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.     

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.     

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.     

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.     

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.     

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.     

Pre-attentive detection of a target defined by stereoscopic slant.

Does the visual system represent stereoscopic depth purely as a map of local disparities, or does it explicitly represent local relationships of disparity, such as disparity gradients? Experiments are reported in which visual search for a target containing the same disparity range as other elements in the display, but differing in the relationship of the disparities (stereo slant), was used to determine whether the target showed 'pop-out' like a unitary feature, or the serial search characteristic of feature conjunctions. Each stereo pair of elements was selected randomly from a range of outline parallelograms leaning to the right or to the left, so that the target could not be identified using any monocular shape cue. Response times for detection of the target (present on 50% of the trials) were independent of the number of elements in the display. This result was confirmed by varying element size and spacing, and by using oblique crosses rather than parallelograms as stimuli. It is concluded that stereoscopically defined slant, or disparity gradient, can be processed and compared in parallel across the display, and acts in this respect as an explicit unitary visual property. This contrasts with findings in analogous experiments on movement, which show that targets defined by divergence or deformation of optic flow can only be identified by serial search.     

Differences in influence between pitched-from-vertical lines and slanted-from-frontal horizontal lines on egocentric localization

The visual field exerts powerful effects on egocentric spatial localization along both horizontal and vertical dimensions. Thus, (1) prism-produced visual pitch and visual slant generate similar mislocalizations of visually perceived eye level (VPEL) and visually perceived straight ahead (VPSA) and (2) in darkness curare-produced extraocular muscle paresis under eccentric gaze generates similar mislocalizations in VPEL and VPSA that are essentially eliminated by introducing a normal visual field. In the present experiments, however, a search for influences of real visual slant on VPSA to correspond to the influences of visual pitch on VPEL failed to find one. Although the elevation corresponding to VPEL changes linearly with the pitch of a visual field consisting of two isolated 66.5°-long pitched-from-vertical lines, the corresponding manipulation of change in the slant of either a horizontal two-line or a horizontal four-line visual field on VPSA did not occur. The average slope of the VPEL-versus-pitch function across 5 subjects was +0.40 over a ±30° pitch range, but was indistinguishable from 0.00 for the VPSA-versus-slant function over a ±30° slant range. Possible contributions to the difference between susceptibility of VPEL and VPSA to visual influence from extraretinal eye position information, gravity, and several retinal gradients are discussed.     

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.     

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.     

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.     

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 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.     

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.     

Texture gradient effectiveness in the perception of surface slant

To assess the development of monocular slant perception as well as the relative effectiveness of different sources of information, children in first, third, and fifth grades and college adults were asked to make judgments of surface slant on the basis of monocular texture gradient information. Accuracy of judgment increased with increasing age. In addition, differences in gradient effectiveness were found. Compression gradients were relatively ineffective sources of information, whereas perspective and multiple gradients resulted in greater accuracy. The results suggest limitations on the specificity of certain forms of gradients.     

TWO-DIMENSIONAL FIELD EFFECTS AND STATIC SLANT PERCEPTION

E riksson , E. S. Two-dimensional field effects and static slant perception. Scand. J. Psychol ., 1968, 9, 19–32.—The model for two-dimensional field effects as developed in a previous article makes possible certain predictions concerning perceived shape which, taken together with the subjective slant principle, result in predictions of the perceived slant of a circle or a surface composed of circles. Data were obtained which agreed with these predictions, showing that the geometrical shape slant invariance hypothesis is an inadequate model for depth perception. Some implications for gradient theory, Helmholtzian theories and Gestalt theory are discussed.     

Perceived structure from optic flow: consistent versus variable mapping of 3-D Euclidean structure

In an earlier study (Börjesson & Lind, 1996), the perception of Euclidean structure from polar projected two‐frame apparent motion sequences was studied. The results showed that Euclidean structure is not perceived. However, at larger visual angles a certain consistency in the mapping between distal and perceived structure exists. The aim of the present study was to more precisely examine how this degree of consistency varies as a function of visual angle. In Experiments 1 and 2, slant judgments of simulated and real planes indicated that the degree of consistency is a positive function of visual angle. No definite sign of a Euclidean mapping could, however, be found even in the full view condition. Experiment 3 examined texture gradients and the response method used. The results showed that texture gradients did not influence the degree of consistency of the mapping between distal and judged depth and that the response method was both reliable and valid. However, texture gradients did influence the absolute values of the slant judgments. The role of Euclidean and affine mappings of distal structure is discussed and it is proposed that the perceptually important distinction is not between affine and Euclidean mapping, but rather between two types of affine mappings—consistent and variable.     

Perceiving binocular depth with reference to a common surface

A common surface is a spatial regularity of our terrestrial environment. For instance, we walk on the common ground surface, lay a variety of objects on the table top, and display our favorite paintings on the wall. It has been proposed that the visual system utilizes this regularity as a reference frame for coding objects' distances. Presumably, by treating the common surface as such--i.e. an anticipated constant--the visual system can reduce its coding redundancy, and divert its resources to representing other information. For intermediate-distance space perception, it has been found that absolute distance judgment is most accurate when a common ground surface is available. Here we explored if the common surface also serves as the reference frame for the processing of binocular-disparity information, which is a predominant cue for near-distance space perception. We capitalized on an established observation where the perceived slant of a surface with linear binocular-disparity gradient is underestimated. Clearly, if the visual system utilizes this incorrectly represented slant surface as a reference frame for coding the objects' locations, the perceived depth separation between the objects will be adversely affected. Our results confirm this, by showing that the depth judgment of objects (two laterally separated vertical lines) on, or in the vicinity of, the surface is underestimated. Furthermore, we show that the impact of the common surface on perceived depth separation most likely occurs at the surface-representation level where the visual surface has been explicitly delineated, rather than at the earlier disparity-processing level.     

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.