Journal of Vision - Suppression of monocular visual direction under fused binocular stimulation: Evoked potential measurements, by Norcia, McKee, Bonneh, & Pettet

Anthony M. Norcia	Smith-Kettlewell Eye Research Institute, San Francisco, CA, USA
Suzanne P. McKee	Smith-Kettlewell Eye Research Institute, San Francisco, CA, USA
Yoram Bonneh	Department of Neurobiology, The Weizmann Institute of Science, Rehovot, Israel
Mark W. Pettet	Smith-Kettlewell Eye Research Institute, San Francisco, CA, USA

Visual evoked potentials (VEPs) were recorded in response to a vernier onset/offset target presented to one eye that was combined with matching static targets in the other eye. The monocular response was dominated by a negative peak at 160 ms that occurred after a set of offsets was introduced into a one-dimensional random bar pattern. The static targets produced no discernible VEP response by themselves, but when fused binocularly with the oscillating vernier target, they produced shifts in perceived visual direction that influenced the VEP response. A vernier target fused with static vertical bars was perceived to alternate in depth between a flat surface and one broken into two interleaved surfaces. The response to this “surface-breaking” was as large or larger than the response to the monocular vernier offset. This response was much reduced when the oscillating vernier was fused with a static offset vernier (5’ offset) that produced a percept of segregated regions moving in depth. Apparently, the VEP is strongly driven by shifts in visual direction that alter surface, texture, or contour contiguity.

The lateral placement of the eyes in humans and other species presents each eye with a slightly different view of the world. This disparity between the two images provides the brain with information that can be used to compute depth via stereopsis. The slightly different views also present something of a problem–the brain must assign a unique visual direction to objects to guide action in the environment. The assignment of a single visual direction (allelotropia; von Tschermak-Seysenegg, 1952) involves recoding into a nonretinotopic representation. This recoding is associated with the suppression of sensitivity to monocular displacements. For example, oscillatory motion thresholds are lower when the half-images oscillate in-phase (translation) compared to when they are in anti-phase (i.e., motion in depth) (Sumnall & Harris, 2002; Tyler, 1971; Tyler & Cavanagh, 1991; Westheimer, 1990). Similarly, the half-images of a motion-in-depth stimulus (equal and opposite lateral motions) are much more easily detected amidst noise than their fused combination (Harris, McKee, & Watamaniuk, 1998; Harris & Sumnall, 2000).

McKee and Harrad (1993) found that monocular vernier acuity was much higher than when the same vernier target was interocularly paired with an offset vernier target that produced a standing disparity of 4 arcmin between the upper and lower lines of the target. The precise information about visual location provided by one half-image was lost in the fused binocular combination. McKee and Harrad referred to this phenomenon as “fusional suppression” to distinguish it from other forms of interocular suppression, such as rivalry and the constant suppression found in strabismus.

Taken together, all these results indicate that the visual system has little access to the monocular components of binocularly fused targets, even if the monocular signals provide better information about motion or position. The visual system thus appears to sacrifice some sensitivity to monocular information in favor of single binocular vision.

In the present study, we recorded visual evoked potentials in a variant of the McKee and Harrad task. The goal of the study was to determine if there is an analogous reduction in the evoked response under conditions that support fusion with an accompanying shift in visual direction, and if so, whether all or only part of the response is suppressed. We find that the monocular response to vernier offset is strongly reduced by the introduction of a standing disparity between the target components, especially at later time points. This suppression is not due simply to the presence of a high-contrast image in the other eye (dichoptic contrast masking) because suppression is not observed when there is no standing disparity offset.

Eleven visually normal adult observers participated, one of whom was excluded due to poor signal-to-noise ratio. Each observer had a visual acuity in each eye of 6/6 or higher and demonstrated normal stereopsis on the Frisby free-space stereo-test and on a random-dot stereoacuity test. Informed consent was obtained from each observer, and the research reported here complied with the principles set forth in the Helsinki Declaration.

