Stereoscopic Surface Research Articles

The stereoscopic anisotropy affects manual pointing.

Although binocular disparity can in principle provide absolute depth information, perceived stereoscopic depth depends on the relative disparities between points and their spatial arrangement. An example of this is the stereoscopic anisotropy--observers typically perceive less depth for stereoscopic surfaces when depth varies in the horizontal direction than in the vertical direction. We investigated whether this anisotropy also affects manual pointing. Participants were presented with stereograms depicting surfaces that were slanted in depth about either a horizontal axis (inclination) or a vertical axis (slant), and were asked either to point to the edge of a surface, or to estimate its inclination or slant. For both tasks, a clear anisotropy was observed, with participants perceiving greater depth, and also pointing out steeper surfaces, for inclined surfaces than for slanted surfaces. We conclude that both perception and the control of action are subject to a similar stereoscopic anisotropy, and that performance on the two tasks relies on similar depth processing mechanisms.

The absence of depth constancy in contour stereograms.

Stereoscopic surfaces constructed from Kanizsa-type illusory contours or explicit luminance contours were tested for three-dimensional (3-D) shape constancy. The curvature of the contours and the apparent viewing distance between the surface and the observer were manipulated. Observers judged which of two surfaces appeared more curved. Experiment 1 allowed eye movements and revealed a bias in 3-D shape judgment with changes in apparent viewing distance, such that surfaces presented far from the observer appeared less curved than surfaces presented close to the observer. The lack of depth constancy was approximately the same for illusory-contour surfaces and for explicit-contour surfaces. Experiment 2 showed that depth constancy for explicit-contour surfaces improved slightly when fixation was required and eye movements were restricted. These experiments suggest that curvature in depth is misperceived, and that illusory-contour surfaces are particularly sensitive to this distortion.

ステレオマッチング法の改善によるＳＥＭ３次元破面解析

ステレオマッチング法の改善によるＳＥＭ３次元破面解析

Aftereffects and the representation of stereoscopic surfaces.

The structure of human disparity representation is examined through (i) adaptation experiments and (ii) model simulations of the data. Section 3 presents results of adaptation experiments designed to illuminate the structure of human disparity representation. Section 4 presents model simulations of three different disparity representation schemes. In the experiments, participants adapted to a 0.133 cycle deg-1 sinusoidally corrugated surface with 10 min of arc peak-to-trough disparity. A flat test surface was briefly presented, in which the aftereffect surface was perceived. Adapt and test surfaces were placed on disparity pedestals and thus presented in front of or behind the plane of fixation. The adapt surface could be offset from the fixation plane by +/- 8 to 24 min of arc. The test surface could be offset from the fixation plane by +/- 8 to 48 min of arc. The depth aftereffect was measured in different disparity planes by a nulling method and 'topping-up' procedure. Aftereffect tuning functions were obtained whose bandwidths, magnitudes, and tuning depended on the disparity planes of both the adapt and test surfaces. These parameters were used to constrain the models tested in section 4. On the basis of the two studies, it is argued that the human stereoscopic system encodes spatial changes of disparity using channels localised within disparity planes. A localised disparity-gradient model of the human representation of disparity is proposed.

Disparity minimisation, cyclovergence, and the validity of nonius lines as a technique for measuring torsional alignment.

Frisby et al (1993 Perception 22 Supplement, 115) proposed that the visual system might make cyclovergent eye movements in order to minimise the overall pattern of both vertical and horizontal disparities when an observer views an inclined stereoscopic surface. Their measurements of cyclovergence, which used vertically oriented nonius lines, were found to be consistent with that proposal. In our experiment 1, we measured torsional eye movements objectively, using scleral coils, and found no evidence of a cyclovergent response to either a real inclined surface or to a simulated inclined surface in which the two stereoscopic images were related by a horizontal shear transformation. These results are inconsistent with the disparity minimisation hypothesis. In order to account for the discrepant findings of the two studies, we propose that vertically oriented nonius lines may not be a valid method for assessing cyclovergence because the lines can be seen as lying 'within' the inclined surface. In experiment 2, we tested the predictions of the cyclovergence hypothesis of Frisby et al against our own 'within surface' explanation, using both horizontally and vertically oriented nonius lines and dichoptic images related by either a horizontal or a vertical shear. If cyclovergence were the cause of the misalignment, both horizontal and vertical nonius lines should appear misaligned to the same extent. This was not found to be the case. We conclude that vertical nonius lines may not be a valid technique for measuring cyclovergence when the lines are seen against a background of an inclined surface.

