Perceiving surface slant from deformation of optic flow

Perceived surface orientation and angular velocity were investigated for orthographic projections of 3-D rotating random-dot planes. It was found that (a) tilt was accurately perceived and (b) slant and angular velocity were systematically misperceived. It was hypothesized that these misperceptions are the product of a heuristic analysis based on the deformation, one of the differential invariants of the first-order optic flow. According to this heuristic, surface attitude and angular velocity are recovered by determining the magnitudes of these parameters that most likely produce the deformation of the velocity field, under the assumption that all slant and angular velocity magnitudes have the same a priori probability. The results of the present investigation support this hypothesis. Residual orientation anisotropies not accounted for by the proposed heuristic were also found.     

Perceiving geographical slant

People judged the inclination of hills viewed either out-of-doors or in a computer-simulated virtual environment. Angle judgments were obtained by having people (1) provide verbal estimates, (2) adjust a representation of the hill’s cross-section, and (3) adjust a tilt board with their unseen hand. Geographical slant was greatly overestimated according to the first two measures, but not the third. Apparent slant judgments conformed to ratio scales, thereby enhancing sensitivity to the small inclines that must actually be traversed in everyday experience. It is proposed that the perceived exaggeration of geographical slant preserves the relationship between distal inclination and people’s behavioral potential. Hills are harder to traverse as people become tired; hence, apparent slant increased with fatigue. Visually guided actions must be accommodated to the actual distal properties of the environment; consequently, the tilt board adjustments did not reflect apparent slant overestimations, nor were they influenced by fatigue. Consistent with the fact that steep hills are more difficult to descend than to ascend, these hills appeared steeper when viewed from the top.     

Perceived motion in structure from motion: Pointing responses to the axis of rotation

We investigated the ability to match finger orientation to the direction of the axis of rotation in structure-from-motion displays. Preliminary experiments verified that subjects could accurately use the index finger to report direction. The remainder of the experiments studied the perception of the axis of rotation from full rotations of a group of discrete points, the profiles of a rotating ellipsoid, and two views of a group of discrete points. Subjects’ responses were analyzed by decomposing the pointing responses into their slant and tilt components. Overall, the results indicated that subjects were sensitive to both slant and tilt. However, when the axis of rotation was near the viewing direction, subjects had difficulty reporting tilt with profiles and two views and showed a large bias in their slant judgments with two views and full rotations. These results are not entirely consistent with theoretical predictions. The results, particularly for two views, suggest that additional constraints are used by humans in the recovery of structure from motion.     

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.     

Apparent extended body motions in depth.

Five experiments were designed to investigate the influence of three-dimensional (3-D) orientation change on apparent motion. Projections of an orientation-specific 3-D object were sequentially flashed in different locations and at different orientations. Such an occurrence could be resolved by perceiving a rotational motion in depth around an axis external to the object. Consistent with this proposal, it was found that observers perceived curved paths in depth. Although the magnitude of perceived trajectory curvature often fell short of that required for rotational motions in depth (3-D circularity), judgments of the slant of the virtual plane on which apparent motions occurred were quite close to the predictions of a model that proposes circular paths in depth.     

The role of balance dynamics in the active perception of orientation.

The Stoffregen and Riccio (1988) hypothesis that perceived orientation is determined primarily by balance dynamics was tested. Perception of orientation was evaluated in the context of a task that required Ss to control the roll orientation of a device in which they were seated. The device's direction of balance was manipulated across trials and thus was independent of gravity. Eighteen Ss participated in the investigation. After each trial, Ss estimated their mean tilt with respect to upright. Correlations of perceived tilt with tilt from balance were consistently higher than the correlations with gravity tilt. The dominance of balance over gravity depended on the magnitude of tilt from balance.     

