3-D shape perception

In this paper, we analyze and test three theories of 3-D shape perception: (1) Helmholtzian theory, which assumes that perception of the shape of an object involves reconstructing Euclidean structure of the object (up to size scaling) from the object’s retinal image after taking into account the object’s orientation relative to the observer, (2) Gibsonian theory, which assumes that shape perception involves invariants (projective or affine) computed directly from the object’s retinal image, and (3) perspective invariants theory, which assumes that shape perception involves a new kind of invariants of perspective transformation. Predictions of these three theories were tested in four experiments. In the first experiment, we showed that reliable discrimination between a perspective and nonperspective image of a random polygon is possible even when information only about the contour of the image is present. In the second experiment, we showed that discrimination performance did not benefit from the presence of a textured surface, providing information about the 3-D orientation of the polygon, and that the subjects could not reliably discriminate between the 3-D orientation of the textured surface and that of a shape. In the third experiment, we compared discrimination for solid shapes that either had flat contours (cuboids) or did not have visible flat contours (cylinders). The discrimination was very reliable in the case of cuboids but not in the case of cylinders. In the fourth experiment, we tested the effectiveness of planar motion in perception of distances and showed that the discrimination threshold was large and similar to thresholds when other cues to 3-D orientation were used. All these results support perspective invariants as a model of 3-D shape perception.     

Salient features in 3-D haptic shape perception

Shape is an important cue for recognizing an object by touch. Several features, such as edges, curvature, surface area, and aspect ratio, are associated with 3-D shape. To investigate the saliency of 3-D shape features, we developed a haptic search task. The target and distractor items consisted of shapes (cube, sphere, tetrahedron, cylinder, and ellipsoid) that differed in several of these features. Exploratory movements were left as unconstrained as possible. Our results show that this type of haptic search task can be performed very efficiently (25 msec/item) and that edges and vertices are the most salient features. Furthermore, very salient local features, such as edges, can also be perceived through enclosure, an exploratory procedure usually associated with global shape. Since the subjects had to answer as quickly as possible, this suggests that speed may be a factor in selecting the appropriate exploratory procedure.     

The perception of 3-D shape from shadows cast onto curved surfaces

In a natural environment, cast shadows abound. Objects cast shadows both upon themselves and upon background surfaces. Previous research on the perception of 3-D shape from cast shadows has only examined the informativeness of shadows cast upon flat background surfaces. In outdoor environments, however, background surfaces often possess significant curvature (large rocks, trees, hills, etc.), and this background curvature distorts the shape of cast shadows. The purpose of this study was to determine the extent to which observers can “discount” the distorting effects of curved background surfaces. In our experiments, observers viewed deforming or static shadows of naturally shaped objects, which were cast upon flat and curved background surfaces. The results showed that the discrimination of 3-D object shape from cast shadows was generally invariant over the distortions produced by hemispherical background surfaces. The observers often had difficulty, however, in identifying the shadows cast onto saddle-shaped background surfaces. The variations in curvature which occur in different directions on saddle-shaped background surfaces cause shadow distortions that lead to difficulties in object recognition and discrimination.     

Aging and the perception of depth and 3-D shape from motion parallax

The ability of younger and older observers to perceive 3-D shape and depth from motion parallax was investigated. In Experiment 1, the observers discriminated among differently curved 3-dimensional (3-D) surfaces in the presence of noise. In Experiment 2, the surfaces' shape was held constant and the amount of front-to-back depth was varied; the observers estimated the amount of depth they perceived. The effects of age were strongly task dependent. The younger observers' performance in Experiment 1 was almost 60% higher than that of the older observers. In contrast, no age effect was obtained in Experiment 2. Older observers can effectively perceive variations in depth from patterns of motion parallax, but their ability to discriminate 3-D shape is significantly compromised.     

