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.     

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.     

Static and dynamic factors in the perception of rotary motion

Direction of rotation and static slant judgments were collected for a series of outline plane forms in four experiments with 106 subjects. Direction was judged more accurately for forms displaying the same perspective gradients as trapezoids, but with right-angled contours, than for trapezoids. There were no consistent differences among these forms in judged slant. Direction of rotation judgments were affected by a static false interposition cue, with interposition increasing the proportion of veridical judgments when placed in conflict with a relative size gradient and decreasing this proportion when a size gradient was absent. Both a dynamic factor (contour angle change) and a static factor (misperceived relative distance of the vertical sides) were found to affect perceived direction of rotation, with direction judgments based primarily on the dynamic factor.     

The framing effect with rectangular and trapezoidal surfaces: actual and pictorial surface slant, frame orientation, and viewing condition

The perceived slant of a surface relative to the frontal plane can be reduced when the surface is viewed through a frame between the observer and the surface. Aspects of this framing effect were investigated in three experiments in which observers judged the orientations-in-depth of rectangular and trapezoidal surfaces which were matched for pictorial depth. In experiments 1 and 2, viewing was stationary-monocular. In experiment 1, a frontal rectangular frame was present or absent during viewing. The perceived slants of the surfaces were reduced in the presence of the frame; the reduction for the trapezoidal surface was greater, suggesting that conflict in stimulus information contributes to the phenomenon. In experiment 2, the rectangular frame was either frontal or slanted; in a third condition, a frame was trapezoidal and frontal. The conditions all elicited similar results, suggesting that the framing effect is not explained by pictorial perception of the display, or by assimilation of the surface orientation to the frame orientation. In experiment 3, viewing was moving-monocular to introduce motion parallax; the framing effect was reduced, being appreciable only for a trapezoidal surface. The results are related to other phenomena in which depth perception of points in space tends towards a frontal plane; this frontal-plane tendency is attributed to heavy experimental demands, mainly concerning impoverished, conflicting, and distracting information.     

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.     

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.     

Grounding the figure: Surface attachment influences figure-ground organization

We investigated whether the lower region effect on figure-ground organization (Vecera, Vogel, & Woodman, 2002) would generalize to contextual depth planes in vertical orientations, as is predicted by a theoretical analysis based on the ecological statistics of edges arising from objects that are attached to surfaces of support. Observers viewed left/right ambiguous figure-ground displays that occluded middle sections of four types of contextual inducers: two types of attached, receding, vertical planes (walls) that used linear perspective and/or texture gradients to induce perceived depth and two types of similar trapezoidal control figures that used either uniform color or random texture to reduce or eliminate perceived depth. The results showed a reliable bias toward seeing as “figure” the side of the figure-ground display that was attached to the receding depth plane, but no such bias for the corresponding side in either of the control conditions. The results are interpreted as being consistent with the attachment hypothesis that the lower region cue to figure-ground organization results from ecological biases in edge interpretation that arise when objects are attached to supporting surfaces in the terrestrial gravitational field.     

Cueing the interpretation of a Necker Cube: a way to inspect fundamental cognitive processes

The term perceptual bistability refers to all those conditions in which an observer looks at an ambiguous stimulus that can have two or more distinct but equally reliable interpretations. In this work, we investigate perception of Necker Cube in which bistability consists of the possibility to interpret the cube depth in two different ways. We manipulated the cube ambiguity by darkening one of the cube faces (cue) to provide a clear cube interpretation due to the occlusion depth index. When the position of the cue is stationary the cube perceived perspective is steady and driven by the cue position. However, when we alternated in time the cue position (i.e. we changed the position of the darkened cube face) two different perceptual phenomena occurred: for low frequencies the cube perspective alternated in line with the position of the cue; however for high frequencies the cue was no longer able to bias the perception but it appears as a floating feature traveling across the solid with the cube whole perspective that returns to be bistable as in the conventional, bias-free, case.     

