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Research Article  |   March 2008
Cross-orientation interactions in human vision
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Journal of Vision March 2008, Vol.8, 15. doi:10.1167/8.3.15
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      Urte Roeber, Elaine M. Y. Wong, Alan W. Freeman; Cross-orientation interactions in human vision. Journal of Vision 2008;8(3):15. doi: 10.1167/8.3.15.

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Abstract

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.

Introduction
One of the fundamental properties of the mammalian visual system is its ability to discriminate one contour from another on the basis of a difference in orientation. Humans, for example, can reliably judge the alignment of two contours to within about 0.5° (Andrews, 1967; Westheimer, Shimamura, & McKee, 1976). A widely accepted model for this capability holds that the visual system contains multiple neural channels, each of which responds best to a narrow band of orientations, and that together the channels span all possible orientations (Wilson & Wilkinson, 2004). Subthreshold summation and masking experiments (Blake & Holopigian, 1985; Phillips & Wilson, 1984) have shown that in the human visual system the bandwidth of these channels varies from 30° to 62°, depending on the coarseness of the contour. 
What neural mechanisms might account for the narrowness of orientation tuning? Hubel and Wiesel (1962) suggested that orientation selectivity arises through geniculo-cortical connections: Excitatory input to a cortical cell comes from several lateral geniculate nucleus cells with aligned receptive fields. Psychophysical work, however, suggested that the mechanisms involved were not all excitatory. Blakemore, Carpenter, and Georgeson (1970) noted that several visual illusions (including those of Hering and Zöllner) could be explained by assuming that acute angles between contours are perceived to be larger than they are. They found that when two contours are separated by an acute angle, subjects overestimated the angle. In the model they used to explain their results, orientation detectors are excited by a narrow range of orientations and inhibited by a broader range of orientations. 
The model used by Blakemore et al. (1970) assumed that an orientation detector is inhibited by orientations differing by an acute angle from the preferred value but is less affected by orthogonal orientations. This model has been challenged by measurements from single cortical cells stimulated by a grating with the preferred orientation and masked by a second grating at a differing orientation. The cross-orientation suppression that results is largely independent of the orientation of the mask (Bonds, 1989; DeAngelis, Robson, Ohzawa, & Freeman, 1992). The lack of orientation selectivity in the suppressive effect has lead to the idea that cross-orientation suppression arises pre-cortically (Freeman, Durand, Kiper, & Carandini, 2002), an idea supported by recent intracellular data from cortical cells (Priebe & Ferster, 2006). 
Ringach (1998) described a new psychophysical technique for studying orientation tuning. He presented human subjects with a rapid stream of randomly oriented gratings and asked the subjects to press a key each time they saw a target orientation. Examination of the orientations present 300 or 400 ms before the key-press showed that the most probable orientation was the target, and that orientations at about 45° from the target were least probable. This “Mexican hat” probability density suggests that gratings at an acute angle to the target have a greater suppressive influence than orthogonal ones. An alternative possibility, however, is that the reduced probability of off-target orientations results not from suppression but simply from reduced excitation of target detectors. 
We have taken Ringach's method further in two ways. First, we analyze cross-orientation interactions by examining the joint influence of two orientations presented in the stream preceding the key-press. Using the interaction between two orientations allows us to demonstrate both excitatory and suppressive influences and adds extra weight to the idea that cross-orientation suppression is non-oriented. Second, by delivering an orientation stream to one eye and an independent stream to the other eye, we are able to measure interocular interactions. Previous studies of interocular suppression used a masking stimulus to one eye and an aligned test stimulus to the other eye (Legge, 1979; McKee, Bravo, Taylor, & Legge, 1994). We have generalized these results by measuring the interactive effects of two gratings, one delivered to each eye, and differing in orientation by angles ranging from 0° to 90°. 
Methods
Subjects
Ten undergraduate psychology students (mean age, 22.4 years; range 19 to 29 years, 1 male) participated in the study in partial fulfillment of course requirements. All had normal or corrected-to-normal visual acuity and stereopsis. Subjects gave written informed consent once the methodology had been explained to them but were naive as to the purpose and the results of the study. 
Stimuli
The experiment was run with the ERTS software package (BeriSoft). The stimuli were presented on a Belinea 106080 computer screen with a video frame rate of 60 Hz. Left and right eye stimuli were presented on the left and right sides of the screen, respectively. The view presented to one eye was kept separate from that to the other eye by using a mirror stereoscope. The optical distance from screen to eye was 41.5 cm, and the subject's head was stabilized by a chin rest. Stimuli to each eye were presented on a gray background (58 cd/m 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. 
Protocol
Figure 1A illustrates the stimulus. An experimental run consisted of a stream of gratings presented to each eye at the rate of 30 per second for 1 min. Each grating was chosen from the 40 available, with all choices having the same probability. The grating stream presented to one eye was independent of that presented to the other eye, and both streams on a run were independent of those presented on other runs. Subjects were asked to press a key whenever they saw an orientation nominated as the target, and key-press times were captured using the ERTS reaction time clock. Three target orientations were used: horizontal, vertical, or oblique. For five subjects, the oblique target was 45° left of vertical, and for the other five subjects, it was 45° right of vertical. Each subject participated for nine experimental sessions of approximately 1.5 hr duration. Each session was devoted to a single target orientation, the order of targets in successive sessions was horizontal, vertical, and oblique, and the target on the first session was counter-balanced across subjects. Each session consisted of 57 runs, so that there were 171 runs (171 min) of recording time per target orientation. 
Figure 1
 