Perceived range, perceived velocity, and perceived duration of the body rotating in the frontal plane

We investigated perceived range, perceived velocity, and perceived duration of the body rotating in the frontal plane (in roll). Specifically, to examine how shear to the otoliths in the inner ears and tactile pressure to the trunk affect judgments of range and velocity, in two experiments, we manipulated rotating range (30°–160°), rotating velocity (1.8°/sec to 9.6°/sec), mean tilt of the body (?60°, 0°, and 60°), and exposure to the visual vertical. Thirty-three normal or blindfolded participants made verbal judgments of range, velocity, and duration for each combination of these factors. The exponents of the power functions fitted to these judgments were, as a first approximation, .94, .61, and .84 for range, velocity, and duration, respectively, and perceived velocity was proportional to the ratio of perceived range to perceived duration (r = .91). These results suggest that the vestibular and somatosensory inputs are effective on judgments of range, but less so on judgments of velocity, and that perceived velocity may be determined as a ratio of perceived range to perceived duration. In addition, we found that (1) when the range the body has traveled is constant, the perceived range increases as the objective velocity decreases (proprioceptive τ effect); (2) self-motion through the tilted roll sometimes enlarges perceived range and perceived duration but reduces perceived velocity; and (3) the exposure to the visual vertical reduces variability of judgments for range and velocity and also reduces perceived range and perceived velocity of self-motion within a small range through the vertical roll.     

Surface tilt (the direction of slant): A neglected psychophysical variable

Surface slant (the angle between the line of sight and the surface normal) is an important psychophysical variable. However, slant angle captures only one of the two degrees of freedom of surface orientation, the other being thedirection of slant. Slant direction, measured in the image plane, coincides with the direction of the gradient of distance from viewer to surface and, equivalently, with the direction the surface normal would point if projected onto the image plane. Since slant direction may be quantified by the tilt of the projected normal (which ranges over 360 deg in the frontal plane), it is referred to here assurface tilt. (Note that slant angle is measured perpendicular to the image plane, whereas tilt angle is measured in the image plane.) Compared with slant angle’s popularity as a psychophysical variable, the attention paid to surface tilt seems undeservedly scant. Experiments that demonstrate a technique for measuring apparent surface tilt are reported. The experimental stimuli were oblique crosses and parallelograms, which suggest oriented planes in 3-D. The apparent tilt of the plane might be probed by orienting a needle in 3-D so as to appear normal, projecting the normal onto the image plane, and measuring its direction (e.g., relative to the horizontal). It is shown to be preferable, however, to merely rotate a line segment in 2-D, superimposed on the display, until it appears normal to the perceived surface. The apparent surface tilt recorded in these experiments corresponded closely to that predicted by assuming the 3-D configurations consist of equal-length lines and perpendicular intersections.     

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.     

Distortions of depth-order relations and parallelism in structure from motion

Four experiments related human perception of depth-order relations in structure-from-motion dis-plays to current Euclidean and affine theories of depth recovery from motion. Discrimination between parallel and nonparallel lines and relative-depth judgments was observed for orthographic projections of rigidly oscillating random-dot surfaces. We found that (1) depth-order relations were perceived veridically for surfaces with the same slant magnitudes, but were systematically biased for surfaces with different slant magnitudes. (2) Parallel (virtual) lines defined by probe dots on surfaces with different slant magnitudes were judged to be nonparallel. (3) Relative-depth judgments were internally inconsistent for probe dots on surfaces with different slant magnitudes. It is argued that both veridical performance and systematic misperceptions may be accounted for by a heuristic analysis of the first-order optic flow.     

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.     

Apparent body tilt and postural aftereffect

Apparent orientation of the body tilted laterally in the frontal plane was studied with the methods of absolute judgments in four experiments. In Experiment 1, 17 subjects, who maintained the normal adaptation of body to gravity, estimated their body tilts under the condition of seeing the gravitational vertical and under the condition of eliminating it. The results showed that (1) there was not a significant difference between the two conditions and (2) the small tilts of less than 45° were exactly estimated, whereas the large tilts of 45°–108° were overestimated. In Experiment 2,10 subjects estimated their body tilts under three velocities of a rotating chair on which each subject was placed. Although both body tilt and chair velocity were found to influence tilt estimation, the effect of body tilt was overwhelmingly greater than that of chair velocity. In Experiment 3, 11 subjects adapted their bodies to a 72° left tilt for 10 min and then estimated various body tilts around the adapting tilt. The estimations obtained under the 72° adaptation were lower than those obtained under the 0° adaptation, and this reduction was greater for the test tilt that was farther away from the adapting tilt. In Experiment 4, 11 subjects adjusted their own body tilts to designated angles. The results confirmed the outcomes of absolute estimation in Experiments 1-3. From these findings and past literature, the judgments of body tilt were considered to be subserved by a single sensory process that was based on the cutaneous and muscular proprioceptors, rather than the vestibular and joint proprioceptors.     

