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.     

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.     

Binocular shape constancy from novel views: the role of a priori constraints

We tested shape constancy from novel views in the case of binocular viewing, using a variety of stimuli, including polyhedra, polygonal lines, and points in 3-D. The results of the psychophysical experiments show that constraints such as planarity of surface contours and symmetry are critical for reliable shape constancy. These results are consistent with the results obtained in our previous psychophysical experiments on shape constancy from novel views in the presence of a kinetic depth effect (Pizlo & Stevenson, 1999). On the basis of these results, we developed a new model of binocular shape reconstruction. The model is based on the assumption that binocular reconstruction is a difficult inverse problem, whose solution requires imposing a priori constraints on the family of possible interpretations. In the model, binocular disparity is used to correct monocularly reconstructed shape. The new model was tested on the same shapes as those used in the psychophysical experiments. The reconstructions produced by this model are substantially more reliable than the reconstructions produced by models that do not use constraints. Interestingly, monocular (but not binocular) reconstructions produced by this model correlate well with both monocular and binocular performance of human subjects. This fact suggests that binocular and monocular reconstructions of shapes in the human visual system involve similar mechanisms based on monocular shape constraints.     

Constancy and illusion of apparent direction of rotary motion in depth: Tests of a theory

An explanation of apparent direction of rotary motion in depth derived from a general theory of perceptual constancy and illusion is proposed with experimental data in its support. Apparent direction of movement is conceived of as exhibiting-perceptual constancy or illusion as a function of apparent direction of orientation m depth for plane objects and apparent relative depth for three-dimensional objects. Apparent reversals of movement direction represent either regular fluctuations between constancy and illusion of direction as a function of valid and invalid stimuli for orientation, or irregular and random fluctuations in their absence. In three preliminary experiments, the apparent movement direction of plane ellipses was investigated as a function of surface pattern information for orientation, and in Experiment I apparent reversals during 20-revolution trials were studied. In Experiment II, apparent movement direction of 3D elliptical V shapes as a function of surface pattern information for relative depth was investigated. In addition to supporting the explanation proposed, the data offer a resolution of a conflict between different theories of apparent reversal of motion in depth.     

Shape from shading from images rendered with various surface types and light fields

Shape constancy is referred to as the tendency for the perceived shape of an object to remain unchanged even under changed viewing and illumination conditions. We investigated, in two experiments, whether shape constancy would hold for images of 3-D solid objects defined by shading only, whose renderings differed in terms of surface material type (bi-directional reflectance distribution functions), light field, light direction, shape, and specularity. Observers were presented with the image of a sphere or an ellipsoid and required to set perceived orientation and cross-section profile on designated points of the image. Results showed that shape judgments varied with all the aforementioned variables except specularity. Shape estimates were more precise with specular than asperity scattering surfaces, collimated than hemispherical diffuse lighting conditions, lower than higher elevations, spherical than ellipsoidal shapes, but not different between surfaces having differing specularity. These results suggest that shape judgments are made largely on the basis of the overall intensity distribution of shading, and that the portions of intensity distribution that are due to nonstructural variables such as surface material type or light field are not excluded in the process of shape estimation, as if being due to structural components. It is concluded that little constancy is expected in the perception of shape from shading.     

Shape constancy from novel views

Prior experiments on shape constancy from novel views are inconclusive: Some show that shapes of objects can be recognized reliably from novel views, whereas others show just the opposite. Our analysis of prior results suggests that shape constancy from novel views is reliable when the object has properties that constrain its shape: The object has volumetric primitives, it has surfaces, it is symmetrical, it is composed of geons, its contours are planar, and its images provide useful topological information about its three-dimensional structure. To test the role of some of these constraints, we performed a set of experiments. Solid shapes (polyhedra) were shown on a computer monitor by means of kinetic depth effect. Experiment 1 showed that shape constancy can be reliably achieved when a polyhedron is represented by its contours (most of the constraints are present), but not when it is represented by vertices or by a polygonal line connecting the vertices in a random order (all the constraints are absent). Experiments 2 and 3 tested the role of individual constraints. Results of these experiments show that shape constancy from novel views is reliable when the object has planar contours and when the shapes of the contours together with topological information about the relations among the contours constrain the possible interpretations of the shape. Symmetry of the object and the topological stability of its image also contribute to shape constancy.     

