In this paper we investigate properties of digital spaces which are represented by graphs. We find conditions for digital spaces to be digital n-manifolds and n-spheres. We study properties of partitions of digital spaces and prove a digital analog of the Jordan-Brouwer theorem for the normal digital n-space Z n .
A point of a digital space is called simple if it can be deleted from the space without altering topology. This paper introduces the notion simple set of points of a digital space. The definition is based on contractible spaces and contractible transformations. A set of points in a digital space is called simple if it can be contracted to a point without… (More)
This paper proposes a new cubical space model for the representation of continuous objects and surfaces in the n-dimensional Euclidean space by discrete sets of points. The cubical space model concerns the process of converting a continuous object in its digital counterpart, which is a graph, enabling us to apply notions and operations used in digital… (More)
Methods of digital topology are widely used in various image processing operations including topology-preserving thinning, skeletonization, simplification, border and surface tracing and region filling and growing. Usually, transformations of digital objects preserve topological properties. One of the ways to do this is to use simple points, edges and… (More)
One of the aims in the field of computer vision is to find a digitization process, which preserves main features of continuous objects in their digital models and study the mathematical structure of digital models by discrete methods which do not require the existence of continuous sources. Several approaches based on discrete frameworks have been proposed… (More)
In this work, we define a parabolic equation on digital spaces and study its properties. The equation can be used in investigation of mechanical, aerodynamic, structural and technological properties of a Moebius strip, which is used as a basic element of a new configuration of an airplane wing. Condition for existence of exact solutions by a matrix method… (More)