A Bayesian model for perception of surfaces from binocular disparity

We propose a computational model for the perception of surfaces from binocular disparity within a Bayesian framework. The model attempts to reconstruct the perceived surfaces from their differential structure, which is concurrently estimated from initial data of given binocular disparity. To achieve this, the model consists of four processes: a continuous-valued process that represents the surface depth, and three binary processes that represent the presence or absence of depth discontinuities, nonzero second spatial derivatives of the surfaces, and outliers in given disparity data. By strongly coupling these four processes, the perceived surface is reconstructed within regions bounded by salient stereo features such as the discontinuities and nonzero second spatial derivatives of the surface, while rejecting outlying points from the surface. We show through simulations that the model is consistent with some psychophysical experiments that address the perception of stereoscopic surface. © 1999 Scripta Technica, Syst Comp Jpn, 30(1): 32–42, 1999

Aftereffects and the representation of stereoscopic surfaces

Aftereffects and the representation of stereoscopic surfaces

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.

Anisotropic Temporal Integration in the Perception of Stereoscopic Corrugations

Disparity sensitivity for horizontal depth corrugations increases with exposure duration for presentations of up to 1 s (Tyler, 1990 Vision Research30 1877 – 1895). To extend the work of Parton et al (1996 Perception25 67) we investigated whether differences existed in the effects of exposure for corrugations at different orientations. Disparity thresholds were measured for horizontal, vertical, and diagonal gratings with spatial frequencies ranging between 0.1 cycle deg−1 and 0.8 cycle deg−1, as a function of stimulus duration. Stimuli were presented for exposures of between 50 ms and 32 s, and were followed by a random disparity mask, which served the important function of disrupting further processing of stimulus disparity. Thresholds were greatest for vertical gratings. This effect was particularly pronounced for the lowest frequencies. In all conditions, disparity sensitivity improved as exposure duration increased, and continued to do so for all durations tested. For vertical and diagonal gratings, log - log plots of threshold against time showed a linear relationship with a slope of −1 up to 1.0 s, after which time improvements in sensitivity reduced. Horizontal gratings showed a similar relationship, but with thresholds ceasing to decrease significantly after 0.5 s. Temporal integration limits differ with surface orientation, and represent another important difference in our ability to detect and encode depth in stereoscopic surfaces.

Scaling of Frontoparallel Surfaces by Vertical Disparities: Effects of Field Size, Location, and Eccentricity

Since the pattern of horizontal disparities created by a frontal surface depends on the distance of the surface from the observer, additional information about distance is needed in order to judge whether a surface lies in a frontal plane. Rogers and Bradshaw (1995 Perception24 155 – 179) showed that both vertical disparities and vergence angle can be used to scale the curvature of surfaces in a horizontal direction. In the present experiments, we measured the extent of frontal plane scaling as a function of the location and eccentricity of the vertical disparity information. Observers were presented with a series of random-textured stereoscopic surfaces with vertical disparity information appropriate for surfaces located at distances between 28 cm and infinity. The observer's task was to vary the pattern of horizontal disparities until the surface appeared to lie in a frontal plane. The stereoscopic images were masked to reveal either a circular, or an annular, or a rectangular patch with dimensions between 10 deg and 70 deg. Maximum scaling was found for the 70 deg diameter circular patch; it decreased by 50% when the patch was masked down to 20 deg in diameter. Scaling remained at over 80% when the central 60,deg of the display were masked. Scaling was reduced more when the horizontal width of the rectangle was made smaller than when the vertical height was made smaller. Vertical disparities are most effective for frontal plane scaling when they are present in more eccentric regions of the visual field, especially in a horizontal direction.

