**Patterns in the two eyes' views that are not identical in hue or contrast often elicit an impression of luster, providing a cue for discriminating them from perfectly matched patterns. Here we attempt to determine the mechanisms for detecting interocular differences in luminance contrast, in particular in relation to the possible contributions of binocular differencing and binocular summing channels. Test patterns were horizontally oriented multi-spatial-frequency luminance-grating patterns subject to variable amounts of interocular difference in grating phase, resulting in varying degrees of local interocular contrast difference. Two types of experiment were conducted. In the first, subjects discriminated between a pedestal with an interocular difference that ranged upward from zero (i.e., binocularly correlated) and a test pattern that contained a bigger interocular difference. In the second type of experiment, subjects discriminated between a pedestal with an interocular difference that ranged downward from a maximum (i.e., binocularly anticorrelated) and a test pattern that contained smaller interocular difference. The two types of task could be mediated by a binocular differencing and a binocular summing channel, respectively. However, we found that the results from both experiments were well described by a simpler model in which a single, linear binocular differencing channel is followed by a standard nonlinear transducer that is expansive for small signals but strongly compressive for large ones. Possible reasons for the lack of involvement of a binocular summing channel are discussed in the context of a model that incorporates the responses of both monocular and binocular channels.**

*interocular (de)-correlations*(Cormack et al., 1991; Stevenson et al., 1992; Reynaud & Hess, 2018),

*dichoptic differences*(e.g., Yoonessi & Kingdom, 2009; Malkoc & Kingdom, 2012)

*binocular luminance disparities*(Formankiewicz & Mollon, 2009), and simply

*interocular differences*, the term we will employ here. An interocular difference in contrast or hue can generate an impression of luster, a cue that has been argued to enable detection of interocular differences (Formankiewicz & Mollon, 2009; Yoonessi & Kingdom, 2009; Malkoc & Kingdom, 2012; Jennings & Kingdom, 2016; Kingdom et al., 2018). Recent studies have suggested models for interocular difference detection based on luster (Georgeson et al., 2016; Jennings & Kingdom, 2016) and have furthermore demonstrated that interocular difference detection is an adaptable dimension of vision (Kingdom et al., 2018).

*C*

_{diff}(Kingdom et al., 2018), we use this as our measure here. For the situation in which the contrasts in the two eyes are the same,

*C*

_{diff}is given by

*C*is the RMS contrast of the image for each eye,

*ϕ*is the interocular difference in grating phase, and contrast is the same for all the component spatial frequencies of the image.

*ϕ*and

*C*

_{diff}of zero—and the other with a nonzero

*ϕ*and hence positive

*C*

_{diff}. On the right is shown a second condition, where the upper pair is interocularly anticorrelated—that is, of opposite luminance polarity between the eyes—produced by setting

*ϕ*to 180° and resulting in a maximum

*C*

_{diff}. The other pair has a smaller

*ϕ*and hence smaller

*C*

_{diff}. In the experiments to be described, our observers were required to discriminate between pairs of stimuli with different

*C*

_{diff}, to determine their just-noticeable differences (JNDs). We did this for both the lower range of

*C*

_{diff}, as exemplified by the left-hand figure, and the upper range, as exemplified by the right-hand figure.

*C*

_{diff}we would expect JNDs to be mediated by the B− channel, as it would signal the difference between zero and some positive value, using the early, noncompressive part of its response range. On the other hand, in the upper range of

*C*

_{diff}the JNDs would be best served not by the B− channel, as it would be operating within its compressive response range, but instead by the B+ channel, again because it would be signaling the difference between zero and some positive value. Figure 2 helps to reinforce the point by showing how the binocular contrast difference (in red) and the binocular sum (in green) of a single dichoptic pair change as a function of

*ϕ*, where the binocular sum

*C*

_{sum}is given by

*C*

_{diff}increases and saturates at large phase disparities, whereas

*C*

_{sum}does the opposite. Note that the saturated parts of these curves are a physical property of the way that the sum and difference signals vary with phase disparity, a property that would only be exacerbated by an internal compressive transducer. The main point, however, is that for interocular pairs that fall within the range of

*ϕ*= 0° to 90°, the B− channel (responding to

*C*

_{diff}) would be expected to be most differentially responsive, whereas for pairs that fall within the range of

*ϕ*= 90° to 180°, the B+ channel (responding to

*C*

_{sum}) would be expected to be most differentially responsive. Our main aim is to test this prediction by comparing performance found for the two ranges of

*ϕ*illustrated in Figure 1.

