The Basic Topology Model of Spherical Surface Digital Space

SGDM (Sphere Grid Data Model) is an efficient method to deal with the global data because of the advantages of multi-resolution and hierarchy. However, SGDM has no distinct descriptions and lack of round mathematical basis for various applications. What’s more, most of mathematical model about global application have been based on the continuous methods. Although several researchers have considered the digital topology in 2-dimension and 3-dimension Euclidean Plane, complete theoretical foundation of proper theory for spherical surface digital space is still missing. In fact, it’s more convenient and efficient to compute spatial relationship based on spherical surface digital space. Firstly, this paper constructs spherical surface digital space based on manifold, i.e. the digitization of the spherical surface as a common spatial framework just as planar. Secondly, the concept of spherical surface digital topology will be given in the context of adjacency. We define a spherical surface digital image P as a triplet ) , , ( 2 H R T , where H is a finite subset of 2 T and R represents the adjacency relation in the whole lattice in a specific way. Then topological properties and paradox of discrete objects will be discussed in spherical surface digital space. In the end, we give some potential applications about spherical surface digital topology.