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.     

An application of the optic sphere theory in discrimination of slant with minimal information

In Johansson and Börjesson (1989), a new theory of visual space perception—the optic sphere theory—was presented in which the hemispheric shape of the retina is utilized for determination of slant of plane surfaces in wide-angle perception. The process of the optic sphere mechanism can be described as the projection of a translating distal line on the optic sphere, and an extrapolation of this projection to a great circle. The determination of the 3-D slant of the distal line is made by identification of points of no change on the great circle during its rotation. The main objective of the present study was to investigate this process as applied to central stimulation of the retina with reduced and minimal information of slant or horizontal orientation. Each stimulus pattern consisted of either two continuous lines or two pairs of dots in motion presented on a computer screen. The pairwise lines and the pairs of dots defined simulated 3-D slants (or horizontal orientations) of different magnitude within each pair, and the subjects' task was to discriminate between these simulated slants. It was shown that the simulations evoke percepts of 3-D slants, and of horizontal orientations, and that it is possible to discriminate between them even from minimal information (pairs of dots). Further, the empirical findings of Börjesson (1994) indicated that longer extrapolations of the projected arc to a point of no change yield less accurate discriminations of slant. We failed to replicate this in Experiment 4, in which case stimulus variables that covaried with extrapolation length were eliminated or minimized. It is suggested that this raises some doubt about discrimination accuracy as dependent on extrapolation length per se. The overall conclusion, however, is that the optic sphere theory represents a possible explanation of, or analogy to, the process utilized by the visual system for determination of the simulated 3-D slants and horizontal orientations in the present study.     

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.     

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.     

坡度知觉及其影响因素的研究进展

人们对于地表斜坡的知觉是非常不准确的,通常表现为对坡度估计过高。但是,研究发现,在以行为的方式对坡度进行模拟时,所模拟的坡度值却与实际坡度基本一致。这种面对同一视觉线索出现的视知觉与行为不一致的现象即为坡度知觉中的“知觉-行为分离”。本文回顾了影响坡度知觉的各种因素,涉及视觉线索、认知判断、感觉通道、生理状态以及报告方式等方面的研究,并对坡度知觉的未来研究进行了展望。     

Change in perceived spatial directions due to context

We examined the influence of context on exocentric pointing. In a virtual three-dimensional set-up, we asked our subjects to aim a pointer toward a target in two conditions. The target and the pointer were visible alone, or they were visible with planes through each of them. The planes consisted of a regular grid of horizontal and vertical lines. The presence of the planes had a significant influence on the indicated direction. These changes in indicated direction depended systematically on the orientation of the planes relative to the subject and on the angle between the planes. When the orientation of the (perpendicular) planes varied from asymmetrical to symmetrical to the frontoparallel plane, the indicated direction varied over a range of 15 degrees--from a slightly larger slant to a smaller slant--as compared with the condition without the contextual planes. When the dihedral angle between the two planes varied from 90 degrees to 40 degrees, the indicated direction varied over a range of less than 5 degrees: A smaller angle led to a slightly larger slant. The standard deviations in the indicated directions (about 3 degrees) did not change systematically. The additional structure provided by the planes did not lead to more consistent pointing. The systematic changes in the indicated direction contradict all theories that assume that the perceived distance between any two given points is independent of whatever else is present in the visual field--that is, they contradict all theories of visual space that assume that its geometry is independent of its contents (e.g., Gilinsky, 1951; Luneburg, 1947; Wagner, 1985).     

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.     

Factors involved in visual capture.

Visual capture was explored using three types of vision-"touch" conflicts. The results indicated that the amount of visual capture differed for the three tasks. In one task (slant judgments) strong, but incomplete, visual capture occurred, in another (a length judgment task) an approximate compromise between the two modalities was found, and in the third task (texture judgments) a trend toward touch capture occurred. In two additional experiments using the slant task, the effects of brief training with one of the competing modalities and the effects of manipulating certain aspects of the stimulus display were explored. The bried training did not alter the resolution of the conflict but varying visual clarity and felt texture of the rod whose slant was being judged did affect visual capture.     

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.     

Texture gradient registration and the development of slant perception.

The processes underlying the development of slant perception were investigated by manipulating the degree of texture element variability. Subjects at four grade levels were required to make judgments of physical slant of surfaces with three levels of variability. Absolute error of judgment decreased with age, but texture variability had no effect at any grade level. The results suggest that there is no improvement in the ability to extract gradient information. Rather, improvement in the consistency of judgment reflects a developmental change in the relationship between stimulus information and judgment.     

Perceptual depth synthesis in the visual system as revealed by selective adaptation

Selective adaptations was used to determine the degree of interactions between channels processing relative depth from stereopsis, motion parallax, and texture. Monocular adaptations with motion parallax or binocular stationary adaptation caused test surfaces, viewed either stationary binocularly or monocularly with motion parallax, to appear to slant in the opposite direction compared with the slant initially adapted to. Monocular adaptations on frontoparallel surfaces covered with a pattern of texture gradients caused a subsequently viewed test surface, viewed either monocularly with motion parallax or stationary binocularly, to appear to slant in the opposite direction as the slant indicated by the texture in the adaptation condition. No aftereffect emerged in the monocular stationary test condition. A mechanism of independent channels for relative depth perception is dismissed in favor of a view of an asymmetrical interactive processing of different information sources. The results suggest asymmetrical inhibitory interactions among habituating slant detector units receiving inputs from static disparity, dynamic disparity, and texture gradients.     

