Effects of context on a visual 3-D pointing task

We examined the effects of egocentric and contextual references on a 3-D exocentric pointing task. Large systematic deviations were found for the slant (angle in the horizontal plane). For most observers, the deviations were smaller when the veridical pointing direction was parallel to a wall. For some observers the size of the deviations was also dependent on whether the veridical pointing direction was frontoparallel or not. For the tilt (angle in the vertical plane), the deviations were smaller and less systematic. Hence, although observers show comparable systematic deviations, the way in which the presence of structure in an environment is used for judging positions of objects is observer-dependent.     

Extraction of relief from visual motion

We quantified the ability of human subjects to discriminate the relative distance of two points from a slanted plane when viewing the projected velocities of this scene (orthographic projection). The relative distance from a plane (called relief) is a 3-D property that is invariant under linear (affine) transformations. As such, relief canin principle be extracted from the instantaneous projected velocity field; a metric representation, which requires the extraction of visual acceleration, is not required. The stimulus consisted of a slanted planeP (specified by three points) and two pointsQ ₁ andQ ₂ that are non-coplanar withP. This configuration of points oscillated rigidly around the vertical axis. We have measured thesystematic error andaccuracy with which human subjects estimate the relative distance of pointsQ ₁ andQ ₂ from planeP as a function of the slant of_P. The systematic error varies with slant: it is low for small slant values, reaches a maximum for medium slant values, and drops again for high slant values. The accuracy covaries with the systematic error and is thus high for small and large slant values and low for medium slant values. These results are successfully modeled by a simple relief-from-motion computation based on local estimates of projected velocities. The data are well predicted by assuming (1) a measurement error in velocity estimation that varies proportionally to velocity (Weber’s law) and (2) an eccentricity-dependent underestimation of velocity.     

Three gradients and the perception of flat and curved surfaces

Researchers of visual perception have long been interested in the perceived slant of a surface and in the gradients that purportedly specify it. Slant is the angle between the line of sight and the tangent to the planar surface at any point, also called the surface normal. Gradients are the sources of information that grade, or change, with visual angle as one looks from one's feet upward to the horizon. The present article explores three gradients--perspective, compression, and density--and the phenomenal impression of flat and curved surfaces. The perspective gradient is measured at right angles to the axis of tilt at any point in the optic array; that is, when looking down a hallway at the tiles of a floor receding in the distance, perspective is measured by the x-axis width of each tile projected on the image plane orthogonal to the line of sight. The compression gradient is the ratio of y/x axis measures on the projected plane. The density gradient is measured by the number of tiles per unit solid visual angle. For flat surfaces and many others, perspective and compression gradients decrease with distance, and the density gradient increases. We discuss the manner in which these gradients change for various types of surfaces. Each gradient is founded on a different assumption about textures on the surfaces around us. In Experiment 1, viewers assessed the three-dimensional character of projections of flat and curved surfaces receding in the distance. They made pairwise judgments of preference and of dissimilarity among eight stimuli in each of four sets. The presence of each gradient was manipulated orthogonally such that each stimulus had zero, one, two, or three gradients appropriate for either a flat surface or a curved surface. Judgments were made were made for surfaces with both regularly shaped and irregularly shaped textures scattered on them. All viewer assessment were then scaled in one dimension. Multiple correlation and regression on the scale values revealed that greater than 98% of the variance in scale values was accounted for by the gradients. For the flat surfaces a mean of 65% of the variance was accounted for by the perspective gradient, 28% by the density gradient, and 6% by the compression gradient. For curved surfaces, on the other hand, a mean of 96% of the variance was accounted for by the compression gradient, and less than 2% by either the perspective gradient or the density gradient.(ABSTRACT TRUNCATED AT 400 WORDS)     

2-D tilt and 3-D slant illusions in perception and action tasks

There is now a well established dissociation between perception and action based primarily on neuropsychological evidence [Milner and Goodale, 1995 The Visual Brain in Action (Oxford: Oxford University Press)]. Although equivocal, an important source of evidence from normal observers is that 'perceptual illusions' may affect the systems differently. We investigated the relative effects of 2-D tilt and 3-D slant illusions in the two domains, using similar tasks to those employed originally by Milner and Goodale. Subjects were required to either post a card through, or set a paddle to match the orientation of, a plane that was presented in two conditions: surrounded by a striped surface tilted between +90 degrees and -90 degrees (2-D tilt contrast), or surrounded by a disparity defined surface slanted in depth between +60 degrees and -60 degrees (3-D depth contrast). For 2-D tilt, action and perception were equally affected by the illusion, whereas in the 3-D condition they were not. Here, the illusion appeared greater in the posting than in the perceptual task. We conclude that, although no qualitative differences exist, there were quantitative differences between perception and action tasks in the binocular condition.     

