Binocular depth-from-motion in infantile and late-onset esotropia patients with poor stereopsis

PURPOSE

There are at least two possible ways to detect motion-in-depth binocular without monocular cues: the binocular disparities at different times and a mechanism that detects interocular velocity differences. The perception of interocular velocity differences (Binocular depth-from-motion [BDFM]) depends on the relative velocity of the images on the retina of the left and right eyes, and this information can be experienced by normal and some strabismic patients. The purpose of this study was to determine the characteristics of esotropic patients who have BDFM but have poor stereopsis.

METHODS

Forty-one infantile and 28 late-onset esotropia patients with poor stereopsis were studied. Dynamic stereopsis and BDFM were tested with computer-generated random dot stereograms and kinematograms. The correlations between BDFM and other binocular functional tests were determined.

RESULTS

A total of 31 (44.9%) patients, 15 (36.5%) of the infantile and 16 (57.1%) of the late-onset esotropia group, passed the BDFM test. None of these patients passed the random dot stereo test under static or dynamic conditions. Fusion of the Worth four dot test at near 0.3 m was correlated with the presence of BDFM. Three of the 15 infantile and 10 of the 16 late-onset esotropic patients with positive BDFM showed gross stereopsis as measured by the Titmus Fly. The angle of strabismus was significantly smaller in the patients with positive BDFM for the infantile and the late-onset esotropia groups.

CONCLUSIONS

BDFM was present in about half of the esotropic patients who do not have fine stereopsis. Ocular alignment within 10 to 15 prism diopters is an important factor in obtaining BDFM. Strabismus surgery still provides some binocular benefit for infantile esotropia patients who were bypassed for early surgery. Separate mechanisms may underlie static stereopsis and BDFM.

The interaction of binocular disparity and motion parallax in determining perceived depth and perceived size

Although binocular disparity and motion parallax are powerful cues for depth, neither, in isolation, can specify information about both object size and depth. It has been shown that information from both cues can be combined to specify the size, depth, and distance of an object in a scene (Richards, 1985 Journal of the Optical Society of America A 2 343-349). Experiments are reported in which natural viewing and physical stimuli have been used to investigate the nature of size and depth perception on the basis of disparity and parallax presented separately and together at a range of viewing distances. Observers adjusted the relative position of three bright LEDs, which were constrained to form a triangle in plan view with the apex pointing toward the observer, so its dimensions matched that of a standard held by the subject. With static monocular viewing, depth settings were inaccurate and erratic. When both cues were present together accuracy increased and the perceptual outcome was consistent with an averaging of the information provided by both cues. When an apparent bias evident in the observers' responses (the tendency to under-estimate the size of the standard) was taken into account, accuracy was high and size and depth constancy were close to 100%. In addition, given this assumption, the same estimate of viewing distance was used to scale size and depth estimates.

Temporal aspects of slant and inclination perception

Linear transformations (shear or scale transformations) of either horizontal or vertical disparity give rise to the percept of slant or inclination. It has been proposed that the percept of slant induced by vertical size disparity, known as Ogle's induced-size effect, and the analogous induced-shear effect, compensate for scale and shear distortions arising from aniseikonia, eccentric viewing, and cyclodisparity. We hypothesised that these linear transformations of vertical disparity are processed more slowly than equivalent transformations of horizontal disparity (horizontal shear and size disparity). We studied the temporal properties of the stereoscopic slant and inclination percepts that arose when subjects viewed stereograms with various combinations of horizontal and vertical size or shear disparities. We found no evidence to support our hypothesis. There were no clear differences in the build-up of percepts of slant or inclination induced by step changes in horizontal size or shear disparity and those induced by step changes in vertical size or shear disparity. Perceived slant and inclination decreased in a similar manner with increasing temporal frequency for modulations of transformations of both horizontal and vertical disparity. Considerable individual differences were found and several subjects experienced slant reversal, particularly with oscillating stimuli. An interesting finding was that perceived slant induced by modulations of dilation disparity was in the direction of the vertical component. This suggests the vertical size disparity mechanism has a higher temporal bandwidth than the horizontal size disparity mechanism. However, conflicting perspective information may play a dominant role in determining the temporal properties of perceived slant and inclination.

