Does vertical disparity scale the perception of stereoscopic depth?

It has been suggested that a measure of the gradients of vertical disparity over a surface may scale the mapping between horizontal disparity and perceived depth. We have investigated this possibility by obtaining estimates of the depth within stereograms that simulated two apposed fronto-parallel planes placed at different distances from an observer. The gradients of vertical disparity in a stereogram were set to simulate those appropriate to a viewing distance of 12.5 cm, 25 cm, 50 cm or 100 cm, whereas the distance specified by vergence and accommodative cues was always fixed at 50 cm. Judgements of the perceived depth between the two planes were uninfluenced by changes in the gradients of vertical disparity. It thus seems that the human visual system does not employ vertical disparity as a scaling parameter in stereoscopic depth judgements.     

Linear and nonlinear transparencies in binocular vision.

When the product of a vertical square-wave grating (contrast envelope) and a horizontal sinusoidal grating (carrier) are viewed binocularly with different disparity cues they can be perceived transparently at different depths. We found, however, that the transparency was asymmetric; it only occurred when the envelope was perceived to be the overlaying surface. When the same two signals were added, the percept of transparency was symmetrical; either signal could be seen in front of or behind the other at different depths. Differences between these multiplicative and additive signal combinations were examined in two experiments. In one, we measured disparity thresholds for transparency as a function of the spatial frequency of the envelope. In the other, we measured disparity discrimination thresholds. In both experiments the thresholds for the multiplicative condition, unlike the additive condition, showed distinct minima at low envelope frequencies. The different sensitivity curves found for multiplicative and additive signal combinations suggest that different processes mediated the disparity signal. The data are consistent with a two-channel model of binocular matching, with multiple depth cues represented at single retinal locations.     

Detecting binocular 3D motion in static 3D noise: no effect of viewing distance

Relative binocular disparity cannot tell us the absolute 3D shape of an object, nor the 3D trajectory of its motion, unless the visual system has independent access to how far away the object is at any moment. Indeed, as the viewing distance is changed, the same disparate retinal motions will correspond to very different real 3D trajectories. In this paper we were interested in whether binocular 3D motion detection is affected by viewing distance. A visual search task was used, in which the observer is asked to detect a target dot, moving in 3D, amidst 3D stationary distractor dots. We found that distance does not affect detection performance. Motion-in-depth is consistently harder to detect than the equivalent lateral motion, for all viewing distances. For a constant retinal motion with both lateral and motion-in-depth components, detection performance is constant despite variations in viewing distance that produce large changes in the direction of the 3D trajectory. We conclude that binocular 3D motion detection relies on retinal, not absolute, visual signals.     

Perceptual distance and the constancy of size and stereoscopic depth

The relationship between distance and size perception is unclear because of conflicting results of tests investigating the size-distance invariance hypothesis (SDIH), according to which perceived size is proportional to perceived distance. We propose that response bias with regard to measures of perceived distance is at the root of the conflict. Rather than employ the usual method of magnitude estimation, the bias-free two-alternative forced choice (2AFC) method was used to determine the precision (1/sigma) of discriminating depth at different distances. The results led us to define perceptual distance as a bias free power function of physical distance, with an exponent of approximately 0.5. Similar measures involving size differences among stimuli of equal angular size yield the same power function of distance. In addition, size discrimination is noisier than depth discrimination, suggesting that distance information is processed prior to angular size. Size constancy implies that the perceived size is proportional to perceptual distance. Moreover, given a constant relative disparity, depth constancy implies that perceived depth is proportional to the square of perceptual distance. However, the function relating the uncertainties of depth and of size discrimination to distance is the same. Hence, depth and size constancy may be accounted for by the same underlying law.     

