Discovering Affinities between Perceptual Granules

Abstract

This paper proposes an approach to detecting affinities between perceptual objects contained in perceptual granules such as images with tolerance near preclasses. A perceptual object is something perceptible to the senses or knowable by the mind. Perceptual objects that have similar appearance are considered perceptually near each other, i.e., perceived objects that have perceived affinities or, at least, similar descriptions.A perceptual granule is a finite, non-empty set containing sample perceptual objects with common descriptions. Perceptual granules originate from observations of the objects in the physical world. Similarities between perceptual granules are measured within the context of what is known as a tolerance near space. This form of tolerance space is inspired by C.E. Zeeman’s work on visual perception and Henri Poincaré’s work on the contrast between mathematical continua and the physical continua in a pragmatic philosophy of science that laid the foundations for tolerance spaces. The perception of nearness or closeness that underlies tolerance near relations is rooted in Maurice Merleau-Ponty’s work on the phenomenology of perception during the mid-1940s, and, especially, philosophical reflections on description of perceived objects and the perception of nearness. Pairs of perceptual granules such as images are considered near each other to the extent that tolerance near preclasses of sufficient magnitude can be found. The contribution of this paper is the introduction of L ₂ norm-based tolerance near preclasses in detecting affinities between images.