Further developments in binocular summation

This paper reviews experiments that bear on the issue of binocular summation, the superiority of binocular over monocular viewing on various visual tasks covering studies published since the appearance of a previous review of this literature by Blake and Fox (1973). The experiments are grouped into three main categories—those that deal with the specificity of binocular summation (i.e., the extent to which inputs to the two eyes must coincide spatially and temporally), those that study binocular summation on suprathreshold tasks, and those that correlate binocular summation with other aspects of binocular function. The last section of the paper critically reviews several models of binocular summation.     

Suprathreshold binocular interactions for grating patterns

Binocular interactions of suprathreshold grating patterns have been investigated using a reaction time measure of contrast detection. Simple reaction times were determined for monocular and binocular viewing conditions over a contrast range from .63 to near threshold. The results from all subjects showed binocular summation for contrast levels near threshold, but there was considerable variation across subjects for contrast levels above threshold. Some subjects showed summation over the entire contrast range, but other subjects showed either binocular inhibition or binocular facilitation for some range of contrast levels. The pattern of binocular interaction for a given subject was consistent for several spatial frequencies. The differences in types of interaction between subjects, the variation in magnitude of binocular interaction with contrast level for each subject, and the data from experiments involving stimulation of noncorresponding retinal areas show that the binocular interactions found for suprathreshold stimuli cannot be accounted for on the basis of probability, and must, therefore, result from physiological interactions between the two eyes. These interactions have been investigated further under conditions of (1) induced fixation disparity, (2) horizontal gratings, and (3) orthogonally oriented gratings.     

Binocular summation of equal-energy flashes of unequal duration

To determine if binocular summation occurs when increment flashes are of equal energy (Bloch’s law) but unequal in luminance-duration parameters, three Ss made temporal forced-choice judgments: (1) monocularly, (2) binocularly when the flashes to each eye were identical, (3) binocularly when the flashes to each eye were of equal energy but different in terms of their luminance and duration parameters, and (4) binocularly when flashes to each eye were separated by 100 msec. Binocular detection rates were consistently superior to monocular detection rates. Similarity in performance between Conditions 2 and 3 indicates that the binocular visual system responds only to the total energy of each monocular flash. The data from two Ss reveal that binocular performance was greater than that predicted on the basis of probability summation.     

Do background luminances interact during binocular fusion?

The question investigated in the experiments reported here was whether monocular background luminances sum during binocular fusion. Fusion was made explicit by using a random-dot stereogram (RDS) as a background stimulus. In the presence of the RDS, differential luminance thresholds were somewhat higher than in the uniform field: a full-field, binocular dot array acted as a mask for a full-field luminance change, but global depth had no effect at threshold. The amount of the binocular advantage at threshold was compared to the basic "threshold response," that is, the change in threshold resulting from raising the background luminance by a factor of 2. It was found that the amount of the binocular advantage was equivalent, on the average, to some 75% of the threshold response--significantly less than the 100% predicted by "simple summation." The amount of the binocular advantage varied substantially among observers and eyes, whereas the threshold response obeyed Weber's law in all cases: the variability was eye-, rather than threshold-dependent. Monocular thresholds did not decrease when taken with the nontest eye occluded rather than viewing a fused background. The proposition that the adaptation state of the visual system is increased during binocular fusion (Cogan, 1982) was not supported. Yet occluding the nontest eye, rather than presenting the test stimulus monocularly against a fused background, did change monocular thresholds in some eyes and observers. These findings are interpreted as evidence for a complex binocular background interaction involving both summation and inhibition.     

The binocular combination of chromatic contrast

How is chromatic contrast combined binocularly? One index of binocularity is the binocular contrast summation ratio (BCSR), which is the improvement in contrast sensitivity with binocular rather than monocular presentation. Simmons and Kingdom (1998, Vision Research 38 1063-1071) noted that BCSRs with some red-green isoluminant stimuli were suggestive of full linear summation. This suggestion was investigated further in four subjects by measuring binocular and monocular contrast thresholds for the detection of 0.5 cycle deg(1) isoluminant (red-green) and isochromatic (yellow-black) Gabor patches. These Gabor patches had either vertically or horizontally oriented carrier gratings and were either dichoptically in phase (same coloured bars in binocular correspondence) or in dichoptic anti-phase (opposite coloured bars in binocular correspondence). Full linear summation would be indicated by BCSRs of 2 for the in-phase and close to 0 for the anti-phase conditions. Mean BCSRs at isoluminance were 1.93 and 0.90, respectively, for the in-phase and anti-phase stimuli with horizontal carriers, the former being consistent with full linear summation, but the latter not. Despite these results, BCSRs obtained with isoluminant and isochromatic stimuli under similar conditions were not statistically distinguishable from each other, although there was a tendency for summation at isoluminance with in-phase stimuli to be higher and anti-phase stimuli to be lower. These data fall short of demonstrating full linear summation of chromatic contrast between the eyes under all presentation conditions, but they do indicate that there are strong binocular interactions at red-green isoluminance, which are similar to, and possibly even stronger than, those obtained with luminance stimuli.     