Stereoscopic depth constancy

Depth constancy is the ability to perceive a fixed depth interval in the world as constant despite changes in viewing distance and the spatial scale of depth variation. It is well known that the spatial frequency of depth variation has a large effect on threshold. In the first experiment, we determined that the visual system compensates for this differential sensitivity when the change in disparity is suprathreshold, thereby attaining constancy similar to contrast constancy in the luminance domain. In a second experiment, we examined the ability to perceive constant depth when the spatial frequency and viewing distance both changed. To attain constancy in this situation, the visual system has to estimate distance. We investigated this ability when vergence, accommodation and vertical disparity are all presented accurately and therefore provided veridical information about viewing distance. We found that constancy is nearly complete across changes in viewing distance. Depth constancy is most complete when the scale of the depth relief is constant in the world rather than when it is constant in angular units at the retina. These results bear on the efficacy of algorithms for creating stereo content.This article is part of the themed issue ‘Vision in our three-dimensional world’.     

Depth resolution in the pigeon

Summary Pigeons possess a binocular visual field and a retinal region of higher cellular density pointing to the center of this overlap. These features and the precision of pecking behavior suggest that in this lateral-eyed bird cues other than monocular ones might participate in depth judgements.Pigeons were trained with an operant procedure to discriminate between luminous points differing in depth which appeared to the observer as floating in the dark. The accuracy of depth judgements was found to be a function of the ratio between the interstimulus distance and the mean eyes-to-stimulus distance. In a first test (experiment I) no external binocular disparity cues were available, the animal only seeing one luminous point at a time (near or far). In a second test (experiment II) where binocular disparity cues were available, the animal having this time to discriminate a pair of points placed at equal depth from a pair placed at unequal depths, only one pair being visible at a time, depth resolution did not improve. This suggests that, at least within the range of distances explored, the pigeon has no stereoscopic vision. Notwithstanding this, binocular cues do play a role, since when tests were done comparing binocular with monocular viewing (experiment III), monocular depth resolution was significantly worse.     

Where Do the Eyes Really Go in the Hollow-Face Illusion?

The hollow-face illusion refers to the finding that people typically perceive a concave (hollow) mask as being convex, despite the presence of binocular disparity cues that indicate the contrary. Unlike other illusions of depth, recent research has suggested that the eyes tend to converge at perceived, rather than actual, depths. However, technical and methodological limitations prevented one from knowing whether disparity cues may still have influenced vergence. In the current study, we presented participants with virtual normal or hollow masks and asked them to fixate the tip of the face's nose until they had indicated whether they perceived it as pointing towards or away from them. The results showed that the direction of vergence was indeed determined by perceived depth, although vergence responses were both somewhat delayed and of smaller amplitude (by a factor of about 0.5) for concave than convex masks. These findings demonstrate how perceived depth can override disparity cues when it comes to vergence, albeit not entirely.     

Stereoscopic correspondence for ambiguous targets is affected by elevation and fixation distance

Binocular correspondence must be determined if disparity is to be used to provide information about three-dimensional shape. The current study investigated whether knowledge of the statistical distribution of disparities in the natural environment is employed in this process. A simple model, which produces distributions of distances similar to those found in the natural environment, was used to predict the distribution of disparities in natural images. This model predicts that crossed disparities will be more likely as (i) stimulus elevation decreases below fixation and (ii) fixation distance increases. To determine whether these factors influence binocular correspondence for human observers, ambiguous stereograms were presented to observers, as stimulus elevation and fixation distance were manipulated. Clear biases were observed in the depth perceived in these stereograms, which were more likely to be seen as closer than fixation (i) for stimuli presented below fixation and (ii) as fixation distance increased. These results suggest that binocular correspondence is determined in a manner consistent with the distributions of disparities expected in natural scenes.     

Evidence for implication of primate area V1 in neural 3-D spatial localization processing.

