The perception of rotated shapes: A process analysis of shape constancy

Ss made objective shape judgments of circular objects rotated in depth to provide a process analysis of shape constancy. The significant finding was that task difficulty, as reflected by proportion errors and correct reaction times; increased with increases in rotation from the frontal-parallel plane. This effect was located at the perceptual encoding stage of the shape judgment process. It was demonstrated that, in contrast to true shape information, the time to interpret slant and two-dimensional projected shape information was not critically dependent on degree of rotation. These results and a number of other additional observations demonstrate that the invariance hypothesis does not provide a sufficient account of shape constancy. Although projected shape and’ slant judgments can be made easily, perception of true shape involves encoding a figure-ground relationship by a process that does not rely exclusively on the discrete values of projected shape and slant.     

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.     

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.     

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.     

Head for the hills: The influence of environmental slant on spatial memory organization

Environmental slant is known to improve navigation performance in humans and other animals. Successful navigation relies on accurate spatial orientation and accurate spatial memory retrieval. The role of environmental slant in spatial orientation has been established, but its role in spatial memory organization is unclear. Two experiments using immersive virtual reality explored the influence of environmental slant on reference frame selection during spatial learning. Participants studied object locations on a sloped surface. When no additional environmental cues were present (Experiment 1), spatial memory retrieval was best from the studied perspective aligned with the direction of slope. When the direction of slope was placed in competition with the axis of the surrounding room (Experiment 2), spatial memory retrieval was best from the initially studied perspective. The latter finding contrasts with the results of research showing that pigeons preferentially rely on environmental slant over room shape. The findings are discussed in the context of spatial memory theory.     

How I managed to hide my shadow

A special type of visual stimulus is described which gives the perceiver the impression that a shadow has been hidden behind a surface in the image, contrary to expectations based on ecological situations in which covering a shadow only passes it on to the cover.     

Stationary visual texture and the estimation of slant angle

Gibson (1950a) has suggested that a gradient of retinal stimulation from an irregularly textured surface is used in the estimation of slant. There are several measures that could form such a gradient. Eight pictures of slanting surfaces were constructed with the aid of a computer. These consisted only of texture elements: in this case, outline circles and ellipses. Subjects studied pairs of pictures and indicated which had the greater tilt. By varying separately the gradients of element size and element density, it was possible to show that only the former contributed appreciably to the impression of slant. Only some of the measures considered are consistent with this result.     

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.     

The perception of cast shadows

When an object casts its shadow on a background surface, the shadow can be informative about the shape of the object, the shape of the background surface and the spatial arrangement of the object relative to the background. Among all these roles, we found that cast shadows were perceptually most relevant for the recovery of spatial arrangement, especially when the shadow is in motion. This finding is intriguing when one considers the ambiguities in the possible ways that shadow motion can be interpreted. We reasoned that the visual system must use a priori constraints to disambiguate the cast shadow motion. One of these constraints is that the light source is stationary. Though simple, the stationary-light-source constraint supports rich, reliable inferences about the qualitative motions of objects in three dimensions.     

Visual impressions of penetration in the perception of objects in motion

Observers viewed visual stimuli in which one object moved to a position of partial occlusion by another. The objects were presented as two-dimensional profiles moving in an undefined space, so the partial occlusion supports several different physical interpretations. In fact some stimuli reliably gave rise to a perceptual impression that the moving object penetrated or pierced the stationary one. This kind of interaction impression has not previously been reported. The impression was maximized by rapid deceleration to a halt with minimal occlusion. If the object decelerated more slowly, so that it was completely occluded or projected from the far side of the stationary object, it was perceived as moving behind the stationary object. The shape of the moving object and its speed prior to occlusion had significant but small effects.     

FACTORS INFLUENCING TWO-DIMENSIONAL FORM PERCEPTION

The perceived shape of a circle and ellipse has been studied as influenced by the size of the figure, size of the reference frame, contrast and intensity. It was found that these factors have a systematic influence upon form perception. The data are considered within the context of the shape slant invariance hypothesis and are interpreted as providing evidence against this hypothesis as applied to the proximal form.     