Aging and the perception of 3-D shape from dynamic patterns of binocular disparity

In two experiments, we investigated the ability of younger and older observers to perceive and discriminate 3-D shape from static and dynamic patterns of binocular disparity. In both experiments, the younger observers' discrimination accuracies were 20% higher than those of the older observers. Despite this quantitative difference, in all other respects the older observers performed similarly to the younger observers. Both age groups were similarly affected by changes in the magnitude of binocular disparity, by reductions in binocular correspondence, and by increases in the speed of stereoscopic motion. In addition, observers in both age groups exhibited an advantage in performance for dynamic stereograms when the patterns of binocular disparity contained significant amounts of correspondence "noise." The process of aging does affect stereopsis, but the effects are quantitative rather than qualitative.     

The visual perception of 3D shape

A fundamental problem for the visual perception of 3D shape is that patterns of optical stimulation are inherently ambiguous. Recent mathematical analyses have shown, however, that these ambiguities can be highly constrained, so that many aspects of 3D structure are uniquely specified even though others might be underdetermined. Empirical results with human observers reveal a similar pattern of performance. Judgments about 3D shape are often systematically distorted relative to the actual structure of an observed scene, but these distortions are typically constrained to a limited class of transformations. These findings suggest that the perceptual representation of 3D shape involves a relatively abstract data structure that is based primarily on qualitative properties that can be reliably determined from visual information.     

Effects of 3-D complexity on the perception of 2-D depictions of objects

In a recent study, Pelli (1999 Science 285 844-846) performed a set of perceptual experiments using portrait paintings by Chuck Close. Close's work is similar to the 'Lincoln' portraits of Harmon and Julesz (1973 Science 180 1194-1197) in that they are composite images consisting of coarsely sampled, individually painted, mostly homogeneous cells. Pelli showed that perceived shape was dependent on size, refuting findings that perception of this type is scale-invariant. In an attempt to broaden this finding we designed a series of experiments to investigate the interaction of 2-D scale and 3-D structure on our perception of 3-D shape. We present a series of experiments where field of view, 3-D object complexity, 2-D image resolution, viewing orientation, and subject matter of the stimulus are manipulated. On each trial, observers indicated if the depicted objects appeared to be 2-D or 3-D. Results for face stimuli are similar to Pelli's, while more geometrically complex stimuli show a further interaction of the 3-D information with distance and image information. Complex objects need more image information to be seen as 3-D when close; however, as they are moved further away from the observer, there is a bias for seeing them as 3-D objects rather than 2-D images. Finally, image orientation, relative to the observer, shows little effect, suggesting the participation of higher-level processes in the determination of the 'solidness' of the depicted object. Thus, we show that the critical image resolution depends systematically on the geometric complexity of the object depicted.     

A system for investigating 3-D form perception

This paper describes a noninvasive, relatively inexpensive, and simple to use system developed by the authors for monitoring the visual inspection behavior of someone free to select any viewing angle of an object by moving about it while at the same time being able to rotate it. A demonstration experiment verifies the potential of the system to study 3-D form perception.     

Discrimination of 3-D shape and 3-D curvature from motion in active vision

We examined the ability of human observers to discriminate between different 3-D quadratic surfaces defined by motion, and with head position fed back to the stimulus to provide an up-to-date dynamical perspective view. We tested whether 3-D shape or 3-D curvature would affect discrimination performance. It appeared that discrimination of 3-D quadratic shape clearly depended on shape but not on the amount of curvature. Even when the amount of curvature was randomized, subjects’ performance was not altered. On the other hand, the discrimination of 3-D curvature clearly depended linearly on curvature with Weber fractions of 20% on the average and, to a small degree, on 3-D shape. The experiment shows that observers can easily separate 3-D shape and 3-D curvature, and that Koenderink’s shape index and curvedness provide a convenient way to specify shape. These results warn us against using just any arbitrary 3-D shape in 3-D shape perception tasks and indicate, for example, that emphasizing 3-D shape in computer displays by exaggerating curvature does not have any effect.     

