Continuous digitization in Khalimsky spaces
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منابع مشابه
Continuous digitization in Khalimsky spaces
A real-valued function defined on R can sometimes be approximated by a Khalimsky-continuous mapping defined on Z. We elucidate when this can be done and give a construction for the approximation. This approximation can be used to define digital Khalimsky hyperplanes that are topological embeddings of Z into Z. In particular, we consider Khalimsky planes in Z and show that the intersection of tw...
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We consider the digital plane of integer points equipped with the Khalimsky topology. We suggest a digitization of straight lines such that the digitized image is homeomorphic to the Khalimsky line and a digitized line segment is a Khalimsky arc. It is demonstrated that a Khalimsky arc is the digitization of a straight line segment if and only if it satisfies a generalized version of the chord ...
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Melin, E. 2008. Digital Geometry and Khalimsky Spaces (Digital geometri och Khalimskyrum). Uppsala Dissertations in Mathematics 54. vii+47 pp. Uppsala. ISBN 978-91-506-1983-6 Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young. Efim Khalimsky’s topology on the integers, invented in t...
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The digital space Z equipped with Efim Khalimsky’s topology is a connected space. We study continuous functions Z ⊃ A→ Z, from a subset of Khalimsky n-space to the Khalimsky line. We give necessary and sufficient condition for such a function to be extendable to a continuous function Z → Z. We classify the subsets A of the digital plane such that every continuous function A → Z can be extended ...
متن کاملConnectedness and continuity in digital spaces with the Khalimsky topology
2 Digital spaces 3 2.1 Topology in digital spaces . . . . . . . . . . . . . . . . . . . . 3 2.2 Spaces with a smallest basis . . . . . . . . . . . . . . . . . . . 4 2.3 Connectedness . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 General topological properties . . . . . . . . . . . . . . . . . . 5 2.5 Topologies on the Digital Line . . . . . . . . . . . . . . . . . . 7 2.6 The Khalim...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2008
ISSN: 0021-9045
DOI: 10.1016/j.jat.2007.06.003