Application of mathematics in the representation of images: From geometry to set theory

Abstract

Mathematics has long been applied to images, especially in a number of ways that rely on categorizing visible properties not just geometrically, that is, spatially, but also algebraically or quantitatively. In Part 1 I have discussed how fuzzy set theory has been applied to the empirical (Zadeh) and conceptual (Smith) understanding of linguistic vagueness as a quantitative, conceptually precise model of categorization practices. Visual description and experience take meaningful place only within the context set by a perceptual system. From a categorization standpoint, it makes sense to claim that linguistic and visual indeterminacy and vagueness are inseparable. As a result, the same formal approaches should be, at least heuristically, and have been applied to images, and this in two different ways I call synthetic and analytic.