Slant Perception Research Articles

Adaptation to the induced effect stimulus normalizes surface slant perception and recalibrates eye position signals for azimuth

A frontoparallel plane viewed with unequal vertical magnification of the two ocular images appears rotated about a vertical axis (i.e., induced effect; Ogle, 1938). Several experiments were conducted to investigate changes in the visual system that occurred after adapting to the induced effect. Adaptation at 57 cm was tested using tall stimuli at various viewing distances to test for the adaptation of vertical size ratio (VSR) information and normalization of the slant percept. When aftereffects were expressed in units of slant, they were larger at 57 cm than other test distances and were not significantly different from each other at other distances. Short stimuli were used to test adaptation of eye position signals for azimuth. The aftereffects were in the opposite direction to those measured with tall stimuli. The combined results suggest that the visual system normalizes slant percepts based on the surface slant of the adaptation stimulus and when there is a conflict between VSR signals and eye position cues for azimuth that the primary eye position signal for azimuth is recalibrated toward the direction indicated by the binocular differential vertical magnification in the adaptation stimulus.

Depth aftereffects mediated by vertical disparities: Evidence for vertical disparity driven calibration of extraretinal signals during stereopsis

Perceptual adaptation often results in a repulsive aftereffect: stimuli are seen as biased away from the adaptation stimulus ( Blakemore & Sutton, 1969). Here we report the absence of a repulsive aftereffect for a vertical gradient of vertical disparity (or vertical size ratio, VSR). We exposed observers to a binocular stimulus consisting of horizontal lines. This stimulus contains vertical, but not horizontal disparities. The visual system was able to measure the VSR of this stimulus: although the lines themselves always appeared unslanted, the VSR carried by the lines had a dramatic effect on the apparent slant of a horizontal row of dots, as predicted by recent accounts of Ogle’s (1938) induced effect (e.g., Backus, Banks, van Ee, & Crowell, 1999). Yet we observed no repulsive aftereffect for the VSR signal: after adaptation to horizontal lines that were vertically larger in one eye, we found an attractive aftereffect, the magnitude of which was largest in stimuli that did not contain a VSR signal. We interpret these results as a case of recalibration: disagreement between extra-retinal eye position signals (EP) and VSR causes a recalibration in the use of EP as used in the stereoscopic perception of slant.

Assessment of cyclodisparity-induced slant perception with a synoptophore

To evaluate with a synoptophore slant perception induced by binocular cyclodisparities in normal subjects and to argue for the possibility of abnormal slant perception in patients with cyclo-vertical strabismus. A vertical line with cyclodisparities that ranged from 0 degrees to +/- 10 degrees was presented to 17 normal subjects (mean +/- SD age, 28.4 +/- 5.6 years; 11 men and 6 women) with a synoptophore, and the perceived slant of the line in the pitch plane was measured by a matching method. Cyclodisparity thresholds for top-away and top-forward slants were also evaluated by the method of limits in a separate experiment. An incyclodisparity induced top-forward, while an excyclodisparity induced top-away, slant perception. The maximum slant angle was 37 degrees on average at a cyclodisparity of 10 degrees , and the mean slant gain (perceived angle/geometrically calculated angle) was 64 +/- 13%. The mean cyclodisparity thresholds for top-away and top-forward slants were -1.1 degrees and 0.6 degrees , respectively. The slant perception induced by cyclodisparities was reasonably assessed with the synoptophore. The cyclodisparity thresholds obtained in this experiment were much lower than the cyclodeviation range of the patients, indicating that a considerable number of patients may have abnormal slant perception once they achieve sensory fusion.

The effects of field of view on the perception of 3D slant from texture

Observers judged the apparent signs and magnitudes of surface slant from monocular textured images of convex or concave dihedral angles with varying fields of view between 5° and 60°. The results revealed that increasing the field of view or the regularity of the surface texture produced large increases in the magnitude of the perceptual gain (i.e., the judged slant divided by the ground truth). Additional regression analyses also revealed that observers slant judgments were highly correlated with the range of texture densities (or spatial frequencies) in each display, which accounted for 96% of the variance among the different possible dihedral angles and fields of view.

Voluntarily controlled bi–stable slant perception of real and photographed surfaces

We have quantified voluntarily selected perceived slant of real trapezoidal surfaces (a 'reverse-perspective' scene) and their photographed counterparts (pictorial space). The surfaces were slanted about the vertical axis and observers estimated slant relative to the frontal plane. We were particularly interested in those cases in which binocular disparity and monocular perspective provided conflicting slant information. We varied the monocularly and binocularly specified surface slants independently across stimulus presentations. To eliminate texture and shading cues we used sand-blasted aluminium trapezoidal surfaces illuminated from all directions. When disparity-specified slant and perspective-specified slant were conflicting, observers were able to perceive the surfaces in two ways: they perceived either a trapezoid or a rectangle. Our main finding is twofold. First, when subjects chose to perceive the trapezoid, the slant estimates followed the disparity-predicted slant with only a slight underestimation, as if they selected a pure binocular representation of slant governed only by disparity. Second, when subjects chose to perceive the rectangle their estimates for real surfaces were similar to those for photographed surfaces, as if they selected a representation of slant governed by perspective foreshortening.

