The lost direction in binocular vision: the neglected signs posted by Wells, Towne, and LeConte

Studies of vision have informed theories first in philosophy and then in psychology. Over the centuries, an increasing number of phenomena have been enlisted to refute or reinforce particular theories. Nowhere has this been more evident than in binocular vision. How we see a single world with two eyes is one of the oldest and most consistently studied topics in vision research. It has been discussed at least since the time of Aristotle and it has been examined experimentally since the second century, when Ptolemy defined lines of visual correspondence for the two eyes. Prior to Wheatstone's invention of the stereoscope in the 1830s, binocular vision had been studied in terms of visual directions. The stereoscope established distance (or depth) as well as direction as dimensions of binocular vision. Subsequently, depth rather than direction has been the principal concern of students of vision, and texts in English devoted to analyses of direction rather than depth have been neglected. We examine the experiments on binocular visual direction conducted by Wells before Wheatstone, and by Towne and LeConte after him, and discuss the reasons for their neglect.     

The stereoscopic views of Wheatstone and Brewster

Summary The study of stereopsis, made possible by the invention of the stereoscope, freed binocular vision from the yoke of monocular phenomena. Wheatstone used this freedom to determine the factors involved in the perception of size and distance, and interpreted them within a cognitive framework. He devised an adjustable stereoscope which allowed him to apply the systematic experimental procedures of physics to the phenomena of depth perception. Brewster, by contrast, tried to force the newly discovered binocular phenomena back into the mould of monocular vision, using the lever of visible direction. His interpretations of visual phenomena, be they monocular or binocular, could be reduced to the two fundamental laws of visible direction and distinct vision. While Wheatstone's cognitive approach influenced Helmholtz, and thereby modern cognitive theorists. Brewster's interpretations, based as they were in analyses of the retinal projection, find an echo in modern direct theorists.     

Binocular rivalry and stereoscopic depth perception

An investigation was made of stimulus factors causing retinal rivalry or allowing stereoscopic depth perception, given a requisite positional disparity. It is shown that similar colour information can be “filtered” out from both eyes; that stereopsis is not incompatible with rivalry and suppression of one aspect of the stimulus, and that the strongest cue for perception of stereoscopic depth is intensity difference at the boundaries of the figures in the same direction at each eye. Identity of colour can also act as a cue for stereopsis. The brightness of different monocular figures seen in the stereoscope in different combinations was estimated by a matching technique, and it is suggested that the perceived brightness is a compromise between the monocular brightness difference between figure and ground seen in relation to the binocular fused background, and the mean brightness of the figures. The results are discussed in terms of neurophysiological “on,” “off” and continuous response fibres.     

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.     

A statistical model of binocular disparity

Binocular disparity provides important information about the three-dimensional structure of the environment. The current study sought to complement our geometrical understanding of binocular vision by considering the distributions of horizontal and vertical disparities that might be expected in images of the natural environment, using a simple environmental model. It was observed that the distribution of disparities depends critically on fixation, and varies greatly from one image location to another. The results were considered in relation to computational models of binocular stereopsis, and compared to two known properties of the visual system—the small disparity preference in disparity matching, and the influence of eccentricity on Panum's fusional limit. Overall, the study characterizes the binocular disparities that are likely to be encountered in the real world scenes, and discusses the implications of these for our understanding of binocular visual systems.     

From dichoptic to dichotic: historical contrasts between binocular vision and binaural hearing

Phenomena involving vision with two eyes have been commented upon for several thousand years whereas those concerned with hearing with two ears have a much more recent history. Studies of binocular vision and binaural hearing are contrasted with respect to the singleness of the percept, experimental manipulations of dichoptic and dichotic stimuli, eye and ear dominance, spatial localisation, and the instruments used to stimulate the paired organs. One of the principal phenomena that led to studies of dichotic hearing was dichoptic colour mixing. There was similar disagreement regarding whether colours or sounds could be combined when presented to different paired organs. Direction and distance in visual localisation were analysed before those for auditory localisation, partly due to difficulties in controlling the stimuli. Instruments for investigating binocular vision, like the stereoscope and pseudoscope, were invented before those for binaural hearing, like the stethophone and pseudophone.     

Does direction of walking impact binocular rivalry between competing patterns of optic flow?