The perception of a changing shape

Under specified conditions a pair of simple shapes are matched by a subject when almost all supplementary textural and space cues of depth vision have been removed. Under such conditions it is found that shape constancy is no longer present. However, the effect of regular rotatory motion of the shape is sufficient to restore constancy in the continued absence of other cues. Degree of perceptual constancy appears to be correlated with rate of change of shape. It is suggested that an explanation of the phenomenon is to be sought along the lines of Michotte's concept of “object creation” rather than in terms of gradient variables.     

Vertical disparity affects shape and size judgments across surfaces separated in depth

Vertical binocular disparity provides a useful source of information allowing three-dimensional (3-D) shape to be recovered from horizontal binocular disparity. In order to influence metric shape judgments, a large field of view is required, suggesting that vertical disparity may play a limited role in the perception of objects projecting small retinal images. This limitation could be overcome if vertical disparity information could be pooled over wide areas of 3-D space. This was investigated by assessing the effect of vertical disparity scaling of a large surround surface on the perceived size and 3-D shape of a small, central object. Observers adjusted the size and shape of a virtual, binocularly defined ellipsoid to match those of a real, hand-held tennis ball. The virtual ball was presented at three distances (200, 325, and 450 mm). Vertical disparities in a large surround surface were manipulated to be consistent with a distance of 160 mm or infinity. Both shape and size settings were influenced by this manipulation. This effect did not depend on presenting the surround and target objects at the same distance. These results suggest that the influence of vertical disparity on the perceived distance to a surface also affects the estimated distance of other visible surfaces. Vertical disparities are therefore important in the perception of metric depth, even for objects that in themselves subtend only small retinal images.     

The influence of illumination direction on the pictorial reliefs of Lambertian surfaces

In order to assess the influence of illumination direction on shape constancy, we studied the pictorial relief of computer images of globular 3-D objects. We used two globally convex objects, one with a furrow and one with a dimple. Observers adjusted local surface attitude probes at 200-250 different locations in the image such that they seemed to lie on the pictorial surface. We manipulated the viewing direction and the illumination direction in a 2 x 2 orthogonal design. Viewing directions were chosen such that the image contained only a few, or no, contour singularities. Changes in the illumination direction were found to induce systematic changes in the settings for both viewing directions. Effects were especially pronounced for images that had no contour singularities. The results showed that a change in the illumination direction can change the local shape of the pictorial relief in addition to the bas-relief ambiguities of scaling and shearing in depth. We found that concavities in the pictorial relief are associated with the darker areas in the image. The deviation from shape constancy cannot be explained by bas-relief ambiguity since the required transformation between the shapes is nonlinear.     

Using morphs of familiar objects to examine how shape discriminability influences view sensitivity

We investigated how the difficulty of detecting a shape change influenced the achievement of object constancy across depth rotations for object identification and categorization tasks. In three sequential matching experiments, people saw pictures of morphs between two everyday, nameable objects (e.g., bath-sink morphs, along a continuum between "bath" and "sink" end-point shapes). In each experiment, both view changes and shape changes influenced performance. Furthermore, the deleterious effects of view changes were strongest when shape discrimination was hardest. In our earlier research, using morphs of novel objects, we found a similar interaction between view sensitivity and shape sensitivity (Lawson, 2004b; Lawson & Bülthoff, 2006; Lawson, Bülthoff, & Dumbell, 2003). The present results extend these findings to familiar-object morphs. They suggest that recognition remains view-sensitive at the basic level of identification for everyday, nameable objects, and that the difficulty of shape discrimination plays a critical role in determining the degree of this view sensitivity.     

Matching perceived depth from disparity and from velocity: Modeling and psychophysics

We asked observers to match in depth a disparity-only stimulus with a velocity-only stimulus. The observers’ responses revealed systematic biases: the two stimuli appeared to be matched in depth when they were produced by the projection of different distal depth extents. We discuss two alternative models of depth recovery that could account for these results. (1) Depth matches could be obtained by scaling the image signals by constants not specified by optical information, and (2) depth matches could be obtained by equating the stimuli in terms of their signal-to-noise ratios (see Domini & Caudek, 2009). We show that the systematic failures of shape constancy revealed by observers’ judgments are well accounted for by the hypothesis that the apparent depth of a stimulus is determined by the magnitude of the retinal signals relative to the uncertainty (i.e., internal noise) arising from the measurement of those signals.     