We investigated the neural mechanisms underlying visual localization in 3-D space in area V1 of behaving monkeys. Three different sources of information, retinal disparity, viewing distance and gaze direction, that participate in these neural mechanisms are being reviewed. The way they interact with each other is studied by combining retinal and extraretinal signals. Interactions between retinal disparity and viewing distance have been shown in foveal V1; we have observed a strong modulation of the spontaneous activity and of the visual response of most V1 cells that was highly correlated with the vergence angle. As a consequence of these gain effects, neural horizontal disparity coding is favoured or refined for particular distances of fixation. Changing the gaze direction in the fronto-parallel plane also produces strong gains in the visual response of half of the cells in foveal V1. Cells tested for horizontal disparity and orientation selectivities show gain effects that occur coherently for the same spatial coordinates of the eyes. Shifts in preferred disparity also occurred in several neurons. Cells tested in calcarine V1 at retinal eccentricities larger than 10 degrees , show that horizontal disparity is encoded at least up to 20 degrees around both the horizontal and vertical meridians. At these large retinal eccentricities we found that vertical disparity is also encoded with tuning profiles similar to those of horizontal disparity coding. Combinations of horizontal and vertical disparity signals show that most cells encode both properties. In fact the expression of horizontal disparity coding depends on the vertical disparity signals that produce strong gain effects and frequent changes in peak selectivities. We conclude that the vertical disparity signal and the eye position signal serve to disambiguate the horizontal disparity signal to provide information on 3-D spatial coordinates in terms of distance, gaze direction and retinal eccentricity. We suggest that the relative weight among these different signals is the determining factor involved in the neural processing that gives information on 3-D spatial localization.     

Small or far away? Size and distance perception in the praying mantis

Stereo or ‘3D’ vision is an important but costly process seen in several evolutionarily distinct lineages including primates, birds and insects. Many selective advantages could have led to the evolution of stereo vision, including range finding, camouflage breaking and estimation of object size. In this paper, we investigate the possibility that stereo vision enables praying mantises to estimate the size of prey by using a combination of disparity cues and angular size cues. We used a recently developed insect 3D cinema paradigm to present mantises with virtual prey having differing disparity and angular size cues. We predicted that if they were able to use these cues to gauge the absolute size of objects, we should see evidence for size constancy where they would strike preferentially at prey of a particular physical size, across a range of simulated distances. We found that mantises struck most often when disparity cues implied a prey distance of 2.5 cm; increasing the implied distance caused a significant reduction in the number of strikes. We, however, found no evidence for size constancy. There was a significant interaction effect of the simulated distance and angular size on the number of strikes made by the mantis but this was not in the direction predicted by size constancy. This indicates that mantises do not use their stereo vision to estimate object size. We conclude that other selective advantages, not size constancy, have driven the evolution of stereo vision in the praying mantis.This article is part of the themed issue ‘Vision in our three-dimensional world’.     

Effect of pictorial depth cues, binocular disparity cues and motion parallax depth cues on lightness perception in three-dimensional virtual scenes

Background

Surface lightness perception is affected by scene interpretation. There is some experimental evidence that perceived lightness under bi-ocular viewing conditions is different from perceived lightness in actual scenes but there are also reports that viewing conditions have little or no effect on perceived color. We investigated how mixes of depth cues affect perception of lightness in three-dimensional rendered scenes containing strong gradients of illumination in depth.

Methodology/Principal Findings

Observers viewed a virtual room (4 m width×5 m height×17.5 m depth) with checkerboard walls and floor. In four conditions, the room was presented with or without binocular disparity (BD) depth cues and with or without motion parallax (MP) depth cues. In all conditions, observers were asked to adjust the luminance of a comparison surface to match the lightness of test surfaces placed at seven different depths (8.5–17.5 m) in the scene. We estimated lightness versus depth profiles in all four depth cue conditions. Even when observers had only pictorial depth cues (no MP, no BD), they partially but significantly discounted the illumination gradient in judging lightness. Adding either MP or BD led to significantly greater discounting and both cues together produced the greatest discounting. The effects of MP and BD were approximately additive. BD had greater influence at near distances than far.

