Affiliations: Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, E1-526 EITC, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6, Canada. james.peters3@ad.umanitoba.ca; s.ramanna@uwinnipeg.ca
Note: [] Address for correspondence: Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, E1-526 EITC, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6, Canada. This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grants 185986 and 194376 as well as Network of Excellence grants, 2008-2013, from the Province of Manitoba.
Note: [] Also is a Professor in: Department of Applied Computer Science, University of Winnipeg, 515 Portage Ave., Winnipeg, R3B 2E9, Canada
Abstract: This paper introduces descriptive set patterns that originated from our visits with Zdzisław Pawlak and Andrzej Skowron at Banacha and environs in Warsaw. This paper also celebrates the generosity and caring manner of Andrzej Skowron, who made our visits to Warsaw memorable events. The inspiration for the recent discovery of descriptive set patterns can be traced back to our meetings at Banacha. Descriptive set patterns are collections of near sets that arise rather naturally in the context of an extension of Solomon Leader's uniform topology, which serves as a base topology for compact Hausdorff spaces that are proximity spaces. The particular form of proximity space (called EF-proximity) reported here is an extension of the proximity space introduced by V. Efremovič during the first half of the 1930s. Proximally continuous functions introduced by Yu.V. Smirnov in 1952 lead to pattern generation of comparable set patterns. Set patterns themselves were first considered by T. Pavlidis in 1968 and led to U. Grenander's introduction of pattern generators during the 1990s. This article considers descriptive set patterns in EF-proximity spaces and their application in digital image classification. Images belong to the same class, provided each image in the class contains set patterns that resemble each other. Image classification then reduces to determining if a set pattern in a test image is near a set pattern in a query image.
Keywords: Descriptive set pattern, EF-proximity, Grenander pattern generator, near sets, proximally continuous function, proximity space, uniform topology