When dissimilar monocular images are viewed simultaneously by the two eyes, stable binocular vision gives way to unstable vision characterized by alternations in dominance between the two images in a phenomenon called binocular rivalry. These alternations in perception reveal the existence of inhibitory interactions between neural representations associated with conflicting visual inputs. Binocular rivalry has been studied since the days of Wheatstone, but one recent strategy is to investigate its susceptibility to influences caused by one’s own motor activity. This paper focused on the activity of walking, which produces an expected, characteristic direction of optic flow dependent upon the direction of one’s walking. In a set of experiments, we employed virtual reality technology to present dichoptic stimuli to observers who walked forward, backward, or were sitting. Optic flow was presented to a given eye, and was sometimes congruent with the direction of walking, sometimes incongruent, and sometimes random, except when the participant was sitting. Our results indicate that, while walking had a reliable influence on rivalry dynamics, the predominance of congruent or incongruent motion did not.     

Porterfield and Wells on the motions of our eyes

William Porterfield (ca 1969-1771) and William Charles Wells (1757-1817) conducted experimental investigations on eye movements related to accommodation, binocular vision, and vertigo. Porterfield gave a correct interpretation of Scheiner's experiment and invented an optometer to measure the near and far points of distinct vision. He also demonstrated the involvement of the crystalline lens in accommodation by examining vision in an aphakic person. Wells devised an alternative means of measuring the limits of vision and noted his own deterioration of sight with age; he studied the effects of belladonna on pupil size and accommodation. Their analyses of binocular visual direction contrasted Porterfield's view that perceived location was innately determined with Well's argument that visual direction was innate whereas visual distance was learned. Both Porterfield and Wells investigated the involvement of eye movements in binocular vision and in postrotary visual motion. Porterfield maintained that the eyes did not move following body rotation, whereas Wells, using an afterimage as stabilised retinal image, described the characteristics of postrotary nystagmus and their dependence on head orientation. Despite the neglect of Well's work, he should be considered as laying the foundations for the study of vestibular-visual interaction, even though the function of the vestibular system was not known at that time.     

Transformation of the visual-line value in binocular vision: stimuli on corresponding points can be seen in two different directions

We examined Wheatstone's (1838 Philosophical Transactions of the Royal Society of London 128 371-394) claim that images falling on retinally corresponding points can be seen in two different directions, in violation of Hering's law of identical visual direction. Our analyses showed that random-dot stereograms contain stimulus elements that are conceptually equivalent to the line stimuli in the stereogram from which Wheatstone made his claim. Our experiment demonstrated that two lines embedded in a random-dot stereogram appeared in two different directions when they stimulated retinally corresponding points, if the disparity gradient value of the lines was infinity relative to adjacent elements. To ensure that the two lines stimulated corresponding points, observers made vergence eye movements while maintaining the perception of the two lines in two different directions.     

Sensory and sensori-motor adaptations in strabismus: Their role in space perception

In comitant strabismus many perceptual adaptive processes take place, which involve perception of space. Suppression of the image of the deviated eye and anomalous retinal correspondence (ARC) are the two main antidiplopic mechanisms. ARC may be present without suppression in small-angle strabismus (up to 10 degrees), supporting an anomalous binocular cooperation in spite of the deviation. Both psychophysical and electrophysiological evidence for anomalous binocular vision in strabismus are provided. Sensori-motor adaptations in strabismus develop as well. They are represented by vergence eye movements which, although not identical to, have similar characteristics as normal fusional vergences. These anomalous fusional eye movements tend to return the eyes to their original deviation when elements are introduced to change the position of the eyes, e.g., prisms or surgery. In conjunction with ARC, these movements serve to maintain binocular visual perception despite the strabismus.     

Planar motion permits perception of metric structure in stereopsis.

A fundamental problem in the study of spatial perception concerns whether and how vision might acquire information about the metric structure of surfaces in three-dimensional space from motion and from stereopsis. Theoretical analyses have indicated that stereoscopic perceptions of metric relations in depth require additional information about egocentric viewing distance; and recent experiments by James Todd and his colleagues have indicated that vision acquires only affine but not metric structure from motion--that is, spatial relations ambiguous with regard to scale in depth. The purpose of the present study was to determine whether the metric shape of planar stereoscopic forms might be perceived from congruence under planar rotation. In Experiment 1, observers discriminated between similar planar shapes (ellipses) rotating in a plane with varying slant from the frontal-parallel plane. Experimental conditions varied the presence versus absence of binocular disparities, magnification of the disparity scale, and moving versus stationary patterns. Shape discriminations were accurate in all conditions with moving patterns and were near chance in conditions with stationary patterns; neither the presence nor the magnification of binocular disparities had any reliable effect. In Experiment 2, accuracy decreased as the range of rotation decreased from 80 degrees to 10 degrees. In Experiment 3, small deviations from planarity of the motion produced large decrements in accuracy. In contrast with the critical role of motion in shape discrimination, motion hindered discriminations of the binocular disparity scale in Experiment 4. In general, planar motion provides an intrinsic metric scale that is independent of slant in depth and of the scale of binocular disparities. Vision is sensitive to this intrinsic optical metric.     

