Topology-preserving digitization of n-dimensional objects by constructing cubical models

This paper proposes a new cubical space model for the representation of continuous objects and surfaces in the n-dimensional Euclidean space by discrete sets of points. The cubical space model concerns the process of converting a continuous object in its digital counterpart, which is a graph, enabling us to apply notions and operations used in digital imaging to cubical spaces. We formulate a definition of a simple n-cube and prove that deleting or attaching a simple n-cube does not change the homotopy type of a cubical space. Relying on these results, we design a procedure, which preserves basic topological properties of an n-dimensional object, for constructing compressed cubical and digital models.Comment: 9 pages, 8 figures. arXiv admin note: text overlap with arXiv:1503.0349

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

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;Comment: 12 pages, 10 figure