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Proceedings Paper

Nearly continuous functions in digital images
Author(s): Longin Jan Latecki; Frank Prokop
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Paper Abstract

Starting with the intuitive concept of `nearness' as a binary relation, semi-proximity spaces (sp-spaces) are defined. The restrictions on semi-proximity spaces are weaker than the restrictions on topological proximity spaces. Nevertheless, semi-proximity spaces generalize classical topological spaces. Moreover, it is possible to describe all digital pictures used in computer vision and computer graphics as non-trivial semi-proximity spaces, which is not possible in classical topology. Therefore, we use semi-proximity spaces to establish a formal relationship between the `topological' concepts of digital image processing and their continuous counterparts in Rn. Especially interesting are continuous functions in semi- proximity spaces. The definition of a `nearly' bicontinuous function is given which does not require the function to be one-to-one. A nearly bicontinuous function preserves connectedness in both directions. Therefore, nearly bicontinuous functions can be used for characterizing well-behaved operations on digital images such as thinning. Further, it is shown that the deletion of a simple point can be treated as a nearly bicontinuous function. These properties and the fact that a variety of nearness relations can be defined on digital pictures indicate that nearly continuous functions are a useful tool in the difficult task of shape description.

Paper Details

Date Published: 4 January 1995
PDF: 12 pages
Proc. SPIE 2356, Vision Geometry III, (4 January 1995); doi: 10.1117/12.198618
Show Author Affiliations
Longin Jan Latecki, Univ. of Hamburg (United States)
Frank Prokop, Univ. of Wollongong (Australia)

Published in SPIE Proceedings Vol. 2356:
Vision Geometry III
Robert A. Melter; Angela Y. Wu, Editor(s)

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