The law of perceptual stability: well-definedness and validity.

Axiomatic foundations for a theory of perception have been given in a prior communication [Shiman, L. G. (1978) Proc. Natl. Acad. Sci. USA 75, 2049-2053]. The theory is based on mathematically characterized stable images. Stable images model subjective (psychological) states of observers. We showed there is a universal procedure by which such stable images can be assigned to objects of perception (icons), employing observer-dependent perceptual judgements. We construct an abstract model for an icon from the mathematical structure of a stable image that has been assigned to it. We identify the model with the icon. By identifying the model with the object of perception, we can analyze perception of the icon in terms of the mathematical properties of its associated stable images. Thus subjective phenomena, in this mathematical form, can be used to analyze the mechanisms of sensory processes. Grounds for validity of the stability law are given. The procedures are demonstrably universal. A stable image, although subjectively derived from an icon, is a mathematical entity, and has therefore objective status. Stable images give a natural and potentially complete (mathematical) classification of icons, along nontraditional lines, which includes a classification and account of many well-known "visual illusions."Extension of this (static) theory to include time-dependent (kinetic) cases is outlined. We consider grammar for vision, semantics, and the role of stability theory in constructing a unified theory of vision and natural languages.