A simple account of cyclopean edge responses in macaque v2

Abstract

It has been shown recently that neurons in V2 respond selectively to the edges of figures defined only by disparity (cyclopean edges). These responses are orientation selective, often preferring similar orientations for cyclopean and luminance contours, suggesting that they may support a cue-invariant representation of contours. Here, we investigate the extent to which processing of purely local visual information (in the vicinity of the receptive field) might explain such results, using the most impoverished stimulus possible containing a cyclopean edge (a circular patch of random dots divided into two regions by a single edge). Many V2 cells responded better to the cyclopean edge than to uniform disparities, and most of these were at least broadly selective for the orientation of the cyclopean edge. Two characteristics argue against a cue-invariant contour representation: (1) the cyclopean edge response was frequently abolished by small changes to the component disparities; and (2) although V2 cells frequently responded to both signs of a cyclopean edge (defined by which side of the edge is in front), they did so at different edge locations. These characteristics are consistent with a simple feedforward scheme in which V2 neurons receive inputs from several V1 subunits with different disparity selectivity. We also found a correlation between the preferred orientations for cyclopean edges and contrast stimuli, suggesting that this feedforward wiring is not random. These characteristics suggest that V2 responses to cyclopean edges may be useful in supporting a cue-invariant contour representation higher in the visual pathway.

Figure 1.

Experimental setup. a, Monkeys fixated on a central fixation spot while the stimulus was centered on the receptive field (indicated by the solid black line). Receptive fields were located between 1 and 10° from the fovea in the right visual field. The stimulus was a black and white RDS containing a cyclopean edge created by applying two different disparities to the dots. The actual stimulus contained only black and white dots on a gray background; color is used in a and b for illustrative purposes only (red and green represent the views of the right and left eyes, respectively). b, Reproduction of a stimulus containing a vertical edge (left) and a horizontal edge (right). The line drawings inset to the top right of the stimulus drawings illustrate schematically the displacements that were applied to different regions of the stimulus of each eye. The green dots have been shifted in opposite directions on either side of the cyclopean edge, to produce opposite horizontal disparities across the edge. For the vertical edge (left), this shift results in a gap in the green dots along the location of the cyclopean edge, as shown in the line drawing. The gap is filled with uncorrelated dots (identified here with a black boundary). Note that any step change in horizontal disparity across a vertical border inevitably results in uncorrelated dots (this is not peculiar to our stimulus generation method). When a horizontal disparity step occurs across a horizontal boundary, however, no “gap” is created by the displacement; thus, uncorrelated dots are not present. In all cases, we added uncorrelated dots around the margins of the stimulus so that no monocular displacement was ever present. c, We measured the cyclopean edge response for six equally spaced orientations (rows) and five different edge positions for each orientation, 0.55° apart (columns). Dark and light gray shading represents different disparities (d1 and d2, respectively). Each orientation and edge position was measured for both signs of the cyclopean edge (data not shown); opposite sign edges were created by simply swapping the disparities across the edge.

Figure 2.

Responses of the binocular energy model to stimuli containing cyclopean edges. a, Disparity tuning of the model cell. The disparities used to define the cyclopean edge in b and d are marked with dots at −0.4° (d1; dark gray) and 0° (d2; light gray). The disparities used to define the edge in c are shown with dots at −0.4° (d1; dark gray) and +0.4° (d3; light gray). The dotted black line indicates the response of the model cell to uncorrelated stimuli. b–d, Tuning of the binocular energy model cell for the orientation of a cyclopean edge (solid black line). As in a, the dotted black line indicates the response of the model cell to uncorrelated dots (uc). The dashed gray lines indicate the responses to the component disparities d1 = −0.4 (dark gray) and d2 = 0 (b, d) or d3 = +0.4 (c) (light gray). The line drawings along the x-axis represent the stimulus and receptive field at instructive edge orientations. Light and dark gray shading represent the disparities used to define the edge. The receptive field is shown with a black ellipse. The model V1 cell responds according to the proportions of the different disparities appearing in the receptive field. b, c, Applying different horizontal dot displacements to the right and left of the stimulus creates a vertical cyclopean edge, with a gap at the location of the edge in the view of one eye, which is filled with uncorrelated dots. Applying the same two disparities to the top and bottom of the stimulus creates a horizontal cyclopean edge with no gap at the edge location. In b, the model cell responds relatively weakly to an uncorrelated stimulus. Because the response of the model cell is determined by the combination of stimuli in its receptive field, it responds more strongly to a horizontal edge than to a vertical edge. In contrast, in c, the strongest response of the model is to uncorrelated dots, and the cyclopean edge response shows sharp increases for non-horizontal edges. The size of the uncorrelated region changes smoothly as a function of orientation, causing the response of the model cell to change as a function of orientation. d, Mis-centering the receptive field on the stimulus causes the relative proportions of the two disparities covering the receptive field to change with the orientation of the cyclopean edge. In this example, the receptive field sits over the top half of the stimulus (as shown schematically in the line drawings on the x-axis). The horizontal edge stimulus produces a strong response when the 0° disparity (light gray) is in the top half of the stimulus and a much weaker response when the disparities are swapped.

