Surface tilt (the direction of slant): A neglected psychophysical variable

Surface slant (the angle between the line of sight and the surface normal) is an important psychophysical variable. However, slant angle captures only one of the two degrees of freedom of surface orientation, the other being thedirection of slant. Slant direction, measured in the image plane, coincides with the direction of the gradient of distance from viewer to surface and, equivalently, with the direction the surface normal would point if projected onto the image plane. Since slant direction may be quantified by the tilt of the projected normal (which ranges over 360 deg in the frontal plane), it is referred to here assurface tilt. (Note that slant angle is measured perpendicular to the image plane, whereas tilt angle is measured in the image plane.) Compared with slant angle’s popularity as a psychophysical variable, the attention paid to surface tilt seems undeservedly scant. Experiments that demonstrate a technique for measuring apparent surface tilt are reported. The experimental stimuli were oblique crosses and parallelograms, which suggest oriented planes in 3-D. The apparent tilt of the plane might be probed by orienting a needle in 3-D so as to appear normal, projecting the normal onto the image plane, and measuring its direction (e.g., relative to the horizontal). It is shown to be preferable, however, to merely rotate a line segment in 2-D, superimposed on the display, until it appears normal to the perceived surface. The apparent surface tilt recorded in these experiments corresponded closely to that predicted by assuming the 3-D configurations consist of equal-length lines and perpendicular intersections.     

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.     

The framing effect with rectangular and trapezoidal surfaces: actual and pictorial surface slant, frame orientation, and viewing condition

The perceived slant of a surface relative to the frontal plane can be reduced when the surface is viewed through a frame between the observer and the surface. Aspects of this framing effect were investigated in three experiments in which observers judged the orientations-in-depth of rectangular and trapezoidal surfaces which were matched for pictorial depth. In experiments 1 and 2, viewing was stationary-monocular. In experiment 1, a frontal rectangular frame was present or absent during viewing. The perceived slants of the surfaces were reduced in the presence of the frame; the reduction for the trapezoidal surface was greater, suggesting that conflict in stimulus information contributes to the phenomenon. In experiment 2, the rectangular frame was either frontal or slanted; in a third condition, a frame was trapezoidal and frontal. The conditions all elicited similar results, suggesting that the framing effect is not explained by pictorial perception of the display, or by assimilation of the surface orientation to the frame orientation. In experiment 3, viewing was moving-monocular to introduce motion parallax; the framing effect was reduced, being appreciable only for a trapezoidal surface. The results are related to other phenomena in which depth perception of points in space tends towards a frontal plane; this frontal-plane tendency is attributed to heavy experimental demands, mainly concerning impoverished, conflicting, and distracting information.     

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.     

Cross-modal slant and curvature matching of stereo- and motion-induced surfaces

In many laboratory setups and in many day-to-day situations, a unique solution of the structure-fromtwo-views problem is unobtainable. Yet, when the visual system is presented with two projections in a sequence, it nevertheless appears to generate a reasonably stable percept of structure. In the research reported here, we examined whether the same surface would be perceived when subjects were presented with a pair of views that alternated in time monocularly (two-frame motion) or were shown simultaneously to both eyes (stereo). In Experiment 1, we studiedslant perception: human observers were asked to match the slant of a motion-induced planar surface with its stereo-induced counterpart. In Experiment 2, the perceivedcurvature of parabolic surfaces was matched in a similar way. The results show that motion-induced slant is matched with ahigher value of the stereo-induced slant. However, the curvature experiment showed that motion-induced curvature is matched with alower stereo-induced curvature. One possible explanation may be that the slant and curvature are internally inconsistent in at least one of the modalities.     

Apparent extended body motions in depth.

Five experiments were designed to investigate the influence of three-dimensional (3-D) orientation change on apparent motion. Projections of an orientation-specific 3-D object were sequentially flashed in different locations and at different orientations. Such an occurrence could be resolved by perceiving a rotational motion in depth around an axis external to the object. Consistent with this proposal, it was found that observers perceived curved paths in depth. Although the magnitude of perceived trajectory curvature often fell short of that required for rotational motions in depth (3-D circularity), judgments of the slant of the virtual plane on which apparent motions occurred were quite close to the predictions of a model that proposes circular paths in depth.     

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.     

The effect of perceived distance on perceived movement

Equations were developed to predict the apparent motion of a physically stationary object resulting from head movement as a function of errors in the perceived distances of the object or of its parts. These equations, which specify the apparent motion in terms of relative and common components, were applied to the results of two experiments. In the experiments, the perceived slant of an object was varied with respect to its physical slant by means of perspective cues. In Experiment I, O reported the apparent motion and apparent distance of each end of the object independently. The results are consistent with the equations in terms of apparent relative motion, but not in terms of apparent common motion. The latter results are attributed to the tendency for apparent relative motion to dominate apparent common motion when both are present simultaneously. In Experiment II, a direct report of apparent relative motion (in this case, apparent rotation) was obtained for illusory slants of a physically frontoparallel object. It was found that apparent rotations in the predicted direction occurred as a result of head motion, even though under these conditions no rotary motion was present on the retina.     

