The consistency principle for a digitization procedure. An algorithm for building normal digital spaces of continuous n-dimensional objects

Abstract

This paper considers conditions, which allow to preserve important topological and geometric properties in the process of digitization. For this purpose, we introduce a triplet {C,M,D} consisting of a continuous object C, an intermediate model M, which is a collection of subregions whose union is C, a digital model D, which is the intersection graph of M, and apply the consistency principle and criteria of similarity to M in order to make its mathematical structure consistent with the natural structure of D. Specifically, this paper introduces a locally centered lump collection of subregions and shows that for any locally centered lump cover of an n-dimensional continuous manifold, the digital model of the manifold is a digital normal n-dimensional space. In addition, we give examples of locally centered lump tilings of two-manifolds. We propose an algorithm for constructing normal digital models of continuous objects.