Figure 3.

Model responses to all cyclopean edge orientations and positions for the stimulus/receptive field configuration shown in Figure 2d. In the pseudocolor plot, the angular position of a patch (relative to the horizontal) represents stimulus orientation, whereas radial distance from the center represents edge position. The dotted gray line marks the middle of the five concentric rings, representing a cyclopean edge in the center of the stimulus and corresponding to the orientation tuning curve shown in Figure 2d. The central disc and the outermost rings (delineated by solid gray lines) represent the response to control stimuli with uniform disparity. These conditions can be viewed as edge locations that lie outside the stimulus, as reflected by their radial location. The corner regions outside the outermost ring represent the response to uncorrelated dots (uc). The mapping between radial location and edge position can be more clearly seen in the cross sections shown below and to the right of the pseudocolor plot. The cross section shown to the right represents the response of the model for a cyclopean edge oriented at 0°. The stimulus icons along the x-axis indicate the edge orientation and position for each point in the plot. The two uniform horizontal disparities used to define the edge, d1 and d2, are shown as the extrema of the position tuning curve, and the symbol color matches the color for these data in the pseudocolor plot. Note that d1 and d2 are connected to the position tuning curve using dashed lines, because these controls correspond to a range of edge locations falling outside the stimulus. The dashed line represents the response to uncorrelated dots. A cross section for an orthogonally oriented edge (θ = −90°) is shown below the pseudocolor plot, using the same plotting conventions. In both cross sections, it is clear that the cyclopean edge response never exceeds the response to the most effective uniform component disparity (d2 in this example).

Figure 4.

Example of cyclopean enhancement at a single edge orientation. The solid blue line plots the firing rate as a function of edge position for the preferred orientation (±1 SEM) of the cell. Dashed blue lines indicate the response to the uniform disparity controls (d1 and d2), whereas the dashed black line represents the response to a stimulus containing uncorrelated dots (uc). The receptive field is shown as a black rectangle superimposed on the stimulus icons along the x-axis. For this and all other example cells, the receptive field was measured using narrow strips of grating such as those described by Read and Cumming (2003). The rectangle represents the region enclosing all responses >10% of maximum. The spontaneous firing rate is indicated by the black asterisk on the y-axis. Vertical red lines indicate the extent of cyclopean enhancement (responses in excess of any uniform control). The summed length of the red lines is the total contribution from this orientation to our measure of cyclopean enhancement, r_EDGE (see Materials and Methods). The full value of r_EDGE was summed across all orientations. Sp/sec, Spikes per second; spont, spontaneous.

Figure 5.

Strength of the cyclopean edge response. a, Distribution of the magnitude of cyclopean edge response enhancement relative to the most effective uniform disparity control (summed over orientation and position). Red bars indicate responses that are significantly more responsive to a cyclopean edge stimulus than they are to any of the uniform stimuli used to define the edge (p < 0.05 by resampling). b, Comparison of the maximum cyclopean edge response to the maximum responses for any of the three uniform control disparities (d1, d2, uc). Red data points indicate responses that were significant for cyclopean enhancement. Nonsignificant responses are clustered near the identity line, indicating that they responded about equally to the optimal cyclopean edge stimulus and the best control stimulus. Such equal responses in non-edge-specific cells are not surprising; they occur for locations in which the receptive field is mostly covered by one disparity. In contrast, significant responses (red data points) are generally found considerably below the identity line (paired t test, p < 0.001), reflecting much larger responses for their optimal cyclopean edge than for any of the control stimuli. c, For a subset of cells (n = 112) for which we had both cyclopean edge and disparity tuning curves for the same size stimulus, we compared the maximum cyclopean edge response to the best response to any uniform horizontal disparity. As in b, red data points indicate cells that give enhanced responses for cyclopean edges. In general, cyclopean edge-specific responses tend to be found below the identity line (paired t test, p < 0.001), indicating that they responded better to the cyclopean edge than to any uniform disparity stimulus (ranging from −1.5 to 1.5° of horizontal disparity). Sp/sec, Spikes per second.