Dichoptic viewing was obtained using anaglyphs projected onto a high-gain screen via an Infocus Lite Pro 720 (Experiment 1) or a Sanyo PLC-XU30 LCD projector. Each half-image (red and blue) was generated on alternate video lines of an 800 X 600 pixel raster. Interlacing allowed for 8 bits of brightness resolution for each color. The video frame rate was 72 Hz. Red and blue dichroic, additive color-separation filters (OCLI, Inc., Santa Rosa, CA) were used. Each filter transmitted more than 85% of the light in its pass-band. Transmission dropped to 50% at 592 and 493 nanometers for the red and blue filters, respectively. Cross-talk was not visible psychophysically. It should be noted that these levels of cross-talk were not obtainable with LCD flat panel displays or CRTs. A –0.5-diopter lens was placed in front of the eye with the blue-pass filter to compensate for the difference in focus between red and blue channels caused by chromatic aberration. Luminances through the filters were measured photometrically for each color, and separate gamma correction curves were calculated to both linearize the contrast response of each color channel and to balance the luminances across eyes.

LCD displays differ from conventional CRTs because digital re-processing of the synch and video signals inside the projector causes a delay between the update of the video memory and the opening of the LCD shutter in front of the lamp. Moreover, the LCD takes different amounts of time to go from opaque to clear and vice versa.

We measured the processor and shutter delays for the Infocus 720 with a PIN diode (Figure 1). The processor delays are between 5 and 10 ms with the projectors we have used, based on the time it takes for the light output to change after an update. Secondly, the shutter opening is not instantaneous, but has a rise-time of 40-60 ms on opening and a fall-time of 30-40 ms. Light output was equal on rise and fall phases of the shutter at 20 ms after the video D/A is updated.

Figure 1. Temporal characteristics of the InFocus LCD projector. Rise-time (filled symbols) and fall-time (open symbols) were measured by digitizing the output of a linear photo-diode. Opening and closing of the shutter are delayed relative to the updating of video memory by digital processing delays within the projector and by the characteristics of the liquid crystal shutter.

We also measured temporal modulation transfer functions (gain and phase curves) for the Infocus 720 projector. The gain (contrast vs. temporal frequency) characteristic of the display is shown in Figure 2A. Contrast was maintained to within 20% of nominal up to approximately 10 Hz. The phase versus frequency plot shown in Figure 2B is linear and is consistent with a delay of 17-ms delay for a 72-Hz raster. This value was computed by dividing the slope of the phase plot by 360 deg. This value is similar to the 20-ms time of equal light output on rise and fall phases, and for convenience we have used a 20-ms correction for all waveform data.

Figure 2. Frequency-domain characteristics of the Infocus LCD projector. The contrast of a very low spatial-frequency grating was modulated in a square-wave fashion over a range of temporal frequencies. Light output was measured using synchronous detection. Gain is normalized to 1-Hz output. A. Gain decreases with increasing temporal frequency. B. Phase shows a progressive shift consistent with a 17-ms constant delay at each frequency.

The experiments made use of a reference response technique, in which the same temporally modulated pattern was presented to one eye in all stimulus conditions. The reference or “test” pattern consisted of a high-contrast (70-80% contrast) broadband random bar pattern into which a set of 5 vernier offsets was periodically introduced and withdrawn every 500 ms (stimulus frequency of 1 Hz). In the monocular condition, this image was presented alone and the other eye viewed a blank field, as illustrated schematically in Figure 3 (left). In the remaining conditions, static, fusable patterns were presented to the other eye. These patterns did not generate an evoked response, but their effects were observed as modifications of the response to the constant reference stimulus in the other eye.

Figure 3. Schematic illustration of stimuli. The top panels show schematic stereo half-images for each of the three main stimulus conditions. T1 and T2 indicate the two states of the display, which alternate at 1 Hz. All stimuli were composed of random-bar patterns. In the monocular and zero disparity conditions, segmented bands appear and disappear from a uniform patterned background. In the 5-arcmin pedestal condition, the bands are always segregated from the static background panels. The bottom panels show a top-down view of the motion of a single bar (indicated by the lines between T1 and T2) in the modulated part of the stimulus for monocular (left), binocular zero disparity pedestal (center), and binocular 5-arcmin pedestal (right) conditions.

