In almost every study of the linearity of spatiotemporal summation in simple cells of the cat's visual cortex, there have been systematic mismatches between the experimental observations and the predictions of the linear theory. These mismatches have generally been explained by supposing that the initial spatiotemporal summation stage is strictly linear, but that the following output stage of the simple cell is subject to some contrast-dependent nonlinearity. Two main models of the output nonlinearity have been proposed: the threshold model (e.g. Tolhurst & Dean, 1987) and the contrast-normalization model (e.g. Heeger, 1992a, b). In this paper, the two models are fitted rigorously to a variety of previously published neurophysiological data, in order to determine whether one model is a better explanation of the data. We reexamine data on the interaction between two bar stimuli presented in different parts of the receptive field; on the relationship between the receptive-field map and the inverse Fourier transform of the spatial-frequency 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 suppressive action of gratings moving in a neuron's nonpreferred direction. In many situations, the predictions of the two models are similar, but the contrast-normalization model usually fits the data slightly better than the threshold model, and it is easier to apply the equations of the normalization model. More importantly, the normalization model is naturally able to account very well for the details and subtlety of the results in experiments where the total contrast energy of the stimuli changes; some of these phenomena are completely beyond the scope of the threshold model. Rigorous application of the models' equations has revealed some situations where neither model fits quite well enough, and we must suppose, therefore, that there are some subtle nonlinearities still to be characterized.

Previous studies of cat visual cortex have shown that the spatiotemporal (S-T) structure of simple cell receptive fields correlates with direction selectivity. However, great heterogeneity exists in the relationship and this has implications for models. Here we report a laminar basis for some of the heterogeneity. S-T structure and direction selectivity were measured in 101 cells using stationary counterphasing and drifting gratings, respectively. Two procedures were used to assess S-T structure and its relation to direction selectivity. In the first, the S-T orientations of receptive fields were quantified by fitting response temporal phase versus stimulus spatial phase data. In the second procedure, conventional linear predictions of direction selectivity were computed from the amplitudes and phases of responses to stationary gratings. Extracellular recording locations were reconstructed histologically. Among direction-selective cells, S-T orientation was greatest in layer 4B and it correlated well (r = 0.76) with direction selectivity. In layer 6, S-T orientation was uniformly low, overlapping little with layer 4B, and it was not correlated with directional tuning. Layer 4A was intermediate in S-T orientation and its relation (r = 0.46) to direction selectivity. The same laminar patterns were observed using conventional linear predictions. The patterns do not reflect laminar differences in direction selectivity since the layers were equivalent in directional tuning. We also evaluated a model of linear spatiotemporal summation followed by a static nonlinear amplification (exponent model) to account for direction selectivity. The values of the exponents were estimated from differences between linearly predicted and actual amplitude modulations to counterphasing gratings. Comparing these exponents with another exponent—that required to obtain perfect matches between linearly predicted and measured directional tuning—indicates that an exponent model largely accounts for direction selectivity in most cells in layer 4, particularly layer 4B, but not in layer 6. Dynamic nonlinearities seem essential for cells in layer 6. We suggest that these laminar differences may partly reflect the differential involvement of geniculocortical and intracortical mechanisms.