*C*

_{diff}by varying the interocular phase difference

*ϕ*between the dichoptic images rather than by varying the relative contrasts of the two monocular gratings? Our reasons have been detailed elsewhere (Kingdom et al., 2018), but in brief the use of phase difference is first because it minimizes the possibility that global contrast can be used as a cue to the presence of an interocular difference (because RMS contrast is the same in both eyes and the same for all

*ϕ*) and second because of the simple mathematical relationship between interocular phase difference and local interocular contrast difference, as in Equation 1. Finally, our use of horizontally oriented gratings minimizes stereo-depth cues to the stimulus containing the interocular difference, because horizontally oriented gratings have only vertical disparities, and these appear to play no role in depth perception, at least in central vision.

*a*was randomly 1 or −1 across SF. The randomization of

*a*did introduce random variations in the waveform structure (see Figure 1) but did not perturb the value of

*C*

_{diff}. One member of each two-alternative forced-choice pair comprised a fixed, or pedestal, level of

*C*

_{diff}, and the other a pedestal plus or minus a variable Δ

*C*

_{diff}. In the experiment exploring the lower range of

*C*

_{diff}, the pedestal

*C*

_{diff}involved

*ϕ*ranging from 0° to 90°, with Δ

*C*

_{diff}an increment. In the experiments exploring the upper range of

*C*

_{diff}, the fixed level of

*C*

_{diff}involved

*ϕ*ranging from 180° to 90°, with Δ

*C*

_{diff}a decrement. We will refer to the two types of experiment as the lower- and upper-range

*C*

_{diff}or

*ϕ*experiments.

*C*

_{diff}according to previous responses. The base phase

*C*

_{diff}, the task on each trial was to identify the position (upper or lower) of the patch containing the bigger

*C*

_{diff}—observers were instructed to “select the stimulus with the most luster.” In the experiments exploring the upper range of

*C*

_{diff}, the task was to identify the position of the smaller

*C*

_{diff}—observers were instructed to “choose the stimulus with the least luster.” The different instructions for the two tasks ensured that the two tasks were comparable in terms of what constituted the target stimulus—that is, the one that was varied during the staircase procedure: the more lustrous stimulus for the first task and the less lustrous for the second. The initial difference in

*C*

_{diff}between the members of the forced-choice pair, Δ

*C*

_{diff}, was randomly selected from a range whose average was approximately double the expected threshold Δ

*C*

_{diff}as determined in pilot runs. A 3-up-1-down staircase method was used in which Δ

*C*

_{diff}either increased or decreased proportionately on each trial by a factor of 2.5 for the first five trials and a factor of 1.3 thereafter. Correct and incorrect trial sequences resulted in, respectively, decreases and increases in the magnitude of Δ

*C*

_{diff}, with the sign of Δ

*C*

_{diff}always being positive for the lower and negative for the upper range. There were between five and 10 sessions for each condition, resulting in a total of between 250 and 500 trials per condition. Condition order was randomized.

*C*

_{diff}were fitted with Quick functions using a maximum-likelihood criterion, using routines customized from the Palamedes toolbox (Prins & Kingdom, 2018). Threshold Δ

*C*

_{diff}at the 75% correct level (where performance

*d*′ = 0.954 is close to 1) and associated bootstrap errors were estimated from the fits.

_{diff}with correlated and anticorrelated comparisons

*C*

_{diff}was a decrement, the absolute value is given in the figure to allow a direct comparison with the increment Δ

*C*

_{diff}measured in the 0° comparison condition. The results show that for all observers, Δ

*C*

_{diff}was significantly lower for the 0° condition than the 180° condition. The geometric mean ratio of Δ

*C*

_{diff}values for the two conditions, averaged across the six observers, is 4.37. This shows that Δ

*C*

_{diff}detection is markedly asymmetric, in that detecting a change in

*C*

_{diff}between two image pairs is much easier when one of them is interocularly correlated (

*ϕ*= 0) than when one is interocularly anticorrelated (

*ϕ*= 180).

