Perception of relative depth interval: Systematic biases in perceived depth

Given an estimate of the binocular disparity between a pair of points and an estimate of the viewing distance, or knowledge of eye position, it should be possible to obtain an estimate of their depth separation. Here we show that, when points are arranged in different vertical geometric configurations across two intervals, many observers find this task difficult. Those who can do the task tend to perceive the depth interval in one configuration as very different from depth in the other configuration. We explore two plausible explanations for this effect. The first is the tilt of the empirical vertical horopter: Points perceived along an apparently vertical line correspond to a physical line of points tilted backwards in space. Second, the eyes can rotate in response to a particular stimulus. Without compensation for this rotation, biases in depth perception would result. We measured cyclovergence indirectly, using a standard psychophysical task, while observers viewed our depth configuration. Biases predicted from error due either to cyclovergence or to the tilted vertical horopter were not consistent with the depth configuration results. Our data suggest that, even for the simplest scenes, we do not have ready access to metric depth from binocular disparity.     

The backward inclination of a surface defined by empirical corresponding points

Three experiments were conducted to investigate whether a locus of binocular correspondence extends eccentrically from the vertical horopter. In experiment 1, we investigated whether the backward inclination of the vertical horopter was manifested in the angle at which readers prefer to orient the page. All observers preferred a page inclined backwards to any other orientation. This backward inclination was less than predicted from previous psychophysical reports, however. In experiment 2, we investigated the extent of binocular correspondence, defined by minimal apparent interocular horizontal motion, in the central 24 deg of the binocular field. Our data define a planar surface inclined top-away from the observer as a locus from which psychophysical corresponding points are stimulated. In experiment 3, we measured vertical adjustments required to eliminate apparent vertical motion. Together, the pattern of results from experiments 2 and 3 is most consistent with a planar surface, inclined top-away from the observer. This is consistent with Helmholtz's account of the backward inclination of the vertical horopter and expands the locus of zero horizontal disparity from a single line in the median plane to eccentric loci extending at least +/- 12 deg in the central binocular field.     

Stereoscopic matching and the aperture problem

In order to perceive stereoscopic depth, the visual system must define binocular disparities. Consider an oblique line seen through an aperture formed by flanking occluders. Because the line is perceived behind the aperture, the line must have disparity relative to the aperture. What is the assigned disparity of the line in this aperture problem? To answer this question five observers adjusted the horizontal disparity of a probe until it was perceived at the same depth as the disparate line behind the aperture. The results show that, when both the horizontal and the vertical disparities of the occluders are well-defined, the probe must have the same horizontal disparity as the horizontal separation between the line half-images. However, when the horizontal and vertical disparities of the occluders are ill-defined, the intersections of the line and the occluder borders can determine the matching direction. In the latter case, the matching direction varies with the aperture orientation and there is considerable variability across observers.     

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.     

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.     

The appearance of surfaces specified by motion parallax and binocular disparity

The experiments reported in this paper were designed to investigate how depth information from binocular disparity and motion parallax cues is integrated in the human visual system. Observers viewed simulated 3-D corrugated surfaces that translated to and fro across their line of sight. The depth of the corrugations was specified by either motion parallax, or binocular disparities, or some combination of the two. The amount of perceived depth in the corrugations was measured using a matching technique.

A monocularly viewed surface specified by parallax alone was seen as a rigid, corrugated surface translating along a fronto-parallel path. The perceived depth of the corrugations increased monotonically with the amount of parallax motion, just as if observers were viewing an equivalent real surface that produced the same parallax transformation. With binocular viewing and zero disparities between the images seen by the two eyes, the perceived depth was only about half of that predicted by the monocular cue. In addition, this binocularly viewed surface appeared to rotate about a vertical axis as it translated to and fro. With other combinations of motion parallax and binocular disparity, parallax only affected the perceived depth when the disparity gradients of the corrugations were shallow. The discrepancy between the parallax and disparity signals was typically resolved by an apparent rotation of the surface as it translated to and fro. The results are consistent with the idea that the visual system attempts to minimize the discrepancies between (1) the depth signalled by disparity and that required by a particular interpretation of the parallax transformation and (2) the amount of rotation required by that interpretation and the amount of rotation signalled by other cues in the display.     

The importance of being upright: Use of environmental and viewer-centered reference frames in shape discriminations of novel three-dimensional objects

We investigated the frame of reference that people use to make shape discriminations when their heads are either upright or tilted. Observers madesame-different judgments of pairs of novel threedimensional objects that were aligned along their length within the frontal-parallel plane and rotated in depth around an axis parallel to their own axes of elongation. The aligned objects were displayed vertically, tilted 45°, or horizontally with respect to the environmental upright, but the distance of each pair from the upright was irrelevant to resolving the angular disparity between the stimuli for thesame-different judgment. Nevertheless, when observers’ heads were upright, the time to encode the stimuli was a linear function of the distance of the stimuli from the environmental upright, whereas when observers’ heads were tilted 45°, encoding times for tilted and vertical stimuli did not differ and were faster than the times to encode horizontal stimuli. We interpreted these data to mean that observers either rotate or reference the top of an object to the environmental upright, and they can use either a gravitational or retinal reference frame to do so when either they or the objects are not upright.     