In one condition, the static target was a full-field version of the test pattern presented without any vernier offsets (Panum’s limiting case; Figure 3, center). When viewed binocularly, the observer saw a pattern consisting of bands of static, zero disparity bars that alternated with bands that moved in depth from a collinear background (zero disparity) to a small disparate offset in front of the static bands (crossed 5-min disparity). This offset size is at least 10 times threshold for the VEP (Norcia et al., 1999). In a second type of condition, standing disparities were created by introducing vernier offsets in the static image in the other eye (Figure 3, right). This pedestal created images that matched the dynamic stimulus in all respects, except that a static vernier offset was introduced in correspondence with the moving portions of the pattern in the other eye. In these conditions, the disparate bands appeared to float in front of the static band and move in depth from 5 to 10 arcmin of crossed disparity. Field size was 20-deg wide by 15-deg high at a viewing distance of 190 cm. The vernier offset sections were 2.5-deg high, alternated with static sections of the same height.

The EEG was recorded at 432 Hz over an amplifier bandwidth of 0.3 to 100 Hz (–6 dB) using Grass Instruments model P-511 amplifiers. Recordings were made from O1, Oz, and O2, each referenced to Cz of the International 10-20 system. Electrode impedances were maintained below 5-10 kOhms.

Stimuli were presented in trials that lasted 11 s. The first second of the data record was discarded to avoid start-up transients. Trials were run in blocks of five over each stimulus condition, with two repetitions for a total of 10 trials (100 s) per condition. The order of presentation of the five trial blocks was randomized across conditions. A new random pattern was created at the beginning of each block.

Conventional time-locked averages were computed over 1000-ms time epochs. In the records presented below, the first transition was from the misaligned state to vernier alignment, the second transition at 500 ms was from the aligned state to the offset state (considered in terms of the dynamic half-image). Difference potentials were calculated and the statistical significance of the difference at each time point was tested using permutation methods described in the Appendix. The permutation testing procedure accounts for the correlation between time-samples and points of significant difference are indicated by black dots on the time-averages in Figures 4-6.

Spectral analysis was performed with an adaptive filter technique (Tang & Norcia, 1995). Error statistics for these coherent or vector averages from individual observer data (Figure 9) were calculated using the methods described by Victor and Mast (1991). Grand averages were computed for both time averages and spectrum averages. For the adaptively filtered data, the spectrum averages were incoherent, that is an individual observer's data was averaged as a scalar value number, independent of their response phase, and the error bars in Figures 7 and 8 are conventional SEMs. We also calculated discrete Fourier transforms of the time-averaged data at a spectrum resolution of 0.5 Hz (Figures 4-6, left panels).

Grand average waveforms for seven observers are shown in Figure 4, contrasting the monocular (dark lines) and binocular 5-arcmin disparity conditions (gray lines). The difference potential is shown in the right panels, and the discrete Fourier transform of the waveform data is shown in the left panel. Time zero in Figures 4-6 is the display update, and the data have been shifted to account for the update latency of approximately 20 ms. The waveforms from O₁, O₂, and O_zare similar in each condition, with the monocular response consisting of a smaller multi-phasic response at the transition to the “make” state (alignment) and a larger multi-phasic response at the transition to the “break” state (misalignment). This asymmetry of the vernier onset/offset response was first reported by Levi, Manny, Klein, and Steinman (1983). This asymmetry of the response waveform leads to odd harmonics in the response spectrum.

Figure 4. Group average (n = 7) data for the monocular and binocular 5-arcmin pedestal conditions. The left-hand panels plot amplitude spectra, with the data from the monocular condition plotted above the x-axis (black lines) and the binocular 5-arcmin pedestal condition plotted below the x-axis (gray lines). The response is composed of a series of spikes at exact integer multiples of the 1-Hz stimulus frequency. The addition of the disparate pedestal reduces the amplitude of the evoked response, particularly at low-response frequencies. The middle panels plot the waveforms for the two stimulus conditions using the same color coding. During the first half of the records, the stimulus was in the collinear state and in the second half, the test stimulus contained an offset (noncollinear). The addition of the disparate pedestal reduces the amplitude of the evoked response. Significant differences are indicated by solid circles on the waveforms. Right panel. Difference potential for waveforms in the middle panel. The difference potential is maximal at about 170 ms after the introduction of the offset in the test pattern. Electrode locations were O₁, O_z, and O₂. Time zero is with respect to actual display update.

