The visual perception of smoothly curved surfaces from minimal apparent motion sequences

A series of four experiments was designed to investigate the minimal amounts of information required to perceive the structure of a smoothly curved surface from its pattern of projected motion. In Experiments 1 and 2, observers estimated the amplitudes of sinusoidally corrugated surfaces relative to their periods. Observers’ judgments varied linearly with the depicted surface amplitudes, but the amount of perceived relative depth was systematically overestimated by approximately 30%. The observers’ amplitude judgments were also influenced to a lesser extent by the amount of rotary displacement of a surface at each frame transition, and by increasing the length of the apparent motion sequences from two to eight frames. The latter effect of sequence length was quite small, however, accounting for less than 3% of the variance in the observers’ judgments. Experiments 3 and 4 examined observers’ discrimination thresholds for sinusoidally corrugated surfaces of variable amplitude and for ellipsoid surfaces of variable eccentricity. The results revealed that observers could reliably detect differences of surface structure as small as 5%. The length of the apparent motion sequences had no detectable effect on these tasks, although there were significant effects of angular displacement and surface orientation. These results are considered with respect to the analysis of affine structure from motion proposed by Todd and Bressan (1990).     

The visual perception of smoothly curved surfaces from minimal apparent motion sequences.

A series of four experiments was designed to investigate the minimal amounts of information required to perceive the structure of a smoothly curved surface from its pattern of projected motion. In Experiments 1 and 2, observers estimated the amplitudes of sinusoidally corrugated surfaces relative to their periods. Observers' judgments varied linearly with the depicted surface amplitudes, but the amount of perceived relative depth was systematically overestimated by approximately 30%. The observers' amplitude judgments were also influenced to a lesser extent by the amount of rotary displacement of a surface at each frame transition, and by increasing the length of the apparent motion sequences from two to eight frames. The latter effect of sequence length was quite small, however, accounting for less than 3% of the variance in the observers' judgments. Experiments 3 and 4 examined observers' discrimination thresholds for sinusoidally corrugated surfaces of variable amplitude and for ellipsoid surfaces of variable eccentricity. The results revealed that observers could reliably detect differences of surface structure as small as 5%. The length of the apparent motion sequences had no detectable effect on these tasks, although there were significant effects of angular displacement and surface orientation. These results are considered with respect to the analysis of affine structure from motion proposed by Todd and Bressan (1990).     

Ordinal structure in the visual perception and cognition of smoothly curved surfaces

In theoretical analyses of visual form perception, it is often assumed that the 3-dimensional structures of smoothly curved surfaces are perceptually represented as point-by-point mappings of metric depth and/or orientation relative to the observer. This article describes an alternative theory in which it is argued that our visual knowledge of smoothly curved surfaces can also be defined in terms of local, nonmetric order relations. A fundamental prediction of this analysis is that relative depth judgments between any two surface regions should be dramatically influenced by monotonicity of depth change (or lack of it) along the intervening portions of the surface through which they are separated. This prediction is confirmed in a series of experiments using surfaces depicted with either shading or texture. Additional experiments are reported, moreover, that demonstrate that smooth occlusion contours are a primary source of information about the ordinal structure of a surface and that the depth extrema in between contours can be optically specified by differences in luminance at the points of occlusion.     

The perception of doubly curved surfaces from anisotropic textures

Abstract— Most existing computational models of the visual perception of three-dimensional shape from texture are based on assumed constraints about how texture is distributed on visible surfaces. The research described in the present article was designed to investigate how violations of these assumptions influence human perception. Observers were presented with images of smoothly curved surfaces depicted with different types of texture, whose distribution of surface markings could be both anisotropic and inhomogeneous. Observers judged the pattern of ordinal depth on each object by marking local maxima and minima along designated scan lines. They also judged the apparent magnitudes of relative depth between designated probe points on the surface. The results revealed a high degree of accuracy and reliability in all conditions, except for a systematic underestimation of the overall magnitude of surface relief. These findings suggest that human perception of three-dimensional shape from texture is much more robust than would be reasonable to expect based on current computational models of this phenomenon.     

Perceived depth inversion of smoothly curved surfaces due to image orientation

A relative depth judgement task was used to distinguish perceived reversals in depth due to image orientation from spontaneous reversals such as those observed with a Necker cube. Results demonstrate that inversion effects due to image orientation can occur for several different types of pictorial representation and that many of these effects are incompatible with traditional explanations involving a perceptual bias for overhead illumination. When this bias was neutralized by placing the light source at the point of observation, the effects of image orientation were just as large as with overhead illumination. Similar results were also obtained for surfaces depicted with texture or motion in which all relevant shading information was eliminated. These results can be explained by a perceptual bias for backward slanting surfaces, but additional evidence suggests that this bias can be attenuated by the presence of smooth occlusion contours.     

