Temporal aspects of binocular slant perception

Crowding in depth for binocular and monocular observation

Crowding refers to the phenomenon of reduced recognition performance for peripherally presented targets that are flanked by similar stimuli. Crowding is known to vary with lateral distances (i.e., effects of target eccentricity and inter-character spacing). In the present experiment, we examined how crowding is affected by the distance of the stimuli in depth for natural viewing, i.e., for binocular observation of a real depth presentation. Superimposing the displays of two orthogonally arranged screens with a half-transparent mirror created real-depth presentation. We measured recognition performance of flanked compared to isolated targets that were presented at fixation depth, or in depths deviating from fixation depth (defocused). For both defocused directions (i.e., in front of and behind fixation depth), a near as well as a far distance from fixation was applied. Participants' task was to fixate a central cross at a constant distance (190 cm), and to indicate the gap position of an isolated or flanked Landolt ring that was presented at an eccentricity of 2°, on, in front of, or behind fixation depth. Results for natural binocular observation revealed increased crowding effects when stimuli were far compared to near from the fixation plane in depth. This resembles the common effect of eccentricity. Under monocular viewing, that is, without disparity information, crowding did not increase with increased depth distance. Thus, the result seemed to be an effect of binocular observation in real depth. This suggests that crowding in natural viewing might serve as a mechanism to stabilize and orient attention efficiently in three-dimensional space.

Vertical size disparity induces enhanced neural responses in good stereo observers

Stereoscopic three-dimensional vision requires cortical processing for horizontal binocular disparity between the two eyes' retinal images. Behavioral and theoretical studies suggest that vertical size disparity is used to recover the viewing geometry and to generate the slant of a large surface. However, unlike horizontal disparity, the relation between stereopsis and neural responses to vertical disparity remains controversial. To determine the role of cortical processing for vertical size disparity in stereopsis, we measured neuromagnetic responses to disparities in people with good and poor stereopsis, using magnetoencephalography (MEG). Healthy adult participants viewed stereograms with a horizontal or vertical size disparity, and judged the perceived slant of the pattern. We assessed neural activity in response to disparities in the visual cortex and the phase locking of oscillatory responses including the alpha frequency range using MEG. For participants with good stereopsis, activity in the visual areas was significantly higher in response to vertical size disparity than to horizontal size disparity. The time-frequency analysis revealed that early neural responses to vertical size disparity were more phase-locked in good stereo participants than in poor stereo participants. These results provide neuromagnetic evidence that vertical-size disparity processing plays a role in good stereo vision.

Orientation-specific learning of the prior assumption for 3D slant perception

We usually interpret a trapezoidal image on our retina as a slanted rectangle rather than a frontoparallel trapezoid, because we use a statistical assumption (i.e. rectangles are more common than trapezoids), called a 'prior', for recovering the 3D world from ambiguous 2D images. Here we report that the shape prior for recovering 3D slant can be updated differently depending on the slant axis orientation (horizontal vs. vertical). The participants were exposed to a variety of trapezoidal images surrounded by a stereoscopic reference plane. The perspective transformation of the images was interpreted as 2D shape, rather than 3D slant because the surrounding plane enhanced disparity. We found that, after continuous exposure to such images, the participants relied less on the shape information for recovering 3D slant, suggesting the update of priors via experience (i.e., rectangles are less common than trapezoids). Importantly, the learning effect was context (slant-axis) specific although partially transferred across contexts; the training with horizontal-axis slant reduced the reliance on perspective even in vertical-axis slant estimation but not vice versa. The results suggest that context-specific training is vital to update the prior for the horizontal-axis slant, whereas it is not required to update the prior for a vertical-axis slant.

Searching for invariance: Geographical and optical slant

When we move through rigid environments, surface orientations of static objects do not appear to change. Most studies have investigated the perception of optical slant which is dependent on the perspective of the observer. We investigated the perception of geographical slant, which is invariant across different viewing perspectives, and compared it to optical slant. In Experiment 1, participants viewed a 3D triangular target surface with triangular phosphorescent texture elements presented at eye level at one of 5 slants from 0° to 90°, at 0° or 40° tilt. Participants turned around to adjust a 2D line or a 3D surface to match the slant of the target surface. In Experiment 2, the difference between optical and geographical slant was increased by changing the height of the surface to be judged. In Experiment 3, target surfaces were rotated by 50° (±25°) and viewed in both a dark and lighted room. In Experiment 1, the overall pattern of judgments exhibited only slight differences between response measures. In Experiment 2, slant judgments were slightly overestimated when the surface was at a low height and at 0° tilt. We compared optical slants of the surfaces to geographical slants. While sometimes inaccurate, participants' slant judgments remained invariant across changes in viewing perspective. In Experiment 3, judgments were the same in the dark and lighted conditions. There was no effect of target motion on judgments, although variability decreased. We conclude that participants' judgments were predicted by geographical slant, not optical slant.

Stereoscopic Slant Contrast and the Perception of Inducer Slant at Brief Stimulus Presentations

Slant contrast refers to a stereoscopic phenomenon in which the perceived slant of a test object is affected by the disparity of a surrounding inducer object. Slant contrast has been proposed to involve cue conflict, but it is unclear whether this idea is useful in explaining slant contrast at short stimulus presentations (<1 s). We measured both slant contrast and perceived inducer slant while varying the presentation duration (100-800 ms) of stereograms with several spatial configurations. In three psychophysical experiments, we found that (a) both slant contrast and perceived inducer slant increased as a function of stimulus duration, and (b) slant contrast was relatively stable across different test and inducer shapes at each short stimulus duration, whereas perceived inducer slant increased when cue conflict was reduced. These results suggest that at brief, not long stimulus presentations, the cue conflict between disparity and perspective plays a smaller role in slant contrast than other depth cues.