When the image containing 5-arcmin offsets is added to the other eye, there is a small but nonsignificant suppression of the response at the make transition, and a larger, statistically significant suppression peaking 170 ms after the break transition (Figure 4). Suppression occurs without changing peak latencies.

Figure 5 compares grand average waveforms for the same seven observers in the monocular and zero disparity pedestal conditions. The results with the zero disparity pedestal differ from those in the 5-arcmin condition in that the amplitude of the peak at 670-170 ms is only mildly suppressed but it is shifted in latency by about 20 ms. Note that this display (second in Figure 3) appears to be shifting from a flat surface to a broken plane at the break transition. Generally, the response to the broken plane was similar in magnitude to the response to the broken contour (i.e., the vernier offset).

Figure 5. Group average (n = 7) data for the monocular and binocular 0-arcmin pedestal conditions. The left-hand panels plot amplitude spectra, with the data from the monocular condition plotted above the x-axis (black lines) and the binocular 0-arcmin pedestal condition plotted below the x-axis (gray lines). The addition of the 0-disparity pedestal does not produce the general amplitude reduction seen with the 5-arcmin pedestal. The middle panels plot the waveforms for the two stimulus conditions using the same color coding. The addition of the 0-disparity pedestal produces a small reduction of the amplitude of the major negative peak, along with a latency shift. Significant differences are indicated by solid circles on the waveforms. Right. Difference potential for waveforms in the middle panel. The difference potential is maximal at about 150 ms after the introduction of the offset in the test pattern. Time zero is with respect to actual display update.

Photometric tests indicated that the image updating was not affected by the addition of the pedestals–the pedestal effects thus have a neural origin. The difference potential reflects the latency shift as a negative going potential peaking at ca 150 ms . In contrast to the 5-min offset condition, the difference potential is positive rather than negative after 180 ms. This was due to the activity centered around 280 ms being larger than the monocular control in the zero disparity condition, rather than being smaller as in the 5-arcmin condition.

Finally, Figure 6 compares the waveforms from the two binocular conditions that differ only in the standing disparity created by the pedestal. The pattern of results is very similar to that seen in Figure 4 where the monocular response was compared to that from the disparate pedestal condition. The standing disparity caused an overall suppression of response amplitudes without changing the peak latencies. In this comparison, significant differences are also seen about 300 ms after the make transition. There was a nonsignificant trend in this direction in Figure 4.

Figure 6. Group average (n = 7) data for the binocular 0-arcmin and binocular 5-arcmin pedestal conditions. The left-hand panels plot amplitude spectra, with the data from the monocular condition plotted above the x-axis (black lines), and the binocular 0-arcmin pedestal condition plotted below the x-axis (gray lines). The comparison of 0- and 5-arcmin conditions (middle panels) shows relatively larger late positive activity after the noncollinear to collinear transition (first half), as well as greater relative negativity after the collinear to noncollinear transition (second half). Significant differences are indicated by solid circles on the waveforms. Right. Difference potential for waveforms in the middle panel show the sustained relative positivity and the broad transient relative negativity. Time zero is with respect to actual display update.

In the time domain, the monocular response to the onset of vernier misalignment was substantially larger than the response at the return to alignment. The response itself is a complex waveform with peaks of different polarity and latency that are not directly interpretable in functional terms. Response peaks are a concatenation of responses to motion, vernier onset, and disparity, when present. However, by considering symmetry relationships, one can decompose the different response components in the frequency domain. The basic response asymmetry yields a response spectrum that contains both odd and even harmonics when temporally periodic stimuli are used (Norcia, Wesemann, & Manny, 1999). The odd-harmonic components are associated with a nonlinear response to the change in spatial configuration of the stimulus (the alignment-to-misalignment transition yields a different response than the reverse). Motion cues, local contrast changes, and any other processing that is common to the two states contribute to the even harmonics in the spectrum. Spectral analysis thus provides an alternative method of defining components based on their symmetry relationships, which in this context are related to figural (asymmetric component/odd-harmonics) and nonfigural (symmetric components/even harmonics) processing.