Starry night: a texture devoid of depth cues

From a modern Bayesian point of view, the classic Julesz random-dot stereogram is a cue-conflict stimulus: Texture cues specify an unbroken, unslanted surface, in conflict with any variation in depth specified by binocular disparity. We introduce a new visual texture-the starry night texture (SNT)--that is incapable of conveying slant, depth edges, or texture boundaries, in a single view. For SNT, changing density is equivalent to changing intensity, so an instance of the texture is characterized (up to the random locations of the texture elements) by what we call its densintensity. We consider deviations from the ideal that are needed to realize the texture in practice. In three experiments with computer-generated stimuli we examined human perception of SNT to show that (1) the deviations from the ideal that were needed to realize SNT do not affect the invariance of its appearance across changes in distance of several orders of magnitude; (2) as predicted, observers match SNT across changes in distance better than other textures; and (3) the use of SNT in a slant perception experiment did not reliably increase observers' reliance on stereoscopic slant cues, as compared with the sparse random-dot displays that have been commonly employed to study human perception of shape from binocular disparity and motion.

Perceiving virtual geographical slant: action influences perception.

In 4 experiments, the authors varied the extent and nature of participant movement in a virtual environment to examine the influence of action on estimates of geographical slant. Previous studies showed that people consciously overestimate hill slant but can still accurately guide an action toward the hill (D. R. Proffitt, M. Bhalla, R. Gossweiler, & J. Midgett, 1995). Related studies suggest that one's potential to act may influence perception of slant and that distinct representations may independently inform perceptual and motoric responses. The authors found that in all conditions, perceptual judgments were overestimated and motoric adjustments were more accurate. The virtual environment allowed manipulation of the effort required to walk up simulated hills. Walking with the effort appropriate to the visual slant led to increased perceptual overestimation of slant compared with active walking with the effort appropriate to level ground, while visually guided actions remained accurate.

Slant perception produced by vertical and horizontal size disparities with short duration

Slant perception produced by vertical and horizontal size disparities with short duration

Sensitivity to depth relief on slanted surfaces.

The finest stereoacuity is known to depend on the disparity of a target relative to other visible points. Here we show that a more important factor in determining sensitivity to displacement can be the disparity of a target relative to an invisible interpolation plane through other neighboring points. We tested the sensitivity of observers to displacements of the central column of a regular grid of dots that was either fronto-parallel or slanted about a vertical axis. We found that subjects' sensitivity to displacement was better predicted by a model based on the disparity of a target with respect to the grid plane than it was by a model based on disparity with respect to other reference points. In control conditions carried out on one subject, we found that this result did not depend on adaptation to the grid slant because it also occurred when the direction of grid slant varied from trial to trial. Nor did it depend on the perception of slant, because the data were similar for trials on which the grid was perceived as approximately fronto-parallel or markedly slanted. Our results indicate that sensitivity to the depth component of the target displacement is based on disparity relative to a local reference plane.

Bayesian modeling of cue interaction: bistability in stereoscopic slant perception.

Our two eyes receive different views of a visual scene, and the resulting binocular disparities enable us to reconstruct its three-dimensional layout. However, the visual environment is also rich in monocular depth cues. We examined the resulting percept when observers view a scene in which there are large conflicts between the surface slant signaled by binocular disparities and the slant signaled by monocular perspective. For a range of disparity-perspective cue conflicts, many observers experience bistability: They are able to perceive two distinct slants and to flip between the two percepts in a controlled way. We present a Bayesian model that describes the quantitative aspects of perceived slant on the basis of the likelihoods of both perspective and disparity slant information combined with prior assumptions about the shape and orientation of objects in the scene. Our Bayesian approach can be regarded as an overarching framework that allows researchers to study all cue integration aspects-including perceptual decisions--in a unified manner.

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.

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.

Synthesis of binocular disparity with motion parallax in depth slant perception: statistical efficiency approach

Statistical efficiency approach is used in order to investigate sampling properties of both binocular disparity and motion parallax processes in depth slant perception and to examine the independent decisions model (Mulligan & Shaw, 1980) consisting of these processes. We carried out two experiments in which each cue was displayed solely (i.e., single condition) and both cues were displayed simultaneously (i.e., multiple condition). A two-alternative forced-choice (2AFC) task was used under the situation where a Gaussian noise was added to the stimulus value of depth slant. Statistical efficiencies were calculated in each experiment. The results showed that sampling size from binocular disparity was at least comparable or larger by a factor of 2.5-3.5 with that from motion parallax and that efficiencies of the multiple condition considerably exceeded those of the single condition. This suggests invalidity of the independent decisions model.

Vertical gaze angle: absolute height-in-scene information for the programming of prehension.