_{diff}as a function of pedestal

_{diff}

*C*

_{diff}as a function of a pedestal

*C*

_{diff}for both the lower and upper ranges of

*C*

_{diff}. Figure 4 illustrates the conditions for the two parts of the experiment and the terms we will use for the graphical presentation of the data. As the figure shows, for the lower-range experiment the discriminand pairs comprised

*C*

_{diff}and

*C*

_{diff}+ Δ

*C*

_{diff}, which we designate respectively as the smaller and larger

*C*

_{diff}of a just-discriminable pair. For the upper-range data, the discriminand pairs are

*C*

_{diff}and

*C*

_{diff}− Δ

*C*

_{diff}, which invites the opposite designation of, respectively, larger and smaller. The smaller-versus-larger designation enables the two sets of data to be directly compared in an intuitive manner.

*C*

_{diff}results for both lower- (blue) and upper-range (magenta) data. Thus, these graphs plot on the two axes the just-discriminable

*C*

_{diff}pairs across the full range of

*C*

_{diff}. Note that the orientations of the error bars differ for the two ranges. This reflects the fact that for the lower-range data, Δ

*C*

_{diff}varies along the ordinate, as it is part of the larger

*C*

_{diff}, but for the upper-range data it varies along the abscissa, as it is part of the smaller. For three observers (1, 2, 7) the just-noticeably larger

*C*

_{diff}rises smoothly with increasing values of the smaller

*C*

_{diff}until the physical limit (dashed green line) is reached, suggesting that these thresholds for the lower and upper ranges of

*C*

_{diff}lie on a single monotonic function. The continuous gray curves show fits of a B− model to be described later.

*C*

_{diff}when the comparison stimulus was interocularly correlated than when it was interocularly anticorrelated. This finding was further supported by a second experiment in which we measured JNDs across the full range of interocular difference.

*R*that can be modeled similarly to the well-known contrast transduction model suggested originally by Legge and Foley (1980). In the terms of this study, the model is

*p*,

*q*, and

*z*determine the shape of the response function. With a suitable choice of parameters the function is able to capture the idea that

*R*first accelerates and then decelerates as a function of

*C*

_{diff}, thus providing one possible explanation for the dipper function observed in our lower-range data. To apply the model, we assumed that the Δ

*C*

_{diff}at 75% correct elicits a constant threshold change in response Δ

*R*, which we term

*k*. This is equivalent to assuming that performance is limited by late additive noise with constant variance

*σ*

^{2}. The model's threshold Δ

*C*

_{diff}is then found for each pedestal

*C*

_{diff}by adjusting Δ

*C*

_{diff}until Δ

*R*=

*k*. That is, for a given set of parameters

*p*,

*q*,

*z*,

*k*, we find Δ

*C*

_{diff}based on the following equation:

*fminsearch*in Matlab), we found the best-fitting parameter sets for each observer that minimized the sum of squared differences between model and observed thresholds. The best fit was taken over 50 repeated runs with jittered starting values, to avoid finding local minima in the error surface. The model fitting could minimize the squared error in either Δ

*C*

_{diff}or Δ

*ϕ*. Because of the compressive relation between

*C*

_{diff}and

*ϕ*(Figure 2), we chose to minimize errors in Δ

*ϕ*. Table 1 gives the values of the fitted parameters and the coefficient of determination

*R*

^{2}for each fit. Resulting model fits, re-expressed as

*C*

_{diff}or Δ

*C*

_{diff}, are the continuous gray lines in Figures 5 and 6.

*R*

^{2}values indicate that this simple model, assuming a B− channel with a nonlinear transducer, gave a good fit to the data for all four observers. Figure 7 shows the estimated transducer functions for

*C*

_{diff}for the four observers. The functions are moderately compressive, and fairly similar for observers 1, 2, and 7. But observer 3 (FAAK) shows a more extreme, nonmonotonic transducer with saturation followed by decline for

*C*

_{diff}> 0.2, corresponding to the very steep rise in thresholds seen in Figures 5 and 6. In Appendix 1 we consider whether the nonmonotonic transducer for Observer 3 might be the result of overfitting (having more free parameters than are warranted by the data). For completeness, we report the results of an Akaike information criterion model-selection analysis, comparing three versions of the transducer model applied to the data from each observer. We conclude that the transducer shapes shown in Figure 7 are not distorted by overfitting.