Binocular interactions in suprathreshold contrast perception

Suprathreshold binocular contrast interactions were studied psychophysically. A split-screen CRT display was used to present separate sine-wave gratings to the observer’s left and right eyes. The method of constant stimuli and a modified method of adjustment were used to find sets of binoculartest patterns that matched a given binocularstandard. Test patterns consisted of the simultaneous presentation of sine-wave gratings that differed in contrast to the left and right eyes. Standard patterns consisted of identical sine-wave gratings presented to the two eyes, and had the same spatial frequency as the test patterns. Binocular contrast matching functions were obtained for several standard contrasts at 1 and 8 c/deg. Binocular matching functions were obtained for luminance increments as well. The binocular contrast matching functions departed from a simple binocular averaging rule, and behaved as if the eye receiving the higher contrast disproportionately dominated the binocular contrast percept. Departures from the binocular averaging rule were slightly greater for higher standard contrasts. Spatial frequency had little effect, and the luminance increment matching functions also departed from the binocular averaging rule. There was evidence for a contrast version of Fechner’s paradox and for substantial individual differences in a form of ocular dominance. In a further experiment, additivity of suprathreshold binocular contrast summation was examined by testing the double-cancellation condition. We found no systematic violations of additivity at 1 and 8 c/deg. Models of suprathreshold binocular contrast summation were examined.     

Binocular summation of chromatic changes as measured by visual reaction time

We determined visual reaction times to monocular and binocular changes in the luminance of isochromatic stimuli and to monocular and binocular changes in the color of isoluminant stimuli. Two isoluminant color changes were tested: chromatic variations along the red-green axis of Boynton's (1986) two-stage color vision model and chromatic variations along the yellow-blue axis of the same model. The results indicate a greater degree of binocular summation for luminance change than for color change. This result was largely independent of the motor component of reaction time.     

Brightness function: Binocular versus monocular stimulation

A dozen observers matched numbers to the apparent brightness of a target viewed by one eye or by both eyes. Brightness grew as a power function of luminance, and the functions were practically identical for the two modes of viewing. Throughout its course, the obtained binocular function tended to fall about a decibel above the monocular function. This small degree of binocular summation, of the order of a jnd, mayor may not be significant.     

The psychophysical inquiry into binocular summation

Experiments that compare monocular and binocular visual performance of human psychophysical Os on a variety of visual tasks are reviewed. The review attempts to include all experiments published in English in this century, excluding work on stereopsis, rivalry, and evoked potentials. The concept of probability summation as a baseline for assessing the presence of neural summation is discussed, and the assumptions of several models for estimating probability summation are considered. Experiments are classified in terms of visual task, major categories being increment detection, flicker fusion, brightness magnitude, and contour resolution. A major conclusion is that binocular performance is superior for essentially all task categories and in most cases by a magnitude greater than that predicted by appropriate probability summation models.     

Binocular unmasking with vertical disparity

We recently found (Schneider, Moraglia, & Jepson, 1989) that the contrast threshold for the detection of a visual signal in a noisy background can be considerably lower when binocular cues are available then when monocular cues only are present. Here, we investigated the occurrence of binocular unmasking with vertical interocular disparities. Subjects reported about the presence of Gabor signals in fields of two-dimensional broadband Gaussian noise surrounded by a frame of uniform noise. They saw these stimuli through a stereoscope; in all cases, the right-eye noise field was vertically displaced relative to the left one in either an upward or a downward direction, by up to 67.6'. In one condition, the right-eye signal was displaced by an amount equal to that of the noise, so that no opportunities for binocular unmasking existed; in the other, it appeared in exactly corresponding locations in the two fields--here, binocular disparities could be used to unmask the signal. Enhanced signal detectability, by up to 12.7 dB, was observed in the latter case for both directions of displacement, but only for displacements of 13.52' and only when the signal's orientation was horizontal. We argue that these effects result from the summation of monocular inputs carried out by linear binocular mechanisms.     