Binocular Depth Judgments on Smoothly Curved Surfaces

Binocular disparity is an important cue to depth, allowing us to make very fine discriminations of the relative depth of objects. In complex scenes, this sensitivity depends on the particular shape and layout of the objects viewed. For example, judgments of the relative depths of points on a smoothly curved surface are less accurate than those for points in empty space. It has been argued that this occurs because depth relationships are represented accurately only within a local spatial area. A consequence of this is that, when judging the relative depths of points separated by depth maxima and minima, information must be integrated across separate local representations. This integration, by adding more stages of processing, might be expected to reduce the accuracy of depth judgements. We tested this idea directly by measuring how accurately human participants could report the relative depths of two dots, presented with different binocular disparities. In the first, Two Dot condition the two dots were presented in front of a square grid. In the second, Three Dot condition, an additional dot was presented midway between the target dots, at a range of depths, both nearer and further than the target dots. In the final, Surface condition, the target dots were placed on a smooth surface defined by binocular disparity cues. In some trials, this contained a depth maximum or minimum between the target dots. In the Three Dot condition, performance was impaired when the central dot was presented with a large disparity, in line with predictions. In the Surface condition, performance was worst when the midpoint of the surface was at a similar distance to the targets, and relatively unaffected when there was a large depth maximum or minimum present. These results are not consistent with the idea that depth order is represented only within a local spatial area.

Monocular and binocular edges enhance the perception of stereoscopic slant

Gradients of absolute binocular disparity across a slanted surface are often considered the basis for stereoscopic slant perception. However, perceived stereo slant around a vertical axis is usually slow and significantly under-estimated for isolated surfaces. Perceived slant is enhanced when surrounding surfaces provide a relative disparity gradient or depth step at the edges of the slanted surface, and also in the presence of monocular occlusion regions (sidebands). Here we investigate how different kinds of depth information at surface edges enhance stereo slant about a vertical axis. In Experiment 1, perceived slant decreased with increasing surface width, suggesting that the relative disparity between the left and right edges was used to judge slant. Adding monocular sidebands increased perceived slant for all surface widths. In Experiment 2, observers matched the slant of surfaces that were isolated or had a context of either monocular or binocular sidebands in the frontal plane. Both types of sidebands significantly increased perceived slant, but the effect was greater with binocular sidebands. These results were replicated in a second paradigm in which observers matched the depth of two probe dots positioned in front of slanted surfaces (Experiment 3). A large bias occurred for the surface without sidebands, yet this bias was reduced when monocular sidebands were present, and was nearly eliminated with binocular sidebands. Our results provide evidence for the importance of edges in stereo slant perception, and show that depth from monocular occlusion geometry and binocular disparity may interact to resolve complex 3D scenes.

The effects of vertical gradient of disparity and combination mode of features on the occurrence of double fusion in Panum's limiting case

Panum's limiting case generally refers to the phenomenon that two features presented to one eye and a single feature presented to the other are combined and then perceived as two features at different depths. It is still not clear why experimental results derived from the Panum-type configuration (all lines parallel) support a double fusion viewpoint, but they do not for the Wheatstone-type configuration (one line not parallel to the others). Some experimental results support the double fusion theory, while others do not, even under a small disparity. Here we report that, under a small disparity, when the vertical gradients of the horizontal disparity ofdichoptic feature pairs in previous Wheatstone-type configurations were increased or decreased, the evidence which was considered to be very convincing in previous studies, either supporting or against the double fusion viewpoint, was challenged, and even turned to support the opposite view. Moreover, it was discovered that changes in the way features were arranged altered the results. Together, these results indicate that double fusion is the common basis for all kinds of Panum-type configurations. But for the Wheatstone-type configurations double fusion is also constrained by the vertical gradient of disparity of the configurations in addition to disparity and influenced by the degree of similarity/conflict between binocular cues and monocular cues resulting from different arrangements of features.

Alternation frequency thresholds for stereopsis as a technique for exploring stereoscopic difficulties

When stereoscopic images are presented alternately to the two eyes, stereopsis occurs at F ≥ 1 Hz full-cycle frequencies for very simple stimuli, and F ≥ 3 Hz full-cycle frequencies for random-dot stereograms (eg Ludwig I, Pieper W, Lachnit H, 2007 “Temporal integration of monocular images separated in time: stereopsis, stereoacuity, and binocular luster” Perception & Psychophysics69 92–102). Using twenty different stereograms presented through liquid crystal shutters, we studied the transition to stereopsis with fifteen subjects. The onset of stereopsis was observed during a stepwise increase of the alternation frequency, and its disappearance was observed during a stepwise decrease in frequency. The lowest F values (around 2.5 Hz) were observed with stimuli involving two to four simple disjoint elements (circles, arcs, rectangles). Higher F values were needed for stimuli containing slanted elements or curved surfaces (about 1 Hz increment), overlapping elements at two different depths (about 2.5 Hz increment), or camouflaged overlapping surfaces (> 7 Hz increment). A textured cylindrical surface with a horizontal axis appeared easier to interpret (5.7 Hz) than a pair of slanted segments separated in depth but forming a cross in projection (8 Hz). Training effects were minimal, and F usually increased as disparities were reduced. The hierarchy of difficulties revealed in the study may shed light on various problems that the brain needs to solve during stereoscopic interpretation. During the construction of the three-dimensional percept, the loss of information due to natural decay of the stimuli traces must be compensated by refreshes of visual input. In the discussion an attempt is made to link our results with recent advances in the comprehension of visual scene memory.

Paradoxical fusion of two images and depth perception with a squinting eye

Some strabismic patients with inconstant squint can fuse two images in a single eye, and experience lustre and depth. One of these images is foveal and the other extrafoveal. Depth perception was tested on 30 such subjects. Relief was perceived mostly on the fixated image. Camouflaged continuous surfaces (hemispheres, cylinders) were perceived as bumps or hollows, without detail. Camouflaged rectangles could not be separated in depth from the background, while their explicit counterparts could. Slanted bars were mostly interpreted as frontoparallel near or remote bars. Depth responses were more frequent with stimuli involving inward rather than outward disparities, and were then heavily biased towards "near" judgements. All monocular fusion effects were markedly reduced after the recovery of normal stereoscopic vision following an orthoptic treatment. The depth effects reported here may provide clues on what stereoscopic pathways may or may not accomplish with incomplete retinal and misleading vergence information.