Conclusions/Significance

These results suggest the surface lightness perception is modulated by three-dimensional perception/interpretation using pictorial, binocular-disparity, and motion-parallax cues additively. We propose a two-stage (2D and 3D) processing model for lightness perception.     

Probing depth in monocular images

It is generally expected that depth (distance) is the internal representational primitive that corresponds to much of the perception of 3D. We tested this assumption in monocular surface stimuli that are devoid of distance information (due to orthographic projection and the chosen surface shape, with perspective projection used as a control) and yet are vividly three-dimensional. Slant judgments were found to be in close correspondence with the actual geometric slant of the stimuli; the spatial orientation of the surfaces was perceived accurately. The apparent depth in these stimuli was then tested by superimposing a stereo depth probe over the monocular surface. In both the perspective and orthographic projection the gradient of perceived depth, measured by matching the apparent depth of the stereo probe with that of the monocular surface at a series of locations, was substantial. The experiments demonstrate that in orthographic projection the visual system can compute from local surface orientation a depth quantity that is commensurate with the relative depth derived from stereo disparity. The depth data suggests that, at least in the near field, the zero value for relative depth lies at the same absolute depth as the stereo horopter (locus of zero stereo disparity). Relative to this zero value, the depth-from-slant computation seems to provide an estimate of distance information that is independent of the absolute distance to the surface.Supproted by Office of Naval Research Contract N00014-K-84-0533. We gratefully acknowledge the suggestions of Jacob Beck regarding the experimental design, and the assistance provided by Cathryn Stanford     

Finding the relevant scale: clonality and genetic structure in a marine invertebrate (Crambe crambe, Porifera)

Important changes in genetic relatedness may occur at extremely small scales in benthic invertebrates, providing key information about structuring processes in populations of these organisms. We performed a small-scale study of the population structure of the sponge Crambe crambe, in which 177 individuals from the same rocky wall (interindividual distances from 0 to 7 m) were genotyped using six microsatellite markers. 101 sponges had unique genotypes and the remaining 76 individuals formed 24 groups of sponges sharing genotypes (clones). Mean intraclone distances were found to be c. 20 cm. Spatial autocorrelation analyses showed a drastic decrease in genetic relatedness over the first 100 cm of distance. If the contribution of clonality to this pattern was eliminated, the trend was attenuated, but remained a marked one and was still significant within the first distance classes (30-40 cm). Estimated mean dispersal distances per generation were c. 35 cm, and neighbourhood sizes were estimated at c. 33 sponges. Genetic similarities with sponges of the same locality, or from other Mediterranean localities, were within the same range as those found in sponges 2-7 m apart. It is concluded that asexual reproduction plays an important role in structuring populations in this species. However, over and above the effects of clonality, a strong fine-scale genetic structure was present at distances in the range of tens of centimetres, probably as a result of short dispersal of larvae. This fine-scale genetic structure may be common in invertebrates with lecitotrophic larvae.     

Shading Beats Binocular Disparity in Depth from Luminance Gradients: Evidence against a Maximum Likelihood Principle for Cue Combination

Perceived depth is conveyed by multiple cues, including binocular disparity and luminance shading. Depth perception from luminance shading information depends on the perceptual assumption for the incident light, which has been shown to default to a diffuse illumination assumption. We focus on the case of sinusoidally corrugated surfaces to ask how shading and disparity cues combine defined by the joint luminance gradients and intrinsic disparity modulation that would occur in viewing the physical corrugation of a uniform surface under diffuse illumination. Such surfaces were simulated with a sinusoidal luminance modulation (0.26 or 1.8 cy/deg, contrast 20%-80%) modulated either in-phase or in opposite phase with a sinusoidal disparity of the same corrugation frequency, with disparity amplitudes ranging from 0’-20’. The observers’ task was to adjust the binocular disparity of a comparison random-dot stereogram surface to match the perceived depth of the joint luminance/disparity-modulated corrugation target. Regardless of target spatial frequency, the perceived target depth increased with the luminance contrast and depended on luminance phase but was largely unaffected by the luminance disparity modulation. These results validate the idea that human observers can use the diffuse illumination assumption to perceive depth from luminance gradients alone without making an assumption of light direction. For depth judgments with combined cues, the observers gave much greater weighting to the luminance shading than to the disparity modulation of the targets. The results were not well-fit by a Bayesian cue-combination model weighted in proportion to the variance of the measurements for each cue in isolation. Instead, they suggest that the visual system uses disjunctive mechanisms to process these two types of information rather than combining them according to their likelihood ratios.     

