Nearness of covering uniformities: theory and application in image analysis. (English) Zbl 1262.68173
Summary: This paper applies the concepts of proximity and uniform spaces in an image processing (IP) application [J. R. Isbell, Uniform spaces. Mathematical Surveys. 12. Providence, R.I.: American Mathematical Society (AMS) (1964; Zbl 0124.15601); A. Di Concilio, Contemp. Math. 486, 89–114 (2009; Zbl 1192.54010)]. 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 Am. Math. Soc. 59, No. 4, 536–542 (2012; Zbl 1251.68301)].
MSC:
| 68U10 | Computing methodologies for image processing |
| 54E05 | Proximity structures and generalizations |
| 54E17 | Nearness spaces |
Software:
SIMPLIcityReferences:
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