Planar motion permits perception of metric structure in stereopsis

A fundamental problem in the study of spatial perception concerns whether and how vision might acquire information about the metric structure of surfaces in three-dimensional space from motion and from stereopsis. Theoretical analyses have indicated that stereoscopic perceptions of metric relations in depth require additional information about egocentric viewing distance; and recent experiments by James Todd and his colleagues have indicated that vision acquires only affine but not metric structure from motion—that is, spatial relations ambiguous with regard to scale in depth. The purpose of the present study was to determine whether the metric shape of planar stereoscopic forms might be perceived from congruence under planar rotation. In Experiment 1, observers discriminated between similar planar shapes (ellipses) rotating in a plane with varying slant from the frontal-parallel plane. Experimental conditions varied the presence versus absence of binocular disparities, magnification of the disparity scale, and moving versus stationary patterns. Shape discriminations were accurate in all conditions with moving patterns and were near chance in conditions with stationary patterns; neither the presence nor the magnification of binocular disparities had any reliable effect. In Experiment 2, accuracy decreased as the range of rotation decreased from 80° to 10°. In Experiment 3, small deviations from planarity of the motion produced large decrements in accuracy. In contrast with the critical role of motion in shape discrimination, motion hindered discriminations of the binocular disparity scale in Experiment 4. In general, planar motion provides an intrinsic metric scale that is independent of slant in depth and of the scale of binocular disparities. Vision is sensitive to this intrinsic optical metric.     

Seeing double and depth with Wheatstone's stereograms

Charles Wheatstone, in his classic paper on the invention of the stereoscope, concluded "... objects whose pictures do not fall on corresponding points of the two retinae may still appear single" (1838 Philosophical Transactions of the Royal Society of London 128 384). Soon after, Ernst Brücke, Alexandre Prévost, David Brewster, Joseph Towne, and Joseph LeConte all published disagreements with this conclusion. LeConte's objections were most frequent and most prolonged. To understand the basis of the disagreements, we conducted three experiments using Wheatstone's original stereograms and found that most stereograms produced depth perception with diplopia, which partially explains the consistency among his critics' conclusions. Most of the criticism at variance with Wheatstone's conclusion was based on research conducted outside Germany. We argue that LeConte's lack of knowledge of the German literature on vision research prevented him from considering investigating Wheatstone's experiment with a stereogram having a smaller disparity.     

Binocular disparity magnitude affects perceived depth magnitude despite inversion of depth order

The hollow-face illusion involves a misperception of depth order: our perception follows our top-down knowledge that faces are convex, even though bottom-up depth information reflects the actual concave surface structure. While pictorial cues can be ambiguous, stereopsis should unambiguously indicate the actual depth order. We used computer-generated stereo images to investigate how, if at all, the sign and magnitude of binocular disparities affect the perceived depth of the illusory convex face. In experiment 1 participants adjusted the disparity of a convex comparison face until it matched a reference face. The reference face was either convex or hollow and had binocular disparities consistent with an average face or had disparities exaggerated, consistent with a face stretched in depth. We observed that apparent depth increased with disparity magnitude, even when the hollow faces were seen as convex (ie when perceived depth order was inconsistent with disparity sign). As expected, concave faces appeared flatter than convex faces, suggesting that disparity sign also affects perceived depth. In experiment 2, participants were presented with pairs of real and illusory convex faces. In each case, their task was to judge which of the two stimuli appeared to have the greater depth. Hollow faces with exaggerated disparities were again perceived as deeper.     

Binocular stereopsis without spatial disparity

Binocular stereopsis has traditionally been studied mainly under static viewing conditions. There has consequently been the tendency to view binocular stereopsis only in terms of the pickup of purely spatial (time-frozen) disparity. However, whenever there is movement of objects or the 0, the structure of the light entering each eye undergoes continuous change, and so a different type of disparity—kinetic disparity—is made potentially available to the binocular system. That kinetic disparity can, in fact, be picked up is shown by the present experiment, in which there was no spatial disparity information available about the three-dimensional motion path of an object; only kinetic disparity information was available. This suggests that a clear distinction should be made between binocular-static and binocular-kinetic space perception.     