Depth generalization from stereo to motion parallax in the owl

Although many sources of three-dimensional information have been isolated and demonstrated to contribute independently, to depth vision in animal studies, it is not clear whether these distinct cues are perceived to be perceptually equivalent. Such ability is observed in humans and would seem to be advantageous for animals as well in coping with the often co-varying (or ambiguous) information about the layout of physical space. We introduce the expression primary-depth-cue equivalence to refer to the ability to perceive mutually consistent information about differences in depth from either stereopsis or motion-parallax. We found that owls trained to detect relative depth as a perceptual category (objects versus holes) when specified by binocular disparity alone (stereopsis), immediately transferred this discrimination to novel stimuli where the equivalent depth categories were available only through differences in motion information produced by head movements (observer-produced motion-parallax). Motion-parallax discrimination did occur under monocular viewing conditions and reliable performance depended heavily on the amplitude of side-to-side head movements. The presence of primary-depth-cue equivalence in the visual system of the owl provides further conformation of the hypothesis that neural systems evolved to detect differences in either disparity or motion information are likely to share similar processing mechanisms.     

Stereoscopic and contrast-defined motion in human vision.

There is considerable evidence for the existence of a specialized mechanism in human vision for detecting moving contrast modulations and some evidence for a mechanism for detecting moving stereoscopic depth modulations. It is unclear whether a single second-order motion mechanism detects both types of stimulus or whether they are detected separately. We show that sensitivity to stereo-defined motion resembles that to contrast-defined motion in two important ways. First, when a missing-fundamental disparity waveform is moved in steps of 0.25 cycles, its perceived direction tends to reverse. This is a property of both luminance-defined and contrast-defined motion and is consistent with independent detection of motion at different spatial scales. Second, thresholds for detecting the direction of a smoothly drifting sinusoidal disparity modulation are much higher than those for detecting its orientation. This is a property of contrast-modulated gratings but not luminance-modulated gratings, for which the two thresholds are normally identical. The results suggest that stereo-defined and contrast-defined motion stimuli are detected either by a common mechanism or by separate mechanisms sharing a common principle of operation.     

Distance discrimination during active electrolocation in the weakly electric fish Gnathonemus petersii.

Weakly electric fish use active electrolocation for orientation at night. They emit electric signals (electric organ discharges) which generate an electrical field around their body. By sensing field distortions, fish can detect objects and analyze their properties. It is unclear, however, how accurately they can determine the distance of unknown objects. Four Gnathonemus petersii were trained in two-alternative forced-choice procedures to discriminate between two objects differing in their distances to a gate. The fish learned to pass through the gate behind which the corresponding object was farther away. Distance discrimination thresholds for different types of objects were determined. Locomotor and electromotor activity during distance measurement were monitored. Our results revealed that all individuals quickly learned to measure object distance irrespective of size, shape or electrical conductivity of the object material. However, the distances of hollow, water-filled cubes and spheres were consistently misjudged in comparison with solid or more angular objects, being perceived as farther away than they really were. As training continued, fish learned to compensate for these 'electrosensory illusions' and erroneous choices disappeared with time. Distance discrimination thresholds depended on object size and overall object distance. During distance measurement, the fish produced a fast regular rhythm of EOD discharges. A mechanisms for distance determination during active electrolocation is proposed.     

