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

TL;DR

This paper develops digital models of closed 2D surfaces using digital topology, enabling topology-preserving representations and minimal point models for classification and analysis.

Contribution

It introduces a method to construct digital models of closed surfaces as intersection graphs of LCL covers, preserving topology and geometry, and identifies minimal point models.

Findings

Digital models are topology-preserving and geometrically faithful.

Existence of compressed models with minimal points for any closed surface.

Framework applicable to medical imaging and surface classification.

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;