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.     

Perceptual slant induced through optical contact

Stimuli simulating a corridor with a pole inside it were presented. The positions of the ends of the pole within the ceiling and ground of the corridor were the optical contacts of concern. The main hypothesis was that a difference between the simulated distances of these optical contacts may influence the apparent slant in depth of the pole. Two experiments were conducted, with 30 and 20 participants (university students). The tasks were a choice between three alternative responses (upward, downward, or no apparent slant) in the first experiment and matching by adjustment in the second. The results supported the hypothesized dependence of apparent slant on differences in optical contacts. The results also revealed a dependence of apparent slant on the interaction between the optical tilt of the pole and its position to the right or left of the vertical median through the stimulus. Comparisons between both effects showed that they combine in a cumulative way and that the former is weightier than the latter. Further findings were a privileged association between null optical tilt of the pole and the no apparent slant response and a bias (for poles with nonnull optical tilt) in favor of the upward apparent slant response.     

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 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.     

Exocentric pointing in three-dimensional space

A study is reported of an exocentric pointing task in all three dimensions, in near space, with only two visible luminous objects--a pointer and a target. The task of the subject was to aim a pointer at a target. The results clearly show that visual space is not isotropic, since every set direction appeared to consist of two independent components--one in the projection onto a frontoparallel plane (tilt), the other in depth (slant). The tilt component shows a general trend across subjects, an oblique effect, and can be judged monocularly. The slant component is symmetrical in the mid-sagittal plane, requires the use of binocular information, and shows considerable differences between subjects. These differences seem to depend on the amount of binocular information used by each subject. There was a remarkably high level of consistency in the exocentric pointing, despite the absence of environmental cues. The within-subject consistency in the settings of the pointer corresponds to a consistency of about 1 min of arc in disparity of its tip, even though the pointer and target are separated by more than 5 deg.     

Distortions of perceived visual out of pictures

Two experiments are reported examining judgments from 16 subjects who indicated the apparent direction of a photographed pointer that was rotated to different physical positions while being photographed. The photographs themselves were rotated about a vertical axis to several positions with respect to the subjects’ central viewing axis. The results replicate the well-known distortion in apparent direction associated with photographed pointers positioned to project directly out of the plane of the photograph. This effect has been described by Goldstein (1979) as the “differential rotation effect” because its magnitude is reduced as the depicted angle of the pointer becomes less orthogonal to the photograph. Analysis of the two-dimensional properties of the projected images shows that this differential rotation is related to projected angles on the surface of the photograph. This analysis may explain why circular objects often do not appear to be correctly drawn in the periphery of geometrically correct projections.     

Adaptation in the constancy of visual direction measured by a one-trial method

Adaptation to field displacement during head movements in the direction with the head rotation and in the direction against it was produced under otherwise identical conditions and compared; the field displacement rate was also varied. A rapid training procedure was used, and a novel one-trial test was employed that could measure the adaptation well enough to compare the effects of various training conditions. The one-trial test measured the magnitude of one of the manifestations of adaptation, the apparent displacement of a stationary target during head movements. This apparent horizontal target displacement was transformed into an oblique one by having the head movements that brought forth the apparent target displacement simultaneously cause an objective vertical target displacement. The slant of the resultant apparent motion path varied with the magnitude of the apparent horizontal target displacement. It was measured by having S reproduce its slant angle. It was found that adaptation to field displacement in the direction with the head rotation was consistently greater than adaptation to the opposite displacement conditions. An explanation for this result is offered.     

Adaptation to field displacement during head movement unrelated to the constancy of visual direction

Adaptation to vertical field displacements dependent on head turning about a vertical axis was demonstrated under two conditions, rapid training with 100 head movements and 1-h-long training with continuous head turning. The effect of rapid training was measured with the slant estimation method. Adaptation after the longer training was ascertained by comparing the uncertainty ranges for apparent target immobility before and after the adaptation period. Adaptation to field displacements in directions parallel to the plane of the head rotation obtained under corresponding conditions was also measured and found to be somewhat greater than adaptation to vertical field displacements. The result of work by Wallach and Frey that adaptation to field displacement in the direction with the head rotation is greater than to displacement against it was corroborated. While the previous result had, been obtained with rapid adaptation and with the slant estimation method, we confirmed it with 1-h training and by measuring the uncertainty ranges before and after the adaptation period.     

