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.     

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.     

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.     

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.     

Factors influencing perceived angular velocity.

The assumption that humans are able to perceive and process angular kinematics is critical to many structure-from-motion and optical flow models. The current studies investigate this sensitivity, and examine several factors likely to influence angular velocity perception. In particular, three factors are considered: (1) the extent to which perceived angular velocity is determined by edge transitions of surface elements, (2) the extent to which angular velocity estimates are influenced by instantaneous linear velocities of surface elements, and (3) whether element-velocity effects are related to three-dimensional (3-D) tangential velocities or to two-dimensional (2-D) image velocities. Edge-transition rate biased angular velocity estimates only when edges were highly salient. Element velocities influenced perceived angular velocity; this bias was related to 2-D image velocity rather than 3-D tangential velocity. Despite these biases, however, judgments were most strongly determined by the true angular velocity. Sensitivity to this higher order motion parameter was surprisingly good, for rotations both in depth (y-axis) and parallel to the line of sight (z-axis).     

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.     

Factors influencing perceived angular velocity

The assumption that humans are able to perceive and process-angular kinematics is critical to many structure-from-motion and optical flow models. The current studies investigate this sensitivity, and examine several factors likely to influence angular velocity perception. In particular, three factors are considered: (1) the extent to which perceived angular velocity is determined by edge transitions of surface elements, (2) the extent to which angular velocity estimates are influenced by instantaneous linear velocities of surface elements, and (3) whether element-velocity effects are related to three-dimensional (3-D) tangential velocities or to two-dimensional (2-D) image velocities. Edge-transition rate biased angular velocity estimates only when edges were highly salient. Element velocities influenced perceived angular velocity; this bias was related to 2-D image velocity rather than 3-D tangential velocity. Despite these biases, however, judgments were most strongly determined by the true angular velocity. Sensitivity to this higher order motion parameter was surprisingly good, for rotations both in depth (y-axis) and parallel to the line of sight (z-axis).     

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.     

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.     

Perspective based on stereopsis and occlusion

Perspective is usually considered a monocular pictorial cue, distinct from other cues such as occlusion and stereopsis. We cut across these distinctions by asking whether purely binocular (cyclopean) contours, created by stereoscopically shifting a region of homogeneous texture nearer or further than its surround, can act as a linear-perspective cue and whether the contours' ability to do this is influenced by their surface belongingness. We found that the left/right orientation of cyclopean trapezoids nearer than a surround strongly influenced perceived slant, showing that perspective constraints are applied to stereoscopically derived contours. Further regions, however, appeared as surfaces seen through a trapezoidal aperture. Because the aperture "owned" the trapezoidal contours, their orientation had little effect on perceived slant. We conclude that the application of perspective constraints depends critically on how contours are classified by stereo-specified occlusion relationships among surfaces and that perspective, stereopsis, and occlusion are not distinct processing systems.     

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.     

Discriminating constant from variable angular velocities in structure from motion

We investigated accuracy in discriminating between constant and variable angular velocities for orthographic projections of three-dimensional rotating objects. The reported judgments of “constant” or “variable” angular velocity were only slightly influenced by the projected angular velocities, but they were greatly affected by the variations of the deformation, a first-order component of the optic flow. When viewing either a rotating ellipsoidal volume or a planar surface that accelerated and decelerated over the course of rotation, observers’ tendencies to report a variable angular velocity were increased when the temporal phase of the acceleration pattern increased the range of variation of the median deformation; the tendencies were decreased when the same acceleration pattern was used to decrease the range of variation of the median deformation. These results provide evidence contrary to the hypothesis that the visual system performs a mathematically correct analysis of the optic flow.     

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.     

Shape constancy and slant perception at birth

Two experiments are described the object of which was to investigate whether perception of shape at birth is determined solely by proximal (retinal) stimulation, or whether newborn babies have the ability to perceive objective, real shape across changes in slant. In experiment 1 looking at (ie preference for) one stimulus, a square, when paired with either of two trapeziums, was found to change in a consistent manner with changes in slant, indicating that these changes in stimulation are detected and can cause considerable changes in looking behaviour. In experiment 2 newborns were desensitized to changes in slant during familiarization trials, and subsequently strongly preferred a different shape to the familiarized shape in a new orientation. This suggests that the real shape had been perceived as invariant across the retinal changes caused by the changes in slant, and further suggests that shape constancy is an organizing feature of perception which is present at birth.     

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.     

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.     

Understanding collision dynamics

In two experiments we investigated people's ability to judge the relative mass of two objects involved in a collision. It was found that judgments of relative mass were made on the basis of two heuristics. Roughly stated, these heuristics were (a) an object that ricochets backward upon impact is less massive than the object that it hit, and (b) faster moving objects are less massive. A heuristic model of judgment is proposed that postulates that different sources of information in any event may have different levels of salience for observers and that heuristic access is controlled by the rank ordering of salience. It was found that observers ranked dissimilarity in mass on the basis of the relative salience of angle and velocity information and not proportionally to the distal mass ratio. This heuristic model was contrasted with the notion that people can veridically extract dynamic properties of motion events when the kinematic data are sufficient for their specification.     

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.     

Aging and the perception of local surface orientation from optical patterns of shading and specular highlights

Younger and older observers' ability to perceive local surface orientation from optical patterns of shading and specular highlights was investigated in two experiments. On each trial, the observers viewed a randomly generated, smoothly curved 3-D object and manipulated an adjustable gauge figure until its orientation matched that of a specific local region on the object's surface (cf. Koenderink, van Doom, & Kappers, 1992). The performance of both age groups was facilitated by the presence of binocular disparity (Experiment 1) and object rotation in depth (Experiment 2). Observers in both age groups were able to judge the surface tilt component of orientation more precisely than the slant component. Significant, but modest, effects of age were found in Experiment 1, but not in Experiment 2. The ability to perceive local surface orientation appears to be relatively well preserved with increasing age, at least through the age of 80.