Distance discrimination during active electrolocation in the weakly electric fish Gnathonemus petersii

Weakly electric fish use active electrolocation for orientation at night. They emit electric signals (electric organ discharges) which generate an electrical field around their body. By sensing field distortions, fish can detect objects and analyze their properties. It is unclear, however, how accurately they can determine the distance of unknown objects. Four Gnathonemus petersii were trained in two-alternative forced-choice procedures to discriminate between two objects differing in their distances to a gate. The fish learned to pass through the gate behind which the corresponding object was farther away. Distance discrimination thresholds for different types of objects were determined. Locomotor and electromotor activity during distance measurement were monitored. Our results revealed that all individuals quickly learned to measure object distance irrespective of size, shape or electrical conductivity of the object material. However, the distances of hollow, water-filled cubes and spheres were consistently misjudged in comparison with solid or more angular objects, being perceived as farther away than they really were. As training continued, fish learned to compensate for these 'electrosensory illusions' and erroneous choices disappeared with time. Distance discrimination thresholds depended on object size and overall object distance. During distance measurement, the fish produced a fast regular rhythm of EOD discharges. A mechanisms for distance determination during active electrolocation is proposed.     

Dyslexic children are confronted with unstable binocular fixation while reading

Reading requires three-dimensional motor control: saccades bring the eyes from left to right, fixating word after word; and oblique saccades bring the eyes to the next line of the text. The angle of vergence of the two optic axes should be adjusted to the depth of the book or screen and--most importantly--should be maintained in a sustained manner during saccades and fixations. Maintenance of vergence is important as it is a prerequisite for a single clear image of each word to be projected onto the fovea of the eyes. Deficits in the binocular control of saccades and of vergence in dyslexics have been reported previously but only for tasks using single targets. This study examines saccades and vergence control during real text reading. Thirteen dyslexic and seven non-dyslexic children read the French text "L'Allouette" in two viewing distances (40 cm vs. 100 cm), while binocular eye movements were measured with the Chronos Eye-tracking system. We found that the binocular yoking of reading saccades was poor in dyslexic children (relative to non-dyslexics) resulting in vergence errors; their disconjugate drift during fixations was not correlated with the disconjugacy during their saccades, causing considerable variability of vergence angle from fixation to fixation. Due to such poor oculomotor adjustments during reading, the overall fixation disparity was larger for dyslexic children, putting larger demand on their sensory fusion processes. Moreover, for dyslexics the standard deviation of fixation disparity was larger particularly when reading at near distance. We conclude that besides documented phoneme processing disorders, visual/ocular motor imperfections may exist in dyslexics that lead to fixation instability and thus, to instability of the letters or words during reading; such instability may perturb fusional processes and might--in part--complicate letter/word identification.     

Interocular orientation disparity and the stereoscopic perception of slanted surfaces

The orientation threshold for two-dimensional filtered noise stimuli was estimated using forced-choice procedures with both dioptic and dichoptic viewing. In the dioptic case the two patterns were co-rotated. In the dichoptic case the stimuli were counter-rotated to produce an orientation disparity, which yields a percept of slant about the horizontal axis orthogonal to the cyclopean line of sight. Dioptic thresholds increased with the orientation bandwidth of the stimuli. In contrast, dichoptic thresholds were essentially constant across a wide range of conditions. In all cases, dichoptic orientation acuity was much finer than conventional estimates. In a second experiment, the dichoptic threshold was estimated for patterns superimposed on a depth pedestal. Acuity was affected significantly by the presence of the pedestal, and was an inverse function of pedestal amplitude. The results suggest that stereoscopic slant caused by dichoptic counter-rotation arises because of neural processing of the overall pattern of disparities of position produced by counter-rotation, rather than specialised encoding of orientation disparity.