The Interaction of Stereopsis and Perspective in the Perception of Depth

When only stereoscopic information is available, the slant of a single isolated surface around a vertical axis is often greatly underestimated. If two small objects (probes), separated horizontally by several degrees, are displayed in front of such a surface, the depth of the probes is perceived relative to the perceived slant of the background surface, leading to systematic misperception of the point of subjective equality (PSE) of the distances of the probes from the observer (Mitchison and Westheimer, 1984 Vision Research24 1063 – 1073; Gillam et al, 1993 Perception22 Supplement, 35). In the present study we found that when we added global perspective information to the background surface, thus increasing its perceived slant, this substantially improved the PSE of the probes. Alternatively, when we added frontal stereoscopic surfaces above and below the background surface, thus providing gradients of disparity discontinuities across the surface boundaries, this also produced an improvement in the perceived slant of the background surface, but produced an even greater improvement in the PSE of the probes. These results imply that the local stereoscopic information specifying the depth of each probe relative to the background surface is integrated with the perceived slant of the background surface, whether specified by global stereoscopic information or by global perspective information, to determine the relative depth of the probes. This integration of local stereoscopic information with global slant information appears to be more complete, however, when the global information is provided by stereopsis rather than by perspective.

Disparity scaling and the perception of frontoparallel surfaces.

Binocular disparity can be defined in a variety of ways and its measurement depends upon the particular coordinate framework chosen. As a result of the inverse square law, binocular disparities need to be scaled by some estimate of absolute distance if they are to be interpreted correctly. The experiments described in this paper investigated the extent to which (i) the vergence angle and (ii) the horizontal gradient of vertical disparities or 'differential perspective' provide the necessary information for judging that a stereoscopic surface is flat and frontoparallel. For small displays (< 20 deg) vergence is more effective than differential perspective in scaling frontoparallel surfaces but for larger displays (> 30 deg), differential perspective plays the major role. When both cues together specify the viewing distance, the constancy of frontoparallel-surface scaling is close to perfect for all sizes of display up to 80 deg. Analysis of the geometry of stereoscopic images shows that when a surface patch lies in a frontal plane, the binocular horizontal size ratio of any surface feature is equal to the square of its binocular vertical size ratio, whatever its distance from the observer.

Cue conflict and stereoscopic surface slant about horizontal and vertical axes.

The way in which a planar surface is defined or configured may affect its apparent slant about a given axis, and the magnitude of slant-axis anisotropies. The authors have previously suggested that (i) these within-axis and between-axis configuration effects may be attributable, in part at least, to the perspective-disparity conflict generated when geometrically frontoparallel configured surfaces are slanted stereoscopically; and (ii) that implicit contours, defined by line endings or conjunctions, may have effects analogous to those seen with explicit contours. These possibilities were directly examined in two experiments. In experiment 1, slant-axis anisotropy was progressively induced by adding horizontal lines to a vertical-line (zero anisotropy) grid under conditions of cue conflict; slants about the vertical (but not the horizontal) were attenuated-demonstrating a clear and systematic nexus between surface configuration and slant-axis anisotropy. The presence of regular implicit horizontals similarly and selectively attenuated the slant perceived about the vertical. In experiment 2, cue conflict was seen to exacerbate slant-axis anisotropy, but clearly could not fully account for it. There was an axis asymmetry in the effect of degrading implicit contours: degradation had a marked impact on perceived slant about the horizontal but not the vertical axis.

Apparent motion determined by surface layout not by disparity or three-dimensional distance.

The most meaningful events ecologically, including the motion of objects, occur in relation to or on surfaces. We run along the ground, cars travel on roads, balls roll across lawns, and so on. Even though there are other motions, such as flying of birds, it is likely that motion along surfaces is more frequent and more significant biologically. To examine whether events occurring in relation to surfaces have a preferred status in terms of visual representation, we asked whether the phenomenon of apparent motion would show a preference for motion attached to surfaces. We used a competitive three-dimensional motion paradigm and found that there is a preference to see motion between tokens placed within the same disparity as opposed to different planes. Supporting our surface-layout hypothesis, the effect of disparity was eliminated either by slanting the tokens so that they were all seen within the same surface plane or by inserting a single slanted background surface upon which the tokens could rest. Additionally, a highly curved stereoscopic surface led to the perception of a more circuitous motion path defined by that surface, instead of the shortest path in three-dimensional space.

Asymmetrical effect of crossed and uncrossed disparity on stereoscopic capture.