Cueing the interpretation of a Necker Cube: a way to inspect fundamental cognitive processes

The term perceptual bistability refers to all those conditions in which an observer looks at an ambiguous stimulus that can have two or more distinct but equally reliable interpretations. In this work, we investigate perception of Necker Cube in which bistability consists of the possibility to interpret the cube depth in two different ways. We manipulated the cube ambiguity by darkening one of the cube faces (cue) to provide a clear cube interpretation due to the occlusion depth index. When the position of the cue is stationary the cube perceived perspective is steady and driven by the cue position. However, when we alternated in time the cue position (i.e. we changed the position of the darkened cube face) two different perceptual phenomena occurred: for low frequencies the cube perspective alternated in line with the position of the cue; however for high frequencies the cue was no longer able to bias the perception but it appears as a floating feature traveling across the solid with the cube whole perspective that returns to be bistable as in the conventional, bias-free, case.     

When texture takes precedence over motion in depth perception

Both texture and motion can be strong cues to depth, and estimating slant from texture cues can be considered analogous to calculating slant from motion parallax (Malik and Rosenholtz 1994, report UCB/CSD 93/775, University of California, Berkeley, CA). A series of experiments was conducted to determine the relative weight of texture and motion cues in the perception of planar-surface slant when both texture and motion convey similar information. Stimuli were monocularly viewed images of planar surfaces slanted in depth, defined by texture and motion information that could be varied independently. Slant discrimination biases and thresholds were measured by a method of single-stimuli binary-choice procedure. When the motion and texture cues depicted surfaces of identical slants, it was found that the depth-from-motion information neither reduced slant discrimination thresholds, nor altered slant discrimination bias, compared to texture cues presented alone. When there was a difference in the slant depicted by motion and by texture, perceived slant was determined almost entirely by the texture cue. The regularity of the texture pattern did not affect this weighting. Results are discussed in terms of models of cue combination and previous results with different types of texture and motion information.     

Perception of local orientation from shaded images

The perception of local orientation from shaded images was examined. In Experiment 1, subjects viewed a boundaryless Gaussian hill and judged local orientation using both a gauge figure and a pointing method. One subject reported an internally consistent surface which was incompatible with the judged light-source direction and model used to generate the image. The remaining subjects reported a surface similar to the generating one, and analysis of their results indicated a contour of zero difference between response and generating slants. This contour of zero slant difference was explored in three subsequent experiments using the pointing technique. These experiments investigated possible influences of luminance artifact (Experiment 2), perception of global orientation (Experiment 3), and self-occluding contours (Experiment 4). All three of these experiments yielded results similar to those of Experiment 1, with distinct contours of zero slant difference. This contour was explored for relationships with the simulated slant of the generating surface and the differential structure of image intensity. This analysis indicated that the contour of zero slant difference was approximately a line of constant slant which shared large regions of adjacency to the zero crossings of the second directional derivative of image intensity.     

Ordinal structure in the visual perception and cognition of smoothly curved surfaces

In theoretical analyses of visual form perception, it is often assumed that the 3-dimensional structures of smoothly curved surfaces are perceptually represented as point-by-point mappings of metric depth and/or orientation relative to the observer. This article describes an alternative theory in which it is argued that our visual knowledge of smoothly curved surfaces can also be defined in terms of local, nonmetric order relations. A fundamental prediction of this analysis is that relative depth judgments between any two surface regions should be dramatically influenced by monotonicity of depth change (or lack of it) along the intervening portions of the surface through which they are separated. This prediction is confirmed in a series of experiments using surfaces depicted with either shading or texture. Additional experiments are reported, moreover, that demonstrate that smooth occlusion contours are a primary source of information about the ordinal structure of a surface and that the depth extrema in between contours can be optically specified by differences in luminance at the points of occlusion.     

Integrating multiple cues to depth order at object boundaries

We examined the interaction between motion and stereo cues to depth order along object boundaries. Relative depth was conveyed by a change in the speed of image motion across a boundary (motion parallax), the disappearance of features on a surface moving behind an occluding object (motion occlusion), or a difference in the stereo disparity of adjacent surfaces. We compared the perceived depth orders for different combinations of cues, incorporating conditions with conflicting depth orders and conditions with varying reliability of the individual cues. We observed large differences in performance between subjects, ranging from those whose depth order judgments were driven largely by the stereo disparity cues to those whose judgments were dominated by motion occlusion. The relative strength of these cues influenced individual subjects' behavior in conditions of cue conflict and reduced reliability.     

Shifts of spatial attention in perceived 3-D space.