Binocular spatial induction for the perception of depth does not cross the midline

Although horizontal binocular retinal disparity between images in the two eyes resulting from their different views of the world has long been the centerpiece for understanding the unique characteristics of stereovision, it does not suffice to explain many binocular phenomena. Binocular depth contrast (BDC), the induction of an appearance of visual pitch in a centrally located line by pitched-from-vertical flanking lines, has particularly been the subject of a good deal of attention in this regard. In the present article, we show that BDC does not cross the median plane but is restricted to the side of the visual field containing a unilateral inducer. These results cannot be explained by the use of retinal disparity alone or in combination with any additional factors or processes previously suggested to account for stereovision. We present a two-channel three-stage neuromathematical model that accounts quantitatively for present and previous BDC results and also accounts for a large number of the most prominent features of binocular pitch perception: Stage 1 of the differencing channel obtains the difference between the retinal orientations of the images in the two eyes separately for the inducer and the test line; stage 1 of the summing channel obtains the corresponding sums. Signals from inducer and test stimuli are combined linearly in each channel in stage 2, and in stage 3 the outputs from the two channels are combined along with a bias signal from the body-referenced mechanism to yield ', the model's prediction for the perception of pitch.

Hinge versus twist: the effects of 'reference surfaces' and discontinuities on stereoscopic slant perception

Stereoscopic slant perception around a vertical axis (horizontal slant) is often found to be strongly attenuated relative to geometric prediction. Stereo slant is much greater, however, when an adjacent surface, stereoscopically in the frontal plane, is added. This slant enhancement is often attributed to the presence of a 'reference surface' or to a spatial change in the disparity gradient (introducing second and higher derivatives of disparity). Gillam, Chambers, and Russo (1988 Journal of Experimental Psychology: Human Perception and Performance 14 163-175) questioned the role of these factors in that placement of the frontal-plane surface in a direction collinear with the slant axis (twist configuration) sharply reduced latency for perceiving slant whereas placing the same surface in a direction orthogonal to the slant axis (hinge configuration) had little effect. We here confirm these findings for slant magnitude, showing a striking advantage for twist over hinge configurations. We also examined contrast slant measured on the frontal-plane surface in the hinge and twist configurations. Under conditions where test and inducer surfaces have centres at the same depth for twist and hinge, we found that twist configurations produced strong negative slant contrast, while hinge configurations produced significant positive contrast or slant assimilation. We conclude that stereo slant and contrast effects for neighbouring surfaces can only be understood from the patterns and gradients of step disparities present. It is not adequate to consider the second surface merely as a reference slant for the first or as having its effect via a spatial change in the disparity gradient.

Vertical-size disparities are temporally integrated for slant perception

We investigated temporal properties of vertical-size and horizontal-size disparity processing for slant perception. Subjects indicated perceived slants for a stereoscopic stimulus in which the two magnitudes of vertical-size or horizontal-size disparities were oscillated stepwise with various frequencies (from 0.2 to 10 Hz). For the stimulus with vertical-size disparity oscillation, two slants corresponding to the two magnitudes of disparity were perceived for low-frequency conditions, whereas only a static mean slant of the two slants was perceived for high frequencies (5 and 10 Hz). For the stimulus with horizontal-size disparity oscillation, two slants were perceived for all the temporal frequency conditions. These results indicate that temporal properties of vertical- and horizontal-size disparity processing are clearly different and vertical-size disparities are temporally integrated over a period of around 500 ms for slant perception.

Slant perception, and its voluntary control, do not govern the slant aftereffect: multiple slant signals adapt independently

Although it is known that high-level spatial attention affects adaptation for a variety of stimulus features (including binocular disparity), the influence of voluntary attentional control-and the associated awareness-on adaptation has remained unexplored. We developed an ambiguous surface slant adaptation stimulus with conflicting monocular and binocular slant signals that instigated two mutually exclusive surface percepts with opposite slants. Using intermittent stimulus removal, subjects were able to voluntarily select one of the two rivaling slant percepts for extended adaptation periods, enabling us to dissociate slant adaptation due to awareness from stimulus-induced slant adaptation. We found that slant aftereffects (SAE) for monocular and binocular test patterns had opposite signs when measured simultaneously. There was no significant influence of voluntarily controlled perceptual state during adaptation on SAEs of monocular or binocular signals. In addition, the magnitude of the binocular SAE did not correlate with the magnitude of perceived slant. Using adaptation to one slant cue, and testing with the other cue, we demonstrated that multiple slant signals adapt independently. We conclude that slant adaptation occurs before the level of slant awareness. Our findings place the site of stereoscopic slant adaptation after disparity and eye posture are interpreted for slant [as demonstrated by Berends et al. (Berends, E. M., Liu, B., & Schor, C. M. (2005). Stereo-slant adaptation is high level and does not involve disparity coding. Journal of Vision 5 (1), 71-80), using that disparity scales with distance], but before other slant signals are integrated for the resulting awareness of the presented slant stimulus.

The role of (micro)saccades and blinks in perceptual bi-stability from slant rivalry

We exposed the visual system to an ambiguous 3D slant rivalry stimulus consisting of a grid for which monocular (perspective) and binocular (disparity) cues independently specified a slant about a horizontal axis. When those cues specified similar slants, observers perceived a single slant. When the difference between the specified slants was large, observers alternatively perceived a perspective- or a disparity-dominated slant. Eye movement measurements revealed that there was no positive correlation between a perceptual flip and both saccades (microsaccades as well as larger saccades) and blinks that occurred prior to a perceptual flip. We also found that changes in horizontal vergence were not responsible for perceptual flips. Thus, eye movements were not essential to flip from one percept to the other. After the moment of a perceptual flip the occurrence probabilities of both saccades and blinks were reduced. The reduced probability of saccades mainly occurred for larger voluntary saccades, rather than for involuntary microsaccades. We suggest that the reduced probability of voluntary saccades reflects a reset of saccade planning.

The effect of surface placement and surface overlap on stereo slant contrast and enhancement

Stereoscopic slant contrast is an apparent slant induced in a stereoscopically frontal plane surface (the test) opposite in direction to the specified stereoscopic slant of a neighbouring surface (the inducer). Test surfaces offset from the inducer in a direction collinear with the axis of slant (twist) show more contrast than those offset in a direction orthogonal to the axis of slant (hinge). We attribute this anisotropy to the presence and extent of a gradient of relative disparity in twist configurations and the absence of such a gradient in hinge configurations. This hypothesis was tested by measuring the perceived slant of the test and inducer surfaces for horizontal and vertical axes of inducer slant and collinear and orthogonal surface offsets. For vertical axis slant, the hypothesis was supported; contrast variations with position of the test surface could be explained by variations in relative slant. For horizontal axis slant, variations in contrast could be accounted for by normalisation of the slanted surface, with relative slant remaining constant. Two further experiments showed that the extent of the gradient of relative disparity rather than the area of texture overlap of the two surfaces best predicted the contrast results and that perceived relative slant did not vary with the absolute slants of the two surfaces. The arrangement of stereo surfaces is critical in predicting their relative slant.

