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

2005/11/16 by Alexander V. Evako, Evako, Alexander V.
Computer Science · #Computer Vision and Pattern Recognition (cs.CV) #Digital Image Processing Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #G.2.2 #I.3.5 #I.5.1 #cs.CV #cs.DM

paper · pdf · doi:10.48550/arxiv.cs/0511064

13 pages, 11 figures

arxiv created 2005/11/16 · openalex publication_date 2005/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Topology-preserving digitization of n-dimensional objects by constructing cubical models
• Simple pairs of points in digital spaces. Topology-preserving transformations of digital spaces by contracting simple pairs of points
• Variable density preserving topology grids and the digital models for the plane
• The Poincare conjecture for digital spaces. Properties of digital n-dimensional disks and spheres
• Introduction to the theory of digital spaces