(A) Both eyes were presented with a stream of randomly oriented gratings at a rate of 30 per second. The two monocular streams were independent of each other. The subject's task was to press a key when a target orientation (for example, horizontal) was seen. (B) The data were analyzed by finding the orientations present at a specific time prior to the key-press. Examples are shown here for one subject and three target orientations: The horizontal axes show the available orientations, and the vertical axes show the number of times each orientation appeared 367 ms prior to the key-press. Data for both the left eye (continuous lines) and the right eye (dashed lines) are given. These histograms peak at, or close to, the target orientation.
Figure 1
 
(A) Both eyes were presented with a stream of randomly oriented gratings at a rate of 30 per second. The two monocular streams were independent of each other. The subject's task was to press a key when a target orientation (for example, horizontal) was seen. (B) The data were analyzed by finding the orientations present at a specific time prior to the key-press. Examples are shown here for one subject and three target orientations: The horizontal axes show the available orientations, and the vertical axes show the number of times each orientation appeared 367 ms prior to the key-press. Data for both the left eye (continuous lines) and the right eye (dashed lines) are given. These histograms peak at, or close to, the target orientation.
Analysis
The average key-pressing rate across nine of the subjects was 0.32 Hz. The average rate at which the target orientation appeared was 6 Hz (3 Hz in each eye), indicating that these subjects responded to about 1 in 19 target occurrences. The remaining subject (number 8) had an unusually high key-press rate, 3.0 Hz. This subject's data were discarded for reasons discussed in the Results section. Key-presses were analyzed to find the orientations that preceded them. For each time prior to a key-press, a frequency histogram was compiled for the orientations presented to each eye at that time. Compilation took no regard of grating spatial phase, and the results are therefore averaged across the four phases. Examples are shown in Figure 1B for one subject and three targets. Grating orientation relative to the target is shown on the horizontal axis. The vertical axis gives the number of times an orientation was presented 367 ms prior to a key-press. Data for the left eye and right eye are shown with solid and dashed lines, respectively. The left and right eye histograms were compared using a Kolmogorov–Smirnov two-sample test. The hypothesis that the two samples came from the same population could not be rejected at the 5% significance level in 93% of comparisons; the data were therefore averaged across the two eyes. The one exception to this rule was subject 9, whose right eye was strongly dominant; data from this subject's non-dominant eye were discarded. Probability densities were calculated from each histogram by dividing the count for each orientation by the sum of counts across all orientations. 
Results
Figure 1A shows the stimulus used; the task of the subjects was to press a key when they saw an orientation previously designated as the target. Responses were analyzed by finding the orientations present at a specific time prior to the key-press, as described in the Methods section. As an example, Figure 1B shows a frequency histogram of orientations present 367 ms before a key-press for one subject. As previously shown by Ringach (1998), the histograms peak at, or close to, target orientation. 
Reaction time
Figure 2A shows orientation probability densities at a number of times prior to the key-press. The horizontal axis gives grating orientation relative to the target, and the vertical axis gives the probability that a given orientation precedes a key-press. The third dimension, represented obliquely, is the time prior to the key-press at which the probability density was measured. At 100 ms prior to the key-press, the density is essentially flat because visual stimuli take longer than this to influence motor behavior. Similarly, there is a flat density at 800 ms because reaction times are generally less than this value. In between these limits, the density peaks at the target orientation, indicating that a target grating is more likely to produce a key-press than is a grating at an angle to the target. 
Figure 2
 
Reaction time. (A) Each profile in this plot represents a probability density, showing the probability that an orientation occurred at a specific time prior to a key-press. The orientation is shown on the horizontal axis, probability on the vertical axis, and time prior to a key-press is shown obliquely. Data for one subject and one target orientation (horizontal) are shown. The density deviates most from a flat line at about 400 ms prior to the key-press, which is therefore defined as the reaction time. (B) The vertical axis in these graphs gives the extent to which the orientation probability density deviates from a flat line. Deviation is given as a function of time prior to a key-press for five subjects. Reaction time, the time at which the function peaks, differs slightly from subject to subject.
Figure 2
 