Effective 3-D shape discrimination survives retinal blur

A single experiment evaluated observers’ ability to visually discriminate 3-D object shape, where the 3-D structure was defined by motion, texture, Lambertian shading, and occluding contours. The observers’ vision was degraded to varying degrees by blurring the experimental stimuli, using 2.0-, 2.5-, and 3.0-diopter convex lenses. The lenses reduced the observers’ acuity from ?0.091 LogMAR (in the no-blur conditions) to 0.924 LogMAR (in the conditions with the most blur; 3.0-diopter lenses). This visual degradation, although producing severe reductions in visual acuity, had only small (but significant) effects on the observers’ ability to discriminate 3-D shape. The observers’ shape discrimination performance was facilitated by the objects’ rotation in depth, regardless of the presence or absence of blur. Our results indicate that accurate global shape discrimination survives a considerable amount of retinal blur.     

Recovery of 3-D shape from deforming contours

Three experiments were conducted to examine the accuracy of 3-D shape recovery from deforming-contour displays. The displays simulated silhouettes of ellipsoids rotating about a vertical axis. Subjects judged the horizontal cross-section of the ellipsoids. The shape of the ellipsoid, the position of the axis of rotation, and the type of projection were manipulated in Experiment 1. The results indicated relatively accurate shape recovery when the major axis of the ellipsoid was small. In Experiment 2, the shape of the ellipsoid and the velocity and curvature of the contour were manipulated. When the rate of deformation of curvature was decreased, more eccentric shapes were reported. In Experiment 3, the shape of the object and the amount of simulated rotation were manipulated. Subjects made both shape and extent of rotation judgments. The results showed that eccentricity of shape responses could be accurately predicted from rotation responses, suggesting that the recovery of 3-D shape from smooth, deforming contours is dependent on the perceived extent of rotation.     

2-D tilt and 3-D slant illusions in perception and action tasks

There is now a well established dissociation between perception and action based primarily on neuropsychological evidence [Milner and Goodale, 1995 The Visual Brain in Action (Oxford: Oxford University Press)]. Although equivocal, an important source of evidence from normal observers is that 'perceptual illusions' may affect the systems differently. We investigated the relative effects of 2-D tilt and 3-D slant illusions in the two domains, using similar tasks to those employed originally by Milner and Goodale. Subjects were required to either post a card through, or set a paddle to match the orientation of, a plane that was presented in two conditions: surrounded by a striped surface tilted between +90 degrees and -90 degrees (2-D tilt contrast), or surrounded by a disparity defined surface slanted in depth between +60 degrees and -60 degrees (3-D depth contrast). For 2-D tilt, action and perception were equally affected by the illusion, whereas in the 3-D condition they were not. Here, the illusion appeared greater in the posting than in the perceptual task. We conclude that, although no qualitative differences exist, there were quantitative differences between perception and action tasks in the binocular condition.     

The effects of age upon the perception of depth and 3-D shape from differential motion and binocular disparity

The ability of younger and older adults to perceive the 3-D shape, depth, and curvature of smooth surfaces defined by differential motion and binocular disparity was evaluated in six experiments. The number of points defining the surfaces and their spatial and temporal correspondences were manipulated. For stereoscopic sinusoidal surfaces, the spatial frequency of the corrugations was also varied. For surfaces defined by motion, the lifetimes of the individual points in the patterns were varied, and comparisons were made between the perception of surfaces defined by points and that of more ecologically valid textured surfaces. In all experiments, the older observers were less sensitive to the depths and curvatures of the surfaces, although the deficits were much larger for motion-defined surfaces. The results demonstrate that older adults can extract depth and shape from optical patterns containing only differential motion or binocular disparity, but these abilities are often manifested at reduced levels of performance.     

Neural dynamics of 3-D surface perception: figure-ground separation and lightness perception

This article develops the FACADE theory of three-dimensional (3-D) vision to simulate data concerning how two-dimensional pictures give rise to 3-D percepts of occluded and occluding surfaces. The theory suggests how geometrical and contrastive properties of an image can either cooperate or compete when forming the boundary and surface representations that subserve conscious visual percepts. Spatially long-range cooperation and short-range competition work together to separate boundaries of occluding figures from their occluded neighbors, thereby providing sensitivity to T-junctions without the need to assume that T-junction "detectors" exist. Both boundary and surface representations of occluded objects may be amodally completed, whereas the surface representations of unoccluded objects become visible through modal processes. Computer simulations include Bregman-Kanizsa figure-ground separation, Kanizsa stratification, and various lightness percepts, including the Münker-White, Benary cross, and checkerboard percepts.     