Disparity detection in anticorrelated stereograms

Recent physiological observations in which stimuli with opposite contrast signs in the two eyes have been used (anticorrelated stereograms) show that these stimuli evoke responses in primary visual cortex which are the reverse of responses to correlated stimuli. Psychophysical investigations reveal no such reversals: reversed-contrast bars with crossed disparities are seen in front of those with uncrossed disparities. For anticorrelated random-dot stereograms human subjects perceive no depth at all, except at low dot densities. However, these human studies were carried out with stimuli that differed in several ways from those used in physiological studies. We therefore reexamined psychophysical responses using stimuli similar to those used for physiological recordings. Our results confirm the previous findings: there is no evidence of a reversed depth sensation for bar stereograms (crossed disparities are never seen behind uncrossed disparities), and subjects are unable to detect depth in anticorrelated random-dot stereograms at the densities used for the physiological recordings. The discrepancy between the psychophysical data and the responses of single neurons in primary visual cortex suggests that further processing outside area V1 is necessary to provide the signals that produce the sensation of stereoscopic depth.

Surface separation decreases stereoscopic slant but a monocular aperture increases it

When an isolated surface is stereoscopically slanted around its vertical axis, perceived slant is attenuated relative to prediction, whereas when a frontal-plane surface is placed above or below the slanted surface, slant is close to the predicted magnitude. Gillam et al (1988 Journal of Experimental Psychology: Human Perception and Performance 14 163-175) have argued that this slant enhancement is due to the introduction of a gradient of relative disparities across the abutment of the two surfaces which is a more effective stimulus for slant than is the gradient of absolute disparities present when the slanted surface is presented alone. To test this claim we varied the separation between the two surfaces, along either the vertical or depth axis. Since these manipulations have been reported to reduce the depth response to individual relative disparities, they should similarly affect any slant response based on a gradient of relative disparities. As predicted, increasing the separation, vertically or in depth, systematically reduced both the perceived slant of the stereoscopically slanted surface and also the stereo contrast slant induced in the frontal-plane surface. These results are not predicted by alternative accounts of slant enhancement (disparity-gradient contrast, normalisation, frame of reference). We also demonstrated that sidebands of monocular texture, when added to equate the half-image widths of the slanted surface, increased the perceived slant of this surface (particularly when presented alone) and reduced the contrast slant. Monocular texture, by signalling occlusion, appeared to provide absolute slant information which determined how the total relative slant perceived between the surfaces was allocated to each.

Cues to viewing distance for stereoscopic depth constancy

A veridical estimate of viewing distance is required in order to determine the metric structure of objects from binocular stereopsis. One example of a judgment of metric structure, which we used in our experiment, is the apparently circular cylinder task (E B Johnston, 1991 Vision Research 31 1351-1360). Most studies report underconstancy in this task when the stimulus is defined purely by binocular disparities. We examined the effect of two factors on performance: (i) the richness of the cues to viewing distance (using either a naturalistic setting with many cues to viewing distance or a condition in which the room and the monitors were obscured from view), and (ii) the range of stimulus disparities (cylinder depths) presented during an experimental run. We tested both experienced subjects (who had performed the task many times before under full-cue conditions) and naïve subjects. Depth constancy was reduced for the naïve subjects (from 62% to 46%) when the position of the monitors was obscured. Under similar conditions, the experienced subjects showed no reduction in constancy. In a second experiment, using a forced-choice method of constant stimuli, we found that depth constancy was reduced from 64% to 23% in naïve subjects and from 77% to 55% in experienced subjects when the same set of images was presented at all viewing distances rather than using a set of stimulus disparities proportional to the correct setting. One possible explanation of these results is that, under reduced-cue conditions, the range of disparities presented is used by the visual system as a cue to viewing distance.

