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.     

The unknown Fechner

Summary Despite Fechner's universal fame as the founder of psychophysics, his work is not very well known among contemporary psycholgists. To correct this situation, the present issue of Psychological Research contains some excerpts from previously untranslated works of Fechner. By way of introduction to the translations, some popular misconceptions about Fechner's outer psychophysics are corrected, and a brief introduction to his inner psychophysics is given.     

Mutual information, perceptual independence, and holistic face perception

The concept of perceptual independence is ubiquitous in psychology. It addresses the question of whether two (or more) dimensions are perceived independently. Several authors have proposed perceptual independence (or its lack thereof) as a viable measure of holistic face perception (Loftus, Oberg, & Dillon, Psychological Review 111:835–863, 2004; Wenger & Ingvalson, Learning, Memory, and Cognition 28:872–892, 2002). According to this notion, the processing of facial features occurs in an interactive manner. Here, I examine this idea from the perspective of two theories of perceptual independence: the multivariate uncertainty analysis (MUA; Garner & Morton, Definitions, models, and experimental paradigms. Psychological Bulletin 72:233–259, 1969), and the general recognition theory (GRT; Ashby & Townsend, Psychological Review 93:154–179, 1986). The goals of the study were to (1) introduce the MUA, (2) examine various possible relations between MUA and GRT using numerical simulations, and (3) apply the MUA to two consensual markers of holistic face perception^—recognition of facial features (Farah, Wilson, Drain, & Tanaka, Psychological Review 105:482–498, 1998) and the composite face effect (Young, Hellawell, & Hay, Perception 16:747–759, 1987). The results suggest that facial holism is generated by violations of several types of perceptual independence. They highlight the important theoretical role played by converging operations in the study of holistic face perception.     

Anisotropy in haptic curvature and shape perception

An investigation was undertaken into whether haptic comparison of curvature and of shape is influenced by the length/width ratio of the hand. For this purpose three experiments were conducted to test the curvature matching of curved strips (experiment 1), the curvature matching of cylindrically curved hand-sized surfaces (experiment 2), and the shape discrimination of elliptically curved hand-sized surfaces (experiment 3). The orientation of the stimuli with respect to the fingers was varied. The results of the two matching experiments showed that a given curvature is judged to be more curved when touched along the fingers than when touched across the fingers. The phenomenal flatness along and across the fingers was found to be different and subject dependent. The results of the shape-discrimination experiment showed that the orientation of ellipsoidal surfaces influences the judgments of the shapes of these surfaces. This influence could be predicted on the basis of results of the second matching experiment. It is concluded that similar mechanisms underlie the (anisotropic) perception of curvature and shape. For the major part the trends in the results can be explained by the length/width ratio of the hand and the phenomenal flatnesses.     

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.     

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.     

Aging and the visual, haptic, and cross-modal perception of natural object shape

One hundred observers participated in two experiments designed to investigate aging and the perception of natural object shape. In the experiments, younger and older observers performed either a same/different shape discrimination task (experiment 1) or a cross-modal matching task (experiment 2). Quantitative effects of age were found in both experiments. The effect of age in experiment 1 was limited to cross-modal shape discrimination: there was no effect of age upon unimodal (ie within a single perceptual modality) shape discrimination. The effect of age in experiment 2 was eliminated when the older observers were either given an unlimited amount of time to perform the task or when the number of response alternatives was decreased. Overall, the results of the experiments reveal that older observers can effectively perceive 3-D shape from both vision and haptics.     

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.     

Fechner as a statistician

The work of Gustav Theodor Fechner (1801–1887) related to probability and statistics and, in particular, to the treatment of observations is described. From a mathematical point of view his arguments were often insufficient, but his work proved to be highly fruitful, and the relevant comments of such scholars as Pearson and von Mises are presented. As the originator of psychophysics, Fechner opened up a new field for quantification. Subsequent workers rejected some of his findings, while at the same time acknowledging their debt to him.     

Curvature and the visual perception of shape: theory on information along object boundaries and the minima rule revisited

Previous empirical studies have shown that information along visual contours is known to be concentrated in regions of high magnitude of curvature, and, for closed contours, segments of negative curvature (i.e., concave segments) carry greater perceptual relevance than corresponding regions of positive curvature (i.e., convex segments). Lately, Feldman and Singh (2005, Psychological Review, 112, 243-252) proposed a mathematical derivation to yield information content as a function of curvature along a contour. Here, we highlight several fundamental errors in their derivation and in its associated implementation, which are problematic in both mathematical and psychological senses. Instead, we propose an alternative mathematical formulation for information measure of contour curvature that addresses these issues. Additionally, unlike in previous work, we extend this approach to 3-dimensional (3D) shape by providing a formal measure of information content for surface curvature and outline a modified version of the minima rule relating to part segmentation using curvature in 3D shape.     

