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

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

The visual perception of rigid motion from constant flow fields

Four experiments investigated observers’ judgments of rigidity for different types of optical motion. The depicted structural deformations were of two types: (1) those with nonparallel image trajectories that are detectable from the first-order spatiotemporal relations between pairs of views; and (2) those with parallel image trajectories that can only be detected from higher order relations among three or more views. Patterns were composed of smooth flow fields in Experiments 1 and 3, and of wire frame figures in Experiments 2 and 4. For both types of display, the nonrigidity detectable from the first-order spatiotemporal structure of the motion sequence was much more salient than the deformation detectable only from the higher order spatiotemporal structure. These results indicate that observers’ judgments of rigidity are based primarily on a two-view analysis, but that some useful information can be obtained under appropriate circumstances from higher order spatiotemporal relations among three or more views.     

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.     

A test of the gravity lens theory.

Naito and Cole [1994, in Contributions to Mathematical Psychology: Psychometrics and Methodology Eds G H Fischer and D Laming (New York: Springer)] provide a configuration which they describe as the Gravity Lens illusion. In this configuration, four small dots are presented in proximity to four large disks, and one is asked to compare the slope of an imaginary line which connects one pair of dots with the slope of a line which connects the other pair. In fact the slopes are the same, i.e. their axes are parallel, but because of the positioning of the large disks they appear to be at different orientations. Naito and Cole propose that the perceptual bias is analogous to the effects of gravity on the metrics of physical space, such that mental projections in the vicinity of a disk (or an open circle) are distorted just as the path of light is bent as it passes a massive body such as a star. Here we provide a simple test of this concept by having subjects judge alignments of dots which lie near tangents to a circle. Subjects were asked to project straight lines through pairs of stimulus dots, selecting and marking points in open space which were collinear with each pair. As would be predicted by the Gravity Lens theory, the locations selected by subjects were displaced from straight lines. However, the error magnitudes were substantially larger for judgments of dot pairs which had an oblique alignment, as compared with dot pairs which were aligned with a cardinal axis. This differential of effect as a function of stimulus orientation is not predicted by the gravity concept.     

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.     

Bantams (Gallus gallus domesticus) also perceive a reversed Zöllner illusion

Although pigeons have been shown to be susceptible to several size and length illusions, other avian species have not been tested intensively for illusory perception. Here we report how bantams perceive the Zöllner figure, in which parallel lines look nonparallel due to short crosshatches superimposed on the lines. Watanabe et al. (Cognition 119:137–141, 2011) showed that pigeons, like humans, perceived parallel lines as nonparallel but that the orientation of subjective convergence was opposite to that of humans. We trained three bantams to peck at the narrower (or wider) of the two gaps at the end of a pair of nonparallel lines. After adapting them to target lines with randomly oriented crosshatches (which result in no apparent illusion to humans), we tested the bantams’ responses on randomly inserted probe trials, in which crosshatches that should induce the standard Zöllner-like illusion for humans replaced the randomly oriented ones. The results suggested bantams, like pigeons, perceive a reversed Zöllner illusion.     

The effect of pattern and texture gradient on slant and shape judgments

The experiment reported was designed to explore the relationship between gradient of texture and monocular slantshape perception. The effects of instructional set and order of slant and shape judgments were studied in interaction with four patterns differing in regularity of texture. Judgments of slant and shape were made by the same Ss for all patterns at 20°, 45°, 60°slant for slant judgments and 0°, 20°, 45°, 60° for width judgments. There were three instructional groups. Within each group one half of the Ss made slant judgments first, the other half shape judgments first. For all patterns, accurate perception of the slant of patterned material resulted in increased compensation in width judgments. Apparent width was found to be a function of pattern and also subject to instructional manipulation.     

Studies of open-loop pointing in the presence of induced motion

In the present research, we examined the influence of induced motion (IM) on open-loop pointing responses and the possibility that IM alters the registration of either eye or trunk position. In two experiments, subjects tracked a dot that oscillated vertically while a rectangular stimulus oscillated horizontally. The pairing of frame and dot motion caused the dot to appear to move on a slant, due to IM. In the first experiment, the subjects made judgments of the apparent slant of the dot's motion and, on separate trials, pointed open loop at the apparent location of the dot at the endpoints of its motion. Both responses were influenced by IM, although the effect on dot localization was less than the amount predicted by the IM, as indicated by the slant responses. Results were similar immediately following IM and after a 5-sec delay. In the second experiment, the subjects pointed open loop either at the apparent location of the endpoints of the tracked dot's motion or at the apparent location of one of three other briefly flashed stationary dots. The pointing responses directed toward the fixated IM target were influenced by IM to a greater extent than the responses directed toward the stationary dots. The results of the two experiments are inconsistent with the hypothesis that the effect of IM on open-loop pointing at the IM target results completely from altered perception of either eye or trunk position, since misregistration of either would be expected to influence, in a similar fashion, pointing at both the tracked dot and the briefly flashed, stationary targets.     

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.     

Texture gradient registration and the development of slant perception.

