An Analytical Derivation of Visual Nonlinearity

Many visual phenomena, in particular, visual discrimination performance as a function of light intensity, have been attributed to a, nonlinearity in the retinal stages of the visual system. A comprehensive analytical quantified derivation of the nonlinearity based upon an optimum processor approach to visual perception is presented. The account follows optimum decision rules described by likelihood ratio tests applied to Poisson processes. The processor is constrained in ways inferred from empirical phenomena, particularly visual discrimination performance. A nonlinearity of the type y(x) = [log (x)]2, x 1, is mathematically derived applying rigorous engineering principles from statistical communications and signal detection theory. It is shown that this nonlinearity is in full conformity with known visual performance and the ideal detection hypothesis. The results are then confronted with actual physiological data to fimd a visual-system mechanistic correlate.