[Retroequatorial myopexy combined with bimedial recession for near-distance disparity esotropia]

PURPOSE

In cases of esotropia combined with a high AC/A ratio, partly accommodative convergence excess or with nonaccommodative convergence excess, two methods of surgical therapy are possible: recession of the medial recti (Parks) and retroequatorial myopexy (Cüppers). Our aim was to answer the question whether retroequatorial myopexy alone and in combination with bimedial recession are appropriate methods of reducing the strabismic angle at near and distant fixation to values under 10 PD and near-distance disparity to less than 10 PD to form the basis for single binocular vision without bifocals.

PATIENTS AND METHODS

Eighty-three patients, aged 2-14 years (39 boys and 44 girls), were included in the study: 37 children (group A) with early-onset near-distance esotropia of 14-48 PD for distance and 26-65 PD for near objects and 46 children (group B) with acquired near-distance esotropia of 8-45 PD for distance and 26-70 PD for near objects. Inclusion criteria were a near-distanced disparity of at least 10 PD (range 10-33 PD), a follow-up of at least 3 months (median 5 months, range 3-69 months), retinoscopy in cycloplegia and full refractive correction. The amount of conventional surgery was chiefly based on the distance angle of esotropia. The myopexy was placed 12, 13 and 14 mm behind the insertion of the medial rectus.

RESULTS

In 73 of 83 patients (88%) we were able to reduce the strabismic angle for distance and near fixation to less than 10 PD and in 73 cases even under 5 PD. In 77 of 83 patients (93%) the near-distance disparity was reduced to less than 10 PD and in 72 patients (87%) even under 5 PD. Postoperatively, 9 children had bifocals, but 3 of them have meanwhile discarded them. Two cases were slightly ocvercorrected and 1 case undercorrected. Seventy children (84%) attained grade of binocularity.

CONCLUSION

Retroequatorial myopexy (fadenoperation) alone and combined with bimedial recession is an effective procedure in treating esotropia with abnormal near-distance disparity.

Stereothresholds in persons wtih congenital nystagmus and in normal observers during comparable retinal image motion

Despite rapid oscillations of the eyes, visual acuity is close to normal in many observers with congenital nystagmus (CN). This study investigated whether binocular hyperacuity thresholds are also close to normal in observers with CN. To do so, we assessed stereothresholds for horizontally and vertically separated line targets in three normal observers and six observers with idiopathic horizontal CN. Stereothresholds in normal observers are better than in the observers with CN, especially for horizontally-separated targets and very small inter-line separations. Stereothresholds remain better in normal observers than in the observers with CN, even in the presence of conjugate retinal image motion simulating that in jerk nystagmus. However, when the simulated CN wave form also includes disconjugate position variability of the foveation periods, normal observers' stereothresholds become similar to those of approximately half of the observers with CN. We conclude that stereothresholds in observers with CN are degraded by the more-or-less constant motion of the retinal image, by excessive vergence instability and, in some observers, by a neural sensory deficit.

Two processes in stereoscopic apparent motion

This study investigated the human ability to discriminate the motion direction of sequentially presented depth patterns produced by random-dot stereograms. The stereoscopic (cyclopean) patterns used here consisted of 256 rectangle patches, each of which had an alternative depth position (near or far). Two successive frames of correlated depth patterns made impressions of lateral motion when the pattern position in the second frame shifted laterally. The density of the patches that were near was varied. The Dmax that was measured using the 2AFC method was short when the density was high. The effect of depth reversing in the second frame was also tested. Under low density conditions, the performance was still good against reversing 3-D polarity. However, when the density was high, with depth reversal, motion in the reversed direction was perceived. Reversed motion was observed more often when SOA was small and when the density of near patches was near 1/2. Two strategies seem to exist in stereoscopic motion detecting: a polarity-independent process which matches figures, ignoring their depth polarity, and a polarity-dependent process which operates locally, ignoring 2-D shapes. The latter suggests the existence of a passive process in stereoscopic motion.