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

Aging and the perception of slant from optical texture, motion parallax, and binocular disparity

The ability of younger and older observers to perceive surface slant was investigated in four experiments. The surfaces possessed slants of 20°, 35°, 50°, and 65°, relative to the frontoparallel plane. The observers judged the slants using either a palm board (Experiments 1, 3, and 4) or magnitude estimation (Experiment 2). In Experiments 1–3, physically slanted surfaces were used (the surfaces possessed marble, granite, pebble, and circle textures), whereas computer-generated 3-D surfaces (defined by motion parallax and binocular disparity) were utilized in Experiment 4. The results showed that the younger and older observers' performance was essentially identical with regard to accuracy. The younger and older age groups, however, differed in terms of precision in Experiments 1 and 2: The judgments of the older observers were more variable across repeated trials. When taken as a whole, the results demonstrate that older observers (at least through the age of 83 years) can effectively extract information about slant in depth from optical patterns containing texture, motion parallax, or binocular disparity.     

Perceiving geographical slant

People judged the inclination of hills viewed either out-of-doors or in a computer-simulated virtual environment. Angle judgments were obtained by having people (1) provide verbal estimates, (2) adjust a representation of the hill’s cross-section, and (3) adjust a tilt board with their unseen hand. Geographical slant was greatly overestimated according to the first two measures, but not the third. Apparent slant judgments conformed to ratio scales, thereby enhancing sensitivity to the small inclines that must actually be traversed in everyday experience. It is proposed that the perceived exaggeration of geographical slant preserves the relationship between distal inclination and people’s behavioral potential. Hills are harder to traverse as people become tired; hence, apparent slant increased with fatigue. Visually guided actions must be accommodated to the actual distal properties of the environment; consequently, the tilt board adjustments did not reflect apparent slant overestimations, nor were they influenced by fatigue. Consistent with the fact that steep hills are more difficult to descend than to ascend, these hills appeared steeper when viewed from the top.     

The perception of doubly curved surfaces from anisotropic textures

Abstract— Most existing computational models of the visual perception of three-dimensional shape from texture are based on assumed constraints about how texture is distributed on visible surfaces. The research described in the present article was designed to investigate how violations of these assumptions influence human perception. Observers were presented with images of smoothly curved surfaces depicted with different types of texture, whose distribution of surface markings could be both anisotropic and inhomogeneous. Observers judged the pattern of ordinal depth on each object by marking local maxima and minima along designated scan lines. They also judged the apparent magnitudes of relative depth between designated probe points on the surface. The results revealed a high degree of accuracy and reliability in all conditions, except for a systematic underestimation of the overall magnitude of surface relief. These findings suggest that human perception of three-dimensional shape from texture is much more robust than would be reasonable to expect based on current computational models of this phenomenon.     

Further experiments on the perception of growth in three dimensions

Mark and Todd (1983) reported an experiment in which the cardioidal strain transformation was extended to three dimensions and applied to a three-dimensional (3-D) representation of the head of a 15-year-old girl in a direction that made the transformed head appear younger to the vast majority of their subjects. The experiments reported here extend this research in order to examine whether subjects are indeed detecting cardioidal strain in three dimensions, rather than detecting changes in head slant or making 2-D comparisons of the shape of the occluding contour. Three-dimensional surfaces were obtained by measuring a real head manually (Experiment 1) and with a laser scanner (Experiment 2), and transformed to different age levels using the 3-D strain transformation described by Mark and Todd (1983). There were no statistically significant differences in the accuracy with which relative age judgments could be made in response to pairs of profiles, pairs of 3/4 views, or pairs of mixed views (profile plus 3/4 view), suggesting that subjects can indeed extract the cardioidal strain level of the head in three dimensions. However, an additional effect that emerged in these studies was that judgments were crucially affected by the instructions given to subjects, which suggests that factors other than cardioidal strain are important in making judgments about rich data structures.     

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.     

Static and dynamic factors in the perception of rotary motion

Direction of rotation and static slant judgments were collected for a series of outline plane forms in four experiments with 106 subjects. Direction was judged more accurately for forms displaying the same perspective gradients as trapezoids, but with right-angled contours, than for trapezoids. There were no consistent differences among these forms in judged slant. Direction of rotation judgments were affected by a static false interposition cue, with interposition increasing the proportion of veridical judgments when placed in conflict with a relative size gradient and decreasing this proportion when a size gradient was absent. Both a dynamic factor (contour angle change) and a static factor (misperceived relative distance of the vertical sides) were found to affect perceived direction of rotation, with direction judgments based primarily on the dynamic factor.     

Visual perception of touchdown point during simulated landing

Experiments examined the accuracy of visual touchdown point perception during oblique descents (1.5 degrees -15 degrees ) toward a ground plane consisting of (a) randomly positioned dots, (b) a runway outline, or (c) a grid. Participants judged whether the perceived touchdown point was above or below a probe that appeared at a random position following each display. Although judgments were unacceptably imprecise and biased for moving dot and runway displays, accurate and unbiased judgments were found for grid displays. It is concluded that optic flow per se does not appear to be sufficient for a pilot to land an airplane and that the systematic errors associated with optic flow under sparse conditions may be responsible for the common occurrence of landing incidents in so-called "black hole" situations.     

Perceiving surface slant from deformation of optic flow

Perceived surface orientation and angular velocity were investigated for orthographic projections of 3-D rotating random-dot planes. It was found that (a) tilt was accurately perceived and (b) slant and angular velocity were systematically misperceived. It was hypothesized that these misperceptions are the product of a heuristic analysis based on the deformation, one of the differential invariants of the first-order optic flow. According to this heuristic, surface attitude and angular velocity are recovered by determining the magnitudes of these parameters that most likely produce the deformation of the velocity field, under the assumption that all slant and angular velocity magnitudes have the same a priori probability. The results of the present investigation support this hypothesis. Residual orientation anisotropies not accounted for by the proposed heuristic were also found.     

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.