Nearby contours abolish the binocular advantage

That binocular viewing confers an advantage over monocular viewing for detecting isolated low luminance or low contrast objects, has been known for well over a century; however, the processes involved in combining the images from the two eyes are still not fully understood. Importantly, in natural vision, objects are rarely isolated but appear in context. It is well known that nearby contours can either facilitate or suppress detection, depending on their distance from the target and the global configuration. Here we report that at close distances collinear (but not orthogonal) flanking contours suppress detection more under binocular compared to monocular viewing, thus completely abolishing the binocular advantage, both at threshold and suprathreshold levels. In contrast, more distant flankers facilitate both monocular and binocular detection, preserving a binocular advantage up to about four times the detection threshold. Our results for monocular and binocular viewing, for threshold contrast discrimination without nearby flankers, can be explained by a gain control model with uncertainty and internal multiplicative noise adding additional constraints on detection. However, in context with nearby flankers, both contrast detection threshold and suprathreshold contrast appearance matching require the addition of both target-to-target and flank-to-target interactions occurring before the site of binocular combination. To test an alternative model, in which the interactions occur after the site of binocular combination, we performed a dichoptic contrast matching experiment, with the target presented to one eye, and the flanks to the other eye. The two models make very different predictions for abutting flanks under dichoptic conditions. Interactions after the combination site predict that the perceived contrast of the flanked target will be strongly suppressed, while interactions before the site predict the perceived contrast will be more or less veridical. The data are consistent with the latter model, strongly suggesting that the interactions take place before the site of binocular combination.

. DS gain-control model 4,35 with (A) a flanker as an equivalent weak pedestal (AM2); (B) monocular flank-to-target gain-control (AM3); (C) monocular flank-to-target gainenhancement (AM4); (D) both monocular flank-to-target gain-control and gain-enhancement (AM5). given by Eq. A18, where and are given by Eq. A2, and are given by Eq. A9, and are given by Eq. A16, and and are given by Eq. A20.  Figure A4. A). The model output is given by: (3) flank's gain-control of binocularly combined target with interocular target's gain-control of flank's gain-control ( Figure A4. B). The model output is given by: , (A22) where and are given by Eq. A2, and are given by Eq. A9, and are given by Eq. A16, and and are given by Eq. A13.  Model comparison.

Supplementary Information B. The AIC for comparison of different models
We used the Akaike Information Criterion (AIC) 3 , a measure of the relative goodness of fit of a statistical model developed by Akaike 4 , to compare different models. Let K be the number of estimated parameters in the model and be the maximized value of the likelihood function for the model, AIC is defined as . Assuming that the errors are normally distributed and independent, after ignoring the constant term, AIC is given by is the residual sum of square in the least squares fitting and N is the number of observed data points. To give a greater penalty for additional parameters, we applied a correction for finite sample sizes (AICc) 71 which is given by, .
(B2) For the set of R models, the one with the lowest AICc score is most likely to be the best model of those considered. The relative likelihood of model i is proportional to , where is the AICc difference between model i and the best model (with the lowest AICc). Given the data and the set of R models, the relative likelihood or Akaike weight 71 , given by: . (B3)

Supplementary Information C. Model and Modeling for contrast detection and discrimination
GUM model for contrast discrimination Let ) * and ) + be binocular contrast output of the DS model with and without targets, respectively. Based on Eqs. A1 and A2, we have: and where ! and & are pedestal contrast presented to the LE and RE, respectively. Based on Eqs. 9 and 10, the internal noises are given by:   With weak pedestal assumption of flank, the alternative GUM (aGUM: Fig. C1) was tested for contrast detection with flank (dotted lines in Figs. 1 and 2). Let 9 (Eq. A4) be a flank-target distance weighting function to transfer a flanker to an equivalent weak pedestal. The equivalent weak pedestals of flank F L and F R are given by: where r is the flank-target distance in SDU. Taking Eq. C10 into Eqs. C1-C9, we have the predictions of aGUM (dotted lines in Figs. 1-2) for contrast detection thresholds.

GUMI model
Let " be target binocular contrast output of GI model (Fig. 5D), and " * and " + be flank binocular contrast output of GI with and without targets, respectively, which can be calculated by Eq. 6. For a 2AFC task, the internal noise of the interval without target is given by,  Where -&+ , 34+ , -&* , and 34* are given by Eqs. C11 -C14, and -&*,7 , and 34*,7 are given by Eqs. C7 and C8. Table C1 shows fitting statistics of aGUM and GUMI models for data sets of contrast detection shown in Figs. 1 and 2. For contrast discrimination (Figs. 3B and 3C), GUMI is simplified to be GUM without flank-target interactions (flank contrast = 0), and aGUM becomes GUM with flanktarget distance = 0. As shown in Table C1, with a weak equivalent pedestal of flank but without separated flank-target interactions, aGUM has poor fitting performance. After including flanktarget interactions, GUMI significantly improves fitting performance. Tables C2 -C5 show the best fitting model parameters. Please note that, because the data in Figs. 1-3 are limited, some model parameters are fixed during modeling.