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.     

The perception and recognition of natural object shape from deforming and static shadows

In this study of the informativeness of shadows for the perception of object shape, observers viewed shadows cast by a set of natural solid objects and were required to discriminate between them. In some conditions the objects underwent rotation in depth while in other conditions they remained stationary, thus producing both deforming and static shadows. The orientation of the light source casting the shadows was also varied, leading to further alterations in the shape of the shadows. When deformations in the shadow boundary were present, the observers were able to reliably recognize and discriminate between the objects, invariant over the shadow distortions produced by movements of the light source. The recognition performance for the static shadows depended critically upon the content of the specific views that were shown. These results support the idea that there are invariant features of shadow boundaries that permit the recognition of shape (cf Koenderink, 1984 Perception 13 321-330).     

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.     

How little do we need for 3-D shape perception?

How little do we need to perceive 3-D shape in monocular natural images? The shape-from-texture and shape-from-shading perspectives would motivate that 3-D perception vanishes once low-level cues are disrupted. Is this the case in human vision? Or can top-down influences salvage the percept? In this study we probe this question by employing a gauge-figure paradigm similar to that used by Koenderink et al (1992, Perception & Psychophysics 52 487-496). Subjects were presented degraded natural images and instructed to make local assessments of slant and tilt at various locations thereby quantifying their internal 3-D percept. Analysis of subjects' responses reveals recognition to be a significant influence thereby allowing subjects to perceive 3-D shape at high levels of degradation. Specifically, we identify the 'medium-blur' condition, images approximately 32 pixels on a side, to be the limit for accurate 3-D shape perception. In addition, we find that degradation affects the perceived slant of point-estimates making images look flatter as degradation increases. A subsequent condition that eliminates texture and shading but preserves contour and recognition reveals how bottom-up and top-down cues can combine for accurate 3-D shape 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.     

Shape from shadows

The colors, textures, and shapes of shadows are physically constrained in several ways in natural scenes. The visual system appears to ignore these constraints, however, and to accept many patterns as shadows even though they could not occur naturally. In the stimuli that we have studied, the only requirements for the perception of depth due to shadows were that shadow regions be darker than the surrounding, nonshadow regions and that there be consistent contrast polarity along the shadow border. Three-dimensional shape due to shadows was perceived when shadow areas were filled with colors or textures that could not occur in natural scenes, when shadow and nonshadow regions had textures that moved in different directions, or when they were presented on different depth planes. The results suggest that the interpretation of shadows begins with the identification of acceptable shadow borders by a cooperative process that requires consistent contrast polarity across a range of scales at each point along the border. Finally, we discuss how the identification of a shadow region can help the visual system to patch together areas that are separated by shadow boundaries, to identify directions of surface curvature, and to select a preferred three-dimensional interpretation while rejecting others.     

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.     

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.     

Rapid processing of cast and attached shadows

We used a visual-search method to investigate the role of shadows in the rapid discrimination of scene properties. Targets and distractors were light or dark 2-D crescents of identical shape and size, on a mid-grey background. From the dark stimuli, illusory 3-D shapes can be created by blurring one arc of the crescent. If the inner arc is blurred, the stimulus is perceived as a curved surface with attached shadow. If the outer arc is blurred, the stimulus is perceived as a flat surface casting a shadow. In a series of five experiments, we used this simple stimulus to map out the shadow properties that the human visual system can rapidly detect and discriminate. To subtract out 2-D image factors, we compared search performance for dark-shadow stimuli with performance for light-shadow stimuli which generally do not elicit strong 3-D percepts. We found that the human visual system is capable of rapid discrimination based upon a number of different shadow properties, including the type of the shadow (cast or attached), the direction of the shadow, and the displacement of the shadow. While it is clear that shadows are not simply discounted in rapid search, it is unclear at this stage whether rapid discrimination is acting upon shadows per se or upon representations of 3-D object shape and position elicited by perceived shadows.