When a real or subjective contour is superimposed on a repetitive texture or 'wallpaper pattern', the apparent depth of the elements of the wallpaper pattern may be influenced by the contour. When the contour has crossed disparity, the elements inside the contour are seen floating in the plane of the contour. This is called 'stereoscopic capture'. On the other hand, when the contour has uncrossed disparity a different, somewhat unstable, percept is seen. The wallpaper elements are either seen to form a transparent surface floating in front of the contour, or all of the elements inside and outside of the contour are seen to lie in the uncrossed plane of the inducing contour. We suggest that the asymmetry between crossed and uncrossed stereo capture is a by-product of the different roles played by crossed and uncrossed disparity in stereoscopic surface construction: specifically, crossed and, perhaps, zero disparity spreads one-directionally into a figure from a contour whereas uncrossed disparity spreads out from a figure in all directions. These points are illustrated with a series of demonstrations.

Vertical disparities, differential perspective and binocular stereopsis.

To calculate the depth difference between a pair of points on a three-dimensional surface from binocular disparities, it is necessary to know the absolute distance to the surface. Traditionally, it has been assumed that this information is derived from non-visual sources such as the vergence angle of the eyes. It has been shown that the horizontal gradient of vertical disparity between the images in the two eyes also contains information about the fixation distance. Recent results, however indicated that manipulations of the vertical disparity gradient have no effect on either the perceived shape or the perceived depth of surfaces defined by horizontal disparities. Following the reasoning of Longuet-Higgins and Tyler, we suggest that vertical disparities are best understood as a consequence of perspective viewing from two different vantage points and the results we report here show that the human visual system is able to exploit vertical disparities and use them to scale the perceived depth and size of stereoscopic surfaces, if the field of view is sufficiently large.

The Discriminability of Smooth Stereoscopic Surfaces

In this study the sensitivity of human vision to the smoothness of stereoscopic surface structure was investigated. In experiments 1 and 2 random-dot stereograms were used to evaluate the discrimination of smooth versus 'noisy' sinusoidal surfaces differing in the percentages of points on a single smooth surface. Fully coherent smooth surfaces were found to be much more discriminable than other less smooth randomly perturbed surfaces. In experiment 3 the discrimination between discontinuous triangle-wave surfaces and similarly shaped smoothly curved surfaces obtained from the addition of the fundamental and the third harmonic of the corresponding triangle-wave surface was evaluated. The triangle-wave surfaces were found to be more accurately discriminated from the smoothly curved surfaces than would be predicted from the detectability of the difference in their Fourier power spectra. This superior discriminability was attributed to differences between the curvature and/or discontinuity of the two surfaces. In experiment 3 the effects of incoherent 'noise' points on the discrimination between the two surface types were also evaluated. These randomly positioned noise points had a relatively small effect on the discrimination between the two surfaces. In general, the results of these experiments indicate that smooth surfaces are salient for stereopsis and that isolated local violations of smoothness are highly discriminable.

Postfusional latency in stereoscopic slant perception and the primitives of stereopsis.

Random dot stereograms of slanted surfaces were constructed, each representing one or two slanted surfaces in different relative arrangements and with different axes. Latency to fusion and from fusion to stereoscopic resolution was measured for each stimulus. It was found that latency to fusion was always very brief but that latency to stereoscopic resolution varied markedly, depending upon the orientation and arrangement of the stereoscopic surfaces. A gradient of discontinuities at a surface boundary produced an instant slant response for that surface, whereas a gradient of absolute disparities across the surface did not, except under conditions where vertical declination (a form of orientation disparity) was present. We conclude that stereopsis is not based on the primitives used in matching the images for fusion and that it is, at least initially, a response to disparity discontinuities which play no role in the fusion process. We also conclude that vertical declination is responded to globally as a slant around a horizontal axis but that other forms of orientation disparity are ineffective. The evidence from our experiments does not support the existence of a stereoscopic ability to respond globally to differences in magnification (or spatial frequency). It is suggested that stereoscopic perception of slant around a vertical axis is slow because it results from the integration of local processes.

Scanning electron microscopy of the nasal glands and vessels

The trypsin-HCl method of Uehara was applied to the respiratory nasal mucosa of rats and guinea pigs, and the stereoscopic surface view of the nasal glands, vessels, and associated nerve fibers were observed under the scanning electron microscope (SEM).