Sphere digital space based on manifold: definition, properties and applications

SGDM (Sphere Grid Data Model) is an efficient method of dealing with global data because of its advantages of multiple resolution and hierarchy. Several studies have been examined many aspects of the model. However, SGDM has no distinct descriptions and lack of round mathematical basis for various applications. To overcome this deficiency, this paper constructs a regular mesh structure for sphere; i.e., the digitization of the spherical surface as a common spatial framework, such as a planar. First, the definition of sphere digital space based on manifold is given. The characteristics of sphere digital space are then presented in detail, and compared with planar digital space in the aspects of topology, metric and order relationships. In the end, some potential applications and possible future studies are discussed briefly. Computers are digital, and most efforts at image acquisition and communication are currently directed towards digital approaches. Therefore, it is convenient to analyse the global data and make decisions in sphere digital space.