Previous studies have shown that spatial attention can shift in three-dimensional (3-D) space determined by binocular disparity. Using Posner's precueing paradigm, the current work examined whether attentional selection occurs in perceived 3-D space defined by occlusion. Experiment 1 showed that shifts of spatial attention induced by central cues between two surfaces in the left and right visual fields did not differ between the conditions when the two surfaces were located at the same or different perceptual depth. In contrast, Experiment 2 found that peripheral cues generated a stronger cue validity effect when the two surfaces were perceived at a different rather than at the same perceptual depth. The results suggest that exogenous but not endogenous attention operates in perceived 3-D space.     

Effects of partial occlusion on perceived surface segregation

Tests are reported of the possibility that local information from contour junctions and from corners of intersecting surfaces is used for perceived surface segregation. Stimuli were two intersecting squares with small disks occluding different parts of the squares. The perceived segregation of the squares from one another decreased as the amount of occlusion of parts of the squares increased. This segregation was less when disks occluded parts of contours than when disks occluded parts entirely inside the squares. Occlusion of parts of contours reduced segregation independently of whether contour junctions or corners were visible or invisible, both where the intersecting surfaces were transparent squares and when they were outlined squares. The present findings show that local information from contour junctions or from corners is not used for surface segregation, and confirm that this segregation is determined by global processes of grouping of areas and of extrapolation of contours.     

Perceived depth inversion of smoothly curved surfaces due to image orientation

A relative depth judgement task was used to distinguish perceived reversals in depth due to image orientation from spontaneous reversals such as those observed with a Necker cube. Results demonstrate that inversion effects due to image orientation can occur for several different types of pictorial representation and that many of these effects are incompatible with traditional explanations involving a perceptual bias for overhead illumination. When this bias was neutralized by placing the light source at the point of observation, the effects of image orientation were just as large as with overhead illumination. Similar results were also obtained for surfaces depicted with texture or motion in which all relevant shading information was eliminated. These results can be explained by a perceptual bias for backward slanting surfaces, but additional evidence suggests that this bias can be attenuated by the presence of smooth occlusion contours.     

Measurement and modelling of perceived slant in surfaces represented by freely viewed line drawings

Simple pictures under everyday viewing conditions evoke impressions of surfaces oriented in depth. These impressions have been studied by measuring the slants of perceived surfaces, with probes (rotating arrowheads) designed to respect the distinctive character of depicted scenes. Converging arguments indicated that the perceived orientation of the probes was near theoretical values. A series of experiments showed that subjects formed well-defined impressions of depicted surface orientation. The literature suggests that perceived objects might be 'flattened', but that was not the general rule. Instead, both mean slant and uncertainty fitted models in which slant estimates are derived in a relatively straightforward way from local relations in the picture. Simplifying pictures tended to make orientation estimates less certain, particularly away from the natural anchor points (vertical and horizontal). The shape of the object affected all aspects of the observed-object/percept relationship. Individual differences were large, and suggest that different individuals used different relationships as a basis for their estimates. Overall, data suggest that everyday picture perception is strongly selective and weakly integrative. In particular, depicted slant is estimated by finding a picture feature which will be strongly related to it if the object contains a particular regularity, not by additive integration of evidence from multiple directly and indirectly relevant sources.     

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.     

Visual inertia of rotating 3-D objects

Five experiments were designed to determine whether a rotating, transparent 3-D cloud of dots (simulated sphere) could influence the perceived direction of rotation of a subsequent sphere. Experiment 1 established conditions under which the direction of rotation of a virtual sphere was perceived unambiguously. When a near-far luminance difference and perspective depth cues were present, observers consistently saw the sphere rotate in the intended direction. In Experiment 2, a near-far luminance difference was used to create an unambiguous rotation sequence that was followed by a directionally ambiguous rotation sequence that lacked both the near-far luminance cue and the perspective cue. Observers consistently saw the second sequence as rotating in the same direction as the first, indicating the presence of 3-D visual inertia. Experiment 3 showed that 3-D visual inertia was sufficiently powerful to bias the perceived direction of a rotation sequence made unambiguous by a near-far luminance cue. Experiment 5 showed that 3-D visual inertia could be obtained using an occlusion depth cue to create an unambiguous inertia-inducing sequence. Finally, Experiments 2, 4, and 5 all revealed a fast-decay phase of inertia that lasted for approximately 800 msec, followed by an asymptotic phase that lasted for periods as long as 1,600 msec. The implications of these findings are examined with respect to motion mechanisms of 3-D visual inertia.     

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.