Humans can discriminate one visual contour from another on the basis of small differences in orientation. This capability depends on cortical detectors that are selective for a small range of orientations. We have measured this orientation bandwidth and the suppression that helps to shape it, with a reverse correlation technique. Human subjects were presented with a stream of randomly oriented gratings at a rate of 30 per second. Their task was to press a key whenever they saw an orientation nominated as the target. We analyzed the data by finding the probability density of two orientations: One preceded the key-press by the reaction time, and the second preceded the first by up to 100 ms. The results were as follows: (1) One grating facilitated the following one in producing a key-press when the gratings differed little in orientation. The estimate of orientation bandwidth resulting from this facilitation was 38°. (2) A large angle between the two orientations reduced the probability of a key-press. This finding was best modelled as a suppression that did not vary with orientation, consistent with the idea that cross-orientation suppression is non-oriented. (3) Analysis of non-consecutive grating pairs showed that cross-orientation interactions lasted no longer than 67 ms.

^{2}) and contained a black fusion circle with an inner diameter of 3° and a width of 0.25°. Subjects adjusted the horizontal separation of the monocular stimuli to obtain comfortable binocular fusion. The stimuli within the fusion circle consisted of sinusoidal gratings with a spatial frequency of 2 cycles/deg and a contrast of 99.8%. Each grating had one of 10 orientations spaced 18° apart and one of four spatial phases spaced a quarter of a cycle apart, yielding a total of 40 possible gratings.

*n*(= 10), the deviation at a specific time is conveniently measured with a squared-error statistic:

*cause*a key-press. We will refer to the orientation/key-press relationship as causal in what follows.

*θ*

_{1}in Figure 1A has a direct effect on key-presses, is it also true that a preceding orientation

*θ*

_{2}influences key pressing through its interaction with

*θ*

_{1}? To answer this question, we constructed two-dimensional probability plots such as the one at the top of Figure 4. The horizontal axis gives orientation

*θ*

_{1}and the other axis gives the orientation

*θ*

_{2}, which immediately precedes

*θ*

_{1}(that is, with an inter-stimulus interval of 33 ms). The gray level at point (

*θ*

_{1},

*θ*

_{2}) indicates the probability that a key-press is preceded by the consecutive orientations

*θ*

_{2}and

*θ*

_{1}. A probability scale for the gray levels is shown at the right.

*θ*

_{1}and

*θ*

_{2}have independent influences on key pressing was calculated as follows. The influence of

*θ*

_{1}acting alone can be calculated by summing the probabilities across all values of

*θ*

_{2}. The resulting marginal density,

*p*

_{1}(

*θ*

_{1}), is shown underneath the two-dimensional plot. Similarly, the marginal density,

*p*

_{2}(

*θ*

_{2}), was obtained by summing across all values of

*θ*

_{1}and is shown at the right of the two-dimensional plot. The probability that a key-press will result from the independent effects of

*θ*

_{1}and

*θ*

_{2}is the product of the marginal densities (Papoulis & Pillai, 2002):

*θ*

_{1}and

*θ*

_{2}had independent effects on a key-press, the difference plot would be uniformly gray. The presence of light and dark therefore indicates cross-orientation facilitation and suppression, respectively.

*θ*

_{1}−

*θ*

_{2}, indicating that it might be easier to visualize the plot by graphing the probabilities obtained with constant orientation differences. This is done in Figure 5, which shows the observations and the independence model along two diagonals,

*θ*

_{1}−

*θ*

_{2}= 0° and

*θ*

_{1}−

*θ*

_{2}= 90°. The result is quite different for these two cases. In the first case,

*θ*

_{1}and

*θ*

_{2}are equal, and the observed probabilities exceed the predictions of the independence model. The two gratings are more likely to be aligned than is expected from their independent effects, indicating that alignment leads to facilitation. When the two gratings are misaligned, however, the observed probabilities fall below the independence model, indicating cross-orientation suppression.

*θ*

_{1}and

*θ*

_{2}are equal, or nearly so, and fall below the independence model when

*θ*

_{1}and

*θ*

_{2}differ markedly. The difference between observations and independence model is provided explicitly in Figure 6B for three targets, the mean across targets is shown in Figure 6C, and data for all five subjects are shown in Figure 6D. The magnitude of the cross-orientation interaction differs between subjects, but the results agree in that there is facilitation between the two gratings when their orientations differ by no more than 36° and that there is cross-orientation suppression otherwise.

*t*-test,

*P*= 0.037).

*θ*

_{1}, and another,

*θ*

_{2}, that precedes it by the interval shown at right. The vertical axis gives the probability that this combination precedes a key-press, less the probability predicted by the independence model. The curves are therefore in the same format as those of Figure 6D, except that they have been averaged over the five subjects. When the inter-stimulus interval is 67 ms, facilitation and suppression are much less than for 33 ms, indicating that cross-orientation interactions have largely decayed over the longer interval. For the inter-stimulus interval of 100 ms, the interactions appear to be reversed in sign: Aligned gratings result in suppression, and misaligned gratings result in facilitation. This result is reminiscent of the reversal in probability densities found in single-cell recordings (Ringach, Hawken, & Shapley, 1997). A

*t*-test, however, showed that the data at 67 and 100 ms did not differ from zero at the 5% significance level. We therefore conclude that cross-orientation interactions last no longer than 67 ms.

*θ*

_{1}is presented to one eye and orientation

*θ*

_{2}is presented simultaneously to the other eye. The observed probabilities clearly differ from the independence model, as shown in the graph on the left. The difference between the observations and the independence model, shown on the right, indicates facilitation and suppression of the same form as that seen with the intraocular interactions. The same pattern of interocular suppression was seen in another three subjects. The fifth subject (number 9) was not included in this analysis because of a strongly dominant right eye, as described in the Methods section. While the interocular effects were significant, a comparison of Figures 6 and 9 shows that they were relatively small. They were smaller still when

*θ*

_{2}occurred prior to

*θ*

_{1}rather than simultaneously with it. Possible reasons for the low magnitude of the interocular interactions are taken up in the Discussion section.

*ρ*= −0.62,

*P*= 0.000). It seems therefore that some subjects were key pressing too rapidly to be able to modulate their responses according to the stimulus. We gave our subjects no feedback on their responses. In future experiments, feedback would clearly be useful in slowing down key pressing to yield higher correlations between stimuli and responses.