Affiliations: Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6 Canada. jfpeters@ee.umanitoba.ca | Institute of Mathematics, The University of Warsaw, Banacha 2, 02-097 Warsaw, Poland. skowron@mimuw.edu.pl | Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland. j.stepaniuk@pb.edu.pl
Note: [] Address for correspondence: Institute of Mathematics, The University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Abstract: The problem considered in this paper is how to describe and compare visual objects. The solution to this problem stems from a consideration of nearness relations in two different forms of Efremovič proximity spaces. In this paper, the visual objects are picture elements in digital images. In particular, this problem is solved in terms of the application of rough sets in proximity spaces. The basic approach is to consider the nearness of the upper and lower approximation of a set introduced by Z. Pawlak during the early 1980s as a foundation for rough sets. Two forms of nearness relations are considered, namely, a spatial EF- and a descriptive EF-relation. This leads to a study of the nearness of objects either spatially or descriptively in the approximation of a set. The nearness approximation space model developed in 2007 is refined and extended in this paper, leading to new forms of nearness approximation spaces. There is a natural transition from the two forms of nearness relations introduced in this article to the study of nearness granules.