Infants’ perception of curved illusory contour with motion

Recently, Masuda et al. (submitted for publication) showed that adults perceive moving rigid or nonrigid motion from illusory contour with neon color spreading in which the inducer has pendular motion with or without phase difference. In Experiment 1, we used the preferential looking method to investigate whether 3–8-month-old infants can discriminate illusory and non-illusory contour figures, and found that the 7–8-month-old, but not the 3–6-month-old, infants showed significant preference for illusory contour with phase difference. In Experiment 2, we tested the validity of the visual stimuli in the present study, and whether infants could detect illusory contour from the current neon color spreading figures. The results showed that all infants might detect illusory contour figure with neon color spreading figures. The results of Experiments 1 and 2 suggest that 7–8-month-old infants potentially perceive illusory contour from the visual stimulus with phase-different movement of inducers, which elicits the perception of nonrigid dynamic subjective contour in adults.     

Simulation of curved surfaces from patterns of optical texture

Previous research on the perceptual analysis of optical texture has been severely restricted by the lack of an appropriate technique for distributing texture on curved surfaces in a uniform manner. In an effort to overcome this problem, the present article presents a new algorithm for generating stochastically regular distributions of texture on any smooth surface regardless of its curvature. We also present a new technique for representing the global organization of a textured image based on the formal concept of a projected area field.     

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.     

The perception of length on curved and flat surfaces

In three experiments, observers judged the apparent extents of spatial intervals along the surface of a curved cylinder or a flat plane that was binocularly viewed in a natural, indoor environment. The observers' judgments of surface lengths were precise and reliable but were also inaccurate and subject to relatively large constant errors. These distortions differed among the observers, but they tended to perceive lengths oriented along the curved dimension of the cylinder as being longer than physically equivalent lengths in the noncurved dimension. This phenomenon did not occur when the observers judged curved and noncurved paths on the flat surface. In addition, some observers' judgments of length were affected by changes in the distance to the cylinder, whereas others were affected by the cylinder's orientation in space. These results demonstrate that the perception of length on surfaces is highly dependent on the particular context in which the length occurs.     

The visual perception of length along intrinsically curved surfaces

The ability of observers to perceive three-dimensional (3-D) distances or lengths along intrinsically curved surfaces was investigated in three experiments. Three physically curved surfaces were used: convex and/or concave hemispheres (Experiments 1 and 3) and a hyperbolic paraboloid (Experiment 2). The first two experiments employed a visual length-matching task, but in the final experiment the observers estimated the surface lengths motorically by varying the separation between their two index fingers. In general, the observers' judgments of surface length in both tasks (perceptual vs. motoric matching) were very precise but were not necessarily accurate. Large individual differences (overestimation, underestimation, etc.) in the perception of length occurred. There were also significant effects of viewing distance, type of surface, and orientation of the spatial intervals on the observers' judgments of surface length. The individual differences and failures of perceptual constancy that were obtained indicate that there is no single relationship between physical and perceived distances on 3-D surfaces that is consistent across observers.     

Three gradients and the perception of flat and curved surfaces

Researchers of visual perception have long been interested in the perceived slant of a surface and in the gradients that purportedly specify it. Slant is the angle between the line of sight and the tangent to the planar surface at any point, also called the surface normal. Gradients are the sources of information that grade, or change, with visual angle as one looks from one's feet upward to the horizon. The present article explores three gradients--perspective, compression, and density--and the phenomenal impression of flat and curved surfaces. The perspective gradient is measured at right angles to the axis of tilt at any point in the optic array; that is, when looking down a hallway at the tiles of a floor receding in the distance, perspective is measured by the x-axis width of each tile projected on the image plane orthogonal to the line of sight. The compression gradient is the ratio of y/x axis measures on the projected plane. The density gradient is measured by the number of tiles per unit solid visual angle. For flat surfaces and many others, perspective and compression gradients decrease with distance, and the density gradient increases. We discuss the manner in which these gradients change for various types of surfaces. Each gradient is founded on a different assumption about textures on the surfaces around us. In Experiment 1, viewers assessed the three-dimensional character of projections of flat and curved surfaces receding in the distance. They made pairwise judgments of preference and of dissimilarity among eight stimuli in each of four sets. The presence of each gradient was manipulated orthogonally such that each stimulus had zero, one, two, or three gradients appropriate for either a flat surface or a curved surface. Judgments were made were made for surfaces with both regularly shaped and irregularly shaped textures scattered on them. All viewer assessment were then scaled in one dimension. Multiple correlation and regression on the scale values revealed that greater than 98% of the variance in scale values was accounted for by the gradients. For the flat surfaces a mean of 65% of the variance was accounted for by the perspective gradient, 28% by the density gradient, and 6% by the compression gradient. For curved surfaces, on the other hand, a mean of 96% of the variance was accounted for by the compression gradient, and less than 2% by either the perspective gradient or the density gradient.(ABSTRACT TRUNCATED AT 400 WORDS)     

2-D contour perception resulting from kinetic occlusion

Kinetic occlusion, the progressive deletion or accretion of texture elements as one surface covers or uncovers another, has been shown to be an important source of information for determining depth order. In the present study, the importance of this information for 2-D contour perception was examined. In Experiment 1, subjects were asked to discriminate four different target shapes defined solely by kinetic occlusion. Discrimination increased with an increase in texture density and velocity, with density as the major factor. In Experiment 2, the targets were defined by static untextured regions as well as by kinetic occlusion. Overall, accuracy was similar to that found in Experiment 1, indicating that the presence of static information had little impact on accuracy. In Experiment 3, subjects were unable to discriminate among the four targets when presented with static versions of the displays used in Experiment 2. The results from these experiments indicate that kinetic occlusion can be used for discrimination of different 2-D shapes and that density has a more important role in determining accuracy than velocity.     

