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

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dc.creatorEvako, Alexander V.
dc.date2005-11-16
dc.date.accessioned2026-07-07T06:49:36Z
dc.date.available2026-07-07T06:49:36Z
dc.descriptionThis 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.
dc.description13 pages, 11 figures
dc.identifierhttps://arxiv.org/abs/cs/0511064
dc.identifierhttp://arxiv.org/abs/cs/0511064
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104411
dc.subjectComputer Vision and Pattern Recognition
dc.subjectDiscrete Mathematics
dc.subjectI.3.5; I.5.1; G.2.2
dc.titleThe consistency principle for a digitization procedure. An algorithm for building normal digital spaces of continuous n-dimensional objects
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