Topology preserving representations of compact 2D manifolds by digital 2-surfaces. Compressed digital models and digital weights of compact 2D manifolds. Classification of closed surfaces by digital tools

Abstract

Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the geometry and topology of their continuous counterparts. In the framework of the proposed models, we show that for any closed surface there exists a compressed model of this surface with the minimal number of points. Key words: Closed Surface; Digital space; Cover; Graph; Digital model; Medical imaging;