The consistency principle for a digitization procedure An algorithm for building normal digital spaces of continuous n-dimensional objects
<|reference_start|>The consistency principle for a digitization procedure An algorithm for building normal digital spaces of continuous n-dimensional objects: 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.<|reference_end|>
@article{evako2005the,
    title={The consistency principle for a digitization procedure. An algorithm for
  building normal digital spaces of continuous n-dimensional objects},
    author={Alexander V. Evako},
    journal={arXiv preprint arXiv:cs/0511064},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0511064},
    primaryClass={cs.CV cs.DM}
}