The Human Contrast Sensitivity Function Reflects Nonlinear Dynamics

Many processes of visual perception may be modelled by nonlinear systems. I here present a novel nonlinear analysis of contrast sensitivity data. My point of departure was the similarity in shape of (i) curves giving threshold contrast as a function of spatial modulation frequency, and (ii) the envelope of bifurcational diagrams obtained from the logistic equation. It should be noted that the well-known changes of curvature for spatial frequencies above 20 cycles deg⁻¹ are now being discussed in the literature as a problem of the last or finest channel [Kulikowski, 1991, in Limits of Vision Eds J J Kulikowski, V Walsh, I J Murray, volume 5 of Vision and Visual Dysfunction Ed. J Cronly-Dillon (London: Macmillan) pp 286–329].

Numerical simulations of threshold contrast as a function of spatial frequency were carried out on the basis of the logistic equation appropriately adapted to the problem. Several linear transformations of the equation were used for determining the parameters that would provide the best fit to the experimental data. The model introduces the concept of perceptual cycle that can be used for characterising the dynamics of selectivity in the spatial frequency domain in its dependence on grating contrast.