A macintosh interface to teach 3-D perception cues

I present an interface between a Macintosh computer and a pair of glasses with liquid crystal shutter lenses that allow interactive demonstration and investigation of the visual system. This equipment allows a graphic image to be presented to a subject’s eyes in a variety of ways. A primary application of this apparatus has been to create binocular disparity that results in a convincing illusion of depth. Other possible applications include tachistoscopic functions and monocular visual presentations.     

The perception of lightness in 3-D curved objects

Lightness constancy in complex scenes requires that the visual system take account of information concerning variations of illumination falling on visible surfaces. Three experiments on the perception of lightness for three-dimensional (3-D) curved objects show that human observers are better able to perform this accounting for certain scenes than for others. The experiments investigate the effect of object curvature, illumination direction, and object shape on lightness perception. Lightness constancy was quite good when a rich local gray-level context was provided. Deviations occurred when both illumination and reflectance changed along the surface of the objects. Does the perception of a 3-D surface and illuminant layout help calibrate lightness judgments? Our results showed a small but consistent improvement between lightness matches on ellipsoid shapes, relative to flat rectangle shapes, under illumination conditions that produce similar image gradients. Illumination change over 3-D forms is therefore taken into account in lightness perception.     

Accuracy and precision of binocular 3-D motion perception

In principle, information for 3-D motion perception is provided by the differences in position and motion between left- and right-eye images of the world. It is known that observers can precisely judge between different 3-D motion trajectories, but the accuracy of binocular 3-D motion perception has not been studied. The authors measured the accuracy of 3-D motion perception. In 4 different tasks, observers were inaccurate, overestimating trajectory angle, despite consistently choosing similar angles (high precision). Errors did not vary consistently with target distance, as would be expected had inaccuracy been due to misestimates of viewing distance. Observers appeared to rely strongly on the lateral position of the target, almost to the exclusion of the use of depth information. For the present tasks, these data suggest that neither an accurate estimate of 3-D motion direction nor one of passing distance can be obtained using only binocular cues to motion in depth. ((c) 2003 APA, all rights reserved)     

Aging and visual 3-D shape recognition from motion

Two experiments were conducted to evaluate the ability of younger and older adults to recognize 3-D object shape from patterns of optical motion. In Experiment 1, participants were required to identify dotted surfaces that rotated in depth (i.e., surface structure portrayed using the kinetic depth effect). The task difficulty was manipulated by limiting the surface point lifetimes within the stimulus apparent motion sequences. In Experiment 2, the participants identified solid, naturally shaped objects (replicas of bell peppers, Capsicum annuum) that were defined by occlusion boundary contours, patterns of specular highlights, or combined optical patterns containing both boundary contours and specular highlights. Significant and adverse effects of increased age were found in both experiments. Despite the fact that previous research has found that increases in age do not reduce solid shape discrimination, our current results indicated that the same conclusion does not hold for shape identification. We demonstrated that aging results in a reduction in the ability to visually recognize 3-D shape independent of how the 3-D structure is defined (motions of isolated points, deformations of smooth optical fields containing specular highlights, etc.).     

The perception of 3-D structure from contradictory optical patterns

Two experiments investigated observers’ perceptions of 3-D structure when optical sources of information were contradictory. When motion and stereoscopic disparities specified different surfaces, the perceptual outcome depended strongly on the direction of curvature present within each modality. Previous research has shown that the perception of surface slant and curvature is anisotropic for both motion and stereo and that it depends on the direction in which it takes place. In the present experiments, the modality with the “effective” direction of curvature tended to dominate or suppress the perception of surfaces in the other modality with less effective curvatures. The results have implications for models which attempt to combine 3-D data from different optical sources.