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 perception of distances and spatial relationships in natural outdoor environments

The ability of observers to perceive distances and spatial relationships in outdoor environments was investigated in two experiments. In experiment 1, the observers adjusted triangular configurations to appear equilateral, while in experiment 2, they adjusted the depth of triangles to match their base width. The results of both experiments revealed that there are large individual differences in how observers perceive distances in outdoor settings. The observers' judgments were greatly affected by the particular task they were asked to perform. The observers who had shown no evidence of perceptual distortions in experiment 1 (with binocular vision) demonstrated large perceptual distortions in experiment 2 when the task was changed to match distances in depth to frontal distances perpendicular to the observers' line of sight. Considered as a whole, the results indicate that there is no single relationship between physical and perceived space that is consistent with observers' judgments of distances in ordinary outdoor contexts.     

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).     

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.     

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.     

Curvature affects haptic length perception

One possible way of haptically perceiving length is to trace a path with one’s index finger and estimate the distance traversed. Here, we present an experiment in which observers judge the lengths of paths across cylindrically curved surfaces. We found that convex and concave surfaces had qualitatively different effects: convex lengths were overestimated, whereas concave lengths were underestimated. In addition, we observed that the index finger moved more slowly across the convex surface than across the concave one. As a result, movement times for convex lengths were longer. The considerable correlation between movement times and length estimates suggests that observers take the duration of movement as their primary measure of perceived length, but disregard movement speeds. Several mechanisms that could underlie observers’ failure to account for speed differences are considered.     

Ontological issues in distance perception: cue use under full cue conditions cannot be inferred from use under controlled conditions

Phosphorescent square tiles (arranged to yield a single image size) were viewed in the dark by 56 monocular observers who utilized a chinrest. The targets were placed at one of three horizontal distances and at one of three eye heights, allowing us to study the relative effect of height in the visual field (HVF) and sagittal distance on observers' verbal reports of the horizontal distance at which the object lay (near, middle, or far). In Experiment 1, we found that reports covaried primarily with HVF and, as predicted, they exhibited a weak paradoxical inverse relation with horizontal distance. In a second and third experiment, a visible surface was placed under the targets at the three eye heights in both dark and fully lighted conditions. In this situation, the inverse distance relation disappeared, and HVF no longer influenced the judgments of most observers. The results show that information projected from relevant support surfaces is essential for veridical information about object distance. These results raise fundamental issues for perceptual researchers regarding how to decide when a cue has been properly delineated, given the assumption that the relation between a cue and what it specifies is probabilistic.     

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 perception and discrimination of local 3-D surface structure from deforming and disparate boundary contours

In a series of four experiments, we evaluated observers' abilities to perceive and discriminate ordinal depth relationships between separated local surface regions for objects depicted by static, deforming, and disparate boundary contours or silhouettes. Comparisons were also made between judgments made for silhouettes and for objects defined by surface texture, which permits judgment based on conventional static texture gradients, conventional stereopsis, and conventional structure-from-motion. In all the experiments, the observers were able to detect, with relatively high precision, ordinal depth relationships, an aspect of local three-dimensional (3-D) structure, from boundary contours or silhouettes. The results of the experiments clearly demonstrate that the static, disparate, and deforming boundary contours of solid objects are perceptually important optical sources of information about 3-D shape. Other factors that were found to affect performance were the amount of separation between the local surface regions, the proximity or closeness of the regions to the boundary contour itself, and for the conditions with deforming contours, the overall magnitude of the boundary deformation.     

Perception of three-dimensional form from patterns of optical texture

The research described in the present article was designed to investigate how patterns of optical texture provide information about the three-dimensional structure of objects in space. Four experiments were performed in which observers were asked to judge the perceived depth of simulated ellipsoid surfaces under a variety of experimental conditions. The results revealed that judged depth increases linearly with simulated depth although the slope of this relation varies significantly among different types of texture patterns. Random variations in the sizes and shapes of individual surface elements have no detectable effect on observers' judgments. The perception of three-dimensional form is quite strong for surfaces displayed under parallel projection, but the amount of apparent depth is slightly less than for identical surfaces displayed under polar projection. Finally, the perceived depth of a surface is eliminated if the optical elements in a display are not sufficiently elongated or if they are not approximately aligned with one another. A theoretical explanation of these findings is proposed based on the neural network analysis of Grossberg and Mingolla.     

Learning to perceive differences in solid shape through vision and touch

A single experiment was designed to investigate perceptual learning and the discrimination of 3-D object shape. Ninety-six observers were presented with naturally shaped solid objects either visually, haptically, or across the modalities of vision and touch. The observers' task was to judge whether the two sequentially presented objects on any given trial possessed the same or different 3-D shapes. The results of the experiment revealed that significant perceptual learning occurred in all modality conditions, both unimodal and cross-modal. The amount of the observers' perceptual learning, as indexed by increases in hit rate and d', was similar for all of the modality conditions. The observers' hit rates were highest for the unimodal conditions and lowest in the cross-modal conditions. Lengthening the inter-stimulus interval from 3 to 15 s led to increases in hit rates and decreases in response bias. The results also revealed the existence of an asymmetry between two otherwise equivalent cross-modal conditions: in particular, the observers' perceptual sensitivity was higher for the vision-haptic condition and lower for the haptic-vision condition. In general, the results indicate that effective cross-modal shape comparisons can be made between the modalities of vision and active touch, but that complete information transfer does not occur.     

