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Nearness of Covering Uniformities: Theory and Application in Image Analysis

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Abstract

This paper applies the concepts of proximity and uniform spaces in an image processing (IP) application (Isbell, Uniform spaces, vol 12, American Mathematical Society, Providence, 1964; Di Concilio, Beyond Topology, AMS Contemporary Mathematics, vol. 486, Amer. Math. Soc. pp. 89–114, 2009). Application of these mathematical concepts to a digital image space and considering the time constraint of IP applications requires some modifications to the actual definitions. The paper presents a method to find a nearness measure between images based on these concepts. Given a pair of digital images, the basic approach starts with the approximation of the covering uniformity (\({\hat{\mathcal{C}}}\)) of the first image and then restricts the search on the second image based on proximities between the elements of \({\hat{\mathcal{C}}}\) and descriptive neighborhoods in the second image. This work carries forward the basic approach to descriptively near sets from the work by J.F. Peters and S.A. Naimpally (Notices Amer. Math. Soc, vol. 59(4), pp. 536–542, 2012).

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  1. Department of Applied Computer Science, University of Winnipeg, Winnipeg, R3B 2E9, Canada

    Homa Fashandi

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  1. Homa Fashandi
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Fashandi, H. Nearness of Covering Uniformities: Theory and Application in Image Analysis. Math.Comput.Sci. 7, 43–50 (2013). https://doi.org/10.1007/s11786-013-0142-0

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