Further studies in the perception of a changing shape

Koffka's hypothesis of “invariant relation” holding between tilt and perceived shape of an object is discussed from the standpoints both of logical tenability and of experimental findings.

After discussion of certain shortcomings in the method of investigation devised by Stavrianos, two experiments are suggested, the first, of a simple character, intended to follow out in practice the hypothetical conclusions of Koffka's argument, the second to test the hypothesis under conditions which attempt to ensure the preservation of the perceptual object throughout the arc of tilt. For this purpose subjects attempt to match two shapes, one of which is stationary whilst the other revolves at a constant speed. The comparison shapes cover the range of the possible arc of tilt.

The results of the first experiment, whilst appearing to contradict the requirements of the hypothesis, are by no means conclusive. The second experiment, though not absolutely conclusive, gives little support to Koffka. The main conclusion drawn is that there occur non-systematic variations in perceptual constancy throughout the arc of tilt. These are of a phasic character and are qualitatively different from results obtained by matching stationary shapes. There appears to be no simple function which would result in exhibiting a uniform constancy value for the entire arc of orientation.     

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 changing emotion expressions

The utility of recognising emotion expressions for coordinating social interactions is well documented, but less is known about how continuously changing emotion displays are perceived. The nonlinear dynamic systems view of emotions suggests that mixed emotion expressions in the middle of displays of changing expressions may be decoded differently depending on the expression origin. Hysteresis is when an impression (e.g., disgust) persists well after changes in facial expressions that favour an alternative impression (e.g., anger). In expression changes based on photographs (Study 1) and avatar images (Studies 2a-c, 3), we found hystereses particularly in changes between emotions that are perceptually similar (e.g., anger-disgust). We also consistently found uncertainty (neither emotion contributing to the mixed expression was perceived), which was more prevalent in expression sequences than in static images. Uncertainty occurred particularly in changes between emotions that are perceptually dissimilar, such as changes between happiness and negative emotions. This suggests that the perceptual similarity of emotion expressions may determine the extent to which hysteresis and uncertainty occur. Both hysteresis and uncertainty effects support our premise that emotion decoding is state dependent, a characteristic of dynamic systems. We propose avenues to test possible underlying mechanisms.     

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.     

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.     

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 visual and haptic perception of natural object shape

In this study, we evaluated observers' ability to compare naturally shaped three-dimensional (3-D) objects, using their senses of vision and touch. In one experiment, the observers haptically manipulated 1 object and then indicated which of 12 visible objects possessed the same shape. In the second experiment, pairs of objects were presented, and the observers indicated whether their 3-D shape was the same or different. The 2 objects were presented either unimodally (vision-vision or haptic-haptic) or cross-modally (vision-haptic or haptic-vision). In both experiments, the observers were able to compare 3-D shape across modalities with reasonably high levels of accuracy. In Experiment 1, for example, the observers' matching performance rose to 72% correct (chance performance was 8.3%) after five experimental sessions. In Experiment 2, small (but significant) differences in performance were obtained between the unimodal vision-vision condition and the two cross-modal conditions. Taken together, the results suggest that vision and touch have functionally overlapping, but not necessarily equivalent, representations of 3-D shape.     

The effects of figurai shape on the perception of area

It was hypothesized that figures of equal area and different shapes are perceived as differing in area and that these apparent differences in area are due to the interaction of certain shape variables. Thirty figures were presented to 45 Ss for paired comparisons. Forty-five sets of 30 Choice scores were calculated. The performance of each S was tested for consistency by the Method of Circular Triads (p>.01). A Coefficient of Agreement (u) indicated that the Ss agreed among themselves (p>.01). Fifteen Ss were tested twice for test-retest reliability (p>.01). The 45 sets of Choice scores were then converted to rank values and averaged over all Ss. The mean rank values of the 30 figures were treated with the two-way analysis of variance by ranks to determine the significance of the differences among them (p>.01). A Coefficient of Concordance (W) was calculated on the 45 sets of rank values to support the results of the analysis of variance (p>.01). Subsequently, the 30 mean rank values were treated as the dependent variable in a multiple correlation (R) with the shape variables as the independent variables (p>.01). The apparent area of the figures was found to vary inversely with perimeter, number of turns, breadth, and external area.     

