COMPARISON OF CONTRAST-NORMALIZATION AND THRESHOLD MODELS OF THE RESPONSES OF SIMPLE CELLS IN CAT STRIATE CORTEX

In almost every study of the linearity of spatiotemporal summation in simple cells of the cat's visual cortex, there have been systematic mi smatches between the experimental observations and the predictions of the linear theory. These mismatches have generally been explained by s upposing that the initial spatiotemporal summation stage is strictly l inear, but that the following output stage of the simple cell is subje ct to some contrast-dependent nonlinearity. Two main models of the out put nonlinearity have been proposed: the threshold model (e.g. Tolhurs t & Dean, 1987) and the contrast-normalization model (e.g. Heeger, 199 2a,b). In this paper, the two models are fitted rigorously to a variet y of previously published neurophysiological data, in order to determi ne whether one model is a better explanation of the data. We reexamine data on the interaction between two bar stimuli presented in differen t parts of the receptive field; on the relationship between the recept ive-field map and the inverse Fourier transform of the spatial-frequen cy tuning curve; on the dependence of response amplitude and phase on the spatial phase of stationary gratings; on the relationships between the responses to moving and modulated gratings; and on the suppressiv e action of gratings moving in a neuron's nonpreferred direction. In m any situations, the predictions of the two models are similar, but the contrast-normalization model usually fits the data slightly better th an the threshold model, and it is easier to apply the equations of the normalization model. More importantly, the normalization model is nat urally able to account very well for the details and subtlety of the r esults in experiments where the total contrast energy of the stimuli c hanges; some of these phenomena are completely beyond the scope of the threshold model. Rigorous application of the models' equations has re vealed some situations where neither model fits quite well enough, and we must suppose, therefore, that there are some subtle nonlinearities still to characterized.