*r*= 1) to uncorrelation (

*r*= 0) was as brief as 5–10 ms, while the reverse direction, from interocular uncorrelation to correlation, required about five times as long (25–50 ms). Julesz and Tyler coined the term

*neurontropy*to characterize this asymmetry, the idea being that in terms of entropy the switch from correlation to uncorrelation was one of order to disorder, while the reverse was one of disorder to order. Creating order may necessarily be a slower, more difficult process than reducing order to chaos. Julesz and Tyler proposed the interaction of two processes, fusion and rivalry, that operate in parallel and are akin to the B+ and B− channels, respectively. But that model did not directly account for the striking difficulty of detecting an increase compared to a decrease of correlation. Tyler and Julesz (1978) suggested that this difference “must represent some kind of

*adaptation*to the current state” of the visual noise (p. 104). This is consistent with our previous study showing the B− channel to be adaptable (Kingdom et al., 2018). In the Tyler/Julesz experiments the transitions would be detected under different levels of B− channel adaptation. Transition from correlated (

*r*= 1) to uncorrelated (

*r*= 0) would be detected by a B− channel in an unadapted and hence maximally sensitive state, while the opposite transition (

*r*= 0 to

*r*= 1) would be detected by the same channel in an adapted and hence less sensitive state.

*C*

_{diff}appear to be mediated by the same mechanism across the full range of

*C*

_{diff}, we suggest that this mechanism is the B− channel.

*C*

_{diff}with the comparison stimuli at 90° phase difference. Stevenson et al. found that thresholds were elevated by adapting to perfectly correlated images, complementary to our later finding that adapting to uncorrelated as well as anticorrelated images raised thresholds for detecting departures from correlation (Kingdom et al., 2018). The impairment of correlation detection shown by Stevenson et al. was disparity specific: The largest effect was obtained when the test correlation (embedded in uncorrelated noise) had the same disparity as the adapter. They interpreted these results as due to adaptation of disparity-tuned neurons within the stereovision system. This seems very likely, but also suggests that the B+ channel (in addition to the B− channel) might in principle be involved.

*C*

_{diff}. Informal observations by FAAK suggest that, unlike these gratings, stereo cues are quite pronounced in orientationally broadband stimuli with differing amounts of

*C*

_{diff}. So it is possible that the apparent lack of B+ involvement in the present study in comparison to previous related studies (e.g., Stevenson et al. 1992) may be due to the particular stimuli we used.

*not*involved. Recently, Georgeson et al. (2016) put forward a model of binocular combination to account for the appearance of dichoptic mixtures of luminance contrasts and discrimination-threshold measures obtained in dichoptic masking experiments. They suggested that three channels were involved, two monocular (call these L and R) alongside the binocular summing B+ channel. The critical model computation was that the task-relevant visual response was given by the channel with the largest of the three outputs—that is, MAX(L,R,B+). This MAX operation can be envisaged as a form of competition or winner-take-all rivalry between all three signals. Such an operation is

*not*needed to explain simple contrast increment discriminations, either monocular or binocular, but was strongly implicated in tasks where the contrast of a binocular pedestal was incremented in one eye and decremented in the other (see Georgeson et al., 2016, figure 9). It is also consistent with the near-winner-take-all behavior of binocular contrast matching. Ding, Klein, and Levi (2013) and Ding and Levi (2016, 2017) developed a detailed alternative account of binocular combination based solely on a more complex B+ channel, involving several interacting contrast-gain controls. Because it generates, by different means, a near-winner-take-all binocular response surface that fits contrast-matching behavior, the Ding model is likely to be able to predict correctly the critical contrast-decrement discriminations mentioned earlier (see Georgeson et al., figure 6A). But since it is focused entirely on the B+ summation mechanism, it will probably need additional mechanisms for interocular difference detection.

*C*

_{sum}falls to zero with increasing phase disparity (Figure 1), while the monocular contrasts

*C*,

_{L}*C*are invariant with disparity. Thus it seems likely that in the MAX operator, the B+ signal must be silenced by the L, R signals at

_{R}*large*disparities after some critical disparity is reached. At

*smaller*disparities,

*C*

_{sum}is larger, and the B+ signal may win the L,R,B+ competition, depending on how much binocular summation B+ exhibits. But that larger B+ signal is likely to be highly compressed (Figure 1), and so its ability to signal changes may be much lower than the B− signal. Thus the B+ signal may fail to support discrimination for different reasons at small and large disparities. To illustrate and quantify this argument, we developed a simple multichannel model that includes B−, B+, and MAX signals, as follows.