Reaction time. (A) Each profile in this plot represents a probability density, showing the probability that an orientation occurred at a specific time prior to a key-press. The orientation is shown on the horizontal axis, probability on the vertical axis, and time prior to a key-press is shown obliquely. Data for one subject and one target orientation (horizontal) are shown. The density deviates most from a flat line at about 400 ms prior to the key-press, which is therefore defined as the reaction time. (B) The vertical axis in these graphs gives the extent to which the orientation probability density deviates from a flat line. Deviation is given as a function of time prior to a key-press for five subjects. Reaction time, the time at which the function peaks, differs slightly from subject to subject.
Reaction time can be determined as the time prior to a key-press at which the probability density differs most from a flat line. Denoting the number of orientations by n (= 10), the deviation at a specific time is conveniently measured with a squared-error statistic:  
D e v i a t i o n f r o m u n i f o r m d e n s i t y = i = 1 n ( o b s e r v a t i o n i m e a n ) 2 = i = 1 n ( p r o b a b i l i t y i 1 / n ) 2 .
(1)
Deviation versus time prior to a key-press is shown in Figure 2B for five subjects; profiles are normalized so that the sum of deviations is one. There is a peak at around 400 ms, indicating that stimuli at this time correlate best with key-presses. This value corresponds well with previous determinations of reaction time (Ringach, 1998; Zlatkova, Vassilev, & Mitov, 2000). The deviation function also shows how subjects differ in their ability to detect a target grating in that for some subjects the peak deviation is lower than for others. In fact, for 5 of the 10 subjects we tested, a chi-square test showed that deviations were not significant at the 5% level for any of the target orientations. The data for these five subjects (numbers 1, 3, 5, 8, and 10) are not shown and are ignored in the remaining analysis. Reasons for the lack of significance in the discarded data are taken up in the Discussion section. 
The deviations in Figure 2B were used to calculate orientation probability densities that are independent of time prior to a key-press. The density at each time prior to a key-press was weighted by its deviation from uniformity, and the weighted densities were averaged over those times for which the deviation differed significantly from zero. This approach ensures that each density contributes to the average in proportion to its correlation with key-presses. All probability densities shown in the following figures were calculated using this weighted sum procedure. A related issue is causality. Given the observation that particular orientations are well correlated with key-presses, and that these orientations precede the key-presses with little variability in the intervening interval, we claim that the presence of specific orientations in the stimulus stream cause a key-press. We will refer to the orientation/key-press relationship as causal in what follows. 
Orientation probability density
The graph on the left side of Figure 3 shows orientation probability densities for five subjects. As with Ringach's (1998) results, a key-press is more likely to be preceded by the target orientation than by other orientations. Unlike Ringach's results, the densities do not have a “Mexican hat” shape. Instead, the probabilities fall more or less monotonically on either side of the peak. Our method differed from Ringach's mainly in the use of dichoptic stimulation: The orientation stream presented to one eye differed from that to the other eye. To test whether this accounted for the difference in results, we ran the experiment again using binocularly congruent stimulation. In this case, the stimuli to the two eyes were identical. The right side of Figure 3 shows the results for the same five subjects. The densities now have a “Mexican hat” shape, confirming Ringach's finding. Possible reasons for this difference between the results of dichoptic and congruent stimulation are considered in the Discussion section. The remainder of the results, however, deals only with the data from dichoptic stimulation. The reason for this is that while nine sessions of data collection were devoted to dichoptic stimulation of each subject, only one session used congruent stimulation. The dichoptic data therefore had a higher signal to noise ratio. 
Figure 3
 
Orientation probability densities. The graph at left shows probability densities for five subjects stimulated dichoptically, that is, with an orientation stream to one eye and an independent stream to the other eye. The data have been averaged across eyes and targets. In the graph at right, stimulation was binocularly congruent so that the two eyes saw the same orientation stream. The densities are more “Mexican hat” in shape than are the densities obtained with dichoptic stimulation.
Figure 3
 
Orientation probability densities. The graph at left shows probability densities for five subjects stimulated dichoptically, that is, with an orientation stream to one eye and an independent stream to the other eye. The data have been averaged across eyes and targets. In the graph at right, stimulation was binocularly congruent so that the two eyes saw the same orientation stream. The densities are more “Mexican hat” in shape than are the densities obtained with dichoptic stimulation.
Cross-orientation interaction
The main question asked in this paper concerns cross-orientation interaction. While the grating orientation 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. 
Figure 4
 
Cross-orientation interactions. Events leading to a key-press for a single subject and target orientation were analyzed in terms of two orientations. θ 1 is the orientation preceding the key-press by the reaction time, and θ 2 is the orientation immediately preceding (that is, 33 ms before) θ 1. These plots show joint probabilities of these two orientations, with θ 1 on the horizontal axis and θ 2 on the vertical. The top plot shows the observations. Probabilities were summed along columns and rows to determine the marginal probability densities for θ 1, shown below the plot, and θ 2, at right, respectively. The middle plot shows the joint probability density expected if θ 1 and θ 2 have independent effects in producing a key-press: It is obtained by multiplying the marginal densities. The probability scale at the right of this plot applies to both it and the top plot. The bottom plot gives the difference between the observations and the independence model and therefore shows the extent to which the two orientations interact. The deviations from a uniform density are aligned along diagonals, indicating elevated probabilities that the two orientations are aligned and reduced probabilities that they differ substantially.
Figure 4
 
Cross-orientation interactions. Events leading to a key-press for a single subject and target orientation were analyzed in terms of two orientations. θ 1 is the orientation preceding the key-press by the reaction time, and θ 2 is the orientation immediately preceding (that is, 33 ms before) θ 1. These plots show joint probabilities of these two orientations, with θ 1 on the horizontal axis and θ 2 on the vertical. The top plot shows the observations. Probabilities were summed along columns and rows to determine the marginal probability densities for θ 1, shown below the plot, and θ 2, at right, respectively. The middle plot shows the joint probability density expected if θ 1 and θ 2 have independent effects in producing a key-press: It is obtained by multiplying the marginal densities. The probability scale at the right of this plot applies to both it and the top plot. The bottom plot gives the difference between the observations and the independence model and therefore shows the extent to which the two orientations interact. The deviations from a uniform density are aligned along diagonals, indicating elevated probabilities that the two orientations are aligned and reduced probabilities that they differ substantially.
The two-dimensional plot is dominated by a bright spot at its centre, indicating that a key-press is likely to be preceded by consecutive gratings that both align with the target. This is hardly surprising as the two gratings could independently lead to a key-press. What is more interesting is the possibility that facilitatory interactions between the two gratings lead to a probability higher than that expected of their independent effects. The probability expected if 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): 
pind(θ1,θ2)=p1(θ1)p2(θ2).
(2)
The independence model is shown in the middle plot of Figure 4, and the difference between the observations and the independence model is shown at the bottom. If θ1 and θ2 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. 
Close inspection of the difference plot in Figure 4 shows that there is a pattern to the light and the dark areas: The light areas run along the main diagonal, and the dark areas along the minor diagonals. Each diagonal represents a constant orientation difference, θ 1θ 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 1θ 2 = 0° and θ 1θ 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. 
Figure 5
 