Voluntary control and the dynamics of perceptual bi-stability

Voluntary control and conscious perception seem to be related: when we are confronted with ambiguous images we are in some cases and to some extent able to voluntarily select a percept. However, to date voluntary control has not been used in neurophysiological studies on the correlates of conscious perception, presumably because the dynamic of perceptual reversals was not suitable. We exposed the visual system to four ambiguous stimuli that instigate bi-stable perception: slant rivalry, orthogonal grating rivalry, house-face rivalry, and Necker cube rivalry. In the preceding companion paper [van Ee, R. (2005). Dynamics of perceptual bi-stability for stereoscopic slant rivalry and a comparison with grating, house-face, and Necker cube rivalry. Vision Research] we focussed on the temporal dynamics of the perceptual reversals. Here we examined the role of voluntary control in the dynamics of perceptual reversals. We asked subjects to attempt to hold percepts and to speed-up the perceptual reversals. The investigations across the four stimuli revealed qualitative similarities concerning the influence of voluntary control on the temporal dynamics of perceptual reversals. We also found differences. In comparison to the other rivalry stimuli, slant rivalry exhibits: (1) relatively long percept durations; (2) a relatively clear role of voluntary control in modifying the percept durations. We advocate that these aspects, alongside with its metrical (quantitative) aspects, potentially make slant rivalry an interesting tool in studying the neural underpinnings of visual awareness.

Dynamics of perceptual bi-stability for stereoscopic slant rivalry and a comparison with grating, house-face, and Necker cube rivalry

A way to study conscious perception is to expose the visual system to an ambiguous stimulus that instigates bi-stable perception. This provides the opportunity to study neural underpinnings related to the percepts rather than to the stimulus. We have recently developed a slant-rivalry paradigm that has beneficial metrical (quantitative) aspects and that exhibits temporal aspects of perceptual reversals that seemed to be under considerable voluntary control of the observer. Here we examined a range of different aspects of the temporal dynamics of the perceptual reversals of slant rivalry and we compared these with the dynamics of orthogonal grating rivalry, house-face rivalry, and Necker cube rivalry. We found that slant rivalry exhibits a qualitatively similar pattern of dynamics. The drift of the perceptual reversal rate, both across successive experimental repetitions, and across successive 35-s portions of data were similar. The sequential dependence of the durations of perceptual phases, too, revealed very similar patterns. The main quantitative difference, which could make slant rivalry a useful stimulus for future neurophysiological studies, is that the percept durations are relatively long compared to the other rivalry stimuli. In the paper that accompanies this paper [van Ee, R., van Dam, L. C. J., Brouwer, G. J. (2005). Voluntary control and the dynamics of perceptual bi-stability. Vision Research,] we focused on the role of voluntary control in the dynamics of perceptual reversals.

Starry night: a texture devoid of depth cues

From a modern Bayesian point of view, the classic Julesz random-dot stereogram is a cue-conflict stimulus: Texture cues specify an unbroken, unslanted surface, in conflict with any variation in depth specified by binocular disparity. We introduce a new visual texture-the starry night texture (SNT)--that is incapable of conveying slant, depth edges, or texture boundaries, in a single view. For SNT, changing density is equivalent to changing intensity, so an instance of the texture is characterized (up to the random locations of the texture elements) by what we call its densintensity. We consider deviations from the ideal that are needed to realize the texture in practice. In three experiments with computer-generated stimuli we examined human perception of SNT to show that (1) the deviations from the ideal that were needed to realize SNT do not affect the invariance of its appearance across changes in distance of several orders of magnitude; (2) as predicted, observers match SNT across changes in distance better than other textures; and (3) the use of SNT in a slant perception experiment did not reliably increase observers' reliance on stereoscopic slant cues, as compared with the sparse random-dot displays that have been commonly employed to study human perception of shape from binocular disparity and motion.

Measurements of the effect of surface slant on perceived lightness

When a planar object is rotated with respect to a directional light source, the reflected luminance changes. If surface lightness is to be a reliable guide to surface identity, observers must compensate for such changes. To the extent they do, observers are said to be lightness constant. We report data from a lightness matching task that assesses lightness constancy with respect to changes in object slant. On each trial, observers viewed an achromatic standard object and indicated the best match from a palette of 36 grayscale samples. The standard object and the palette were visible simultaneously within an experimental chamber. The chamber illumination was provided from above by a theater stage lamp. The standard objects were uniformly-painted flat cards. Different groups of naive observers made matches under two sets of instructions. In the Neutral Instructions, observers were asked to match the appearance of the standard and palette sample. In the Paint Instructions, observers were asked to choose the palette sample that was painted the same as the standard. Several broad conclusions may be drawn from the results. First, data for most observers were neither luminance matches nor lightness constant matches. Second, there were large and reliable individual differences. To characterize these, a constancy index was obtained for each observer by comparing how well the data were accounted for by both luminance matching and lightness constancy. The index could take on values between 0 (luminance matching) and 1 (lightness constancy). Individual observer indices ranged between 0.17 and 0.63 with mean 0.40 and median 0.40. An auxiliary slant-matching experiment rules out variation in perceived slant as the source of the individual variability. Third, the effect of instructions was small compared to the inter-observer variability. Implications of the data for models of lightness perception are discussed.

Bayesian modeling of cue interaction: bistability in stereoscopic slant perception

Our two eyes receive different views of a visual scene, and the resulting binocular disparities enable us to reconstruct its three-dimensional layout. However, the visual environment is also rich in monocular depth cues. We examined the resulting percept when observers view a scene in which there are large conflicts between the surface slant signaled by binocular disparities and the slant signaled by monocular perspective. For a range of disparity-perspective cue conflicts, many observers experience bistability: They are able to perceive two distinct slants and to flip between the two percepts in a controlled way. We present a Bayesian model that describes the quantitative aspects of perceived slant on the basis of the likelihoods of both perspective and disparity slant information combined with prior assumptions about the shape and orientation of objects in the scene. Our Bayesian approach can be regarded as an overarching framework that allows researchers to study all cue integration aspects-including perceptual decisions--in a unified manner.