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.     

Shape constancy and slant perception at birth

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

Measurement and modelling of perceived slant in surfaces represented by freely viewed line drawings

Simple pictures under everyday viewing conditions evoke impressions of surfaces oriented in depth. These impressions have been studied by measuring the slants of perceived surfaces, with probes (rotating arrowheads) designed to respect the distinctive character of depicted scenes. Converging arguments indicated that the perceived orientation of the probes was near theoretical values. A series of experiments showed that subjects formed well-defined impressions of depicted surface orientation. The literature suggests that perceived objects might be 'flattened', but that was not the general rule. Instead, both mean slant and uncertainty fitted models in which slant estimates are derived in a relatively straightforward way from local relations in the picture. Simplifying pictures tended to make orientation estimates less certain, particularly away from the natural anchor points (vertical and horizontal). The shape of the object affected all aspects of the observed-object/percept relationship. Individual differences were large, and suggest that different individuals used different relationships as a basis for their estimates. Overall, data suggest that everyday picture perception is strongly selective and weakly integrative. In particular, depicted slant is estimated by finding a picture feature which will be strongly related to it if the object contains a particular regularity, not by additive integration of evidence from multiple directly and indirectly relevant sources.     

Effect of viewing plane on perceived distances in real and virtual environments

Three experiments examined perceived absolute distance in a head-mounted display virtual environment (HMD-VE) and a matched real-world environment, as a function of the type and orientation of the distance viewed. In Experiment 1, participants turned and walked, without vision, a distance to match the viewed interval for both egocentric (viewer-to-target) and exocentric (target-to-target) extents. Egocentric distances were underestimated in the HMD-VE while exocentric distances were estimated similarly across environments. Since egocentric distances were displayed in the depth plane and exocentric distances in the frontal plane, the pattern of results could have been related to the orientation of the distance or to the type of distance. Experiments 2 and 3 tested these alternatives. Participants estimated exocentric distances presented along the depth or frontal plane either by turning and walking (Experiment 2) or by turning and throwing a beanbag to indicate the perceived extent (Experiment 3). For both Experiments 2 and 3, depth intervals were underestimated in the HMD-VE compared to the real world. However, frontal intervals were estimated similarly across environments. The findings suggest anisotropy in HMD-VE distance perception such that distance underestimation in the HMD-VE generalizes to intervals in the depth plane, but not to intervals in the frontal plane. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Perceived range, perceived velocity, and perceived duration of the body rotating in the frontal plane

We investigated perceived range, perceived velocity, and perceived duration of the body rotating in the frontal plane (in roll). Specifically, to examine how shear to the otoliths in the inner ears and tactile pressure to the trunk affect judgments of range and velocity, in two experiments, we manipulated rotating range (30°–160°), rotating velocity (1.8°/sec to 9.6°/sec), mean tilt of the body (?60°, 0°, and 60°), and exposure to the visual vertical. Thirty-three normal or blindfolded participants made verbal judgments of range, velocity, and duration for each combination of these factors. The exponents of the power functions fitted to these judgments were, as a first approximation, .94, .61, and .84 for range, velocity, and duration, respectively, and perceived velocity was proportional to the ratio of perceived range to perceived duration (r = .91). These results suggest that the vestibular and somatosensory inputs are effective on judgments of range, but less so on judgments of velocity, and that perceived velocity may be determined as a ratio of perceived range to perceived duration. In addition, we found that (1) when the range the body has traveled is constant, the perceived range increases as the objective velocity decreases (proprioceptive τ effect); (2) self-motion through the tilted roll sometimes enlarges perceived range and perceived duration but reduces perceived velocity; and (3) the exposure to the visual vertical reduces variability of judgments for range and velocity and also reduces perceived range and perceived velocity of self-motion within a small range through the vertical roll.     

The sensing of retinal motion

The apparent relative motion of physically stationary objects that frequently occurs as the head is moved in a frontoparallel plane is almost always in the direction expected from the projection into the distal world of the relative motion of the images on the eye. It is hypothesized that this is the result of the perceptual underestimation of the depth between the objects. If a perceptual overestimation of the depth were produced, it was predicted that the apparent relative motion would be in a direction opposite to that expected from the projection of the retinal motions. This prediction was tested using the binocular disparity cue to produce perceptual overestimation of the slant (depth) of a luminous line. In this case, perceived slant was the indicator of perceived depth, and perceived rotation concomitant with the motion of the head was the indicator of perceived relative motion. The results support the prediction and also provide some support for a theoretically derived equation specifying the relation between these two perceptual variables.     

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.     

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.     

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."