Sex and age modulate the visual perception of distance

An experiment was conducted to evaluate the ability of 28 younger and older adults to visually bisect distances in depth both indoors and outdoors; half of the observers were male and half were female. Observers viewed 15-m and 30-m distance extents in four different environmental settings (two outdoor grassy fields and an indoor hallway and atrium) and were required to adjust the position of a marker to place it at the midpoint of each stimulus distance interval. Overall, the observers’ judgments were more accurate indoors than outdoors. In outdoor environments, many individual observers exhibited perceptual compression of farther distances (e.g., these observers placed the marker closer than the actual physical midpoints of the stimulus distance intervals). There were significant modulatory effects of both age and sex upon the accuracy and precision of the observers’ judgments. The judgments of the male observers were more accurate than those of the female observers and they were less influenced by environmental context. In addition, the accuracies of the younger observers’ judgments were less influenced by context than those of the older observers. With regard to the precision of the observers’ judgments, the older females exhibited much more variability across repeated judgments than the other groups of observers (younger males, younger females, and older males). The results of our study demonstrate that age and sex are important variables that significantly affect the visual perception of distance.     

The role of explicit and implicit standards in visual speed discrimination

Five experiments were designed to investigate visual speed discrimination. Variations of the method of constant stimuli were used to obtain speed discrimination thresholds in experiments 1, 2, 4, and 5, while the method of single stimuli was used in experiment 3. The observers' thresholds were significantly influenced by the choice of psychophysical method and by changes in the standard speed. The observers' judgments were unaffected, however, by changes in the magnitude of random variations in stimulus duration, reinforcing the conclusions of Lappin et al (1975 Journal of Experimental Psychology: Human Perception and Performance 1 383 394). When an implicit standard was used, the observers produced relatively low discrimination thresholds (7.0% of the standard speed), verifying the results of McKee (1981 Vision Research 21 491-500). When an explicit standard was used in a 2AFC variant of the method of constant stimuli, however, the observers' discrimination thresholds increased by 74% (to 12.2%), resembling the high thresholds obtained by Mandriota et al (1962 Science 138 437-438). A subsequent signal-detection analysis revealed that the observers' actual sensitivities to differences in speed were in fact equivalent for both psychophysical methods. The formation of an implicit standard in the method of single stimuli allows human observers to make judgments of speed that are as precise as those obtained when explicit standards are available.     

Aging and the perception of local surface orientation from optical patterns of shading and specular highlights

Younger and older observers' ability to perceive local surface orientation from optical patterns of shading and specular highlights was investigated in two experiments. On each trial, the observers viewed a randomly generated, smoothly curved 3-D object and manipulated an adjustable gauge figure until its orientation matched that of a specific local region on the object's surface (cf. Koenderink, van Doom, & Kappers, 1992). The performance of both age groups was facilitated by the presence of binocular disparity (Experiment 1) and object rotation in depth (Experiment 2). Observers in both age groups were able to judge the surface tilt component of orientation more precisely than the slant component. Significant, but modest, effects of age were found in Experiment 1, but not in Experiment 2. The ability to perceive local surface orientation appears to be relatively well preserved with increasing age, at least through the age of 80.     

Aging and the perception of slant from optical texture, motion parallax, and binocular disparity

The ability of younger and older observers to perceive surface slant was investigated in four experiments. The surfaces possessed slants of 20°, 35°, 50°, and 65°, relative to the frontoparallel plane. The observers judged the slants using either a palm board (Experiments 1, 3, and 4) or magnitude estimation (Experiment 2). In Experiments 1–3, physically slanted surfaces were used (the surfaces possessed marble, granite, pebble, and circle textures), whereas computer-generated 3-D surfaces (defined by motion parallax and binocular disparity) were utilized in Experiment 4. The results showed that the younger and older observers' performance was essentially identical with regard to accuracy. The younger and older age groups, however, differed in terms of precision in Experiments 1 and 2: The judgments of the older observers were more variable across repeated trials. When taken as a whole, the results demonstrate that older observers (at least through the age of 83 years) can effectively extract information about slant in depth from optical patterns containing texture, motion parallax, or binocular disparity.     

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.     

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.     

Apparent extended body motions in depth.

Five experiments were designed to investigate the influence of three-dimensional (3-D) orientation change on apparent motion. Projections of an orientation-specific 3-D object were sequentially flashed in different locations and at different orientations. Such an occurrence could be resolved by perceiving a rotational motion in depth around an axis external to the object. Consistent with this proposal, it was found that observers perceived curved paths in depth. Although the magnitude of perceived trajectory curvature often fell short of that required for rotational motions in depth (3-D circularity), judgments of the slant of the virtual plane on which apparent motions occurred were quite close to the predictions of a model that proposes circular paths in depth.     

The perception of 3-dimensional affine structure from minimal apparent motion sequences

The research described in the present article was designed to identify the minimal conditions for the visual perception of 3-dimensional structure from motion by comparing the theoretical limitations of ideal observers with the perceptual performance of actual human subjects on a variety of psychophysical tasks. The research began with a mathematical analysis, which showed that 2-frame apparent motion sequences are theoretically sufficient to distinguish between rigid and nonrigid motion and to identify structural properties of an object that remain invariant under affine transformations, but that 3 or more distinct frames are theoretically necessary to adequately specify properties of euclidean structure such as the relative 3-dimensional lengths or angles between nonparallel line segments. A series of four experiments was then performed to verify the psychological validity of this analysis. The results demonstrated that the determination of structure from motion in actual human observers may be restricted to the use of first order temporal relations, which are available within 2-frame apparent motion sequences. That is to say, the accuracy of observers' judgments did not improve in any of these experiments as the number of distinct frames in an apparent motion sequence was increased from 2 to 8, and performance on tasks involving affine structure was of an order of magnitude greater than performance on similar tasks involving euclidean structure.