Correlation between stereoanomaly and perceived depth when disparity and motion interact in binocular matching

The aim of this study was to find out to what extent binocular matching is facilitated by motion when stereoanomalous and normal subjects estimate the perceived depth of a 3-D stimulus containing excessive matching candidates. Thirty subjects viewed stimuli that consisted of bars uniformly distributed inside a volume. They judged the perceived depth-to-width ratio of the volume by adjusting the aspect ratio of an outline rectangle (a metrical 3-D task). Although there were large inter-subject differences in the depth perceived, the experimental results yielded a good correlation with stereoanomaly (the inability to distinguish disparities of different magnitudes and/or signs in part of the disparity spectrum). The results cannot be explained solely by depth-cue combination. Since up to 30% of the population is stereoanomalous, stereoscopic experiments would yield more informative results if subjects were first characterized with regard to their stereo capacities. Intriguingly, it was found that motion does not help to define disparities in subjects who are able to perceive depth-from-disparity in half of the disparity spectrum. These stereoanomalous subjects were found to rely completely on the motion signals. This suggests that the perception of volumetric depth in subjects with normal stereoscopic vision requires the joint processing of crossed and uncrossed disparities.

The influence of cyclovergence on unconstrained stereoscopic matching

In order to perceive depth from binocular disparities the visual system has to identify matching features of the two retinal images. Normally, the assigned disparity is unambiguously determined by monocularly visible matching constraints. The assigned disparity is ambiguous when matching is unconstrained, such as when we view an isolated long oblique disparate line. Recently we found that in order to perceive a depth probe at the same depth as the oblique line, the probe needs to have the same horizontal disparity as the line (i.e. matching occurs along horizontal "search-zones" [Vis. Res. 40 (2000) 151]). Here we examined whether the depth probe disparity in unconstrained matching of long lines is influenced by cyclovergence, by cyclorotation between stereogram half-images, or by combinations of the two. We measured retinal rotation (>6 deg in cyclovergence conditions). We found that in those conditions in which the retinal images were the same (a condition with, say, both zero cyclovergence and zero cyclorotation between the half-images, creates the same retinal images as a condition with both 6 deg cyclovergence and 6 deg cyclorotation) assigned depth was the same too, i.e. independent of cyclovergence. Thus, the assigned depth of the test-line seems to be determined solely by the retinal test-line orientation, implying that the binocular matching algorithm does not seem to incorporate the eyes' cyclovergence when matching is unconstrained.

A planar and a volumetric test for stereoanomaly

Stereoanomaly is the failure to see differences in depth when the viewer is presented with stimuli having different magnitudes of stereoscopic disparity. In the absence of eye movements, everyone suffers from stereoanomaly for extremely large disparities. Typically, such disparities are seen at the same depth as monocular stimuli. However, about 30%, of the population exhibit some form of stereoanomaly even for very small disparities, provided eye movements are avoided. In some cases, the sign of the disparity will be confused, and the perceived depth will be incorrectly seen as 'behind' rather than 'in front of' the fixation point, for example. Because anomalies provide useful information about perceptual mechanisms, tests that measure and quantify the extent of a blindness are important investigative tools for research. Here we offer two easy-to-administer tests for stereoanomaly. The first test is based on depth judgments of two bars relative to a fixation point. The second test involves judgments of volumetric stimuli, seen stereoscopically. In each case, subjects indicate depth by setting a rectangle (with fixed base) to match the perceived depth. Although both tests are correlated, some differences in stereo processing are seen, depending upon whether or not the stimuli are presented near the point of fixation.

Perceptual latencies to discriminate surface orientation in stereopsis

The difference in sensitivity to stereoscopic surfaces oriented horizontally or vertically (the stereoscopic orientation anisotropy) can be redescribed as a difference in sensitivity to shear or compression transformations that relate the binocular images. The present experiment was designed to test this by dissociating the image transformation from the orientation of the surface. Surfaces were presented in isolation or in the presence of a surrounding frame that formed step and gradient discontinuities in the disparity field. Without discontinuities, observers required considerably more time to discriminate between surfaces differing in compression than between those differing in shear, irrespective of surface orientation. Disparity discontinuities facilitated the perception of the disparity gradients; minimum stimulus durations were reduced by over an order of magnitude when the reference frame was present. These results support the hypothesis that the disparity field is decomposed into different primitives during the recovery of depth and surface structure.

Perceptual learning without feedback and the stability of stereoscopic slant estimation

Subjects were examined for practice effects in a stereoscopic slant-estimation task involving surfaces that comprised a large portion of the visual field. In most subjects slant estimation was significantly affected by practice, but only when an isolated surface (an absolute disparity gradient) was present in the visual field. When a second, unslanted, surface was visible (providing a second disparity gradient and thereby also a relative disparity gradient) none of the subjects exhibited practice effects. Apparently, stereoscopic slant estimation is more robust or stable over time in the presence of a second surface than in its absence. In order to relate the practice effects, which occurred without feedback, to perceptual learning, results are interpreted within a cue-interaction framework. In this paradigm the contribution of a cue depends on its reliability. It is suggested that normally absolute disparity gradients contribute relatively little to perceived slant and that subjects learn to increase this contribution by utilizing proprioceptive information. It is argued that--given the limited computational power of the brain--a relatively small contribution of absolute disparity gradients in perceived slant enhances the stability of stereoscopic slant perception.

Adaptation to disparity but not to perceived depth

The purpose of the present study was to investigate whether adaptation can occur to disparity per se. The adapting stimuli were large random-dot patterns of which the two half-images were transformed such that the depth effects induced by the vertical transformations were nulled by horizontal transformations. Thus, the adapting stimuli were perceptually the same, whereas the disparity fields differed from each other. The adapting stimuli were presented for five minutes. During that period, the percept of a fronto-parallel surface did not change. After the adapting period, subjects perceived a thin untransformed strip as either slanted or curved depending on the adapting transformation. The thin strips provided negligible information about the vertical disparity field. In a forced-choice task we measured the amount of horizontal transformation that was required to null the acquired adaptation. We found that the amounts of horizontal transformation required to perceive the test strip fronto-parallel were significantly different from zero. We conclude that the visual system can adapt to disparity signals in the absence of a perceptual drive.