Comparing observations with the independence model. These graphs show probabilities along the diagonals in the two-dimensional plots of the preceding figure, representing the case where θ 1 and θ 2 are aligned in the left plot and orthogonal in the right plot. Continuous lines give the observations, and dashed lines give the independence model. Observations are higher than the independence model on the left, indicating that aligned gratings facilitate a key-press. Observations are lower than the independence model on the right, indicating that a grating is less likely to result in a key-press if it is preceded by an orthogonal grating.
Figure 5
 
Comparing observations with the independence model. These graphs show probabilities along the diagonals in the two-dimensional plots of the preceding figure, representing the case where θ 1 and θ 2 are aligned in the left plot and orthogonal in the right plot. Continuous lines give the observations, and dashed lines give the independence model. Observations are higher than the independence model on the left, indicating that aligned gratings facilitate a key-press. Observations are lower than the independence model on the right, indicating that a grating is less likely to result in a key-press if it is preceded by an orthogonal grating.
The difference between the observations and the independence model can be shown more compactly and completely by summing probabilities along each and all diagonals. The results of this calculation are shown in Figure 6. Each point in Figure 6A was obtained by summing the probabilities in the top or the middle plots of Figure 4 along a single diagonal, where the orientation difference defining the diagonal is given on the horizontal axis. The observations exceed the independence model when 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. 
Figure 6
 
Cross-orientation facilitation and suppression. To summarize the two-dimensional plots of Figure 4, probabilities were summed along the diagonals of those plots. The results are shown here, with the identity of each diagonal represented on the horizontal axis by its orientation difference, θ 1θ 2. (A) Data for a single subject and three target orientations are shown. The observations rise above the independence model when the two orientations are aligned, indicating facilitation of a key-press, and they fall below the independence model when the two orientations are misaligned, indicating cross-orientation suppression. (B) This graph gives the difference between observations and independence model for the same subject and target orientations. Points above the dashed line give facilitation, points below it give suppression. (C) The curve shows the data for the same subject averaged over target orientations. (D) Data from the five subjects are shown. All have the same pattern of facilitation and suppression, but to differing extents.
Figure 6
 
Cross-orientation facilitation and suppression. To summarize the two-dimensional plots of Figure 4, probabilities were summed along the diagonals of those plots. The results are shown here, with the identity of each diagonal represented on the horizontal axis by its orientation difference, θ 1θ 2. (A) Data for a single subject and three target orientations are shown. The observations rise above the independence model when the two orientations are aligned, indicating facilitation of a key-press, and they fall below the independence model when the two orientations are misaligned, indicating cross-orientation suppression. (B) This graph gives the difference between observations and independence model for the same subject and target orientations. Points above the dashed line give facilitation, points below it give suppression. (C) The curve shows the data for the same subject averaged over target orientations. (D) Data from the five subjects are shown. All have the same pattern of facilitation and suppression, but to differing extents.
One interesting feature of the curves in Figure 6D is that they generally decline monotonically away from the peak, with no upturns at large orientation difference. In particular, the curves do not have a “Mexican hat” profile. This in turn suggests that the suppression is constant across orientation differences, that is, that the suppression is non-oriented. We used this finding to model the facilitation curve, as shown in Figure 7. Here, facilitation is assumed to be a Gaussian function of orientation difference and to be added to a constant suppression value. The goodness-of-fit of model to observations can be quantified with the root-mean-square error that, for this subject, was 0.0011. Root-mean-square errors for the other four subjects were slightly less than this value, indicating that their fits were no worse than that shown in Figure 7. The most interesting results from data fitting were the model parameters: The bandwidth at half-height averaged across five subjects was 38°, and the suppression constant differed significantly from zero (one-tailed t-test, P = 0.037). 
Figure 7
 
A model for cross-orientation interaction. The experimental data are the probability differences measured for subject 4, as shown in Figure 6C. The model consists of a Gaussian function of orientation difference from which is subtracted a suppression component that does not vary with orientation difference. Values above the dashed line indicate that an orientation facilitates a following one in producing a key-press, and values below the line indicate suppression.
Figure 7
 
A model for cross-orientation interaction. The experimental data are the probability differences measured for subject 4, as shown in Figure 6C. The model consists of a Gaussian function of orientation difference from which is subtracted a suppression component that does not vary with orientation difference. Values above the dashed line indicate that an orientation facilitates a following one in producing a key-press, and values below the line indicate suppression.
Temporal decay
All of the analysis provided thus far applied to the case where the interacting gratings were consecutive; that is, one grating appeared 33 ms after the other. Figure 8 extends this result to other inter-stimulus intervals. The horizontal axis gives the orientation difference between one grating, 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. 
Figure 8
 
Temporal decay of cross-orientation interaction. The horizontal axis gives the difference in two orientations preceding a key-press. The vertical axis gives the probability of the orientation pair, with the prediction of the independence model subtracted. The curves show means over the five subjects and are labeled, on the right, with the inter-stimulus interval between the two orientations. The curve labeled 33 ms is the mean of the five curves in Figure 6D. The curves at longer inter-stimulus intervals have lower amplitude, indicating that cross-orientation interaction has largely disappeared when the two orientations are separated by 67 ms or more.
Figure 8
 
Temporal decay of cross-orientation interaction. The horizontal axis gives the difference in two orientations preceding a key-press. The vertical axis gives the probability of the orientation pair, with the prediction of the independence model subtracted. The curves show means over the five subjects and are labeled, on the right, with the inter-stimulus interval between the two orientations. The curve labeled 33 ms is the mean of the five curves in Figure 6D. The curves at longer inter-stimulus intervals have lower amplitude, indicating that cross-orientation interaction has largely disappeared when the two orientations are separated by 67 ms or more.
Interocular effects
The results thus far have been limited to the interactions between two gratings presented to the same eye. Are there similar interactions when one grating is presented to the left eye and the other grating to the right? The answer is yes, but they are small. Figure 9 shows the interactions for one subject when orientation 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. 
Figure 9
 