The addition of a disparate 5-min pedestal has the effect of lowering both odd and even harmonic components of the response relative to what is measured in either the monocular or zero disparity pedestal conditions (Figures 4 and 6). As aggregate measures of figural and nonfigural response components, we pooled the first 4 odd harmonics by taking the square root of the sum of their powers (quadrature summation) and did the same for the first 4 even harmonics (Figure 7). A repeated measures multivariate ANOVA was used to test for differences between means. There was a significant effect of viewing condition (monocular, binocular 0 disparity, and binocular 5-min disparity; Wilk’s Lambda = 0.04, F(2,5) = 60.56, p < .001), and a significant interaction between viewing condition and the odd versus even harmonic measures (Wilk’s Lambda = 0.18, F(2,5) = 11.04, p = .015).

Figure 7. Group average (n = 7) spectral data for the monocular, binocular 0, and binocular 5-arcmin pedestal conditions. A shows the pooled odd-harmonic responses, and B shows the pooled even-harmonic responses. The addition of a disparate 5-min pedestal (black bars) has the effect of lowering both odd and even harmonic components of the response relative to what is measured in either the monocular (white bars) or zero disparity (gray bars) pedestal conditions.

The interaction effect shown in Figure 7 is driven primarily by the fact that the addition of a nondisparate pedestal causes the odd-harmonics to increase relative to the monocular condition, while the opposite is true for the even harmonics. If one compares the amount of suppression across harmonics, one would conclude that odd-harmonics are relatively more suppressed by the disparate pedestal if the comparison was made to the zero disparity pedestal condition, but not if the comparison was made to the monocular condition.

The original psychophysical studies of fusional suppression (McKee & Harrad, 1993) used a monocular condition for comparison. However, a number of our observers reported transient suppression of the test image when mean luminance fields were used in the monocular control condition, perhaps indicating transient rivalry suppression. In the next experiment, we compared mean luminance monocular controls with monocular controls in which the nonviewing eye was physically occluded. The data from this experiment are plotted in Figure 8A. Response amplitudes were larger with occlusion of the eye that did not receive the test, that is, there was a main effect of occlusion type (F(1,4) = 10.578, p = .031). Even harmonics were larger than odd harmonics (F(1,4) = 47.279, p = .002), but occlusion type did not interact with the harmonic being measured (F(1,4) = 0.117, p = .75). The binocular zero disparity pedestal may thus be a more stable control condition for comparison with disparate pedestals, because it does not induce rivalry.

Figure 8. A. Effect of monocular viewing conditions (n = 5). Response amplitudes were larger with occlusion of the eye that did not receive the test (black) compared to that eye viewing a mean luminance field (mean). Responses from the binocular zero disparity condition (0 disp) are also shown for comparison. B. Disparity tuning of suppression. Disparate pedestals reduced the amplitude of both odd and even harmonic components. Suppression was constant over the range of 5 to 120 arcmin and was larger for odd (filled bars) versus even harmonics (open bars).

McKee and Harrad (1993) found that the amount of suppression was maximal for disparities in the range of 4 to 20 arcmin. In a second experiment, we varied the pedestal disparity between 0 and 120 arcmin. One of the original seven observers participated, along with four new observers.

The disparity tuning function is shown in Figure 8B. Disparate pedestals reduced the amplitude of both odd and even harmonic components. We did not observe tuning over the range of 5 to 120 arcmin. Because of this, we collapsed the data from the 5 to 120 arcmin conditions and tested whether the odd and even harmonics were equally suppressed. As is evident from the figure, the odd harmonics were more suppressed than the even ones by the disparate pedestals; there was a significant disparity by harmonic interaction: F(1,4) = 9.876, p = .035). In McKee and Harrad (1993), single lines rather than extended targets were used. With line stimuli, once the disparity was so large as to be diplopic, the observer simply examined the vernier offset in one half-image and ignored the other. This diplopic percept of the isolated half-image may not be possible with our extended stimuli.