The determination of perceived tridimensional orientation by minimum criteria

The hypothesis investigated is that the perceived tridimensional orientation of an object is determined, in monocular vision, by tendencies to make the perceived object as simple as possible. Line drawings seen as “boxes” were viewed by Os who judged the slant fangle with frontal plane) of various edges. For every such edge, there is a determinate hypothetical slant consistent with perfect homogeneity of values on one or more of three variables (angle, length, and slope) Perceived slant was highly predictable from hypothetical slant, though always with some regression to the frontal plane. Results add support to aPrägnanz or minimum-principle theory of space perception.     

A unified fielder theory for interception of moving objects either above or below the horizon

A unified fielder theory is presented that explains how humans navigate to intercept targets that approach from either above or below the horizon. Despite vastly different physical forces affecting airborne and ground-based moving targets, a common set of invariant perception-action principles appears to guide pursuers. When intercepting airborne projectiles, fielders keep the target image rising at a constant optical speed in a vertical image plane and moving in a constant optical direction in an image plane that remains perpendicular to gaze direction. We confirm that fielders use the same strategies to intercept grounders. Fielders maintained a cotangent of gaze angle that decreases linearly with time (accounting for 98.7% of variance in ball speed) and a linear optical trajectory along an image plane that remains perpendicular to gaze direction (accounting for 98.2% of variance in ball position). The universality of maintaining optical speed and direction for both airborne and ground-based targets supports the theory that these mechanisms are domain independent.     

Horizontal-vertical anisotropy in visual space

We investigated the structure of visual space with a 3D exocentric pointing task. Observers had to direct a pointer towards a ball. Positions of both objects were varied. We measured the deviations from veridical pointing-directions in the horizontal and vertical planes (slant and tilt resp.). The slant increased linearly with an increasing horizontal visual angle. We also examined the effect of relative distance, i.e., the ratio of the distances between the two objects and the observer. When the pointer was further away from the observer than the ball, the observer directed the pointer in between himself and the ball, whereas when the pointer was closer to the observer he directed the pointer too far away. Neither the horizontal visual angle nor the relative distance had an effect on the tilt. The vertical visual angle had no effect on the deviations of the slant, but had a linear effect on the tilt. These results quantify the anisotropy of visual space.     

Slant perception and binocular brightness differences: Some aftereffects of viewing apparent and objective surface slants

Placing a neutral-density filter in front of one eye produces two kinds of distortion in the perceived slant of a binocularly viewed rotating disk: (1) the top or the bottom of a disk rotating in a frontoparallel plane appears displaced toward or away from the observer, depending on the direction of rotation and whether the left or right eye is filtered; and (2) the left or right side of such disk—rotating or stationary—appears closer, depending on whether the left or right eye is filtered. The Pulfrich phenomenon accounts for the first variety of apparent slant, and the Venetian blind effect accounts for the second. Viewing the apparent slant of the rotating disk produces an aftereffect of slant in the third dimension which is greater than the aftereffect of viewing an objective slant of the same direction and magnitude.     

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).     

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.     

Temporal integration in structure from motion

A temporal integration model is proposed that predicts the results reported in 4 psychophysical experiments. The main findings were (a) the initial part of a structure-from-motion (SFM) sequence influences the orientation evoked by the final part of that sequence (an effect lasting for more than 1 s), and (b) for oscillating SFM sequences, perceived slant is affected by the oscillation frequency and by the sign of the final gradient. For contracting optic flows (i.e., rotations away from the image plane), the sequence with the lowest oscillation frequency appeared more slanted; for expanding optic flows (i.e., rotations toward the image plane), the sequence with the highest oscillation frequency appeared more slanted.     

The backward inclination of a surface defined by empirical corresponding points

Three experiments were conducted to investigate whether a locus of binocular correspondence extends eccentrically from the vertical horopter. In experiment 1, we investigated whether the backward inclination of the vertical horopter was manifested in the angle at which readers prefer to orient the page. All observers preferred a page inclined backwards to any other orientation. This backward inclination was less than predicted from previous psychophysical reports, however. In experiment 2, we investigated the extent of binocular correspondence, defined by minimal apparent interocular horizontal motion, in the central 24 deg of the binocular field. Our data define a planar surface inclined top-away from the observer as a locus from which psychophysical corresponding points are stimulated. In experiment 3, we measured vertical adjustments required to eliminate apparent vertical motion. Together, the pattern of results from experiments 2 and 3 is most consistent with a planar surface, inclined top-away from the observer. This is consistent with Helmholtz's account of the backward inclination of the vertical horopter and expands the locus of zero horizontal disparity from a single line in the median plane to eccentric loci extending at least +/- 12 deg in the central binocular field.