The stereoscopic sliver: a comparison of duration thresholds for fully stereoscopic and unmatched versions

Just as positional disparities of image features seen with both eyes provide depth information, the presence of an area visible to one eye but not the other within a binocularly viewed scene can indicate an occlusion at a depth discontinuity. The close geometrical association between these two kinds of cues suggests they may both be exploited by stereopsis. To investigate this, we developed a novel binocular stimulus entirely lacking in classical disparity that contains an unmatched vertical sliver which elicits a warping of the surrounding surface to accommodate a depth discontinuity. We measured depth-discrimination performance at a range of stimulus durations, correcting for variations in stimulus visibility, to characterise the decline of the efficacy of the depth signal with limited integration time. Results show a close correspondence of performance for similar stimuli with unmatched features and classical binocular disparity across a sixtyfold range of viewing durations, supporting the notion of a close association between the two types of cues in human stereopsis. Control experiments excluded simple eye-of-origin cues and long-range false matches as explanatory factors.     

Effects of direction and magnitude of horizontal disparities on binocular unmasking

Conditions under which binocular unmasking (BU), as an analogue of binaural unmasking, occurs have been explored. Observers were to detect through a stereoscope a Gabor signal in patches of two-dimensional broadband gaussian noise surrounded by a frame of uniform noise. The right-eye gaussian field was displaced relative to the left eye so that it appeared either in front of or behind the frame. Performance when signal disparity was equal to that of the noise--a condition functionally equivalent to monocular processing--was compared to that obtained when signal disparity was zero--a case in which BU should occur. Enhanced signal detectability of up to 12 dB and of nearly constant magnitude was observed in the latter condition when uncrossed disparities of up to 67.60 min visual angle and display durations of 1 s were employed. Signal detectability declined appreciably with increasing disparity (both crossed and uncrossed) when display duration was reduced to 90 ms, thus preventing the occurrence of compensatory vergence eye movements. It is suggested that BU effects may result from a process of linear summation of monocular inputs.     

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。     

Two forms of retinal disparity

The retinal disparities in stereograms where the vertical alignment of pairs of homologous points in one eye differs from that in the other eye were found to be more effective than disparities that do not involve that kind of binocular difference. The presence of such “transverse disparities” was found to shorten the time elapsed until perceived depth was reported in four instances, in two simple stereogram pairs and in two different pairs of random dot pattern stereograms. In an experiment where binocular parallax was in conflict with an effect of past experience, the presence of transverse disparities caused binocular parallax to prevail. The presumption that the amount of perceived depth depends only on the amount of disparity (provided distances from the eyes are unchanged) and not on the configuration in which it manifests itself was found not to hold in stereograms containing transverse disparities.     

Suprathreshold stereo-depth matches as a function of contrast and spatial frequency

Thresholds for stereoscopic-depth perception increase with decreasing spatial frequency below 2.5 cycles deg-1. Despite this variation of stereo threshold, suprathreshold stereoscopic-depth perception is independent of spatial frequency down to 0.5 cycle deg-1. Below this frequency the perceived depth of crossed disparities is less than that stimulated by higher spatial frequencies which subtend the same disparities. We have investigated the effects of contrast fading upon this breakdown of stereo-depth invariance at low spatial frequencies. Suprathreshold stereopsis was investigated with spatially filtered vertical bars (difference of Gaussian luminance distribution, or DOG functions) tuned narrowly over a broad range of spatial frequencies (0.15-9.6 cycles deg-1). Disparity subtended by variable width DOGs whose physical contrast ranged from 10-100% was adjusted to match the perceived depth of a standard suprathreshold disparity (5 min visual angle) subtended by a thin black line. Greater amounts of crossed disparity were required to match broad than narrow DOGs to the apparent depth of the standard black line. The matched disparity was greater at low than at high contrast levels. When perceived contrast of all the DOGs was matched to standard contrasts ranging from 5-72%, disparity for depth matches became similar for narrow and broad DOGs. 200 ms pulsed presentations of DOGs with equal perceived contrast further reduced the disparity of low-contrast broad DOGs needed to match the standard depth. A perceived-depth bias in the uncrossed direction at low spatial frequencies was noted in these experiments. This was most pronounced for low-contrast low-spatial-frequency targets, which actually needed crossed disparities to make a depth match to an uncrossed standard. This bias was investigated further by making depth matches to a zero-disparity standard (ie the apparent fronto-parallel plane). Broad DOGs, which are composed of low spatial frequencies, were perceived behind the fixation plane when they actually subtended zero disparity. The magnitude of this low-frequency depth bias increased as contrast was reduced. The distal depth bias was also perceived monocularly, however, it was always greater when viewed binocularly. This investigation indicates that contrast fading of low-spatial-frequency stimuli changes their perceived depth and enhances a depth bias in the uncrossed direction. The depth bias has both a monocular and a binocular component.