Figure 6.

Example neuron showing orientation-selective cyclopean enhancement. a, Response pattern for cyclopean edges with a range of orientations and positions. Plotting conventions are the same as for the pseudocolor plot in Figure 3. The solid blue line indicates the preferred orientation and sign of the cyclopean edge. b, Cyclopean edge response as a function of edge position for the preferred orientation. Error bars indicate ±1 SEM. The component disparity responses (d1 and d2) are indicated at either end of the position tuning curve, and the uncorrelated control response (uc) is shown by the dashed red line. The dotted green line represents the best fit for a binocular energy model cell. The peak of the position tuning curve clearly exceeds the expected response from a binocular energy cell, as well as the response to any of the control stimuli. c, Polar plot of cyclopean enhancement (red line). Although the units are spikes per second, these values are not raw response rates; rather, they indicate the difference between the response rate and the best estimate of the binocular energy cell response, averaged over position. Error bars indicate ±1 SEM. This neuron is only activated by one disparity sign, with a peak near the horizontal. The solid blue arrow marks the direction of the vector average, whereas the flanking dashed lines indicate the angle that contains 95% of these vectors across 1000 resampled values. The circular variance (cv) for this cell was 0.26. d, Polar plot of the contrast response (mean spike rate, red line) as a function of orientation. Manual exploration indicated that this cell was not direction selective, so responses were only measured for stimuli between 90 and 270°. To avoid giving the visual impression of direction selectivity, the data are replicated with a dashed line in the right half of the plot. Plotting conventions are the same as in c. Sp/sec, Spikes per second.

Figure 7.

Example of an orientation-tuned response to both signs of a cyclopean edge. a–c, Plotting conventions are similar to Figure 6. In a and b, the solid and dotted blue lines indicate the responses to both signs of an edge at the preferred orientation. This cell clearly responds to both signs of an optimally oriented edge better than it does to any of the uniform control stimuli (d1, d2, and uc), although in different edge positions. The response to both signs of the edge can be seen in the polar plot shown in c, in which there are peaks near both 90 and −90°. The vector average is shown extending in opposite directions, representing the use of the angle-doubled circular variance. d, Schematic of the type of receptive field organization that could give rise to the pattern of responses seen in a, with two subfields differing only in size and disparity preference. The different disparity tuning curves of the two subfields would produce a receptive field with an optimal response for the rectangular region with a disparity of −0.2°, surrounded by a background with a disparity of 0.2°. When tested with a single cyclopean edge, this receptive field would respond to both signs of the edge, in different locations. Sp/sec, Spikes per second.

Figure 8.

Example of a response that is selective for cyclopean edges but not for their orientation. a, b, Plotting conventions for the pseudocolor and polar plots are the same as in Figure 6, a (pseudocolor plot) and c (polar plot), except that there is no vector average shown in the polar plots (because of the absence of a defined preferred orientation). The examples in a and b were measured using different disparity pairs in the same neuron. c, Disparity tuning curve for this example neuron. The dashed line indicates the response to uncorrelated dots. The disparities used to define the edge in a and b are shown in red and green dots, respectively. Although the disparities used in both cases are similar, the response in a is significant for cyclopean edge response enhancement, whereas the response in b is not. Sp/sec, Spikes per second.

Figure 9.