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.     

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.     

On the Affine Structure of Perceptual Space

Affine geometry is a generalization of Euclidean geometry in which distance can be scaled along parallel directions, though relative distances in different directions may be incommensurable. This article presents a new procedure for testing the intrinsic affine structure of a psychological space by having subjects perform bisection judgments over multiple directions. If those judgments are internally consistent with one another, they must satisfy a theorem first proved by Pierre Varignon around 300 years ago. In the experiment reported here, this procedure was employed to measure the perceived structure of a visual ground surface. The results revealed that observers' judgments were systematically distorted relative to the physical environment, but that the judged bisections in different directions had an internally consistent affine structure. Implications of these findings for other possible response tasks are considered.     

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.     

The influence of texture on judgments of slant and relative distance in a picture with suggested depth

Six surfaces from natural environments with different visual textures were photographed at angles of 60, 65, and 70 deg from perpendicular. Measurements were taken of 24 Ss’ judgments of the inferred angles of slant and inferred midpoints of the six textured surfaces represented in the photographs which were viewed in the frontoparallel plane. Judgments of both slant and relative distance within the photographs were influenced by represented angle of slant and by variations in surface texture.     

The effect of texture relief on perception of slant from texture

Texture can be an effective source of information for perception of slant and curvature. A computational assumption required for some texture cues is that texture must be flat along a surface. There are many textures which violate this assumption, and have some sort of texture relief: variations perpendicular to the surface. Some examples include grass, which has vertical elements, or scattered rocks, which are volumetric elements with 3-D shapes. Previous studies of perception of slant from texture have not addressed the case of textures with relief. The experiments reported here test judgments of slant for textures with various types of relief, including textures composed of bumps, columns, and oriented elements. The presence of texture relief was found to affect judgments, indicating that perception of slant from texture is not robust to violations of the flat-texture assumption. For bumps and oriented elements, slant was underestimated relative to matching flat textures, while for columns textures, which had visible flat top faces, perceived slant was equal or greater than for flat textures. The differences can be explained by the way different types of texture relief affect the amount of optical compression in the projected image, which would be consistent with results from previous experiments using cue conflicts in flat textures. These results provide further evidence that compression contributes to perception of slant from texture.     

Planar motion permits perception of metric structure in stereopsis

A fundamental problem in the study of spatial perception concerns whether and how vision might acquire information about the metric structure of surfaces in three-dimensional space from motion and from stereopsis. Theoretical analyses have indicated that stereoscopic perceptions of metric relations in depth require additional information about egocentric viewing distance; and recent experiments by James Todd and his colleagues have indicated that vision acquires only affine but not metric structure from motion—that is, spatial relations ambiguous with regard to scale in depth. The purpose of the present study was to determine whether the metric shape of planar stereoscopic forms might be perceived from congruence under planar rotation. In Experiment 1, observers discriminated between similar planar shapes (ellipses) rotating in a plane with varying slant from the frontal-parallel plane. Experimental conditions varied the presence versus absence of binocular disparities, magnification of the disparity scale, and moving versus stationary patterns. Shape discriminations were accurate in all conditions with moving patterns and were near chance in conditions with stationary patterns; neither the presence nor the magnification of binocular disparities had any reliable effect. In Experiment 2, accuracy decreased as the range of rotation decreased from 80° to 10°. In Experiment 3, small deviations from planarity of the motion produced large decrements in accuracy. In contrast with the critical role of motion in shape discrimination, motion hindered discriminations of the binocular disparity scale in Experiment 4. In general, planar motion provides an intrinsic metric scale that is independent of slant in depth and of the scale of binocular disparities. Vision is sensitive to this intrinsic optical metric.     

Analogical Mapping by Constraint Satisfaction

A theory of analogical mapping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of isomorphism encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality favors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the analogy is being used. The theory is implemented in a computer program called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A cooperative algorithm for parallel constraint satisfaction identities mapping hypotheses that collectively represent the overall mapping that best fits the interacting constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and pragmatic information if it is available, and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory is able to account for empirical findings regarding the impact of consistency and similarity on human processing of analogies.     

Peak velocity as a cue in audiovisual synchrony perception of rhythmic stimuli

This study investigated audiovisual synchrony perception in a rhythmic context, where the sound was not consequent upon the observed movement. Participants judged synchrony between a bouncing point-light figure and an auditory rhythm in two experiments. Two questions were of interest: (1) whether the reference in the visual movement, with which the auditory beat should coincide, relies on a position or a velocity cue; (2) whether the figure form and motion profile affect synchrony perception. Experiment 1 required synchrony judgment with regard to the same (lowest) position of the movement in four visual conditions: two figure forms (human or non-human) combined with two motion profiles (human or ball trajectory). Whereas figure form did not affect synchrony perception, the point of subjective simultaneity differed between the two motions, suggesting that participants adopted the peak velocity in each downward trajectory as their visual reference. Experiment 2 further demonstrated that, when judgment was required with regard to the highest position, the maximal synchrony response was considerably low for ball motion, which lacked a peak velocity in the upward trajectory. The finding of peak velocity as a cue parallels results of visuomotor synchronization tasks employing biological stimuli, suggesting that synchrony judgment with rhythmic motions relies on the perceived visual beat.