Visual inter-attribute contour completion

A new visual phenomenon, inter-attribute illusory (completed) contours, is demonstrated. Contour completions are perceived between any combination of spatially separate pairs of inducing elements (Kanizsa-like 'pacman' figures) defined either by pictorial cues (luminance contrast or offset gratings), temporal contrast (motion, second-order-motion or 'phantom' contours), or binocular-disparity contrast. In a first experiment, observers reported the perceived occurrence of contour completion for all pair combinations of inducing elements. In a second experiment they rated the perceived clarity of the completed contours. Both methods generated similar results contour completions were perceived even though the inducing elements were defined by different attributes. Ratings of inter-attribute clarity were no lower than in either of the two corresponding intra-attribute conditions and seem to be the average of these two ratings. The results provide evidence for the existence of attribute-invariant Gestalt processes, and on a mechanistic level indicate that the completion process operates on attribute-invariant contour detectors.     

Haptic identification of curved surfaces

In two experiments, the active haptic identification of three-dimensional mathematically welldefined objects is investigated. The objects, quadric surfaces, are defined in terms of the shape index, a quantity describing the shape, and curvedness, a quantity describing overall curvature. Both shape index and curvedness are found to have a significant influence on haptic shape identification . Concave surfaces lead to a larger spread in responses than convex ones. Hyperbolic surfaces show a slight tendency to be identified with more difficulty than elliptic ones. Surfaces with a high curvedness are identified more easily than those with a low curvedness. Results from experiments with constant and with random curvedness are indistinguishable . It is concluded that shape index and curvedness are psychophysically not confounded.     

Visual perception of collinearity

In a metrical space, there exists an intimate relation between collinearity and parallelity. In particular, in a Riemannian space collinearity is just a special case of parallelity. Is this true for visual space as well? We investigated the visual perception of collinearity by having subjects align two bars in the horizontal plane at eye height. The distances of the bars from the subject and the angles at which they were placed were varied. We found deviations of up to 22 degrees. The deviations of the left and right bars could be split into two independent components: namely, the sum and the difference of the deviations of the left and right bars. We found that the former depended only on the ratio between the distances of each bar from the subject, whereas the latter was largely independent of the positions of the bars. The difference in deviations corresponded to the deviation from parallelity. Compared with the results in the parallelity task (Cuijpers, Kappers, & Koenderink, 2000b), the deviations from parallel were much smaller. As a consequence, the results of the two experiments cannot be described by the same Riemannian geometry. This indicates that the intrinsic geometry of visual space differs across tasks. This is conceivable if the intrinsic geometry of visual space is operationally defined.     

Visual perception of markings

Markings, such as designs, writings, diagrams, and depictions, are expressive and communicative human artifacts. The conventional assumption that findings from the study of the visual perception of markings—in particular, of pictures—can be generalized to real-world perception is examined and found to be false. The processes involved in the visual perception of the world and in the visual perception of markings differ in significant ways, and generalizations from one to the other must be undertaken with caution. The visual perception of markings is an identifiable and separate area of study. Implications for a general theory of the perception of markings are examined, and the perception of markings is contrasted with real-world perception.     

Importance of head axes in perception of cutaneous patterns drawn on vertical body surfaces

The "disembodied eye" phenomenon (Corcoran, 1977), that is, the observation that a cutaneous (tactile) pattern is perceived as right-left reversed or not, depending on whether it is presented on the forehead or the back of the head, was extended by incorporating a top-bottom axis into a model of the frame of reference in cutaneous-pattern perception. In two experiments, 21 and 15 subjects were asked to report the letter perceived when one of four letters (p, q, b, or d) was tactually presented. The sites studied were vertical body surfaces (Experiment 1) and hands alongside the body (Experiment 2). The positions for the presentations varied according to the height (head, shoulder, waist, thigh, and calf levels) and the orientation of the surface: forward-, backward-, and side-facing. Although the results for the head and back surfaces supported the notion of a "disembodied eye" behind the individual, other frames were needed: On the forward-facing surfaces below the waist, the prevailing perception was 180 degrees rotated, as if the subjects were looking at the surface by bending forward. An additional frame of reference was introduced for the forward-facing surfaces in lower positions and was described as head axes projected onto body surfaces within the possibility of actual body movements.