Interocular interactions. For this figure, θ 1 is the orientation delivered to one eye and θ 2 is the orientation simultaneously delivered to the other eye. The observations and the independence model are shown separately on the left of the figure for three targets, and the difference between observations and independence model is averaged across the targets on the right of the figure. There is facilitation for like orientations and suppression for unlike orientations, as with intraocular interactions, but the magnitudes of the effects are smaller in the interocular case.
Figure 9
 
Interocular interactions. For this figure, θ 1 is the orientation delivered to one eye and θ 2 is the orientation simultaneously delivered to the other eye. The observations and the independence model are shown separately on the left of the figure for three targets, and the difference between observations and independence model is averaged across the targets on the right of the figure. There is facilitation for like orientations and suppression for unlike orientations, as with intraocular interactions, but the magnitudes of the effects are smaller in the interocular case.
Discussion
Reaction time
We studied ten subjects, but only five of them showed a significant correlation between key-presses and preceding target orientations. Why did the other five subjects fail to reach significance? The answer almost certainly lies in key-press rate: Subjects with high rates were also the ones whose key-presses did not reliably follow target orientations. This can be seen in Figure 10, which plots the chi-square value used to accept or to reject subjects (see the description of Figure 2B) against key-press rate. The correlation between the two variables was negative and statistically significant (Spearman's 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. 
Figure 10
 
Key-press rate. Orientation probability densities differed from uniformity at a range of times prior to a key-press, as shown in Figure 2A. The vertical axis here shows the chi-square value used to test whether the deviation from uniformity was significant; symbols represent ten subjects and three targets per subject. The horizontal axis shows the mean rate at which the subjects pressed the key. Clearly, subjects with higher key-press rates have lower chi-square values, indicating that their responses are less correlated with the stimulus. Subjects that failed the significance test for all three targets are shown as filled symbols, and passing subjects are shown as open symbols.
Figure 10
 
