Results 1 to 10 of about 42,065 (261)
Homotopy Theory in Digital Topology [PDF]
Discrete and Computational Geometry, 2021 Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some of the most basic notions from homotopy theory remain largely absent from the digital topology literature.
Gregory Lupton +2 more
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A Model for Digital Topology [PDF]
Lecture Notes in Computer Science, 1999 In the framework known as digital topology, two different adjacency relations are used for structuring the discrete space Zn.In this paper, we propose a model for digital topology based on the notion of order and discrete topology. We "validate" our model by considering the two fundamental notions of surface and simple point.
Gilles Bertrand +2 more
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Beyond the Hausdorff metric in digital topology
Applied General Topology, 2022 Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar geometric or ...
Laurence Boxer
doaj +6 more sources
A quotient-universal digital topology
Theoretical Computer Science, 2008 The author defines a topology on \(\mathbb Z^{2}\) which has as its quotients three well-known topologies on \(\mathbb Z^{2}\), including both the Marcus and Khalimsky topologies. In Section 3, a quotient closure operator for this topology is studied and a Jordan curve theorem is proved.
Josef Slapal
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Digital Topology on Adaptive Octree Grids [PDF]
Journal of Mathematical Imaging and Vision, 2009 The theory of digital topology is used in many different image processing and computer graphics algorithms. Most of the existing theories apply to uniform cartesian grids, and they are not readily extensible to new algorithms targeting at adaptive cartesian grids.
Ying Bai, Jerry L Prince
exaly +3 more sources
The topology of digital images
Topology and Its Applications, 1992 In digital imaging one wishes to represent a ''subject'', a set \(P\) in a topological (usually Euclidean) space \(S\), by its ''digital image'', a set \(A\) in a discrete space \(E\). In the applications \(E\) models a set of on/off picture elements. In order to recover topological information about a subject from its digital image, the set \(E\) must
exaly +2 more sources
Convexity and freezing sets in digital topology
Applied General Topology, 2021 We continue the study of freezing sets in digital topology, introduced in [4]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that X is convex.
Laurence Boxer
doaj +1 more source
Remarks on fixed point assertions in digital topology, 5
Applied General Topology, 2022 As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in “digital metric spaces” - assertions that are incorrect or incorrectly proven, or reduce to triviality.
Laurence Boxer
doaj +1 more source
Remarks on fixed point assertions in digital topology, 6
Applied General Topology, 2023 This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.
Laurence Boxer
doaj +1 more source
Topology and its Applications, 2023 In this article, we develop the basic theory of digital topological groups. The basic definitions directly lead to two separate categories, based on the details of the continuity required of the group multiplication. We define $\NP_1$- and $\NP_2$-digital topological groups, and investigate their properties and algebraic structure. The $\NP_2$ category
Dae-Woong Lee, P. Christopher Staecker
openaire +3 more sources