Topological properties of closed digital spaces: One method of constructing digital models of closed continuous surfaces by using covers

Evako, Alexander V.

doi:10.1016/j.cviu.2003.11.003

Cited by 17 publications

(20 citation statements)

References 6 publications

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“…This section includes results obtained in [4,5,6,10,13,14] and related to the structure of graphs that are digital ndimensional spaces which were defined in [4].…”

Section: Digital N-dimensional Surfaces and Homeomorphismmentioning

confidence: 99%

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Graph Theoretical Models of Discrete Spaces with Locally Non-spherical Topology

Evako¹

2017

AMP

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A graph theoretical model of a continuous space is a graph with the same topological structure as its continuous counterpart. A digital closed n-dimensional manifold with a locally spherical topology is a graph theoretic model for a continuous closed n-dimensional manifold. This paper defines and studies properties of a new class of digital n-dimensional spaces with a locally non-spherical topology. We prove that such spaces have the dimension n≥3. We define and investigate properties of digital 3-and 5-dimensional closed surfaces with a local toroidal and projective plane topology. These spaces have no direct continuous counterparts among n-dimensional manifolds in classical topology. These results arise questions like what physical, chemical or biological structures can be described by digital n-dimensional surfaces with a locally non-spherical topology. Keywords

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“…This section includes results obtained in [4,5,6,10,13,14] and related to the structure of graphs that are digital ndimensional spaces which were defined in [4].…”

Section: Digital N-dimensional Surfaces and Homeomorphismmentioning

confidence: 99%

“…In paper [4], digital n-surfaces were defined as simple undirected graphs and basic properties of n-surfaces were studied. Properties of digital n-manifolds were investigated in ( [5,6,9,10]). …”

Section: Introductionmentioning

confidence: 99%

Graph Theoretical Models of Discrete Spaces with Locally Non-spherical Topology

Evako¹

2017

AMP

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“…G 7 and G 8 have no simple pairs, and cannot be converted to G 5 by sequential contractions of simple pairs. Properties of a digital sphere, a digital torus and a digital projective plane were studied in [8] [9]. Digital 2-surfaces can be used to construct topologically correct digital models of segmented medical images.…”

Section: Remark 31mentioning

confidence: 99%

“…Collections of 2-cells are depicted in , , In papers [8], locally centered collections were studied it was shown that for a given object, the intersection graphs of all continuous, regular and contractible covers are homotopic to each other. There is a significant number of papers which investigate collections of sets in 2D and 3D (see, e.g., [3]- [5] [9]- [12]).…”

Section: Facts 21mentioning

confidence: 99%

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Topology Preserving Discretization Schemes for Digital Image Segmentation and Digital Models of the Plane

Evako¹

2014

OALib

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In this paper, discretization schemes are defined and studied that allow us to build digital models of 2-dimensional continuous objects with the same topological properties as their continuous counterparts. In particular, it is shown that the digital model of the plane is necessarily the digital 2-surface defined and studied in the context of digital topology. It is shown that in proposed discretization schemes, any required resolution can be used in any area of the object of interest. Finally, we describe a method, which transforms regions of interest produced by the image acquisition process into digital spaces with topological features of the regions.

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