The fact that the pattern of interaction differs between the zero disparity and 5-120 arcmin disparity pedestals indicates that the suppression is not simply due to the presence of a high-contrast image in the other eye. One could still argue that the disparate pedestal images contain spectral components that are in the same spatial frequency and orientation bands as those that generate the test response and that dichoptic pattern masking occurs at these spatial frequencies and orientations.

To differentiate fusional suppression from dichoptic pattern masking, we varied the contrast of the static offset target, while keeping the contrast of the modulating pattern the same as in the previous experiments. Dichoptic contrast masking shows Weber law behavior (Legge, 1984), and if this is the mechanism underlying the suppression we observe, one would expect a proportionate reduction in masking as the static pattern contrast was lowered. As can be seen in Figure 9, there is no significant change in the odd harmonics with contrast reductions of up to a factor of almost 4. The masking of the even harmonics does show an effect of contrast: amplitudes increased in both observers as the contrast of the static pedestal decreased to zero (monocular case). Dichoptic contrast masking, thus, does not explain the suppression of the odd-harmonics, but may well account for the amplitude reduction of the even harmonics.

Figure 9. Effect of pedestal contrast on suppression magnitude. The contrast of a 5-arcmin disparate pedestal was varied over a 4:1 range (20 to 80%). The point at 0 contrast was monocular. Masking was constant for two observers when the first harmonic (1F) was measured (A), but increased with increasing pedestal contrast when the second harmonic (2F) was measured (B).

There have been numerous demonstrations of suppressive binocular interactions in the human VEP. In some of these cases, the two-half-images were not fusable and lead to rivalry (Apkarian, Levi, & Tyler, 1981; Brown, Candy, & Norcia, 1999; Brown & Norcia, 1997; Cobb, Morton, & Ettlinger, 1967; Lansing, 1964; Lennerstrand, 1978b; Norcia, Harrad, & Brown, 2000; Srinivasan, Russell, Edelman, & Tononi, 1999; Tononi, Srinivasan, Russell, & Edelman, 1998; Tyler & Apkarian, 1985; Valle-Inclan, Hackley, de Labra, & Alvarez, 1999). In others, the targets have been different in the two eyes, but presented too briefly to result in rivalry (Lehmann & Fender, 1967; Lehmann & Fender, 1968; Odom & Harter, 1983; Spekreijse, van der Tweel, & Regan, 1972; Towle, Harter, & Previc, 1980). Potentially fusable but nondisparate (flat binocular percept) targets have also been used (Brown et al., 1999; Harter, Seiple, & Musso, 1974; Harter, Towle, & Musso, 1976; Harter, Towle, Zakrzewski, & Moyer, 1977; Lennerstrand, 1978a; Norcia et al., 2000). The suppression observed for the even harmonics (Figure 9B) could be due to contrast masking, similar to that observed in these previous studies. We found that the magnitude of even harmonic suppression was dependent on contrast and the older literature has linked the strength of masking to various measures of stimulus salience. Contrast masking does not underlie the reduction of the odd-harmonics that is the strongest effect in our data (cf. Figure 9).

In our experiments with disparate pedestals, suppression is not observed until well after the evoked response has begun. The magnitude of suppression is maximal at about 200 ms and continues for another 200 ms. It is interesting that this time period is also when the zero disparity condition shows its greatest amplitude increase relative to the monocular condition (positive vs. negative difference potential, Figures 4 and 5. The time-course of suppression by a disparate pedestal appears to be later than previously reported in dichoptic masking studies. For example, Lehmann and Fender (1968) found masking of flash responses by static pattern at 120 ms and Harter et al. (1976) reported effects at 110 ms under similar conditions. de Labra and Valle-Inclan (2001) found rivalry suppression to take effect starting at 100 ms and Valle-Inclan et al. (1999) found effects as early as 70 ms in rivalry.

