  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.
