On the generation of representational spaces in perceptual systems

Abstract

Perceptual Systems are here understood in the sense of Minsky and therefore are structures having three parts: a multisensorial structure facing the environment which provides data fields, a transformation structure acting on data fields through operations which range from analytical to algorithmic, and a projection structure where a dynamic sensory model of the environment is built. Within this context, Mira and Moreno-Díaz, have laid the foundations for the development of a general and theoretical frame, which is very useful not only in the interpretation of neural function but also in the generation and description of Transformations in Artificial Vision. Based on that proposal and considering the visual system as a subsystem of a more general one which includes it, we have developed formal schemes of representation, which allow us to clarify some of their properties. As it is customary in models of early vision, we treat the early representations as linear systems with an optional pointwise nonlinearity applied to the output of the system, under the assumption that the successive stages of processing remap the retinal representation space in a manner that makes similar stimuli closer to each other, and dissimilar stimuli farther apart. We present a theoretical analysis and simulate the visual representations through the successive levels of the visual pathway, from the retina to the nonlinear cortical units, and we present computational experiments at the photoreceptor level. This analysis neglects the essentially nonlinear process of light adaptation in the retina, but it is valid for images in which the mean illumination level is roughly constant.