The role of motion in infants' perception of solid shape

Previous research has shown that infants as young as the first few months of life perceive several aspects of the three-dimensional environment. Yet we know relatively little about the visual depth information which serves as a basis for their spatial capacities. A study is reported in which a visual habituation procedure was used to examine what types of optical depth information four-month-old infants find useful in visually perceiving solid (three-dimensional) shape. Results imply that in the absence of binocular depth cues four-month-olds rely on kinetic depth information to perceive solid shape.     

Intelligence level as a variable in the perception of shape

The relation between shape constancy and intelligence was investigated by determining the functions relating matched shape to the angle of inclination of a circular test-object for groups at four levels of intelligence. Subjects were obtained from groups of institutionalized mental defectives, slow learners from the public schools, unselected undergraduates, and undergraduates who had been awarded scholarships. With increasing intelligence level the matches tend to approach the prediction based on the law of the retinal image thus demonstrating an inverse correlation between intelligence and the extent to which constancy is demonstrated. Since it is known the instructions given to the subject are a variable in shape constancy, it is suggested that the present data are the result of different attitudes adopted by the subjects at the various intelligence levels. The more intelligent subjects are assumed to adopt an analytic attitude in the experimental situation, while the less intelligent tend to maintain their everyday, non-analytic modes of perceiving.     

Effects of unit formation on the perception of a changing sound

The effects of subunit formation on adult listeners' ability to notice changes in a continuous spectral gradient of sound were studied. Results of this experiment support the idea that the auditory system processes information differently within a unit, and that this processing does not occur unless the perceptual system detects unit boundaries. In this experiment, silences were inserted into a continuously changing sound to cause the formation of short units. Listeners noticed the change earlier in conditions with silences inserted than in to conditions where the transition was either unbroken or broken by loud noise bursts. Results are discussed in terms of two processes, one that accentuates stimulus properties present at moments of onset and offset, and a second that uses onsets and offsets to signal the beginnings and ends of units and reduces the change perceived within units.     

How the intentions of the draftsman shape perception of a drawing

The interaction between the recovery of the artist’s intentions and the perception of an artwork is a classic topic for philosophy and history of art. It also frequently, albeit sometimes implicitly, comes up in everyday thought and conversation about art and artworks. Since recent work in cognitive science can help us understand how we perceive and understand the intentions of others, this discipline could fruitfully participate in a multidisciplinary investigation of the role of intention recovery in art perception. The method I propose is to look for cases where recovery of the artist’s intentions interacts with perception of a work of art, and this cannot be explain by a simple top-down influence of conscious propositional knowledge on perception. I will focus on drawing and show that recovery of the draftsman’s intentional actions is handled by a psychological process shaped by the motor system of the observer.     

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.     

Fechner, information, and shape perception

How do retinal images lead to perceived environmental objects? Vision involves a series of spatial and material transformations—from environmental objects to retinal images, to neurophysiological patterns, and finally to perceptual experience and action. A rationale for understanding functional relations among these physically different systems occurred to Gustav Fechner: Differences in sensation correspond to differences in physical stimulation. The concept of information is similar: Relationships in one system may correspond to, and thus represent, those in another. Criteria for identifying and evaluating information include (a)?resolution, or the precision of correspondence; (b)?uncertainty about which input (output) produced a given output (input); and (c)?invariance, or the preservation of correspondence under transformations of input and output. We apply this framework to psychophysical evidence to identify visual information for perceiving surfaces. The elementary spatial structure shared by objects and images is the second-order differential structure of local surface shape. Experiments have shown that human vision is directly sensitive to this higher-order spatial information from interimage disparities (stereopsis and motion parallax), boundary contours, texture, shading, and combined variables. Psychophysical evidence contradicts other common ideas about retinal information for spatial vision and object 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 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 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.