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• W2018987582 abstract "The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the maximal one, corresponding to 3ni1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested." @default.
• W2018987582 created "2016-06-24" @default.
• W2018987582 creator A5059470360 @default.
• W2018987582 date "2006-08-18" @default.
• W2018987582 modified "2023-10-03" @default.
• W2018987582 title "Axiomatic Digital Topology" @default.
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• W2018987582 doi "https://doi.org/10.1007/s10851-006-7453-6" @default.
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