Perspective, orientation disparity, and anisotropy in stereoscopic slant perception.

Stereoscopic depth estimates are not predictable from the geometry of point disparities. The configural properties of surfaces (surface contours) may play an important role in determining, for example, slant responses to a disparity gradient, and the marked anisotropy in favour of slant around a horizontal axis. It has been argued that variation in slant magnitude are attributable to the degree of perspective conflict present and that anisotropy is attributable to orientation disparity, which varies with the axis of slant. Three experiments were conducted in which configural properties were varied to try and tease apart the respective roles of orientation disparity and conflicting perspective in determining stereoscopic slant perception and slant axis anisotropy. The results could not be accounted for by the magnitude of the orientation disparities present. Conflicting perspective cues appeared to play a role but only for slant around a vertical axis. It was concluded that there are important configural effects in stereopsis attributable neither to orientation disparity nor to perspective.     

The stereoscopic anisotropy: individual differences and underlying mechanisms

Observers are more sensitive to variations in the depth of stereoscopic surfaces in a vertical than in a horizontal direction; however, there are large individual differences in this anisotropy. The authors measured discrimination thresholds for surfaces slanted about a vertical axis or inclined about a horizontal axis for 50 observers. Orientation and spatial frequency discrimination thresholds were also measured. For most observers, thresholds were lower for inclination than for slant and lower for orientation than for spatial frequency. There was a positive correlation between the 2 anisotropies, resulting from positive correlations between (a) orientation and inclination thresholds and (b) spatial frequency and slant thresholds. These results support the notion that surface inclination and slant perception is in part limited by the sensitivity of orientation and spatial frequency mechanisms.     

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.     

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.     

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.     

Orientation disparity, deformation, and stereoscopic slant perception.

Koenderink and van Doorn's theory, that the basis of stereoscopic slant perception is the deformation component of the disparity, field, was tested for slant around a horizontal axis, which produces images with a vertical ramp of horizontal disparity (horizontal shear) characterised by a global orientation disparity at the vertical meridian. The disparity field in this case can be parsed into two components, deformation and curl, which each contribute half of the orientation disparity. This case was compared with similar random-dot stimuli in which the deformation component was doubled and the curl component eliminated or vice versa. All three types of stimuli had identical orientation disparity at the vertical meridian. A condition in which there was no such orientation disparity, but deformation was present, was also included. It was found that perceived slant was not related to the deformation present, as Koenderink and van Doorn's theory would predict, but was predictable from the orientation disparity at the vertical meridian per se.     

The induced effect,vertical disparity,and stereoscopic theory

The induced effect is an apparent slant of a frontal plane surface around a vertical axis, resulting from vertical magnification of the image in one eye. It is potentially important in suggesting a role for vertical disparity in stereoscopic vision, as proposed by Helmholtz. The paper first discusses previous theories of the induced effect and their implications. A theory is then developed attributing the effect to the process by which the stereoscopic response to horizontal disparity is scaled for viewing distance and eccentricity. The theory is based on a mathematical analysis of vertical disparity gradients produced by surfaces at various distances and eccentricities relative to the observer. Vertical disparity is shown to be an approximately linear function of eccentricity, with a slope or gradient which decreases with observation distance. The effect of vertical magnification on such gradients is analyzed and shown to be consistent with a change in the eccentricity factor, but not the distance factor, required to scale horizontal disparity. The induced effect is shown to be an appropriate stereoscopic response to a zero horizontal disparity surface at the eccentricity indicated. However, since extraretinal convergence signals provide conflicting evidence about eccentricity, they may attenuate the induced effect from its mathematically predicted value. The discomfort associated with the induced effect is attributed to this conflict.     

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.     

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.     

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.     

Interpolation across surface discontinuities in structure from motion Asad Satdpour

Interpolation across orientation discontinuities in simulated three-dimensional (3-D). surfaces was studied in three experiments with the use of structure-from-motion (SFM). displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap). between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical). of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976). and Kellman and Shipley (1991). and with a model of 3-D interpolation proposed by Grimson (1981).     

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.     

Converging operations revisited: Assessing what infants perceive using discrimination measures

In four experiments, we explored the perception of facial distortions seen in pictures viewed from the side or from above or below. In all four, however, we disguised the slant of the picture surface by using a double-projection technique that removed binocular and monocular cues: Faces were digitized, distorted to mimic a particular slant behind the image plane, cropped to a frame, and presented to viewers for their judgments. In the first experiment, we found that simulated rotations around a horizontal axis (pictures seen as if from above or below) created more noticeable distortions in faces than did simulated rotations around a vertical axis (pictures seen as if from the left or right). In the second experiment, pursuing a result from the first but with a between-subjects design, we found that pictured faces with a slant around a vertical axis of 22° were seen as having no more distortion than unslanted faces. In the third experiment, we placed each image within a frame slanted either in the same way as or differently from the picture, and found no effect of frame. In the fourth experiment, we determined that viewers had little ability to match appropriately slanted frames with slanted pictures. Thus, we claim that part of the reason why one can look at moderately slanted pictures without perceptual interference is that the distortions in the image are subthreshold, or perhaps within the bounds of acceptability. These results contrast with the generally accepted theory that viewers mentally compensate for distortions in moderately slanted pictures.     

JUDGMENTS OF SLANT ON THE BASIS OF FORESHORTENING

By analogy with Stavrianos' (1945) finding for linear perspective, it was proposed that the effectiveness of foreshortening as a slant cue would increase as a function of visual angle. Surfaces of vertical lines slanted around a vertical axis were monocularly viewed at three horizontal visual angles and four angles of slant. An adjustment method was used to record apparent slant. An analysis of variance showed significant F ratios for visual angle and angle of slant thus supporting the hypothesis that increasing visual angle increases the effectiveness of slant judgments. However, subjects' verbal reports indicated that slant may not be perceived when only foreshortening is available as a cue.     