Stereoscopic depth cues can segment motion information

Can the motion system selectively process elements at a particular depth? We attempted to answer this question using global coherence tasks in which signal and noise elements could be given different disparities. In experiment 1 we found that, if all the signal elements had a disparity different from that of the noise elements, performance was far better than when they had the same disparity (at least for stereo-normal observers). In a second experiment we found that adding additional noise elements to the motion task had no effect if they had a different disparity (however, they had a marked effect for stereo-blind observers). We conclude that stereo disparity can be used as a segmentation cue by the motion system.     

The effects of age upon the perception of depth and 3-D shape from differential motion and binocular disparity

The ability of younger and older adults to perceive the 3-D shape, depth, and curvature of smooth surfaces defined by differential motion and binocular disparity was evaluated in six experiments. The number of points defining the surfaces and their spatial and temporal correspondences were manipulated. For stereoscopic sinusoidal surfaces, the spatial frequency of the corrugations was also varied. For surfaces defined by motion, the lifetimes of the individual points in the patterns were varied, and comparisons were made between the perception of surfaces defined by points and that of more ecologically valid textured surfaces. In all experiments, the older observers were less sensitive to the depths and curvatures of the surfaces, although the deficits were much larger for motion-defined surfaces. The results demonstrate that older adults can extract depth and shape from optical patterns containing only differential motion or binocular disparity, but these abilities are often manifested at reduced levels of performance.     

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.     

Relationship between binocular disparity and motion parallax in surface detection

The ability to detect surfaces was studied in a multiple-cue condition in which binocular disparity and motion parallax could specify independent depth configurations. On trials on which binocular disparity and motion parallax were presented together, either binocular disparity or motion parallax could indicate a surface in one of two intervals; in the other interval, both sources indicated a volume of random points. Surface detection when the two sources of information were present and compatible was not better than detection in baseline conditions, in which only one source of information was present. When binocular disparity and motion specified incompatible depths, observers’ ability to detect a surface was severely impaired if motion indicated a surface but binocular disparity did not. Performance was not as severely degraded when binocular disparity indicated a surface and motion did not. This dominance of binocular disparity persisted in the presence of foreknowledge about which source of information would be relevant.     

Attention affects the stereoscopic depth aftereffect

'Preattentive' vision is typically considered to include several low-level processes, including the perception of depth from binocular disparity and motion parallax. However, doubt was cast on this model when it was shown that a secondary attentional task can modulate the motion aftereffect (Chaudhuri, 1990 Nature 344 60-62). Here we investigate whether attention can also affect the depth aftereffect (Blakemore and Julesz, 1971 Science 171 286-288). Subjects adapted to stationary or moving random-dot patterns segmented into depth planes while attention was manipulated with a secondary task (character processing at parametrically varied rates). We found that the duration of the depth aftereffect can be affected by attentional manipulations, and both its duration and that of the motion aftereffect varied with the difficulty of the secondary task. The results are discussed in the context of dynamic feedback models of vision, and support the penetrability of low-level sensory processes by attentional mechanisms.     

Modification of depth and distance perception caused by long-term wearing of left-right reversing spectacles

For 35 to 39 days, four observers wore continuously left-right reversing spectacles which pseudoscopically reverse the order of binocular disparity and direction of convergence. In three tests, we investigated how the visual system copes with the transformation of depth and distance information due to the reversing spectacles. In stereogram observation, after a few days of wearing the spectacles. the observers sometimes perceived a depth order which was opposite to the depth order that they had perceived in the pre-spectacle-wearing period. Monocular depth cues contributed more to depth perception in the spectacle-wearing period than they did in the pre-spectacle-wearing period. While the perceived distance significantly decreased during the spectacle-wearing period, we found no evidence of adaptive change in distance perception. The results indicate that the visual system adapts itself to the transformed situation by not only changing the processing of disparity but also by changing the relative efficiency of each cue in determining apparent depth.     

Perceived depth scales with disparity gradient.

Perceived difference in depth between two adjacent stimuli decreases with increasing disparity gradient even if the disparity stays constant, ie when the stimuli approach each other along paths within fronto-parallel planes. This depth scaling effect is more pronounced with line stimuli than with two isolated points or two small symbols and is insignificant for easily discriminable symbols. The decrease in perceived depth is more pronounced for horizontal orientation than for oblique or vertical orientation. The ratio of perceived depth difference to displayed disparity difference also decreases when the distance between the stimuli increases at a constant gradient in depth. This is to say that we are more correct in our depth estimates for steep gradients in depth when the euclidean distance between the stimuli is short.     

