Nonlinearity in Simple and Complex Cells in Early Biological Visual Systems

The nonlinear model put forward in Mahmoodi (J Math Imaging Vis 54(2):138-161, 2016) for early visual systems is investigated in detail in this paper to explain some nonlinear behaviours of complex and some simple cells. Nonlinear cells are modelled as systems with linear-nonlinear structures where the linear sub-unit is constructed by the layers proposed in Mahmoodi (2016) and nonlinear sub-units are the results of an axon (modelled as a transmission line) carrying a series of spikes. In this paper, the nonlinear sub-systems of complex cells are investigated in more detail to show the mechanism by which nonlinear neurons work. Here the nonlinear systems modelling nonlinear sub-units of complex cells are represented by their first- and second-order responses. Our analytical as well as numerical results show good agreements with biological recordings reported in the literature.