Key-press rate. Orientation probability densities differed from uniformity at a range of times prior to a key-press, as shown in Figure 2A. The vertical axis here shows the chi-square value used to test whether the deviation from uniformity was significant; symbols represent ten subjects and three targets per subject. The horizontal axis shows the mean rate at which the subjects pressed the key. Clearly, subjects with higher key-press rates have lower chi-square values, indicating that their responses are less correlated with the stimulus. Subjects that failed the significance test for all three targets are shown as filled symbols, and passing subjects are shown as open symbols.
Binocularly congruent stimulation
We recorded orientation probability densities both dichoptically and with binocular congruence. The densities differed in shape in that while dichoptic densities fell more or less monotonically on either side of the peak value, the congruent version had a “Mexican hat” shape. The reason for this difference is not clear, but we can suggest one possibility. In the phenomenon known as continuous flash suppression, the presentation of a stream of differing images to one eye results in visual suppression of the other eye's stimulus (Tsuchiya & Koch, 2005). It could be therefore that there was more suppression when we used orientation streams differing between the two eyes than when the two eyes were stimulated identically. This suppression, in turn, could have flattened out the densities for those orientations that differed most from the target orientation. 
The cross-orientation suppression shown in Figure 7 is best modelled as a constant, independent of the orientation difference between the interacting gratings. This non-oriented suppression was obtained from the data produced by dichoptic stimulation. Given the “Mexican hat” shape of the orientation probability density arising from binocularly congruent stimulation, would we also see non-oriented cross-orientation suppression with this type of stimulus? We further analyzed these data to examine this point and found that the resulting cross-orientation interaction functions, while noisier than that in Figure 7, had the same shape. We are therefore confident that our hypothesis of non-oriented cross-orientation suppression applies not only to dichoptic stimulation but also to the binocularly congruent data. 
Cross-orientation facilitation
When randomly oriented gratings are presented in quick succession, a subject is more likely to signal the presence of a target orientation if one of the stimuli aligns with the target (Ringach, 1998). Our results go beyond this finding by showing that two consecutive stimuli have not only independent effects but also an interactive one. In particular, the probability of target detection is facilitated when it is preceded by another target. Given that we removed the effects of probability summation through the use of the independence model, the source of this facilitation is likely to be neural summation. It has previously been shown that a test grating is easier to detect when it is added to a low-contrast grating of the same orientation than when it is presented alone (Legge & Foley, 1980; Nachmias & Sansbury, 1974). Our finding of facilitation between gratings of similar orientation is presumably a reflection of this “dipper effect.” 
According to this argument, the facilitation function in Figure 7 shows the extent to which a specific orientation contributes to the excitation of an orientation-selective channel whose peak sensitivity is at the target orientation. It is of interest therefore to compare our facilitation function with previous measures of orientation tuning. We find a bandwidth at half-height of 38°. (Given the relatively small area of the gratings we used, we have not attempted to correct this value for spatial probability summation.) Phillips and Wilson (1984), who measured orientation tuning with a masking technique, found a bandwidth of 48° for the grating spatial frequency, 2 cycles/deg, equal to the one we used. Blake and Holopigian (1985), who also used a masking technique, found bandwidths from 46° to 62° for a range of spatial frequencies that includes 2 cycles/deg. There is therefore a broad agreement between the psychophysical estimates. At the single-cell level, bandwidths vary widely between cells, and it is therefore not possible to give a single value. De Valois, Yund, and Hepler (1982), however, found a median bandwidth of about 40° among a sizable population of primary visual cortical cells in the macaque. 
Given the orientation selectivity of the channel whose properties are illustrated in Figure 7, it would be useful to know whether it is selective for spatial phase. We were able to check this because the gratings used had four possible phases, spaced a quarter of a cycle apart. Reanalysis of the data showed that the facilitation between two gratings was maximal when they had the same phase and declined progressively as the phase difference between them increased to 90° and 180° (graphs are shown in the Supplementary data). Given this phase sensitivity, it seems that the neuronal population we tested matched the properties of simple cells better than those of complex cells (Movshon, Thompson, & Tolhurst, 1978). 
Cross-orientation suppression
We have shown that a subject is less likely to detect a target orientation that is immediately preceded by a markedly different orientation. The use of the independence model shows that this is due to interaction between the responses to the two orientations, and we therefore use the term cross-orientation suppression to describe the loss of detectability. It should be noted that the method we have used does not assign a unique magnitude to the suppression, for the following reason. The data in Figure 7 represent the difference between two probability densities. By definition, the probabilities making up a density sum to unity, and the data points making up the difference of densities must therefore sum to zero. In other words, the mathematics requires that the facilitation and the suppression in Figure 7 balance each other. This balance does not weaken our demonstration of suppression. We show in Figure 5 that there is suppression when the two gratings are orthogonal, but there is no mathematical requirement that this suppression balances the facilitation shown in the other graph of Figure 5. Furthermore, the suppression in Figure 5 proved to be significant at the 5% level across targets and across subjects. 
We used rapid serial visual presentation for the stimulus. Another issue in interpreting the measured suppression is that it might derive from attentional blinks; that is, loss of saliency in a target when it follows soon after another target (Raymond, Shapiro, & Arnell, 1992). We can rule out this possibility on timing grounds. Attentional blinks affect stimuli separated by up to half a second. The five subjects that we analyzed in detail, however, responded no faster than one key-press every 2 s (Figure 10). 
A number of previous psychophysical studies have provided evidence of cross-orientation suppression. Blakemore et al. (1970) found that when two lines meet at an acute angle, the angle appears to be larger than it is. The authors assumed that each line stimulated a population of orientation-selective channels, and that the angle expansion resulted from mutual inhibition between the two populations of channels. A more direct approach is to overlay an oriented test stimulus with a masking stimulus of differing orientation. This method shows that the threshold for test detection is markedly elevated by the presence of a high-contrast mask (Meese & Holmes, 2007; Petrov, Carandini, & McKee, 2005). 
Clues about the source of the suppression can be gained by examining its variation with orientation. While the data in Figure 7 cannot be unambiguously separated into facilitation and suppression functions, the flatness of the data where the two gratings approach orthogonality suggests that the suppression is a constant function of orientation difference. If this is so, the suppression is non-oriented, consistent with single-cell studies indicating that the cross-orientation suppression resulting from the presentation of two gratings to the same eye varies little with their relative orientation (Bonds, 1989; DeAngelis et al., 1992). Further, it is consistent with evidence that cross-orientation suppression arises pre-cortically (Freeman et al., 2002; Priebe & Ferster, 2006). 
Interocular interaction
Previous work has shown subthreshold summation effects between a grating presented to one eye and an aligned grating simultaneously presented to the other eye (Legge, 1979). It has also been shown that the response to a monocular grating is reduced by simultaneously presenting an orthogonal grating to the other eye (Baker, Meese, & Summers, 2007). The facilitation and the suppression we show in Figure 9 mirror these results. The strength of the interocular interaction we measured, however, was considerably smaller than that of the intraocular variety. There are at least two possible reasons for the small magnitude of the interocular interaction. First, the stimulus delivered to one eye was independent of that delivered to the other eye and may therefore have evoked binocular rivalry. Our subjects did not know whether they experienced rivalry because they could not distinguish one eye's orientation stream from that of the other eye. But if there were rivalry, one eye's stimulus would have been suppressed at any given time, reducing its ability to influence responses to stimuli delivered to the other eye (Blake & Fox, 1974), thereby reducing interocular interactions. 
A second reason for the low magnitude of interocular interactions may lie in the weakness of the stimuli we used. That the stimuli were weak can be seen in two ways. First, the five subjects whose key-presses correlated with target orientations responded to only one in every 30 targets on average. Second, the probability that a target preceded a key-press by the reaction time was of the order of 0.15 ( Figure 3), well short of certainty. It is known that low-contrast orthogonal gratings do not produce binocular rivalry (Liu, Tyler, & Schor, 1992). Thus, the interocular conflict produced by our grating stream may have been insufficient to produce strong interocular suppression. 
Supplementary Materials
Supplementary Figure 1 - Supplementary Figure 1 
Supplementary Figure 1. Sensitivity to spatial phase. The horizontal axis shows the orientation difference between two gratings presented to the same eye, one 33 ms before the other. The vertical axis shows the probability of this combination, less the probability predicted by the independence model. Probability differences are averaged across eyes, targets, and subjects. The two gratings differed in spatial phase by the amount shown in the upper right of each graph. Facilitation between the gratings is reduced when they are out of phase, but cross-orientation suppression appears to be largely unaffected by the phase relationship. 
Acknowledgments
We thank Sandra Hasse, Franziska Wende, and Kathrin Gottlebe for assistance with data collection. This study was supported by a DAAD scholarship and a DFG grant (RO 3061/1-1) to Urte Roeber. 
Commercial relationships: none. 
Corresponding author: Alan Freeman. 
Email: A.Freeman@usyd.edu.au. 
Address: School of Medical Sciences, University of Sydney, PO Box 170, Lidcombe, NSW 1825, Australia. 
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Figure 1
 