In the monocular vernier VEP response, it has been shown that the first harmonic component is likely to be a nonlinear term related to lateral interaction. That is, it is the difference frequency between the moving elements at F1 = 1 Hz and the static element at F2 = 0 Hz (cf. Zemon & Ratliff, 1984). This term is very sensitive to the relative position of static and moving elements. It goes away when the motion is symmetric (symmetric misalignment/misalignment) around the reference (Norcia et al., 1999), and it diminishes considerably when the moving elements are shifted laterally away from collinearity (asymmetric misalignment/misalignment; Zemon & Ratliff, 1982). This term also drops off rapidly when a gap is introduced between the static and moving elements (Norcia et al., 1999; Zemon & Ratliff, 1982). These results suggest that there is a position-selective form of lateral interaction that is specialized for continuous collinear stimuli. In our zero disparity condition, collinearity is broken in the monocular half-image, but with fusion, coplanarity is also broken. We would argue that coplanarity is the more general case. In the monocular case, asymmetric misalignment/misalignment does not evoke the lateral interaction term, notionally because the elements are out of range of the “collinear integration” system. In the disparate pedestal case, one could make an analogous argument that the modulation is between two non-coplanar states, neither of which activates the interaction that is centered on coplanarity.

Coplanarity is not available monocularly and perhaps the sensitivity of the “lateral interaction” to collinearity is a degenerate case of a more general sensitivity to 3D coplanarity. In the real world, vernier breaks are frequently, if not always, associated with depth discontinuities. Faults in real surfaces will typically have a range of depth offsets on either side of them. This may be the “generic view” of discontinuity, with pure vernier offset (no depth discontinuity) being a special case.

The form of the VEP to vernier onset also resembles that recorded in studies of texture segmentation (Bach & Meigen, 1992; Bach & Meigen, 1997; Lamme, Van Dijk, & Spekreijse, 1992), comprising a prominent negative peak around 160-180 ms. Texture segmentation stimuli all have position discontinuities at the texture boundaries, and these may be processed by a mechanism similar to the one that detects offsets in both 2D and 3D. Similar segmentation-related VEPs have been reported for boundaries defined by luminance, orientation motion, and disparity cues (Bach & Meigen, 1997), which also suggests a general purpose mechanism operating on either 2D or 3D inputs.

Coplanarity involves smoothly changing (slants or tilts) or nonchanging disparity (fronto-parallel) gradients. Disparity information appears to be strongly pooled along smooth disparity gradients– Vreven, McKee, and Verghese (2002) have found that disparity increment threshold is poor when the increment is placed on a continuous surface, rather than being presented in isolation at the same standing disparity. This reduction of stereo increment thresholds on smooth surfaces may be a result of the nonlinear interaction observed in the present experiments.

Unlike collinearity, coplanarity cannot be defined in terms of two dimensions on the retina, and, therefore, is not definable on the 2D-cortical representation. The effect of gaps on vernier acuity and the vernier VEP and the windmill dartboard stimulus of Zemon and Ratliff have been interpreted as indicating the spatial scale of 2D-lateral connections. The gap effects on vernier acuity and the VEP are biggest over 3-10 arcmin, which maps onto a cortical distance about the size of a V1 hypercolumn, and previous studies have suggested that this is the fundamental limiting factor (Ratliff & Zemon, 1982). However, in our disparate case, the difference between the zero disparity case and the 5-min case is in the disparity domain, not in the 2D-retinal/cortical representation. Therefore, it is likely that this interaction is a disparity domain rather than a space domain interaction, where the coordinates of the stimuli are computed in three dimensions after the assignment of binocular visual direction (allelotropia). It is thus possible that this computation is done outside of first-tier visual areas where the representation is strongly retinotopic. This interpretation is consistent with the long latency of suppression we have observed.

The significance of time-domain difference potentials was performed using a permutation test based on the work of Blair and Karniski (1993). Given a null hypothesis of no effect due to stimulus condition, the waveform responses for any two conditions from a given subject are exchangeable. Response waveforms were randomly exchanged for each individual in the pool of subjects from a given group. For this permutation sample, we calculated the mean difference potential and the T-value of this difference for each time point in the response waveform. Repeatedly re-randomizing the permutation of condition exchanges for each subject allowed us to accumulate a reference distribution of T-values. From each permutation sample, we noted the maximum T-value over all time points in the response waveforms, and accumulated these maximum T-values into a second reference distribution. The difference potential at a given time point in the original, unexchanged response data was deemed significant if its T-value exceeded 95% of those in the maximum T-value reference distribution.