Kinetic depth effect and identification of shape

We introduce an objective shape-identification task for measuring the kinetic depth effect (KDE). A rigidly rotating surface consisting of hills and valleys on an otherwise flat ground was defined by 300 randomly positioned dots. On each trial, 1 of 53 shapes was presented; the observer's task was to identify the shape and its overall direction of rotation. Identification accuracy was an objective measure, with a low guessing base rate of the observer's perceptual ability to extract 3D structure from 2D motion via KDE. (1) Objective accuracy data were consistent with previously obtained subjective rating judgments of depth and coherence. (2) Along with motion cues, rotating real 3D dot-defined shapes inevitably produced a cue of changing dot density. By shortening dot lifetimes to control dot density, we showed that changing density was neither necessary nor sufficient to account for accuracy; motion alone sufficed. (3) Our shape task was solvable with motion cues from the 6 most relevant locations. We extracted the dots from these locations and used them in a simplified 2D direction-labeling motion task with 6 perceptually flat flow fields. Subjects' performance in the 2D and 3D tasks was equivalent, indicating that the information processing capacity of KDE is not unique. (4) Our proposed structure-from-motion algorithm for the shape task first finds relative minima and maxima of local velocity and then assigns 3D depths proportional to velocity.     

Symmetry in haptic and in visual shape perception

Four experiments tested the hypothesis that bilateral symmetry is an incidental encoding property in vision, but can also be elicited as an incidental effect in touch, provided that sufficient spatial reference information is available initially for haptic inputs to be organized spatially. Experiment 1 showed that symmetry facilitated processing in vision, even though the task required judgments of stimulus closure rather than the detection of symmetry. The same task and stimuli failed to show symmetry effects in tactual scanning by one finger (Experiment 2). Experiment 3 found facilitating effects for vertically symmetric open stimuli, although not for closed patterns, in two-forefinger exploration when the fore-fingers had previously been aligned to the body midaxis to provide body-centered spatial reference. The one-finger exploration condition again failed to show symmetry effects. Experiment 4 replicated the facilitating effects of symmetry for open symmetric shapes in tactual exploration by the two (previously aligned) forefingers. Closed shapes again showed no effect. Spatial-reference information, finger movements, and stimulus factors in shape perception by touch are discussed.     

Revisiting Snodgrass and Vanderwart's object pictorial set: the role of surface detail in basic-level object recognition

Theories of object recognition differ to the extent that they consider object representations as being mediated only by the shape of the object, or shape and surface details, if surface details are part of the representation. In particular, it has been suggested that color information may be helpful at recognizing objects only in very special cases, but not during basic-level object recognition in good viewing conditions. In this study, we collected normative data (naming agreement, familiarity, complexity, and imagery judgments) for Snodgrass and Vanderwart's object database of 260 black-and-white line drawings, and then compared the data to exactly the same shapes but with added gray-level texture and surface details (set 2), and color (set 3). Naming latencies were also recorded. Whereas the addition of texture and shading without color only slightly improved naming agreement scores for the objects, the addition of color information unambiguously improved naming accuracy and speeded correct response times. As shown in previous studies, the advantage provided by color was larger for objects with a diagnostic color, and structurally similar shapes, such as fruits and vegetables, but was also observed for man-made objects with and without a single diagnostic color. These observations show that basic-level 'everyday' object recognition in normal conditions is facilitated by the presence of color information, and support a 'shape + surface' model of object recognition, for which color is an integral part of the object representation. In addition, the new stimuli (sets 2 and 3) and the corresponding normative data provide valuable materials for a wide range of experimental and clinical studies of object recognition.     

Surface-illuminant ambiguity and color constancy: effects of scene complexity and depth cues

Two experiments were conducted to study how scene complexity and cues to depth affect human color constancy. Specifically, two levels of scene complexity were compared. The low-complexity scene contained two walls with the same surface reflectance and a test patch which provided no information about the illuminant. In addition to the surfaces visible in the low-complexity scene, the high-complexity scene contained two rectangular solid objects and 24 paper samples with diverse surface reflectances. Observers viewed illuminated objects in an experimental chamber and adjusted the test patch until it appeared achromatic. Achromatic settings made tinder two different illuminants were used to compute an index that quantified the degree of constancy. Two experiments were conducted: one in which observers viewed the stimuli directly, and one in which they viewed the scenes through an optical system that reduced cues to depth. In each experiment, constancy was assessed for two conditions. In the valid-cue condition, many cues provided valid information about the illuminant change. In the invalid-cue condition, some image cues provided invalid information. Four broad conclusions are drawn from the data: (a) constancy is generally better in the valid-cue condition than in the invalid-cue condition: (b) for the stimulus configuration used, increasing image complexity has little effect in the valid-cue condition but leads to increased constancy in the invalid-cue condition; (c) for the stimulus configuration used, reducing cues to depth has little effect for either constancy condition: and (d) there is moderate individual variation in the degree of constancy exhibited, particularly in the degree to which the complexity manipulation affects performance.     