Orientation tuning of the transient-stereopsis system

Stereo-perception appears to be mediated by at least two systems: a transient system that processes stimuli presented briefly and a sustained one that processes stimuli presented for longer durations. In this paper we investigated the tuning of the transient-stereopsis system to stimulus orientation. Narrowband-gabor targets with a constant envelope size (Gaussian standard deviation of 1 degree) were presented for brief (140 ms) durations at large (from 4 to 8 degrees) disparities. The results were as follows: (1) while observers could extract depth from orthogonally-oriented gabors at above chance levels, their performance was worse than that with gabors of matched orientation; (2) varying the relative contrasts of the two orthogonally oriented gabors of the same spatial frequency resulted in a reduction in performance; (3) varying the relative spatial frequencies of the orthogonally-oriented gabors impaired performance, relative to that for matched frequencies; and (4) varying the relative contrasts of orthogonal gabors that were at different spatial frequencies could improve performance. These results indicate that transient stereo-performance in the orthogonal condition was not mediated by the channels that extracted depth in either the horizontal- or vertically-matched gabor conditions. This apparent lack of orientation tuning is indicative of a second-order pathway. That this performance was mediated by a binocular, as opposed to a monocular channel, is supported by the finding that performance decreased as the contrast of one of the gabors was reduced. The finding that performance with orthogonal gabors of unmatched spatial frequency (0.5 and 4 cpd) could be improved by varying their relative contrasts suggests that the binocular spatial-frequency tuning exhibited by this channel is broadband in nature. Finally, the observation that lowering the contrast of either the high or low spatial-frequency gabor improved performance suggests the presence of at least two broadband channels: one with its peak sensitivity at a low and the other at a high spatial-frequency.

The influence of heterophoria measurements on subsequent associated phoria measurement in a refractive routine

The influence of measuring heterophoria on a subsequent associated phoria measurement was investigated in 50 subjects. After refraction, heterophoria was measured by either von Graefe's technique or Maddox rod and wing. The effect of these procedures was assessed by associated phoria measurements taken before and after the dissociated measures. It is shown that subjects with a history of unstable binocular vision are likely to have an associate phoria induced or changed by the previous dissociated phoria measurement, particularly if von Graefe's technique is employed. It is recommended that, especially for near, associated phoria should be assessed before the dissociated phoria in subjects who are regarded as having a history of unstable binocular vision.

Binocular neurons in V1 of awake monkeys are selective for absolute, not relative, disparity

Most neurophysiological accounts of disparity selectivity in neurons of the primary visual cortex (V1) imply that they are selective for absolute retinal disparities. By contrast, a number of psychophysical observations indicate that relative disparities play a more important role in depth perception. During recordings from disparity selective neurons in area V1 of awake behaving monkeys, we used a disparity feedback loop () to add controlled amounts of absolute disparity to a display containing both absolute and relative disparities. This manipulation changed the absolute disparity of all the visible features in the display but left unchanged the relative disparities signalled by these features. The addition of absolute disparities produced clear changes in the neural responses to unchanged external stimuli, which were well predicted by the measured change in absolute disparity: in 45/53 cases, the neuron maintained a consistent firing pattern with respect to absolute disparity so that the manipulation created no significant change in the absolute disparity preferred by the neuron. No neuron in V1 maintained a consistent relationship with relative disparity. We conclude that the relative disparity signals used in primate depth perception are constructed outside area V1.

The Poggendorff illusion: a bias in the estimation of the orientation of virtual lines by second-stage filters