Effects of disparity-perspective cue conflict on depth contrast

The role of disparity-perspective cue conflict in depth contrast was examined. A central square and a surrounding frame were observed in a stereoscope. Five conditions were compared: (1) only disparity was introduced into either the centre or surround stimulus, (2) only perspective was introduced into the centre or surround, (3) concordant perspective and disparity were introduced into the centre or surround, (4) disparity was introduced into one stimulus and perspective into the other, and (5) only the centre stimulus was presented with horizontal shear disparity and perspective manipulated independently. The results show that individual differences in depth contrast were related to individual differences in the weighting of disparity and perspective in the single-stimulus conditions. We conclude that conflict between disparity and perspective contributes to depth contrast. However, significant depth contrast occurred when there was no disparity-perspective cue conflict, indicating that this cue conflict is not the sole mechanism producing depth contrast.

Strength of depth effects induced by three types of vertical disparity

The goal of the present study is to compare the strengths of depth effects induced by different types of vertical disparity. We use a nulling task, in which the depth effects induced by vertical disparity are nulled by horizontal disparity. The advantage of this method is that it prevents cue conflicts from arising between disparity and other depth cues. The ratios between horizontal and vertical disparity that evoke the percept of a fronto-parallel stimulus vary per type of vertical disparity. The ratios determined for vertical scale and vertical quadratic mix (vertical scale with a horizontal gradient) vary strongly across subjects. The ratios for vertical shear are constant, since all subjects needed the same amount of horizontal and vertical shear to perceive a fronto-parallel plane. In these experiments, one conflict cannot be avoided, namely the conflict between vertical disparity and oculomotor signals. This conflict may cause differential weighting of vertical disparity and oculomotor signals, which could explain the individual differences. The different ratios for different types of vertical disparity suggest that weighting is specific for each type of vertical disparity and the associated oculomotor signal.

Independent mechanisms produce visually perceived eye level (VPEL) and perceived visual pitch (PVP)

Two aspects of the perception of extrapersonal space undergo systematic changes with variations in the pitch of the visual environment: (1) the physical elevation perceived to correspond to eye level (VPEL); and (2) the perception of the pitch of the visual environment (PVP). Thus, one might assume that both discriminations are controlled by a common mechanism utilizing visual information from the pitched surface. In fact this assumption has been made frequently, and - in different forms - underlies three substantial but very different historical streams in the literature. A quantitative theoretical development shows that two of these streams, although derived from very different viewpoints and appearing very different themselves (it is assumed that the basis for both PVP and VPEL is information about the pitch of the visual field in one, and information about the location of the subject's eye level within the visual field in the other), make identical predictions: each requires that the weighted sum of PVP and VPEL equal the magnitude of physical pitch and that the weighted sum of their first derivatives equal a constant. The third stream, which assumes that an internal representation of the visual field gives rise to both PVP and VPEL, requires that a weighted difference of PVP and VPEL be proportional to physical pitch and that the weighted difference of their derivatives equal a constant. In an experiment designed to examine the relation between VPEL and PVP, psychophysical measurements of VPEL and PVP were made on 20 subjects across a range of pitches from -30 degrees to +20 degrees. Contrary to the predictions from all three interpretations, we find no significant correlation between the two perceptual variables when the influence of pitch itself is removed, despite the fact that VPEL and PVP each increased systematically with increasing visual field pitch. The results not only rule out the specific predictions derived from all three historical streams, they also rule out any theoretical viewpoint that requires control of both perceptual responses by a single mechanism. The statistical independence between VPEL and PVP implies independence between the mechanisms that give rise to them. The correlation observed here and elsewhere between individual PVP and VPEL settings when the influence of the systematic variation of pitch is not eliminated is a consequence of the way in which variations in the two perceptions are generated experimentally, and not on an identity of the mechanisms mediating the generation of the two perceptual variables themselves.

Temporal dependencies in resolving monocular and binocular cue conflict in slant perception

Observers viewed large dichoptic patterns undergoing smooth temporal modulations or step changes in simulated slant or inclination under various conditions of disparity-perspective cue conflict and concordance. After presentation of each test surface, subjects adjusted a comparison surface to match the perceived slant or inclination of the test surface. Addition of conflicting perspective to disparity affected slant and inclination perception more for brief than for long presentations. Perspective had more influence for smooth temporal changes than for step changes in slant or inclination and for surfaces presented in isolation rather than with a zero disparity frame. These results indicate that conflicting perspective information plays a dominant role in determining the temporal properties of perceived slant and inclination.

An analysis of binocular slant contrast

When a small frontoparallel surface (a test strip) is surrounded by a larger slanted surface (an inducer), the test strip is perceived as slanted in the direction opposite to the inducer. This has been called the depth-contrast effect, but we call it the slant-contrast effect. In nearly all demonstrations of this effect, the inducer's slant is specified by stereoscopic signals; and other signals, such as the texture gradient, specify that it is frontoparallel. We present a theory of slant estimation that determines surface slant via linear combination of various slant estimators; the weight of each estimator is proportional to its reliability. The theory explains slant contrast because the absolute slant of the inducer and the relative slant between test strip and inducer are both estimated with greater reliability than the absolute slant of the test strip. The theory predicts that slant contrast will be eliminated if the signals specifying the inducer's slant are consistent with one another. It also predicts reversed slant contrast if the inducer's slant is specified by nonstereoscopic signals rather than by stereo signals. These predictions were tested and confirmed in three experiments. The first showed that slant contrast is greatly reduced when the stereo-specified and nonstereo-specified slants of the inducer are made consistent with one another. The second showed that slant contrast is eliminated altogether when the stimulus consists of real planes rather than images on a display screen. The third showed that slant contrast is reversed when the nonstereo-specified slant of the inducer varies and the stereo-specified slant is zero. We conclude that slant contrast is a byproduct of the visual system's reconciliation of conflicting information while it attempts to determine surface slant.

