数字拓扑研究现状及其在GIS中的应用

数字拓扑主要研究栅格空间中离散几何对象的拓扑性质，这些性质在GIS空间分析和栅格数据处理中非常重要。该文从图论、混合拓扑和公理型3方面对数字拓扑的研究现状进行了分类和综述，并讨论数字拓扑在GIS领域的应用，指出三维数字拓扑和球面数字拓扑是数字拓扑在GIS中的两个发展趋势和研究热点。

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.