双眼视差的神经机制与知觉学习效应

双眼瞳距使得空间某物体在左右眼视网膜的成像存在微小位置差异, 这种差异被称为双眼视差(binocular disparity), 是立体视知觉的重要信息来源。对双眼视差的心理物理学研究始于18世纪初, 迄今已有接近两百年的历史。近年来, 双眼视差研究主要集中在两方面。其一是用电生理、脑成像技术考察双眼视差在视觉背、腹侧通路的模块化表征, 其脑区表征反映出视觉系统的层级式、平行式加工规律。其二是应用知觉学习范式研究双眼视差的可塑性。未来研究应综合脑成像和神经调控技术考察双眼视差的神经机制及其学习效应, 包括双眼视差与多种深度线索间的信息整合和交互作用。应用方向上, 可结合虚拟现实等技术优化训练范式, 实现立体视力的康复和增强。     

Binocular summation in detection of contrast flashes

We studied monocular and binocular detection of foveal flashes of different contrast. When background contours were binocularly fused, detectability (d’) of binocular test flashes was, on the average, twice the detectability of monocularly presented flashes. The precise amount of binocular advantage varied with test contrast: binocular improvement exceeded full summation for low test contrast, but fell below full summation at higher test contrasts. In the absence of contours in one eye, background luminances are not expected to sum, yet binocular detection is an average of 41.5% better than monocular detection. This indicates a difference in the functional organization of the fused binocular channel and a monocular channel.     

Binocular information summation and the serial processing model

An experiment was performed to ascertain whether a particular member of the class of sequential processing models (Estes & Taylor, 1964; Townsend, 1966) should be further developed in terms of the contributions of information from the separate eyes. Using the detection paradigm (Estes & Taylor, 1964), nine Ss were each run 576 trials under each of three viewing conditions: (a) monocular left, (b) monocular right, and (c) binocular, after four days of practice and calibration. The serial processing model was used to make predictions for three possible cases of binocular information summation: (a) complete independence of the monocular channels, (b) partial independence of the monocular channels and (c) complete dependence in the monocular channels. Complete dependence provided the best fit to the data with a possible stress on use of a “best” eye, but a marginal level of significance was obtained between a simple average of monocular performance and binocular performance with transformed scores. Thus, although there seems to be little or no information summation in terms of the present model of multi-symbol perception, follow-up experiments were suggested to further delineate monocular-binocular relationships in the detection paradigm.     

The effects of eccentricity and vergence angle upon the relative tilt of corresponding vertical and horizontal meridia revealed using the minimum motion paradigm

When the corresponding horizontal meridia of the two eyes are aligned, the corresponding vertical meridia are tilted outwards in a temporal direction, a phenomenon first described by Helmholtz. However, it is not known if this effect is confined to the principal meridia or whether the same relationship exists between corresponding horizontal and corresponding vertical meridia at eccentric retinal locations. We sought to address this issue by exploiting the technique of Nakayama (1977 Proceedings of the Society of Photo-Optical Instrument Engineers 120 2-9) in which the positions of alternating dichoptic images that produce minimal apparent motion were used to measure the relative tilt of corresponding meridia at a range of eccentricities up to +/- 16 deg away from the fovea. Stimuli were composed of dichoptic images, one containing a blank field and the other a pair of dots, which alternated at a rate of 0.63 Hz and the relative tilt (binocular orientation difference) between the pairs of dots presented to the two eyes was varied between +/- 11 degrees. Nonius lines were used to maintain vergence angle, which was varied between 28 cm and infinity. Subjects judged which pair of alternating images produced the smallest amount of apparent motion (position change). It was found that at all eccentricities examined the corresponding horizontal meridia were generally aligned but the corresponding vertical meridia were consistently offset (extorted) by about +/- 2 degrees. The tilts of corresponding principal meridia were typically unaffected when vergence angle was varied, indicating that little or no cyclovergence accompanied changes in horizontal vergence. The results suggest that the binocular correspondence system appears to be mapped by a horizontal shear distortion that extends to retinal locations at least as far as 16 deg away from the foveae. The invariant extortion of corresponding principal vertical meridia with vergence state is consistent with previous suggestions that the empirical vertical horopter becomes progressively inclined with respect to the vertical as viewing distance increases.     

Integration of Intermittent Visual Samples Over Time and Between the Eyes

The authors investigated the integration of alternate disparate monocular inputs for binocular perception in 1-handed catching experiments (N = 14, 32, 22, and 15 participants, respectively in Experiments 1-4). They varied the no-vision interval between alternate monocular samples to measure catching performance, and they compared the alternating monocular conditions with binocular and monocular conditions with equal no-vision intervals. They found no evidence of a binocular advantage for one-handed catching in the alternating monocular conditions. Performance in monocular and alternating monocular conditions did not differ across no-vision intervals ranging from 0-80 ms and was particularly worse than performance in binocular viewing conditions when the no-vision interval was 40 ms or more. The authors argue that the dissimilarity between disparate monocular inputs created by the approaching object limited the integration of those inputs and subsequent binocular perception.     