*C*

_{diff}(solid) and

*C*

_{sum}(dashed), as in Figure 2. The thick gray curve shows the fitted response of the B− channel (for Observer 1) after nonlinear transduction of

*C*

_{diff}(Equation 3). Responses to the pedestal levels of disparity are marked on this model response curve as white circles. An increase in phase disparity (hence an increase in

*C*

_{diff}) raises the B− response, and discrimination threshold is reached when the rise Δ

*R*equals a constant

*k*(Equation 4) corresponding to 75% correct,

*d*′ = 0.95. Because

*d*′ is nearly 1, and

*d*′ = Δ

*R*/

*σ*, it follows that

*k*almost equals the internal noise level

*σ*(

*k*= 0.95

*σ*).

*k*was around 0.25 (Table 1), but since the full range of model responses was only about 0.8 (Figure 8A), we can see that the task is noisy: Its full range spans only about three standard deviations of the noise

*σ*. Colored circles represent the observed test threshold values (expressed as phase disparity,

*ϕ*

_{ped}+ Δ

*ϕ*) tied to the corresponding pedestal levels (in three selected cases) by black line segments. Figure 8B is similar to Figure 8A, but for discrimination of decreases in phase disparity (or

*C*

_{diff}). Importantly, in both Figure 8A and 8B, the horizontal positions of these threshold points are empirical, not model dependent, while their vertical displacement from the pedestal points is the constant

*k*. The fact that all these threshold points fall on or very close to the same model response curve tells us that the fitted transducer for B− accounts very well for the discrimination of both increases and decreases in interocular phase difference.

*C*

_{diff}, the values of Δ

*C*/

*C*for observers 1, 2, and 7 were about 1.0, 1.5, and 1.5, meaning that the just-detectable increment was as large as or larger than the pedestal itself. These Weber fractions are about five to 10 times higher than for grating-contrast increment detection, where Δ

*C*/

*C*, monocularly or binocularly, is typically about 0.1 to 0.2 (see, e.g., Georgeson et al., 2016, figure 4A, 4B, and 4C). This greater Weber fraction probably reflects a much higher noise level in the

*C*

_{diff}task, because the transducers for

*C*

_{diff}and for grating contrast were broadly similar in shape (cf. Figure 9). How much of the excess noise in the

*C*

_{diff}task might be due to the noisy nature of our compound gratings (the random phase relation between components) is not yet known.

*C*

_{sum}in place of

*C*

_{diff}. The simplex fitting algorithm did not converge on any set of transducer parameters or noise level that could emulate the data, even approximately. Thus, as expected, it seems likely that B+ was not used. To get further insight into why not, we made the simplifying assumption that, for a given observer, the transducers

*T*for L, R, and B+ were the same as for B−. Thus the four channel responses were

*n*= 30 (Georgeson et al., 2016). We then computed

*d*′ for each channel alone, or in combination, as a function of phase disparity, where for the

*i*th channel

*R*is defined as in Equation 4, with the appropriate change of contrast variable. To combine

_{i}*d*′ values across channels

*i*,

*j*, we again used a Minkowski sum:

*m*= 4. A value of

*m*= 2 represents optimal combination for statistically independent cues (the ideal observer; Green & Swets, 1966), but this is unachievable in practice because it requires the observer to have perfect knowledge of the signal means and their detectabilities

*d*′ on each trial in order to weight the cues optimally. A weaker form of summation (

*m*= 4) seems appropriate, and is not crucial to our argument. The resulting

*d*′ tends to track the higher of the two

*d*′ values but shows some summation when the two

*d*′ values are similar. In this way we computed the expected increment thresholds Δ

*ϕ*for single cues (B− or B+) and for pairs of cues—(B−, B+) and (B−, R

_{max})—as shown in Figure 8C and 8D. Thick curves represent the single-cue predictions, as indicated.

