A differential equation model of retinal processing for understanding lightness optical illusions

This paper proposes a differential equation model of the human vision system. Our model has a hierarchical structure in the known retinal cell neural network, and hence, enable to explain what aspects of behaviors of the vision system is affected by which parameters. As the result, our model possesses the following two characteristics: First, it enable the derivation of an integral equation model with a Mexican-hat shape kernel as a necessary result of mechanisms (reduction of the retinal image resolution and a self-control mechanism formed by non-local interaction), in contrast to previous models that assumed various types of Mexican-hat shapes a priori. Second, it can explain two mutually contradicting phenomena called lightness contrast and assimilation. Moreover, our model explains the reason why lightness optical illusions do or do not occur via the magnitude of a control parameter.