Stimulus dependant alterations in the properties of the optimal contrast response function

Purpose. In an earlier component of this work it was shown that the hyperbolic ratio equation, which is a common model for the physiologic contrast response function (CRF), can be derived exactly by considering the trade-off between information flow and the neural resources available for representing that information. These results demonstrated the essential contribution of nonlinearites of this type to maintaining the quality of the biologic image, and established the relationship between the parameters governing the shape of the nonlinearity and the properties of the stimulus ensemble. Given this relationship, it is reasonable to hypothesize that the properties of the theoretical CRF are altered in a physiologic manner as the properties of the stimulus ensemble are varied. Methods. Analytic and computational solutions of the relevant equations were obtained for different sets of stimulus conditions. Results. Phenomena analogous to contrast gain control and contrast gain normalization are present in solutions to the equations. However, it is necessary to consider the effects of the nonlinearity on information flow in order to obtain meaningful results for the full range of possible inputs. In particular, the non-Gaussian statistics induced by the CRF constrain the solution because the range of possible outputs is now finite, and this leads to additional conditions on the location of the semisaturation constant. Conclusions. The shape and important behaviors of the CRF can be accounted for as an effort by the visual system to maximize information flow while conserving available neural resources.