Perceiving shape from profiles

Four experiments related human perception of shape from profiles to current theoretical predictions. In Experiment 1, judgments of structure and motion were obtained for single- and dualellipsoid displays rotating about various axes. Ratings were highest when the axis of rotation was in the image plane and were influenced by the number of ellipsoids and the orientation of a single ellipsoid. The subsequent experiments explored the effect of orientation on shape judgments of a single ellipsoid. The results of Experiments 2 and 3 suggested that the effect of orientation found in Experiment 1 was not due to either the inability of certain orientations to be perceived as three-dimensional objects or to two-dimensional artifacts. It was thus argued that this effect of orientation was due to points of correspondence in relative motion that arise when the major axis is not perpendicular to the axis of rotation. In Experiment 4, subjects provided judgments of both shape and angular velocity. The elevated ellipsoids that were judged as larger were also judged as rotating more slowly. The inverse relationship between size and angular velocity is consistent with current theories. The connection between theory and data was further demonstrated by applying a shape-recovery algorithm to the stimuli used in Experiment 4 and finding a similar tradeoff between angular velocity and shape.     

Stereoscopic shape discrimination is well preserved across changes in object size

A single experiment evaluated human observers’ ability to discriminate the shape of solid objects that varied in size and orientation in depth. The object shapes were defined by binocular disparity, Lambertian shading, and texture. The object surfaces were smoothly curved and had naturalistic shapes, resembling those of water-smoothed granite rocks. On any given trial, two objects were presented that were either the same or different in terms of shape. When the “same” objects were presented, they differed in their orientation in depth by 25°, 45°, or 65°. The observers were required to judge whether any given pair of objects was the “same” or “different” in terms of shape. The size of the objects was also varied by amounts up to ±40% relative to the standard size. The observers’ shape discrimination performance was strongly affected by the magnitude of the orientation changes in depth - thus, their performance was viewpoint dependent. In contrast, the observers’ shape discrimination abilities were only slightly affected by changes in the overall size of the objects. It appears that human observers can recognize the three-dimensional shape of objects in a manner that is relatively independent of size.     

The perception of a rotating shape

A regularly rotated shape was matched to given shapes set in the frontal parallel plane position, under conditions which yielded practically zero constancy. It was found that increases in the rate of rotation resulted in increases in the angular settings at which the subjects matched the rotating shape to the given standard shapes. Thus Langdon's (1951) experimental results were confirmed. However, since matches to the “real” shape also increased with increases in the rate of rotation, Langdon's interpretation of his experimental results is considered to be incorrect. Further theoretical discussion is advanced in support of this conclusion: namely, that regular rotation of a shape, viewed under conditions which usually yield zero constancy, does not restore constancy.     

On how adults identify the orientation of a shape

It is generally assumed that the orientation of a shape is judged only by identifying the location of a particular feature. In contrast, it is argued here that the basis of orientation judgments depends on the task; this proposal is examined for judgments of upside down and sideways. Pictures of mono-oriented objects were presentedone at a time, and adults identified the orientations of each in a RT paradigm. One condition presented successively upright and upside-down pictures or upright and sideways pictures. Another condition presented successively upside-down and sideways pictures. As predicted, the time to identify orientation was longer for the condition presenting two nonuprights, because specific identifications of upside down and sideways were required, whereas the other condition required only that uprightness be distinguished from nonuprightness. The notion that the nature of a judgment of shape orientation depends on the contrasts provided by the task has implications for theory and experimental design that are discussed for both realistic and geometric shapes.     

The importance of being upright: Use of environmental and viewer-centered reference frames in shape discriminations of novel three-dimensional objects

We investigated the frame of reference that people use to make shape discriminations when their heads are either upright or tilted. Observers madesame-different judgments of pairs of novel threedimensional objects that were aligned along their length within the frontal-parallel plane and rotated in depth around an axis parallel to their own axes of elongation. The aligned objects were displayed vertically, tilted 45°, or horizontally with respect to the environmental upright, but the distance of each pair from the upright was irrelevant to resolving the angular disparity between the stimuli for thesame-different judgment. Nevertheless, when observers’ heads were upright, the time to encode the stimuli was a linear function of the distance of the stimuli from the environmental upright, whereas when observers’ heads were tilted 45°, encoding times for tilted and vertical stimuli did not differ and were faster than the times to encode horizontal stimuli. We interpreted these data to mean that observers either rotate or reference the top of an object to the environmental upright, and they can use either a gravitational or retinal reference frame to do so when either they or the objects are not upright.