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- Alexander V. Evako, Ralph Kopperman, Yurii V. Mukhin
- Journal of Mathematical Imaging and Vision
- 1996

Many applications of digital image processing now deal with three- and higher-dimensional images. One way to represent n-dimensional digital images is to use the specialization graphs of subspaces of the Alexandroff topological space ℤn (where ℤ denotes the integers with the Khalimsky line topology). In this paper the dimension of any such graph is defined… (More)

In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by means of axioms, and the axioms are based on an obvious geometrical background. This work presents some discrete models… (More)

- Alexander V. Evako
- Computer Vision and Image Understanding
- 2006

- Alexander V. Evako
- Graphical Models
- 2011

- Alexander V. Evako
- Discrete Mathematics
- 1995

- Alexander V. Evako
- Discrete Applied Mathematics
- 2015

A digital approach to geometry and topology plays an important role in analyzing n-dimensional digitized images arising in computer graphics as well as in many areas of science including neuroscience, medical imaging, industrial inspection, geoscience and fluid dynamics. Concepts and results of the digital approach are used to specify and justify some… (More)

- Alexander V. Evako
- ArXiv
- 2013

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 .

- Alexander V. Evako
- ArXiv
- 2005

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)

- Alexander V. Evako
- ArXiv
- 2014

Methods of digital topology are widely used in various image processing operations including topologypreserving 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)

- Alexander V. Evako
- ArXiv
- 2015

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)