The veridical perception of collinearity between two separated lines is distorted by two parallel lines in the space between them (the Poggendorff illusion). This paper tests the conjecture that the perception of collinearity of separated lines is based on a two-stage mechanism. The first stage encodes the orientation of the virtual line between the proximal terminators of the target lines. The second stage compares this virtual orientation with the orientation of the target lines themselves. Errors can and do arise from either process. Two parallel lines, abutting against the target lines, cause the classical Poggendorff misalignment bias. The magnitude of the bias is increased by Gaussian blur, as is a version of the Poggendorff figure containing only acute angles. In the obtuse-angle figure, on the other hand, blur decreases the misalignment bias. We argue that the acute- and obtuse-angle biases depend upon different mechanisms, and that the obtuse-angle effect is more related to the obtuse-angle version of the Muller-Lyer illusion, which is also decreased by blur. If observers attempt to match the orientation of the virtual line between the two line intersections in the Poggendorff figure they make an error in the same direction as the Poggendorff bias. The orientation of the target lines in the figure, however, is veridically matched to a Gabor-patch probe, unless the target lines are very short, in which case the error is in the same direction as the Poggendorff bias. A small bend in the target lines where they abut the parallels increases the Poggendorff bias if it makes the line more orthogonal to the parallel, but has little effect in the opposite direction. The Poggendorff bias is unlikely to depend upon biases in first-stage linear filters because (a) it still exists in figures composed of short, luminance-balanced lines which are defined by contrast only; and (b) it also exists if the parallels are replaced by grating patches with the same mean luminance as the background. The orientation of the grating in the latter case affects the magnitude of the bias, but even an orientation which should reverse the Poggendorff bias by the mechanism of cross-orientation inhibition fails to do so. The Poggendorff bias is a complex effect arising from several sources. Blurring in second-stage filters with large receptive fields can explain many aspects of the phenomenon.

Emotion space under conditions of perceptual ambiguity

This study examined whether a two-dimensional structure of emotion could be found under the condition of perceptual ambiguity, using a stereoscopic procedure. Two expressions of depicted emotion were presented simultaneously to each different eye of the subjects. Multidimensional scaling yielded results suggesting that the dimensional structure such as valence and arousal was evident even under such an unusual condition as that of the current study.

Motion-transparent inducers have different effects on induced motion and motion capture

To assess the relationship among the underlying mechanisms of induced motion, motion capture, and motion transparency, directions of the former two illusions in the presence of motion-transparent inducers were examined. Two random-dot patterns (inducers) were superimposed upon a stationary disk (target), and moved in orthogonal directions. Either a high-contrast target (for induced motion) or a low-contrast target (for motion capture) was used. The task was to report the perceived direction of the target. The depth order of inducers was controlled either by adding binocular disparity or by asking the subject to report subjective depth order. For induced motion, the target appeared to move in the direction opposite to the inducer that had a disparity closer to the target; when there was no difference in disparity, induced motion occurred oppositely to the 'vector sum' of the inducers' directions. For motion capture, the target was captured by the inducer that subjectively appeared behind. These results suggest that the underlying mechanism of motion capture utilizes the output from the process for motion transparency, whereas induced motion has no clear relationship to the output of the process for motion transparency.

Is the anisotropy of perceived 3-D shape invariant across scale?

A number of studies have resulted in the finding of a 3-D perceptual anisotropy, whereby spatial intervals oriented in depth are perceived to be smaller than physically equal intervals in the frontoparallel plane. In this experiment, we examined whether this anisotropy is scale invariant. The stimuli were L shapes created by two rods placed flat on a level grassy field, with one rod defining a frontoparallel interval, and the other, a depth interval. Observers monocularly and binocularly viewed L shapes at two scales such that they were projectively equivalent under monocular viewing. Observers judged the aspect ratio (depth/width) of each shape. Judged aspect ratio indicated a perceptual anisotropy that was invariant with scale for monocular viewing, but not for binocular viewing. When perspective is kept constant, monocular viewing results in perceptual anisotropy that is invariant across these two scales and presumably across still larger scales. This scale invariance indicates that the perception of shape under these conditions is determined independently of the perception of size.

Stereoscopic occlusion and the aperture problem for motion: a new solution

Recent work has shown that the ability of moving contour terminators to determine the perceived motion of untextured contours is strongly constrained by whether contour terminators are classified as intrinsic (belonging to a moving contour) or extrinsic (belonging to a surface occluding a moving contour). It has also been demonstrated that stereopsis can play a decisive role in this classification. Specifically, Shimojo, Silverman and Nakayama (1989, Vision Research 29, 619-626) argued that the efficacy of stereopsis in classifying moving contour terminators as intrinsic or extrinsic stemmed from the relative depth relationships specified by binocular disparity. Here, evidence is presented which demonstrates that the visual system relies on the presence of unpaired contour terminators to classify stereoscopic contour terminators as extrinsic. The author shows that the tendency to perceive untextured contours translating in a single rectangular aperture in a direction parallel to the longer axis of the aperture (the barberpole illusion) was not abolished by stereoscopic depth differences when the contour terminators were interocularly paired. However, the illusion was abolished when the contours terminators along the longer axis of the aperture were interocularly unpaired. Moreover, contours translated within a square aperture revealed a systematic shift towards the direction of motion signaled by the binocularly paired contour terminators along the horizontal edges of the aperture. These results demonstrate that the classification of stereoscopic contour terminators along an extrinsic-intrinsic dimension results from the presence of local, unpaired contour terminators rather than the relative depth or disparity differences per se, or via the global integration of contour terminators across multiple apertures when multiple apertures are present.

