digital topology plays a very important role in computer vision,image processing and GIS.It is essential to the spatial raster data structure of GIS; in fact,all spatial analysis about raster data is based on the digital topology.Graph-theoretic approach,imbedding approach and axiomatic approach are three main approaches for defining a digital topological analog of the Euclidean space.In this paper,the main contents of digital topology in graph-theoretic approach,imbedding approach and axiomatic approach are introduced.It is pointed out that most of the research results on 2D Euclidean space are related with graph-theoretic approach,in which digital topology is based on the (4,8) adjacency.The application of digital topology to GIS field about graph-theoretic approach is discussed.It is suggested that 3D digital topology and spherical surface digital topology is the two main developing directions.3D digital topology is based on the (6,18,26) adjacency,and the spherical surface digital topology is based on the (3,12) adjacency.