The responses of simple cells were recorded from the visual cortex of cats, as a function of the position and contrast of counterphase and drifting grating patterns, to assess whether direction selectivity can be accounted for on the basis of linear summation. The expected responses to a counterphase grating, given a strictly linear model, would be the sum of the responses to the two drifting components. The measured responses were not consistent with the linear prediction. For example, nearly all cells showed two positions where the responses approached zero (i.e. two “null phase positions”); this was true, even for the most direction selective cells. However, the measured responses were consistent with the hypothesis that direction selectivity is a consequence of the linear spatiotemporal receptive-field structure, coupled with the nonlinearities revealed by the contrast-response function: contrast gain control, halfwave rectification, and expansive exponent. When arranged in a particular sequence, each of these linear and nonlinear mechanisms performs a useful function in a general model of simple cells. The linear spatiotemporal receptive field initiates stimulus selectivity (for direction, orientation, spatial frequency, etc.). The expansive response exponent enhances selectivity. The contrast-set gain control maintains selectivity (over a wide range of contrasts, in spite of the limited dynamic response range and steep slope of the contrast-response function). Rectification conserves metabolic energy.

Cortical neurons selective for the direction of motion often exhibit some limited response to motion in their nonpreferred directions. Here we examine the dependence of neuronal direction selectivity on stimulus contrast, both for first-order (luminance-modulated, sine-wave grating) and second-order (contrast-modulated envelope) stimuli. We measured responses from single neurons in area 18 of cat visual cortex to both kinds of moving stimuli over a wide range of contrasts (1.25–80%). Direction-selective contrast response functions (CRFs) were calculated as the preferred-minus-null difference in average firing frequency as a function of contrast. We also applied receiver operating characteristic analysis to our CRF data to obtain neurometric functions characterizing the potential ability of each neuron to discriminate motion direction at each contrast level tested. CRFs for sine-wave gratings were usually monotonic; however, a substantial minority of neurons (35%) exhibited nonmonotonic CRFs (such that the degree of direction selectivity decreased with increasing contrast). The underlying preferred and nonpreferred direction CRFs were diverse, often having different shapes in a given neuron. Neurometric functions for direction discrimination showed a similar degree of heterogeneity, including instances of nonmonotonicity. For contrast-modulated stimuli, however, CRFs for either carrier or envelope contrast were always monotonic. In a given neuron, neurometric thresholds were typically much higher for second- than for first-order stimuli. These results demonstrate that the degree of a cell's direction selectivity depends on the contrast at which it is measured, and therefore is not a characteristic parameter of a neuron. In general, contrast response functions for first-order stimuli were very heterogeneous in shape and sensitivity, while those for second-order stimuli showed less sensitivity and were quite stereotyped in shape.