Perceptual Tolerance Intersection

This paper elaborates on the introduction of perceptual tolerance intersection of sets as an example of a near set operation. Such operations are motivated by the need to consider similarities between digital images viewed as disjoint sets of points. The proposed approach is in keeping with work by E.C. Zeeman on tolerance spaces and visual perception and work by J.H. Poincare on sets of similar sensations used to define representative spaces (aka tolerance spaces) such as visual, tactile and motile spaces. Perceptual tolerance intersection of sets is a direct consequence of recent work on near sets. The theory of perceptual set intersection has many practical applications such as a solution to the problem of how one goes about measuring the closeness of digital images. The main contribution of this article is a description-based approach to formulating perceptual set intersections between disjoint sets that resemble each other. A practical application of the proposed approach is the discovery of resemblances between sets of points in digital image regions that represent tolerance rough sets.