Stereoscopic depth but not shape perception from second-order stimuli

Depth can be seen using either linear (first-order) or non-linear (second-order) stereo micropatterns when, in the latter, contrast envelopes contain the disparity information. We examined whether a second-order mechanism can contribute to the perception of 3-D surface shape. Using a variety of different stimulus types, we show that for each, shape is easy to see with linear stimuli. Over a wide range of parameters however, none of our observers perceived shape, however faintly, from the non-linear stimuli. To explore why these elements failed, we simplified our stimulus to a step-edge in depth and measured performance while varying the number of elements. We show how performance declined when more than two non-linear elements were used. We discuss reasons for the limitation found for non-matching elements, including a dissociation for stereopsis between seeing surface shape and depth.

Stereopsis, cyclovergence and the backwards tilt of the vertical horopter

It is generally recognized that the vertical horopter has a backwards tilt such that it passes through the fixation point and a point near the feet of the observer. The basis of the tilt has been attributed to either a shear in binocular retinal correspondence along the vertical meridian or the presence of cyclovergence eye movements. In an attempt to determine empirically the mechanisms underlying the tilt of the vertical horopter, retinal correspondence along the vertical meridian was investigated as a function of viewing distance. In addition, binocular measurements of torsional eye position were made in the same observers under similar viewing conditions. The vertical horopter was determined using two criteria. In the first instance, increment depth discrimination thresholds for both crossed and uncrossed disparities were measured as a function of retinal eccentricity along the vertical meridian, up to 5 degrees superiorly and inferiorly, and the horopter was defined by the region in space which had the lowest stereo-threshold. Secondly, subjective alignment of dichoptically presented nonius lines defined the horopter by identical visual directions. Both criteria were used to determine the horopter at 2 m while only the criterion of identical visual direction was used at the nearer distance of 50 cm. The vertical horopter showed a backwards tilt that decreased from an average of about 12 degrees at 2 m to 3 degrees at 50 cm, with some variability between observers. Torsional eye position did not change significantly between fixation distances. These results confirmed the geometric relation between the backwards tilt in the vertical horopter and fixation distance and support Helmholtz's original contention that the tilt is a consequence of a shear in retinal correspondence in the vertical meridian.

Role of spatial and temporal coincidence in depth organization

The linking of spatial information is essential for coherent space perception. A study is reported of the contribution of temporal and spatial alignment for the linkage of spatial elements in terms of depth perception. Stereo half-images were generated on the left and right halves of a large-screen video monitor and viewed through a mirror stereoscope. The half-images portrayed a black vertically oriented bar with two brackets immediately flanking this bar and placed in crossed or uncrossed disparity relative to the bar. A pair of thin white 'bridging lines' could appear on the black bar, always at zero disparity. Brackets and bridging lines could be flickered either in phase or out of phase. Observers judged whether the brackets appeared in front of or behind the black bar, with disparity varied. Compared to conditions when the bridging lines were absent, depth judgments were markedly biased toward "in front" when bridging lines and brackets flashed in temporal phase; this bias was much reduced when the bridging lines and brackets flashed out of phase. This biasing effect also depended on spatial offset of lines and brackets. However, perception was uninfluenced by the lateral separation between object and brackets.

A new stereoscopic illusion: eyes popping out and sinking in

A stereoscopic illusion is produced by manipulating the binocular disparity of the irises in stereo pairs of human faces. These stimuli elicit unnatural percepts of the irises popping out of the face or sinking in inside the head.