Vertical disparity affects shape and size judgments across surfaces separated in depth

Vertical binocular disparity provides a useful source of information allowing three-dimensional (3-D) shape to be recovered from horizontal binocular disparity. In order to influence metric shape judgments, a large field of view is required, suggesting that vertical disparity may play a limited role in the perception of objects projecting small retinal images. This limitation could be overcome if vertical disparity information could be pooled over wide areas of 3-D space. This was investigated by assessing the effect of vertical disparity scaling of a large surround surface on the perceived size and 3-D shape of a small, central object. Observers adjusted the size and shape of a virtual, binocularly defined ellipsoid to match those of a real, hand-held tennis ball. The virtual ball was presented at three distances (200, 325, and 450 mm). Vertical disparities in a large surround surface were manipulated to be consistent with a distance of 160 mm or infinity. Both shape and size settings were influenced by this manipulation. This effect did not depend on presenting the surround and target objects at the same distance. These results suggest that the influence of vertical disparity on the perceived distance to a surface also affects the estimated distance of other visible surfaces. Vertical disparities are therefore important in the perception of metric depth, even for objects that in themselves subtend only small retinal images.     

Independence of sampling of motion parallax and binocular disparity in discrimination of depth1

Abstract: The sampling strategy of the visual system in binocular disparity and motion parallax to discriminate depth was investigated. Human observers were asked to discriminate between the depths of two surfaces defined by both cues. Gaussian noise was added to the depths represented by each cue, and the correlation in noise was manipulated. Human performance was compared with two types of likelihood models. The first was based on independent sampling, in which data from the two cues were gathered from independent sets of points in the display. The second was based on paired sampling, in which data from these cues were gathered from the same set of points. The former model yielded a better fit with human performance. This suggests that the visual system is more likely to adopt independent sampling.     

Shrinkage in the apparent size of cylindrical objects

A novel illusion in apparent size is reported. We asked observers to estimate the width and depth of vertically oriented elliptic cylinders depicted with texture or luminance gradients (experiment 1), or the height of horizontally oriented elliptic cylinders depicted with binocular disparity (experiment 2). The estimated width or height of cylinders showed systematic shrinkage in the direction of the gradual depth change. The dissimilarity of 2-D appearance amongst our stimuli implies a large variation in spatial-frequency components and brightness contrasts, eliminating the possibility that these parameters contributed to the illusion. Also, the mechanism inappropriately triggered by pictorial depth cues (eg size scaling) may be irrelevant, because the illusion was obtained even when binocular disparity alone specified the shape of the cylinders. The illusion demonstrated here suggests that our visual system may determine the size of 3-D objects by accounting for their depth structures.     

Binocular depth from surfaces versus volumes

Subjects were asked to compare the relative depths of two binocular targets embedded in different random dot stereogram backgrounds. The disparities of the background points were either randomized, corresponding to a scattering of points within a volume, or arranged according to a sawtooth (triangle-wave) disparity profile (i.e., a set of slanted planar surfaces separated by sharp depth discontinuities). When the targets were embedded in the random volume, their depths were perceived in accordance with their relative disparities. But when the target points were embedded in the sawtooth surfaces their depths were systematically misperceived in a manner predicted by the incorrect depth interpretation of the background points. Rather than seeing a sawtooth pattern, the background points resembled a staircase in depth, and the targets, which appeared embedded in different steps, were misjudged in depth accordingly. The effect suggests a distinction between the depth processing of isolated binocular features and those associated with continuous surfaces.     

2-D tilt and 3-D slant illusions in perception and action tasks

There is now a well established dissociation between perception and action based primarily on neuropsychological evidence [Milner and Goodale, 1995 The Visual Brain in Action (Oxford: Oxford University Press)]. Although equivocal, an important source of evidence from normal observers is that 'perceptual illusions' may affect the systems differently. We investigated the relative effects of 2-D tilt and 3-D slant illusions in the two domains, using similar tasks to those employed originally by Milner and Goodale. Subjects were required to either post a card through, or set a paddle to match the orientation of, a plane that was presented in two conditions: surrounded by a striped surface tilted between +90 degrees and -90 degrees (2-D tilt contrast), or surrounded by a disparity defined surface slanted in depth between +60 degrees and -60 degrees (3-D depth contrast). For 2-D tilt, action and perception were equally affected by the illusion, whereas in the 3-D condition they were not. Here, the illusion appeared greater in the posting than in the perceptual task. We conclude that, although no qualitative differences exist, there were quantitative differences between perception and action tasks in the binocular condition.     

Oculomotor responses of stereo‐anomalous observers to pulse and ramp disparities

We examined oculomotor responses to binocular disparities of one stereo‐normal and three stereo‐anomalous observers, who were identified through a stereoscopic depth‐discrimination task, in two experimental conditions. In the pulse disparity condition, crossed and uncrossed disparities (1–6°) were briefly presented (for .25–2.0 s). In the ramp disparity condition, disparities were varied continuously with constant velocities (.7–2.0°/s) and with an amplitude of 10°. The stereo‐normal observer showed vergence responses to both pulse and ramp disparities. The three stereo‐anomalous observers showed a marked reduction or absence of vergence responses to pulse disparities but showed vergence responses to ramp disparities. The results suggest the existence of separate sub‐systems mediating disparity vergence eye movements.