One possible source of information regarding the distance of a fixated target is provided by the height of the object within the visual scene. It is accepted that this cue can provide ordinal information, but generally it has been assumed that the nervous system cannot extract "absolute" information from height-in-scene. In order to use height-in-scene, the nervous system would need to be sensitive to ocular position with respect to the head and to head orientation with respect to the shoulders (i.e. vertical gaze angle or VGA). We used a perturbation technique to establish whether the nervous system uses vertical gaze angle as a distance cue. Vertical gaze angle was perturbed using ophthalmic prisms with the base oriented either up or down. In experiment 1, participants were required to carry out an open-loop pointing task whilst wearing: (1) no prisms; (2) a base-up prism; or (3) a base-down prism. In experiment 2, the participants reached to grasp an object under closed-loop viewing conditions whilst wearing: (1) no prisms; (2) a base-up prism; or (3) a base-down prism. Experiment 1 and 2 provided clear evidence that the human nervous system uses vertical gaze angle as a distance cue. It was found that the weighting attached to VGA decreased with increasing target distance. The weighting attached to VGA was also affected by the discrepancy between the height of the target, as specified by all other distance cues, and the height indicated by the initial estimate of the position of the supporting surface. We conclude by considering the use of height-in-scene information in the perception of surface slant and highlight some of the complexities that must be involved in the computation of environmental layout.

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.

Temporal dependencies in resolving monocular and binocular cue conflict in slant perception

Observers viewed large dichoptic patterns undergoing smooth temporal modulations or step changes in simulated slant or inclination under various conditions of disparity–perspective cue conflict and concordance. After presentation of each test surface, subjects adjusted a comparison surface to match the perceived slant or inclination of the test surface. Addition of conflicting perspective to disparity affected slant and inclination perception more for brief than for long presentations. Perspective had more influence for smooth temporal changes than for step changes in slant or inclination and for surfaces presented in isolation rather than with a zero disparity frame. These results indicate that conflicting perspective information plays a dominant role in determining the temporal properties of perceived slant and inclination.

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.

Horizontal and vertical disparity, eye position, and stereoscopic slant perception

The slant of a stereoscopically defined surface cannot be determined solely from horizontal disparities or from derived quantities such as horizontal size ratio (HSR). There are four other signals that, in combination with horizontal disparity, could in principle allow an unambiguous estimate of slant: the vergence and version of the eyes, the vertical size ratio (VSR), and the horizontal gradient of VSR. Another useful signal is provided by perspective slant cues. The determination of perceived slant can be modeled as a weighted combination of three estimates based on those signals: a perspective estimate, a stereoscopic estimate based on HSR and VSR, and a stereoscopic estimate based on HSR and sensed eye position. In a series of experiments, we examined human observers’ use of the two stereoscopic means of estimation. Perspective cues were rendered uninformative. We found that VSR and sensed eye position are both used to interpret the measured horizontal disparities. When the two are placed in conflict, the visual system usually gives more weight to VSR. However, when VSR is made difficult to measure by using short stimuli or stimuli composed of vertical lines, the visual system relies on sensed eye position. A model in which the observer’s slant estimate is a weighted average of the slant estimate based on HSR and VSR and the one based on HSR and eye position accounted well for the data. The weights varied across viewing conditions because the informativeness of the signals they employ vary from one situation to another.

Estimator reliability and distance scaling in stereoscopic slant perception.

When a horizontal or vertical magnifier is placed before one eye, a frontoparallel surface appears slanted. It appears slanted away from the eye with horizontal magnification (geometric effect) and toward the eye with vertical magnification (induced effect). According to current theory, the apparent slant in the geometric and induced effects should increase with viewing distance. The geometric effect does scale with distance, but there are conflicting reports as to whether the induced effect does. Ogle (1938 Archives of Ophthalmology 20 604-623) reported that settings in slant-nulling tasks increase systematically with viewing distance, but Gillam et al (1988 Perception & Psychophysics 44 473-483) and Rogers et al (1995 Perception 24 Supplement, 33) reported that settings in slant-estimation tasks do not. We re-examined this apparent contradiction. First, we conducted two experiments whose results are consistent with the literature and thus replicate the apparent contradiction. Next, we analyzed the signals available for stereoscopic slant perception and developed a general model of perceived slant. The model is based on the assumption that the visual system knows the reliability of various slant-estimation methods for the viewing situation under consideration. The model's behavior explains the contradiction in the literature. The model also predicts that, by manipulating eye position, apparent slant can be made to increase with distance for vertical, but not for horizontal, magnification. This prediction was confirmed experimentally.

The impact of visual exploration of judgments of whether a gap is crossable.

When observers look down into a gap in the ground plane, their judgments of the widest gap they can step across (gapmax) decrease as gap depth increases (Y. Jiang & L. S. Mark, 1994). This study investigated the possibility that Jiang and Mark's viewing conditions did not afford observers a sufficient opportunity to perform exploratory movements needed to detect information about gap width. Experiment 1 showed that the gap depth by gaze interaction disappeared only when restrictions were not imposed on observers' exploratory activities (eye, head, and body movements). Experiment 2 showed that observers tended to see the vertical surface as slanted away from them, which made the bottom of the surface appear farther away from them than the top. Only when observers were able to view the gap binocularly under conditions that did not restrict exploratory activity did their slant perception improve and their gapmax judgments no longer covary with gap depth. The data indicate that the exploratory movements of prospective actors are essential for the pickup of information about their action capabilities.