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.     

Perceiving shape from profiles

Four experiments related human perception of shape from profiles to current theoretical predictions. In Experiment 1, judgments of structure and motion were obtained for single- and dualellipsoid displays rotating about various axes. Ratings were highest when the axis of rotation was in the image plane and were influenced by the number of ellipsoids and the orientation of a single ellipsoid. The subsequent experiments explored the effect of orientation on shape judgments of a single ellipsoid. The results of Experiments 2 and 3 suggested that the effect of orientation found in Experiment 1 was not due to either the inability of certain orientations to be perceived as three-dimensional objects or to two-dimensional artifacts. It was thus argued that this effect of orientation was due to points of correspondence in relative motion that arise when the major axis is not perpendicular to the axis of rotation. In Experiment 4, subjects provided judgments of both shape and angular velocity. The elevated ellipsoids that were judged as larger were also judged as rotating more slowly. The inverse relationship between size and angular velocity is consistent with current theories. The connection between theory and data was further demonstrated by applying a shape-recovery algorithm to the stimuli used in Experiment 4 and finding a similar tradeoff between angular velocity and shape.     

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.     

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.     

Effect of prolonged tilt on visual orientation

Visual orientation during lateral tilt is viewed in terms of orientation constancy. The postural systems involved in the maintenance of constancy are considered to be those of the otolith, neck and trunk. The relative contribution of these systems was investigated by obtaining visual verticality judgments immediately upon and several minutes after head, body, and trunk tilts. Due to the apparent non-adaptation of the otolith system any changes in visual orientation resulting from prolonged tilt would be attributed to adaptation of the proprioceptive system stimulated. For 30° head tilt visual orientation over-constancy was reduced by about 2°, reflecting the influence of the neck system. Prolonged body tilts of 30°, 60° and 90° reduced the constancy operating by approximately 1°, 3° and 8°, respectively. This was taken to indicate the contribution of the trunk system, which increased with increasing degrees of body tilt. The above interpretations received strong support from experiments involving trunk tilt, which stimulates only the neck and trunk systems.     

THE PERCEPTION OF A VISUAL SHAPE AND OF ITS FRAME-SURFACE DURING CONTINUOUS TRANSFORMATION

The procedure differed from that of traditional shape constancy experiments in that cues for the slant of the total frame-surface containing the main figure, a shadow rectangle, were given. The impression of slant was determined by gradients of continuous perspective transformations caused by movable elastic material casting its shadow on a translucent screen. The following hypothesis was confirmed: the tendency to see a shape in its original proportions (i.e., those it has when shown in a frontal-parallel orientation) increases with the increasingly strong impression of the slant of its plane surface.     

The effect of pattern and texture gradient on slant and shape judgments

The experiment reported was designed to explore the relationship between gradient of texture and monocular slantshape perception. The effects of instructional set and order of slant and shape judgments were studied in interaction with four patterns differing in regularity of texture. Judgments of slant and shape were made by the same Ss for all patterns at 20°, 45°, 60°slant for slant judgments and 0°, 20°, 45°, 60° for width judgments. There were three instructional groups. Within each group one half of the Ss made slant judgments first, the other half shape judgments first. For all patterns, accurate perception of the slant of patterned material resulted in increased compensation in width judgments. Apparent width was found to be a function of pattern and also subject to instructional manipulation.     

Visual orientation during and after lateral head,body, and trunk tilt

Visual judgments of orientation were investigated during (effect) and after (aftereffect) different body postures. In Experiment 1 four trained Ss made apparent verticality (AV) judgments before and after 2 min in each of seven orientations: head tilt left and right, body tilt left and right, trunk tilt left and right and a control condition with head ’and body upright. The aftereffect was significant for all postures excepting trunk tilt left and the control. The aftereffect from head tilt was greater than that from the same degree of body tilt, and that in the trunk tilt condition was in the same direction as’ predicted from neck stimulation. In Experiment 2, 30 Ss made AV judgments during tilt in the same seven postures. The E-phenomenon resulted from both head and body tilts, and an effect was found for trunk tilt in the direction predicted from neck stimulation. The results are discussed in terms of the otolith, neck, and trunk receptor systems.