Estimator reliability and distance scaling in stereoscopic slant perception

When a horizontal or vertical magnifier is placed before one eye, a frontoparallel surface appears slanted. It appears slanted away from the eye with horizontal magnification (geometric effect) and toward the eye with vertical magnification (induced effect). According to current theory, the apparent slant in the geometric and induced effects should increase with viewing distance. The geometric effect does scale with distance, but there are conflicting reports as to whether the induced effect does. Ogle (1938 Archives of Ophthalmology 20 604-623) reported that settings in slant-nulling tasks increase systematically with viewing distance, but Gillam et al (1988 Perception & Psychophysics 44 473-483) and Rogers et al (1995 Perception 24 Supplement, 33) reported that settings in slant-estimation tasks do not. We re-examined this apparent contradiction. First, we conducted two experiments whose results are consistent with the literature and thus replicate the apparent contradiction. Next, we analyzed the signals available for stereoscopic slant perception and developed a general model of perceived slant. The model is based on the assumption that the visual system knows the reliability of various slant-estimation methods for the viewing situation under consideration. The model's behavior explains the contradiction in the literature. The model also predicts that, by manipulating eye position, apparent slant can be made to increase with distance for vertical, but not for horizontal, magnification. This prediction was confirmed experimentally.

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.

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.

The influence of large scanning eye movements on stereoscopic slant estimation of large surfaces

The results of several experiments demonstrate that the estimated magnitude of perceived slant of large stereoscopic surfaces increases with the duration of the presentation. In these experiments, subjects were free to make eye movements. A possible explanation for the increase is that the visual system needs to scan the stimulus with eye movements (which take time) before it can make a reliable estimate of slant. We investigated the influence of large scanning eye movements on stereoscopic slant estimation of large surfaces. Six subjects estimated the magnitude of slant about the vertical or horizontal axis induced by large-field stereograms of which one half-image was transformed by horizontal scale, horizontal shear, vertical scale, vertical shear, divergence or rotation relative to the other half-image. The experiment was blocked in three sessions. Each session was devoted to one of the following fixation strategies: central fixation, peripheral (20 deg) fixation and active scanning of the stimulus. The presentation duration in each of the sessions was 0.5, 2 or 8 s. Estimations were done with and without a visual reference. The magnitudes of estimated slant and the perceptual biases were not significantly influenced by the three fixation strategies. Thus, our results provide no support for the hypothesis that the time used for the execution of large scanning eye movements explains the build-up of estimated slant with the duration of the stimulus presentation.

Temporal aspects of stereoscopic slant estimation: an evaluation and extension of Howard and Kaneko's theory

We investigated temporal aspects of stereoscopically perceived slant produced by the following transformations: horizontal scale, horizontal shear, vertical scale, vertical shear, divergence and rotation, between the half-images of a stereogram. Six subjects viewed large field stimuli (70 degrees diameter) both in the presence and in the absence of a visual reference. The presentation duration was: 0.1, 0.4, 1.6, 6.4 or 25.6 s. Without reference we found the following: rotation and divergence evoked considerable perceived slant in a number of subjects. This finding violates the recently published results of Howard and Kaneko. Slant evoked by vertical scale and shear was similar to slant evoked by horizontal scale and shear but was generally less. With reference we found the following: vertical scale and vertical shear did not evoke slant. Slant due to rotation and divergence was similar to slant due to horizontal scale and shear but was generally less. According to the theory of Howard and Kaneko, perceived slant depends on the difference between horizontal and vertical scale and shear disparities. We made their theory more explicit by translating their proposals into linear mathematical expressions that contain weighting factors that allow for both slant evoked by rotation or divergence, subject-dependent underestimation of slant and other related phenomena reported in the literature. Our data for all stimulus durations and for all subjects is explained by this 'unequal-weighting' extension of Howard and Kaneko's theory.

A computational model of depth perception based on headcentric disparity

It is now well established that depth is coded by local horizontal disparity and global vertical disparity. We present a computational model which explains how depth is extracted from these two types of disparities. The model uses the two (one for each eye) headcentric directions of binocular targets, derived from retinal signals and oculomotor signals. Headcentric disparity is defined as the difference between headcentric directions of corresponding features in the left and right eye's images. Using Helmholtz's coordinate systems we decompose headcentric disparity into azimuthal and elevational disparity. Elevational disparities of real objects are zero if the signals which contribute to headcentric disparity do not contain any errors. Azimuthal headcentric disparity is a 1D quantity from which an exact equation relating distance and disparity can be derived. The equation is valid for all headcentric directions and for all binocular fixation positions. Such an equation does not exist if disparity is expressed in retinal coordinates. Possible types of errors in oculomotor signals (six) produce global elevational disparity fields which are characterised by different gradients in the azimuthal and elevational directions. Computations show that the elevational disparity fields uniquely characterise both the type and size of the errors in oculomotor signals. Our model uses a measure of the global elevational disparity field together with local azimuthal disparity to accurately derive headcentric distance throughout the visual field. The model explains existing data on whole-field disparity transformations as well as hitherto unexplained aspects of stereoscopic depth perception.

Types of shear disparity and the perception of surface inclination

A study is reported of (i) the perceived inclination of a textured surface in depth about a horizontal axis as a function of disparity magnitude for horizontal-shear disparity, vertical-shear disparity, and rotation disparity; and (ii) interactions between patterns with shear or rotation disparity and superimposed or adjacent patterns or lines with zero disparity. Horizontal-shear disparity produced strong inclination which was enhanced by superimposed or adjacent zero-disparity stimuli. It produced little or no inclination contrast in superimposed or adjacent zero-disparity stimuli. Vertical-shear disparity produced inclination in the opposite direction (induced effect) which was reduced to near zero by a superimposed zero-disparity pattern. Adjacent vertical-shear and zero-disparity patterns appeared inclined at slightly different angles with a wide curved boundary. This suggests that vertical-shear disparities are averaged over a wide area. Rotation disparity produced minimal inclination. A superimposed or adjacent zero-disparity line appeared strongly inclined. A superimposed or adjacent zero-disparity pattern appeared vertical and caused the pattern with rotation disparity to appear inclined. Four mechanisms are proposed to account for the results: depth contrast, depth enhancement, deformation-disparity processing, and disparity transfer arising from cyclovergence.