Population measures of orientation tuning for cyclopean edges. a, Comparison of the circular variance with the confidence interval of the preferred orientation (α₉₅) for cyclopean edge-selective cells. Cells that responded significantly to both signs of a cyclopean edge are plotted as squares. The cyan, green, and red solid data points indicate the example responses in Figures 6–8, respectively (as they do in b and c). The histogram projected above the scatter plot shows the distribution of the circular variance found in our sample. The histogram projected to the right of the scatter plot indicates the distribution of confidence angles in our data. The majority of cells are found below the horizontal line, indicating confidence angles of <180° and reflecting significant orientation tuning. b, Comparison of the circular variance calculated on the cyclopean edge response (x-axis) and on the average firing rate (y-axis). Almost all data points are located above the identity line, reflecting the large “baseline” component contributed by the response to uniform disparities, which does not change with orientation. c, A more complete picture of the distribution of orientation-selective responses in the population is obtained by comparing the relative cyclopean edge responses for the non-preferred sign (sign index) and the orthogonal orientations (orthogonal index). Each index represents responses relative to the preferred orientation and sign. Points below the identity line responded better to the non-preferred sign of the preferred orientation than to orthogonal orientations (solid squares indicate data points in which this effect was significant). Note that both the orthogonal and sign indices can take negative values, indicating response suppression. The polar diagrams in each corner of the scatter plot represent idealized versions of the expected orientation tuning of a response falling in that quadrant. The solid pink data point is the response that was closest to the mean for both the sign and orthogonal indices. The orientation tuning of this example is shown in the central polar plot. cv, Circular variance.

Figure 10.

The influence of disparity signals and cyclopean edge responses on the location of response maxima. The neural response can be thought of as the combination of a uniform disparity signal (top) and a cyclopean edge signal (middle). Solid and dashed lines reflect responses to opposite sign edge stimuli. The idealized neuron responds in the same spatial location for both response components, as shown by the black oval superimposed on the gray stimulus icons. Summing the response components shown in the top and middle panels produces a response that peaks at different locations for opposite sign responses (bottom).

Figure 11.

Effects of changes in edge sign on the location of cyclopean edge responses. The histograms plot the difference between the center of mass for cyclopean edge responses for opposite signs of the edge (at the preferred orientation). Only cells that showed a significant response to the non-preferred sign of an edge at the preferred orientation were included in this analysis. Gray bars indicate responses in which the center of mass of cyclopean enhancement was significantly different for opposite signs of the edge. a, Cells with an orientation-selective response to both edge signs (respond better to both signs of an edge at the preferred orientation than they do to edges at orientations orthogonal to the preferred). b, Cells only showing orientation-selective responses to the preferred edge sign (respond better or equally well to the orthogonal orientation as they do to the non-preferred sign of an edge at the preferred orientation).

Figure 12.

Comparison of orientation tuning for cyclopean edges and contrast-defined contours. a, Preferred orientation for cyclopean versus contrast contours, for neurons showing significant orientation selectivity to both stimulus types. The solid lines indicate the identity line. To emphasize the circularity of the data (period of 180°), we plotted each data point four times, separated by 180° on the x- and y-axes. A single set of data points is plotted in red. Solid red symbols indicate cells in which the circular variance for both contrast stimuli and cyclopean edges was <0.75. Most of these neurons, for which preferred orientation is clear, lie close to the identity line, indicating similar orientation preferences for cyclopean edges and contrast stimuli. The histogram projected along the diagonal axis indicates the difference between the cyclopean edge and contrast orientation peaks for all cells that were jointly tuned for the orientation of contrast and cyclopean edges. The red line indicates the wrapped normal distribution that best approximates the data (SD = 41°). b, Circular variance for cyclopean edges versus contrast stimuli. The diagonal line indicates the identity. Many neurons are considerably more selective for contrast stimuli than they are for cyclopean edges (indicated by points below the identity line; p < 0.01, paired t test). Solid symbols indicate example cells, shown in Figure 13.

Figure 13.

Examples of orientation tuning for cyclopean edges and contrast stimuli. Blue and red curves represent the responses to cyclopean edges and contrast stimuli, respectively. Note that the two curves have different axes: the axis for cyclopean edge stimuli is shown to the left of the data and indicates cyclopean edge response (see Materials and Methods), whereas the axis for contrast responses is shown to the right of the data and indicates the mean firing rate minus the spontaneous firing rate. Error bars indicate ±1 SEM (by resampling). a, Cell that is well tuned for both types of stimuli. b, Cell that is well tuned for cyclopean edges but not for contrast stimuli. c, Cell that is well tuned for contrast but poorly tuned for cyclopean edges. sp/sec, Spikes per second.