TWO-DIMENSIONAL FIELD EFFECTS AND STATIC SLANT PERCEPTION

E riksson , E. S. Two-dimensional field effects and static slant perception. Scand. J. Psychol ., 1968, 9, 19–32.—The model for two-dimensional field effects as developed in a previous article makes possible certain predictions concerning perceived shape which, taken together with the subjective slant principle, result in predictions of the perceived slant of a circle or a surface composed of circles. Data were obtained which agreed with these predictions, showing that the geometrical shape slant invariance hypothesis is an inadequate model for depth perception. Some implications for gradient theory, Helmholtzian theories and Gestalt theory are discussed.     

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.     

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.     

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.     

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.     

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.     

Surface perception in pictures

Subjects adjusted a local gauge figure such as to perceptually “fit” the apparent surfaces of objects depicted in photographs. We obtained a few hundred data points per session, covering the picture according to a uniform lattice. Settings were repeated 3 times for each of 3 subjects. Almost all of the variability resided in the slant; the relative spread in the slant was about 25% (Weber fraction). The tilt was reproduced with a typical spread of about 10?. The rank correlation of the slant settings of different observers was high, thus the slant settings of different subjects were monotonically related. The variability could be predicted from the scatter in repeated settings by the individual observers. Although repeated settings by a single observer agreed within 5%, observers did not agree on the value of the slant, even on the average. Scaling factors of a doubling in the depth dimension were encountered between different subjects. The data conformed quite well to some hypothetical fiducial global surface, the orientation of which was “probed” by the subject’s local settings. The variability was completely accounted for by singleobserver scatter. These conclusions are based upon an analysis of the internal structure of the local settings. We did not address the problem of veridicality, that is, conformity to some “real object.”     

Surface perception in pictures.

Subjects adjusted a local gauge figure such as to perceptually "fit" the apparent surfaces of objects depicted in photographs. We obtained a few hundred data points per session, covering the picture according to a uniform lattice. Settings were repeated 3 times for each of 3 subjects. Almost all of the variability resided in the slant; the relative spread in the slant was about 25% (Weber fraction). The tilt was reproduced with a typical spread of about 10 degrees. The rank correlation of the slant settings of different observers was high, thus the slant settings of different subjects were monotonically related. The variability could be predicted from the scatter in repeated settings by the individual observers. Although repeated settings by a single observer agreed within 5%, observers did not agree on the value of the slant, even on the average. Scaling factors of a doubling in the depth dimension were encountered between different subjects. The data conformed quite well to some hypothetical fiducial global surface, the orientation of which was "probed" by the subject's local settings. The variability was completely accounted for by single-observer scatter. These conclusions are based upon an analysis of the internal structure of the local settings. We did not address the problem of veridicality, that is, conformity to some "real object."     

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 perception of depth and slant from texture in three-dimensional scenes.

The perception of depth and slant in three-dimensional scenes specified by texture was investigated in five experiments. Subjects were presented with computer-generated scenes of a ground and ceiling plane receding in depth. Compression, convergence, and grid textures were examined. The effect of the presence or absence of a gap in the center of the display was also assessed. Under some conditions perceived slant and depth from compression were greater than those found with convergence. The relative effectiveness of compression in specifying surface slant was greater for surfaces closer to ground planes (80 degrees slant) than for surfaces closer to frontal parallel planes (40 degrees slant). The usefulness of compression was also observed with single-plane displays and with displays with surfaces oriented to reduce information regarding the horizon.     

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.     

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.     

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.     

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.     

Temporal aspects of slant and inclination perception.

Linear transformations (shear or scale transformations) of either horizontal or vertical disparity give rise to the percept of slant or inclination. It has been proposed that the percept of slant induced by vertical size disparity, known as Ogle's induced-size effect, and the analogous induced-shear effect, compensate for scale and shear distortions arising from aniseikonia, eccentric viewing, and cyclodisparity. We hypothesised that these linear transformations of vertical disparity are processed more slowly than equivalent transformations of horizontal disparity (horizontal shear and size disparity). We studied the temporal properties of the stereoscopic slant and inclination percepts that arose when subjects viewed stereograms with various combinations of horizontal and vertical size or shear disparities. We found no evidence to support our hypothesis. There were no clear differences in the build-up of percepts of slant or inclination induced by step changes in horizontal size or shear disparity and those induced by step changes in vertical size or shear disparity. Perceived slant and inclination decreased in a similar manner with increasing temporal frequency for modulations of transformations of both horizontal and vertical disparity. Considerable individual differences were found and several subjects experienced slant reversal, particularly with oscillating stimuli. An interesting finding was that perceived slant induced by modulations of dilation disparity was in the direction of the vertical component. This suggests the vertical size disparity mechanism has a higher temporal bandwidth than the horizontal size disparity mechanism. However, conflicting perspective information may play a dominant role in determining the temporal properties of perceived slant and inclination.     

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.     

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.     

A distance judgment function based on space perception mechanisms: revisiting Gilinsky's (1951) equation

In her seminal article in Psychological Review, A. S. Gilinsky (1951) successfully described the relationship between physical distance (D) and perceived distance (d) with the equation d = DA/(A + D), where A = constant. To understand its theoretical underpinning, the authors of the current article capitalized on space perception mechanisms based on the ground surface to derive the distance equation d = Hcosalpha/sin(alpha + eta), where H is the observer's eye height, alpha is the angular declination below the horizon, and eta is the slant error in representing the ground surface. Their equation predicts that (a) perceived distance is affected by the slant error in representing the ground surface; (b) when the slant error is small, the ground-based equation takes the same form as Gilinsky's equation; and (c) the parameter A in Gilinsky's equation represents the ratio of the observer's eye height to the sine of the slant error. These predictions were empirically confirmed, thus bestowing a theoretical foundation on Gilinsky's equation.     

Summarizing slant perception with words and hands; an empirical alternative to correlations in Shaffer,McManama, Swank,Williams & Durgin (2014)

The paper by Shaffer, McManama, Swank, Williams & Durgin (2014) uses correlations between palm-board and verbal estimates of geographical slant to argue against dissociation of the two measures. This paper reports the correlations between the verbal, visual and palm-board measures of geographical slant used by Proffitt and co-workers as a counterpoint to the analyses presented by Shaffer and colleagues. The data are for slant perception of staircases in a station (N = 269), a shopping mall (N = 229) and a civic square (N = 109). In all three studies, modest correlations between the palm-board matches and the verbal reports were obtained. Multiple-regression analyses of potential contributors to verbal reports, however, indicated no unique association between verbal and palm-board measures. Data from three further studies (combined N = 528) also show no evidence of any relationship. Shared method variance between visual and palm-board matches could account for the modest association between palm-boards and verbal reports.     

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。