*C*

_{sum}and

*C*

_{diff}(thin curves in Figure 8A and 8B), it follows that the threshold curve for B+ with disparity decrements (green curve, Figure 8D) is the mirror image of the B− curve for disparity increments (gray curve, Figure 8C). There is an analogous symmetry between B+ with increments (Figure 8C) and B− with decrements (Figure 8D). But only the B− curves fit the data. With the cue combination (B−, B+), predicted thresholds (thin brown curves) track the better cue across the whole range of pedestal disparities. But the observed thresholds did not do this for any observer. Finally, when the (B−, R

_{max}) cues were combined (thin blue curves), predicted thresholds reverted to being very close to those for B− alone, and close to the data. B+ failed to deliver useful information because the response R

_{max}varied so little with phase disparity (see Figure 9, left, thin blue curve) in relation to the noise level.

*are*an effective cue for interocular difference detection, it follows that they do

*not*pass through a MAX operator in competition with monocular responses. This is broadly in agreement with the previous proposal that a luster signal operates in parallel with the MAX signal (Georgeson et al., 2016).

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*Understanding vision: Theory, models, and data*. Oxford, UK: Oxford University Press.

*p*,

*q*,

*z*plus the noise parameter

*k*) widely used in the context of luminance contrast discrimination, and here applied to

*C*

_{diff}. Let's call this Model 1. For three observers this gave rise to a smoothly saturating transducer function, but for Observer 3 the fitted transducer was, surprisingly, nonmonotonic (Figure 7). We therefore aimed to determine whether a more constrained three-parameter model might also fit the data well, without an unusual transducer shape. We considered two reduced versions of Equation 3: In Model 2,

*q*was fixed (

*q*= 2) while

*p*was free to vary in the model fitting; in Model 3,

*p*and

*q*were yoked (i.e., varied together,

*p*=

*q*). A powerful general procedure for comparing the goodness of different models, especially when they are not nested, is based on the AIC (Akaike information criterion; e.g., Burnham & Anderson, 2002; Wagenmakers & Farrell, 2004; Symonds & Moussalli, 2011). The AICc (AIC corrected for small samples) takes into account both the goodness of fit (deviance or squared error) and the model complexity (number of parameters), and returns Akaike weights that can be interpreted as the probability that a given model is the best of those considered. The outcome of the AIC analysis is shown in Table A1. We can see that for each observer, one of the three-parameter models emerged as best (i.e., more likely to be closest to an unknown true model). For two observers it was Model 2, while for the other two it was Model 3. Clearly it is undesirable to select different models for different observers. But we note that in all four cases (Figure A1) the original model (Model 1) gave transducer functions (red curves) that were very close to those of the best model. It seems reasonable to conclude that Model 1 is a suitable model for all four observers, and that the extra flexibility gained from the fourth parameter did not lead to a distortion in the shape of the transducer function to any serious extent, compared with alternative models that were less flexible.

*C*,

_{L}*C*before the differencing operation. We show here that for our experiments, and for a broad class of possible nonlinearities, such models would give exactly the same predictions as the model with a linear front end that we described, but further experiments could shed new light on this question.

_{R}*ϕ*. We then broadly follow the approach of Ding and colleagues (Ding & Sperling, 2006; Ding et al., 2013; Ding & Levi, 2017) and Jennings and Kingdom (2016) in supposing that multiplicative weights

*T*is a nonlinear transducer function of the kind discussed in the main text and

*std*returns a single number: the standard deviation of values over space

*x*, or some other aggregate measure of response strength over space.

*W*of

*γ*is a constant exponent. Here

*α*,

*β*,

*γ*are constants, then it follows from symmetry that

*W*and no matter how complex it may become (e.g., Ding & Levi, 2017, model 5).

*W*does not vary with phase disparity. Within these broad constraints, we can see that even with arbitrarily complex monocular weight functions

*W*, which may incorporate contrast nonlinearities and interocular suppression, the binocular difference

*k*. More particularly, Equation A5 implies that the standard deviation of

*T*were (trivially) rescaled to allow for the factor

*k*change in input amplitude. This initially seemed surprising, so to confirm our reasoning we ran model fits with the linear front end as usual or with weighting schemes such as Equation A4. The fitted curves and goodness of fit to the data were indistinguishable.

*not*demonstrate that the front-end differencing is linear, only that we could not determine what monocular nonlinearities, if any, were present. This uncertainty arises because the left and right contrasts were constant and equal. Future experiments in which left and right contrasts are systematically varied would shed new light on the monocular weights that precede interocular difference detection.