(A) Both eyes were presented with a stream of randomly oriented gratings at a rate of 30 per second. The two monocular streams were independent of each other. The subject's task was to press a key when a target orientation (for example, horizontal) was seen. (B) The data were analyzed by finding the orientations present at a specific time prior to the key-press. Examples are shown here for one subject and three target orientations: The horizontal axes show the available orientations, and the vertical axes show the number of times each orientation appeared 367 ms prior to the key-press. Data for both the left eye (continuous lines) and the right eye (dashed lines) are given. These histograms peak at, or close to, the target orientation.
Figure 1
 
(A) Both eyes were presented with a stream of randomly oriented gratings at a rate of 30 per second. The two monocular streams were independent of each other. The subject's task was to press a key when a target orientation (for example, horizontal) was seen. (B) The data were analyzed by finding the orientations present at a specific time prior to the key-press. Examples are shown here for one subject and three target orientations: The horizontal axes show the available orientations, and the vertical axes show the number of times each orientation appeared 367 ms prior to the key-press. Data for both the left eye (continuous lines) and the right eye (dashed lines) are given. These histograms peak at, or close to, the target orientation.
Figure 2
 
Reaction time. (A) Each profile in this plot represents a probability density, showing the probability that an orientation occurred at a specific time prior to a key-press. The orientation is shown on the horizontal axis, probability on the vertical axis, and time prior to a key-press is shown obliquely. Data for one subject and one target orientation (horizontal) are shown. The density deviates most from a flat line at about 400 ms prior to the key-press, which is therefore defined as the reaction time. (B) The vertical axis in these graphs gives the extent to which the orientation probability density deviates from a flat line. Deviation is given as a function of time prior to a key-press for five subjects. Reaction time, the time at which the function peaks, differs slightly from subject to subject.
Figure 2
 
Reaction time. (A) Each profile in this plot represents a probability density, showing the probability that an orientation occurred at a specific time prior to a key-press. The orientation is shown on the horizontal axis, probability on the vertical axis, and time prior to a key-press is shown obliquely. Data for one subject and one target orientation (horizontal) are shown. The density deviates most from a flat line at about 400 ms prior to the key-press, which is therefore defined as the reaction time. (B) The vertical axis in these graphs gives the extent to which the orientation probability density deviates from a flat line. Deviation is given as a function of time prior to a key-press for five subjects. Reaction time, the time at which the function peaks, differs slightly from subject to subject.
Figure 3
 
Orientation probability densities. The graph at left shows probability densities for five subjects stimulated dichoptically, that is, with an orientation stream to one eye and an independent stream to the other eye. The data have been averaged across eyes and targets. In the graph at right, stimulation was binocularly congruent so that the two eyes saw the same orientation stream. The densities are more “Mexican hat” in shape than are the densities obtained with dichoptic stimulation.
Figure 3
 
Orientation probability densities. The graph at left shows probability densities for five subjects stimulated dichoptically, that is, with an orientation stream to one eye and an independent stream to the other eye. The data have been averaged across eyes and targets. In the graph at right, stimulation was binocularly congruent so that the two eyes saw the same orientation stream. The densities are more “Mexican hat” in shape than are the densities obtained with dichoptic stimulation.
Figure 4
 
Cross-orientation interactions. Events leading to a key-press for a single subject and target orientation were analyzed in terms of two orientations. θ 1 is the orientation preceding the key-press by the reaction time, and θ 2 is the orientation immediately preceding (that is, 33 ms before) θ 1. These plots show joint probabilities of these two orientations, with θ 1 on the horizontal axis and θ 2 on the vertical. The top plot shows the observations. Probabilities were summed along columns and rows to determine the marginal probability densities for θ 1, shown below the plot, and θ 2, at right, respectively. The middle plot shows the joint probability density expected if θ 1 and θ 2 have independent effects in producing a key-press: It is obtained by multiplying the marginal densities. The probability scale at the right of this plot applies to both it and the top plot. The bottom plot gives the difference between the observations and the independence model and therefore shows the extent to which the two orientations interact. The deviations from a uniform density are aligned along diagonals, indicating elevated probabilities that the two orientations are aligned and reduced probabilities that they differ substantially.
Figure 4
 
Cross-orientation interactions. Events leading to a key-press for a single subject and target orientation were analyzed in terms of two orientations. θ 1 is the orientation preceding the key-press by the reaction time, and θ 2 is the orientation immediately preceding (that is, 33 ms before) θ 1. These plots show joint probabilities of these two orientations, with θ 1 on the horizontal axis and θ 2 on the vertical. The top plot shows the observations. Probabilities were summed along columns and rows to determine the marginal probability densities for θ 1, shown below the plot, and θ 2, at right, respectively. The middle plot shows the joint probability density expected if θ 1 and θ 2 have independent effects in producing a key-press: It is obtained by multiplying the marginal densities. The probability scale at the right of this plot applies to both it and the top plot. The bottom plot gives the difference between the observations and the independence model and therefore shows the extent to which the two orientations interact. The deviations from a uniform density are aligned along diagonals, indicating elevated probabilities that the two orientations are aligned and reduced probabilities that they differ substantially.
Figure 5
 
Comparing observations with the independence model. These graphs show probabilities along the diagonals in the two-dimensional plots of the preceding figure, representing the case where θ 1 and θ 2 are aligned in the left plot and orthogonal in the right plot. Continuous lines give the observations, and dashed lines give the independence model. Observations are higher than the independence model on the left, indicating that aligned gratings facilitate a key-press. Observations are lower than the independence model on the right, indicating that a grating is less likely to result in a key-press if it is preceded by an orthogonal grating.
Figure 5
 