Depth interactions between inclined and slanted surfaces in vertical and horizontal orientations

Depth interactions between a frontal test surface and an adjacent induction surface were measured as a function of the type of disparity in the induction surface and of the vertical/horizontal orientation of the boundary between the surfaces. The types of disparity were 4 degrees horizontal-shear disparity, 4 degrees vertical-shear disparity, and 4 degrees rotation disparity; 4% horizontal-size disparity, 4% vertical-size disparity, and 4% overall-size disparity. Depth contrast in a frontal surface was produced by surfaces containing horizontal-size disparity but not by those containing horizontal-shear disparity. Vertical-shear and vertical-size disparities produced induced effects in both the induction and the test surface, which is here explained in terms of deformation-disparity processing. Effects of rotation disparity on the test surface can be accounted for in terms of cyclovergence, deformation disparity, and perhaps also depth contrast. The fact that horizontal-size disparity produced more depth contrast than horizontal-shear disparity is due to an anisotropy of disparity processing rather than the relative orientation of the surfaces. Ground surfaces appeared more slanted than ceiling surfaces. Surfaces containing horizontal disparities produced a sharp boundary with the test surface because horizontal disparities are processed locally. Surfaces with vertical disparities produced a gradual boundary with the test surface because vertical disparities are processed over a wider area.

Types of size disparity and the perception of surface slant

We examined (i) perceived slant of a textured surface about a vertical axis as a function of disparity magnitude for horizontal-size disparity, vertical-size disparity, and overall-size disparity; and (ii) interactions between patterns with various types and magnitudes of size disparity and superimposed or adjacent zero-disparity stimuli. Horizontal-size disparity produced slant which increased with increasing disparity, was enhanced by superimposed zero-disparity stimuli, and induced contrasting slant in superimposed or adjacent zero-disparity stimuli. Vertical-size disparity produced opposite slant (induced effect) which was reduced to near zero by a superimposed zero-disparity pattern and both patterns appeared as one surface. Adjacent vertical-size-disparity and zero-disparity patterns appeared as separate surfaces with a wide curved boundary. Overall-size disparity produced slant which was enhanced by a superimposed zero-disparity pattern and less so by a zero-disparity line, and induced more slant in a zero-disparity line than in a zero-disparity pattern. The results are discussed in terms of depth underestimation of isolated surfaces, depth enhancement, depth contrast, and the processing of deformation disparity.

Spatial interactions modulate stereoscopic processing of horizontal and vertical disparities

Stereoscopic processing of horizontal and vertical disparities was assessed by measuring how the stereoscopic appearance of test dots near the fixation point was influenced by inducing stimuli in the near periphery. The inducing stimuli were differentially magnified in the two eyes and varied in horizontal eccentricity. As expected, when the inducers were horizontally magnified, the test dots exhibited depth contrast, slanting in depth in a direction opposite the slant of the inducing dots. When the inducers were vertically magnified, the test dots slanted in depth around a vertical axis toward the eye with the larger vertical image (the induced-size effect). However, two lines of evidence suggested that an eccentricity-dependent weighted average of horizontal and vertical components of inducer-dot magnification determined the slant of the test dots. First, as the horizontal eccentricity of the inducing dots was varied, the trend of test-dot slants measured with vertical inducer magnifications was predicted by the trend of test-dot slants measured with horizontal inducer magnifications. Second, test-dot slants measured with a combination of both horizontal and vertical inducer magnification could be predicted by simply adding test-dot slants measured with either horizontal or vertical inducer magnification alone.

Definition and detection of binocular disparity

Stereoacuity experiments tested definitions of binocularly disparate spatial positions by perturbing the binocular correspondence of the two half-images. Dichoptic translations perturbed zero-order retinal positions; expansions perturbed first-order horizontal separations; rotations perturbed first-order orientations; and anisotropic expansions deformed first-order two-dimensional (2D) structure. Each transformation perturbed relative positions in the two half-images by more than 100 arcsec, but stereoacuity thresholds remained about 10 arcsec. Binocular disparity involves second-order 2D differential structure of the monocular half-images, specifying local surface shape. Stereoacuity is much better than nonstereo acuity, suggesting that monocular spatial signals are binocularly correlated.

Spatial limitation of vertical-size disparity processing

We investigated the upper limit of horizontal spatial modulation of vertical-size disparity in a textured surface for the perception of depth. In Experiment 1 subjects matched the appearance of a surface with modulated horizontal-size disparity to that of a surface with modulated vertical-size disparity. In Experiment 2 we determined the threshold amplitude of modulation of vertical-size disparity required for the perception of depth as a function of the spatial frequency of disparity modulation. The results indicate that sensations of depth are not elicited by modulations of vertical-size disparity of any amplitude at spatial frequencies higher than about 0.04 c/deg. We conclude that vertical disparities are averaged within about 20 deg-wide areas and suggest that this global measurement is used to scale local horizontal disparities for the perception of surface slant.

Stability of binocular depth perception with moving head and eyes

We systematically analyse the binocular disparity field under various eye, head and stimulus positions and orientations. From the literature we know that certain classes of disparity which involve the entire disparity field (such as those caused by horizontal lateral shift, differential rotation, horizontal scale and horizontal shear between the entire half-images of a stereogram) lead to relatively poor depth perception in the case of limited observation periods. These classes of disparity are found to be similar to the classes of disparities which are brought about by eye and head movements. Our analysis supports the suggestion that binocular depth perception is based primarily (for the first few hundred milliseconds) on classes of disparity that do not change as a result of ego-movement.

Anisotropy in Werner's binocular depth-contrast effect

We investigated Werner's binocular depth-contrast effect. Subjects viewed stereograms consisting of a test pattern and an inducing pattern. The half-images of the inducing pattern were either horizontally scaled or sheared relative to each other. Subjects judged the (induced) perceived slant of the test pattern. We were interested in what influence the spatial configuration of the test pattern and the inducing pattern had on the depth-contrast effect. We conclude that the depth-contrast effect is a global effect. In other words, it is not restricted to the location of the inducing pattern. The effect decreases with distance, however, in an anisotropic way. The depth-contrast effect was present most prominently when the test pattern was positioned in the direction along the slant (rotation) axis of the inducing pattern. We suggest that Werner's depth-contrast effect can be explained by the (previously reported) findings that: (1) stereopsis is relatively insensitive to whole-field horizontal scale and shear; and (2) stereopsis is very sensitive to horizontal scale and shear of two stimuli relative to each other.