The effect of target size and eccentricity on reflex disparity vergence

This study examined the effects of stimulus size and eccentricity on reflex disparity vergence: the small, involuntary corrections of eye alignment which serve to minimize the binocular disparity of fixated targets. Subjects were instructed to fixate steadily on a small, stationary mark superimposed on the center of a dynamic random dot stereogram. The stereogram was binocularly uncorrelated except for a fully correlated patch whose size and eccentricity were varied systematically across trials. The disparity of the patch was varied sinusoidally over time to stimulate vergence following movements. The overall purpose was to determine the relative contributions of various field loci in controlling binocular fixation by finding the smallest patch which would reliably drive vergence against the effort to fixate steadily. Psychophysical thresholds for detection of the correlated patch stimuli were also measured for comparison to the oculomotor results. Results showed that the smallest effective patch increased with eccentricity similarly for both vergence responses and psychophysical detection, suggesting they depend on a common, presumably cortical matching process. The dependence of response on eccentricity is roughly consistent with changes in the cortical magnification factor, suggesting that the area of cortex stimulated may be the determining factor in vergence responses to this class of stimulus.

Does symmetry structure facilitate the depth separation between stereoscopically overlapped dot planes?

In the present study, we dealt with the problem of whether a symmetrical structure can influence the discrimination of the depth separation of overlapped dot planes. We investigated this problem with the use of both direct and indirect methods. In the direct method, we presented three or two overlapped dot planes consisting of symmetrical or random dots. The subjects were required to discriminate three overlapped from two overlapped planes. In the indirect method, the subjects were required to discriminate the depth positions of a target dot (or a pair of dots) that disappeared during stimulus presentation. Our results, obtained in three experiments, showed that the discrimination performance improved and reached a perfect level in the direct method and a modest plateau level in the indirect method with increasing relative disparity between the two outer planes, irrespective of whether the dot pattern had a symmetrical structure or not. These results suggest that a detection process for symmetry structure on a two-dimensional plane in three-dimensional space will not have a direct or an indirect connection (e.g., via a feedback loop) to a process involved in the depth separation.

Using a synoptophore to test Listing's law during vergence in normal subjects and strabismic patients

The synoptophore was used to measure torsional interocular disparity. This, in turn, was used to compute how much the angle between the Listing's plane (LP) of the two eyes changes as a function of the vergence angle. The ratio of these two angles was defined as G. We measured G in normals and in patients suffering from intermittent horizontal strabismus. Consistent with previous search-coil experiments and with our previous visual test measures, the results using the synoptophore suggest that, for normals, G is less than 1. In the patient group the mean G was similar in magnitude but more variable. The variations in G did not appear to be related to the patient's measurement of ocular deviation. This result suggests that the vergence-related rotation of LP in these patients may be related to other factors besides the effort required to fuse the lines of sight.

Stereoscopic transparency: a test for binocular vision's disambiguating power

It has been suggested that to resolve ambiguities implicit in binocular perception of complex visual scenes, the brain adopts a continuity constraint assuming that disparities change smoothly with eccentricity. Stereoscopic transparency is characterized by abrupt changes of binocular disparity across retinal locations. The focus of the present study is how the brain uses the continuity constraint in the perception of stereoscopic transparency despite the presence of abrupt disparity changes. Observers viewed random-dot stereograms of overlapping transparent plane and cylindrical surfaces and had to distinguish between two orientations of the cylindrical surface under conditions of strictly controlled depth fixation. Surprisingly, maximal dot density of the transparent plane at which perception is still veridical dramatically decreases as depth separation between the surfaces grows. Persistence of this relationship, when binocular matching processes at each surface are separated to on and off brightness channels, suggests at least two stages in the underlying computation binocular matching and inter-surface interactions. We show that these phenomena cannot be accounted for by either higher severity of matching with high dot densities or the ability of the denser surface to pull vergence to its depth. We also measure contrast sensitivity and near-far symmetry of the underlying mechanism and propose a model of competitive interactions between dissimilar disparities.