Enumeration: shape information and expertise

This study examined the interaction between grouping information and expertise in a simple enumeration task. In two experiments, participants made rapid judgements about the number of items present in a visual display. Within each display, items were grouped into a canonical representation (e.g., triangle, square, and pentagon) or were arranged linearly. In both experiments, grouping information facilitated enumeration performance, replicating previous findings in the literature. In Experiment 2, the facilitative effect of grouping information was found to be greater for Air Traffic Controllers (ATCs) than for matched novices, though they were no better than novices on linear arrays. This may be because linear, like canonical arrays, hold unique numerosity information, but only when they contain the minimum number of points necessary to define a line (i.e., 2). So ATCs' performance on linear arrays containing more than two items does not benefit from a facilitative effect of grouping information. That their experience of being ATCs, in terms of years served, was shown to account for the expertise effect suggests that such visuospatial expertise is acquired through frequent exposure to spatial arrays.     

Essential kinematic information,athletic experience,and affordance perception for others

The present study investigated the role of different types of movement in affordance perception, as well as the influence of sports experience. Perception of another actor’s maximum vertical jumping height and horizontal long-jumping distance was evaluated for basketball players, soccer players, and nonplayer controls after viewing point-light representations of the actors’ movements. Perceptual reports were more accurate after jumping-related movements (walking and squatting) were viewed than after nonrelated movements (standing and twisting). Vertical jump reports were more accurate than horizontal jump reports. Basketball and soccer players demonstrated higher accuracy than did controls. This research establishes that point-light displays contain essential kinematic information sufficient to support accurate affordance perception, and athletes appear better attuned to kinematic information specifying affordances for others as a result of their sports experience.     

Variations of the Fechner wheel

The Fechner wheel is a disk that is printed in black and white. When the Fechner wheel spins at an appropriate speed, semicircles on the wheel appear to be in color. Modern computer technology makes it possible to rapidly and repeatedly present a series of images on a monitor screen. A series of still images of a Fechner wheel can be substituted for a Fechner wheel on a motor shaft. Straight lines and lines of text can be substituted for semicircles to obtain a color effect. A color effect can be obtained in small areas of black-and-white pictures.     

The comparative psychophysics of complex shape perception

The authors compared the complex shape perception of humans and monkeys. Members of both species participated in a Same–Different paradigm in which they judged the similarity of shape pairs that could be variations of the same underlying prototype. For both species, similarity gradients were found to be steep going out from the transformational center of psychological space. In contrast, similarity gradients were found to be flat going from the periphery in toward the center of psychological space. These results show that there are important common principles in the shape-perception and shape-comparison processes of humans and monkeys. The same general organization of psychological space is obtained. The same quantifiable metric of psychological distance is applied. Established methods for creating controlled shape variation have the same effect on both species’ similarity judgments. The member of the to-be-judged pair of shapes that is peripheral in psychological space controls the strength of the perceived similarity of the pair. The results have broader implications for the comparative study of perception and categorization.     

Influence of shape on haptic curvature perception

Curvature discrimination of hand-sized doubly curved surfaces by means of static touch was investigated. Stimuli consisted of hyperbolical, cylindrical, elliptical and spherical surfaces of various curvatures. In the first experiment subjects had to discriminate the curvature along a specified orientation (the discrimination orientation) of a doubly curved surface from a flat surface. The curvature to be discriminated was oriented either along the middle finger or across the middle finger of the right hand. Independent of the shape of the surface, thresholds were found to be about 1.6 times smaller along the middle finger than across the middle finger. Discrimination biases were found to be strongly influenced by the shape of the surface; subjects judged a curvature to be more convex when the perpendicular curvature was convex than when this curvature was concave. With the results of the second experiment it could be ruled out that the influence of shape on curvature perception was simply due to a systematic error made by the subject regarding the discrimination orientation.     

On the perception of shape from shading

The extraction of three-dimensional shape from shading is one of the most perceptually compelling, yet poorly understood, aspects of visual perception. In this paper, we report several new experiments on the manner in which the perception of shape from shading interacts with other visual processes such as perceptual grouping, preattentive search (“pop-out”), and motion perception. Our specific findings are as follows: (1) The extraction of shape from shading information incorporates at least two “assumptions” or constraints—first,that there is a single light source illuminating the whole scene, and second, that the light is shining from “above” in relation to retinal coordinates. (2) Tokens defined by shading can serve as a basis for perceptual grouping and segregation. (3) Reaction time for detecting a single convex shape does not increase with the number of items in the display. This “pop-out” effect must be based on shading rather than on differences in luminance polarity, since neither left-right differences nor step changes in luminance resulted in pop-out. (4) When the subjects were experienced, there were no search asymmetries for convex as opposed to concave tokens, but when the subjects were naive, cavities were much easier to detect than convex shapes. (5) The extraction of shape from shading can also provide an input to motion perception. And finally, (6) the assumption of “overhead illumination” that leads to perceptual grouping depends primarily on retinal rather than on “phenomenal” or gravitational coordinates. Taken collectively, these findings imply that the extraction of shape from shading is an “early” visual process that occurs prior to perceptual grouping, motion perception, and vestibular (as well as “cognitive”) correction for head tilt. Hence, there may be neural elements very early in visual processing that are specialized for the extraction of shape from shading.     

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.