Comparing observations with the independence model. These graphs show probabilities along the diagonals in the two-dimensional plots of the preceding figure, representing the case where θ 1 and θ 2 are aligned in the left plot and orthogonal in the right plot. Continuous lines give the observations, and dashed lines give the independence model. Observations are higher than the independence model on the left, indicating that aligned gratings facilitate a key-press. Observations are lower than the independence model on the right, indicating that a grating is less likely to result in a key-press if it is preceded by an orthogonal grating.
Figure 6
 
Cross-orientation facilitation and suppression. To summarize the two-dimensional plots of Figure 4, probabilities were summed along the diagonals of those plots. The results are shown here, with the identity of each diagonal represented on the horizontal axis by its orientation difference, θ 1θ 2. (A) Data for a single subject and three target orientations are shown. The observations rise above the independence model when the two orientations are aligned, indicating facilitation of a key-press, and they fall below the independence model when the two orientations are misaligned, indicating cross-orientation suppression. (B) This graph gives the difference between observations and independence model for the same subject and target orientations. Points above the dashed line give facilitation, points below it give suppression. (C) The curve shows the data for the same subject averaged over target orientations. (D) Data from the five subjects are shown. All have the same pattern of facilitation and suppression, but to differing extents.
Figure 6
 
Cross-orientation facilitation and suppression. To summarize the two-dimensional plots of Figure 4, probabilities were summed along the diagonals of those plots. The results are shown here, with the identity of each diagonal represented on the horizontal axis by its orientation difference, θ 1θ 2. (A) Data for a single subject and three target orientations are shown. The observations rise above the independence model when the two orientations are aligned, indicating facilitation of a key-press, and they fall below the independence model when the two orientations are misaligned, indicating cross-orientation suppression. (B) This graph gives the difference between observations and independence model for the same subject and target orientations. Points above the dashed line give facilitation, points below it give suppression. (C) The curve shows the data for the same subject averaged over target orientations. (D) Data from the five subjects are shown. All have the same pattern of facilitation and suppression, but to differing extents.
Figure 7
 
A model for cross-orientation interaction. The experimental data are the probability differences measured for subject 4, as shown in Figure 6C. The model consists of a Gaussian function of orientation difference from which is subtracted a suppression component that does not vary with orientation difference. Values above the dashed line indicate that an orientation facilitates a following one in producing a key-press, and values below the line indicate suppression.
Figure 7
 
A model for cross-orientation interaction. The experimental data are the probability differences measured for subject 4, as shown in Figure 6C. The model consists of a Gaussian function of orientation difference from which is subtracted a suppression component that does not vary with orientation difference. Values above the dashed line indicate that an orientation facilitates a following one in producing a key-press, and values below the line indicate suppression.
Figure 8
 
Temporal decay of cross-orientation interaction. The horizontal axis gives the difference in two orientations preceding a key-press. The vertical axis gives the probability of the orientation pair, with the prediction of the independence model subtracted. The curves show means over the five subjects and are labeled, on the right, with the inter-stimulus interval between the two orientations. The curve labeled 33 ms is the mean of the five curves in Figure 6D. The curves at longer inter-stimulus intervals have lower amplitude, indicating that cross-orientation interaction has largely disappeared when the two orientations are separated by 67 ms or more.
Figure 8
 
Temporal decay of cross-orientation interaction. The horizontal axis gives the difference in two orientations preceding a key-press. The vertical axis gives the probability of the orientation pair, with the prediction of the independence model subtracted. The curves show means over the five subjects and are labeled, on the right, with the inter-stimulus interval between the two orientations. The curve labeled 33 ms is the mean of the five curves in Figure 6D. The curves at longer inter-stimulus intervals have lower amplitude, indicating that cross-orientation interaction has largely disappeared when the two orientations are separated by 67 ms or more.
Figure 9
 
Interocular interactions. For this figure, θ 1 is the orientation delivered to one eye and θ 2 is the orientation simultaneously delivered to the other eye. The observations and the independence model are shown separately on the left of the figure for three targets, and the difference between observations and independence model is averaged across the targets on the right of the figure. There is facilitation for like orientations and suppression for unlike orientations, as with intraocular interactions, but the magnitudes of the effects are smaller in the interocular case.
Figure 9
 
Interocular interactions. For this figure, θ 1 is the orientation delivered to one eye and θ 2 is the orientation simultaneously delivered to the other eye. The observations and the independence model are shown separately on the left of the figure for three targets, and the difference between observations and independence model is averaged across the targets on the right of the figure. There is facilitation for like orientations and suppression for unlike orientations, as with intraocular interactions, but the magnitudes of the effects are smaller in the interocular case.
Figure 10
 
Key-press rate. Orientation probability densities differed from uniformity at a range of times prior to a key-press, as shown in Figure 2A. The vertical axis here shows the chi-square value used to test whether the deviation from uniformity was significant; symbols represent ten subjects and three targets per subject. The horizontal axis shows the mean rate at which the subjects pressed the key. Clearly, subjects with higher key-press rates have lower chi-square values, indicating that their responses are less correlated with the stimulus. Subjects that failed the significance test for all three targets are shown as filled symbols, and passing subjects are shown as open symbols.
Figure 10
 
Key-press rate. Orientation probability densities differed from uniformity at a range of times prior to a key-press, as shown in Figure 2A. The vertical axis here shows the chi-square value used to test whether the deviation from uniformity was significant; symbols represent ten subjects and three targets per subject. The horizontal axis shows the mean rate at which the subjects pressed the key. Clearly, subjects with higher key-press rates have lower chi-square values, indicating that their responses are less correlated with the stimulus. Subjects that failed the significance test for all three targets are shown as filled symbols, and passing subjects are shown as open symbols.
Supplementary Figure 1
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