Binocular detection by normal and stereoblind observers

Binocular forced-choice detection performance was measured in three stereoblind observers and four observers with normal stereopsis. Detection rates of normal observers were greater than expected from probability summation, while those of the stereoblind observers were near or at a level expected from probability. It is concluded that binocular summation is reduced or absent in stereoblind persons.     

Integration of intermittent visual samples over time and between the eyes

The authors investigated the integration of alternate disparate monocular inputs for binocular perception in 1-handed catching experiments (N = 14, 32, 22, and 15 participants, respectively in Experiments 1-4). They varied the no-vision interval between alternate monocular samples to measure catching performance, and they compared the alternating monocular conditions with binocular and monocular conditions with equal no-vision intervals. They found no evidence of a binocular advantage for one-handed catching in the alternating monocular conditions. Performance in monocular and alternating monocular conditions did not differ across no-vision intervals ranging from 0-80 ms and was particularly worse than performance in binocular viewing conditions when the no-vision interval was 40 ms or more. The authors argue that the dissimilarity between disparate monocular inputs created by the approaching object limited the integration of those inputs and subsequent binocular perception.     

Characteristics of anisometropic suppression: Simple reaction time measurements

The characteristics of artificially induced anisometropic suppression were investigated in observers with normal and abnormal binocular vision (anisometropic amblyopia) by using a simple reaction time paradigm. Reaction time was measured as a function of stimulus intensity for various stimulus durations. For all conditions, the reaction time increased as stimulus intensity decreased toward threshold. We found that traditional techniques for modeling this trend were inadequate, so we developed a simple visuogram method for comparing these functions. Using this technique, reaction time versus intensity functions are shown to be shape-invariant for all conditions examined. This means that, although reaction times are longer during induced anisometropic suppression or in anisometropic amblyopia, they are the same if contrast is normalized to equate threshold. The shape-invariant nature of these functions is also consistent with the notion that a single mechanism mediates detection under these conditions. Temporal summation was investigated at both threshold (method of limits) and suprathreshold (criterion reaction time) levels. Again, because of shape invariance, the suprathreshold results mirror the threshold results. The critical duration (the duration at the intersection of the complete summation and zero summation regions) is not affected by any of the conditions. However, the critical intensity (the intensity for the zero summation region) is higher for the amblyopic eyes, as compared with the normal or nonamblyopic eyes. Induced anisometropic suppression always increases the critical intensity, with a smaller increase occurring for the amblyopic eyes. This suggests that amblyopic eyes do not have a need for strong suppression.     

Seeing in three dimensions: the neurophysiology of stereopsis

From the pair of 2-D images formed on the retinas, the brain is capable of synthesizing a rich 3-D representation of our visual surroundings. The horizontal separation of the two eyes gives rise to small positional differences, called binocular disparities, between corresponding features in the two retinal images. These disparities provide a powerful source of information about 3-D scene structure, and alone are sufficient for depth perception. How do visual cortical areas of the brain extract and process these small retinal disparities, and how is this information transformed into non-retinal coordinates useful for guiding action? Although neurons selective for binocular disparity have been found in several visual areas, the brain circuits that give rise to stereoscopic vision are not very well understood. I review recent electrophysiological studies that address four issues: the encoding of disparity at the first stages of binocular processing, the organization of disparity-selective neurons into topographic maps, the contributions of specific visual areas to different stereoscopic tasks, and the integration of binocular disparity and viewing-distance information to yield egocentric distance. Some of these studies combine traditional electrophysiology with psychophysical and computational approaches, and this convergence promises substantial future gains in our understanding of stereoscopic vision.     

Temporal properties of disparity processing revealed by dynamic random-dot stereograms

In studies of the temporal flexibility of the stereoscopic system, it has been suggested that two different processes of binocular depth perception could be responsible for the flexibility: tolerance for interocular delays and temporal integration of correlation. None has investigated the relationship between tolerance for delays and temporal integration mechanisms and none has revealed which mechanism is responsible for depth perception in dynamic random-dot stereograms. We address these questions in the present study. Across five experiments, we investigated the temporal properties of stereopsis by varying interocular correlation as a function of time in controlled ways. We presented different types of dynamic random-dot stereograms, each consisting of two pairs of alternating random-dot patterns. Our experimental results demonstrate that (i) disparities from simultaneous monocular inputs dominate those from interocular delayed inputs; (ii) stereopsis is limited by temporal properties of monocular luminance mechanisms; and (iii) depth perception in dynamic random-dot stereograms results from cross-correlation-like operation on two simultaneous monocular inputs that represent the retinal images after having been subjected to a process of monocular temporal integration of luminance.