A compression of digital images derived from a Khalimsky topological structure

DOI10.1007/s40314-013-0034-6zbMath1300.54012OpenAlexW2063264830MaRDI QIDQ382455

Sang-Eon Han, Alexander P. Šostak

Publication date: 19 November 2013

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-013-0034-6

zbMATH Keywords

compressiondigital topologydigital geometrydigital image\(A\)-isomorphism\(A\)-mapKhalimsky \(n\mathrm D\) spaceKhalimsky adjacencyKhalimsky homeomorphism

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Continuous maps (54C05) Topological characterizations of particular spaces (54F65) Weak and generalized continuity (54C08) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10)

Related Items (21)

Digital topological rough set structures and topological operators ⋮ Topologies associated with the one point compactifications of Khalimsky topological spaces ⋮ Terse walk sets in graphs and induced closure operators ⋮ Closure operators on graphs for modeling connectedness in digital spaces ⋮ Existence of the category \(\mathit{DTC}_2(k)\) equivalent to the given category \(\mathit{KAC}_2\) ⋮ Semi-topological properties of the \(K\)-topological version of the Jordan curve theorem ⋮ Generalizations of continuity of maps and homeomorphisms for studying 2D digital topological spaces and their applications ⋮ Existence of a proper subspace of \(( \mathbb{Z}^n, ( T_{S_k} )^n)\) which is homeomorphic to the \(n\)-dimensional Khalimsky topological space ⋮ Semi-separation axioms of the infinite Khalimsky topological sphere ⋮ On approximate-type systems generated by \( L\)-relations ⋮ Homotopic properties of $KA$-digitizations of $n$-dimensional Euclidean spaces ⋮ A digitization method of subspaces of the Euclidean \(n\)D space associated with the Khalimsky adjacency structure ⋮ Digitizations associated with several types of digital topological approaches ⋮ Alexandroff pretopologies for structuring the digital plane ⋮ Covering rough set structures for a locally finite covering approximation space ⋮ Digital Space-Type Fixed Point Theory and Its Applications ⋮ Jordan surface theorem for simple closed \textit{SST}-surfaces ⋮ SOME PROPERTIES OF LATTICE-BASED K- AND M-MAPS ⋮ Topological properties of locally finite covering rough sets and \(K\)-topological rough set structures ⋮ The fixed point property of the smallest open neighborhood of the n-dimensional Khalimsky topological space ⋮ Topological graphs based on a new topology on Zn and its applications

Cites Work

• Unnamed Item
• Homotopy equivalence which is suitable for studying Khalimsky \(n\)D spaces
• Computer graphics and connected topologies on finite ordered sets
• A Jordan surface theorem for three-dimensional digital spaces
• CONTINUITIES AND HOMEOMORPHISMS IN COMPUTER TOPOLOGY AND THEIR APPLICATIONS
• ‘Continuous’ functions on digital pictures
• Compression of Khalimsky topological spaces

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