Laterally induced impedance effects in vision

A linear integral equation for a system of mutually impeding points is developed and solved explicitly. Particular solutions are shown to be subharmonic functions for a large class of stimuli. Specialized forms of the general equation presented in this paper occur within a number of mathematical models of Mach bands. In addition to these known spatial properties, our results also show that the time course of this basic equation may be useful in developing models of transient neural activity as well as of temporal psychophysical phenomena, such as the Broca-Sulzer effect. Further, a spatial transfer function much like the low-frequency cutoff of empirically derived modulation transfer functions follows directly from our basic integral equation if the additional assumption of spatial homogeneity is imposed.