Evidence for disparity change as the primary stimulus for stereoscopic processing

Subjects were able to respond to a lens-induced stereoscopic slant more quickly and more accurately when it was imposed on only part of a surface rather than on the whole surface. This shows that the presence of a stereoscopic boundary, where disparity is discontinuous, increases the efficiency of stereoscopic processing. This finding is not consistent with many current models of stereopsis.     

Influence of a stereo surface on the perceived tilt of a monocular line.

This study addressed the issue of how a stereo-specified surface influences the perceived two-dimensional orientation of a monocularly viewed line. In a series of three experiments, it was found that, in general, when a monocular line was embedded in a disparity field specifying a planar surface slanted about the horizontal axis, the tilt of the line depended on the slant of the surface in which it was embedded and on whether the line was presented in the left or in the right visual field. These results, predicted by perspective geometry, are compatible with the hypothesis that the monocular line is perceived as part of the stereo surface. Moreover, it was found that timing is a crucial factor in determining the strength of the effect. The effect was at a maximum when the monocular line and the stereo surface were presented together, with no prior presentation of the surface. The influence of the stereo surface on the monocular line was substantially reduced, however, when the surface alone preceded the combined presentation of the line and the surface.     

Influence of a stereo surface on the perceived tilt of a monocular line

This study addressed the issue of how a stereo-specified surface influences the perceived twodimensional orientation of a monocularly viewed line. In a series of three experiments, it was found that, in general, when a monocular line was embedded in a disparity field specifying a planar surface slanted about the horizontal axis, the tilt of the line depended on the slant of the surface in which it was embedded and on whether the line was presented in the left or in the right visual field. These results, predicted by perspective geometry, are compatible with the hypothesis that the monocular line is perceived as part of the stereo surface. Moreover, it was found that timing is a crucial factor in determining the strength of the effect. The effect was at a maximum when the monocular line and the stereo surface were presented together, with no prior presentation of the surface. The influence of the stereo surface on the monocular line was substantially reduced, however, when the surface alone preceded the combined presentation of the line and the surface.     

Aging and the perception of slant from optical texture, motion parallax, and binocular disparity

The ability of younger and older observers to perceive surface slant was investigated in four experiments. The surfaces possessed slants of 20°, 35°, 50°, and 65°, relative to the frontoparallel plane. The observers judged the slants using either a palm board (Experiments 1, 3, and 4) or magnitude estimation (Experiment 2). In Experiments 1–3, physically slanted surfaces were used (the surfaces possessed marble, granite, pebble, and circle textures), whereas computer-generated 3-D surfaces (defined by motion parallax and binocular disparity) were utilized in Experiment 4. The results showed that the younger and older observers' performance was essentially identical with regard to accuracy. The younger and older age groups, however, differed in terms of precision in Experiments 1 and 2: The judgments of the older observers were more variable across repeated trials. When taken as a whole, the results demonstrate that older observers (at least through the age of 83 years) can effectively extract information about slant in depth from optical patterns containing texture, motion parallax, or binocular disparity.     

The visual perception of surface orientation from optical motion

Observers viewed monocular animations of rotating dihedral angles and were required to indicate their perceived structures by adjusting the magnitude and orientation of a stereoscopic dihedral angle. The motion displays were created by directly manipulating various aspects of the image velocity field, including the mean translation, the horizontal and vertical velocity gradients, and the manner in which these gradients changed over time. The adjusted orientation of each planar facet was decomposed into components of slant and tilt. Although the tilt component was estimated with a high degree of accuracy, the judgments of slant exhibited large systematic errors. The magnitude of perceived slant was determined primarily by the magnitude of the velocity gradient scaled by its direction. The results also indicate that higher order temporal derivatives of the moving elements had little effect on observers' judgments.     

Perceptual space in the dark affected by the intrinsic bias of the visual system

Correct judgment of egocentric/absolute distance in the intermediate distance range requires both the angular declination below the horizon and ground-surface information being represented accurately. This requirement can be met in the light environment but not in the dark, where the ground surface is invisible and hence cannot be represented accurately. We previously showed that a target in the dark is judged at the intersection of the projection line from the eye to the target that defines the angular declination below the horizon and an implicit surface. The implicit surface can be approximated as a slant surface with its far end slanted toward the frontoparallel plane. We hypothesize that the implicit slant surface reflects the intrinsic bias of the visual system and helps to define the perceptual space. Accordingly, we conducted two experiments in the dark to further elucidate the characteristics of the implicit slant surface. In the first experiment we measured the egocentric location of a dimly lit target on, or above, the ground, using the blind-walking-gesturing paradigm. Our results reveal that the judged target locations could be fitted by a line (surface), which indicates an intrinsic bias with a geographical slant of about 12.4 degrees. In the second experiment, with an exocentric/relative-distance task, we measured the judged ratio of aspect ratio of a fluorescent L-shaped target. Using trigonometric analysis, we found that the judged ratio of aspect ratio can be accounted for by assuming that the L-shaped target was perceived on an implicit slant surface with an average geographical slant of 14.4 degrees. That the data from the two experiments with different tasks can be fitted by implicit slant surfaces suggests that the intrinsic bias has a role in determining perceived space in the dark. The possible contribution of the intrinsic bias to representing the ground surface and its impact on space perception in the light environment are also discussed.