Influence of Local Properties on the Perception of Global Object Orientation.

In previous studies, the effect on perception of individual features such as curvature and edges have been studied with specifically designed stimuli. However, the effect of local properties on the perception of the global object has so far received little attention. In this study, cylinders with an elliptical cross section and rectangular blocks were used to investigate the effect and relative importance of curvature, change in curvature and edges, as local properties, on the ability of subjects to determine the orientation of the stimuli, which is a global property. We found that when curvature was present the threshold to determine the orientation was 43 percent lower than when curvature was absent. When, in addition, the change in curvature could be felt, the threshold was 37 percent lower than when only curvature could be felt. Finally, when edges were felt during exploration, the threshold increased by 46 percent compared to when the subjects were instructed to avoid the edges in the blocks. We conclude that the perception of curvature and change in curvature improve the performance of humans in perception of the whole shape, whereas edges, when not directly contributing to the task, disrupt performance.

Visually Guided Haptic Search.

In this study, we investigate the influence of visual feedback on haptic exploration. A haptic search task was designed in which subjects had to haptically explore a virtual display using a force-feedback device and to determine whether a target was present among distractor items. Although the target was recognizable only haptically, visual feedback of finger position or possible target positions could be given. Our results show that subjects could use visual feedback on possible target positions even in the absence of feedback on finger position. When there was no feedback on possible target locations, subjects scanned the whole display systematically. When feedback on finger position was present, subjects could make well-directed movements back to areas of interest. This was not the case without feedback on finger position, indicating that showing finger position helps to form a spatial representation of the display. In addition, we show that response time models of visual serial search do not generally apply for haptic serial search. Consequently, in teleoperation systems, for instance, it is helpful to show the position of the probe even if visual information on the scene is poor.

Local Surface Orientation Dominates Haptic Curvature Discrimination.

Prior studies have shown that local surface orientation is a dominant source of information for haptic curvature perception in static conditions. We show that this dominance holds for dynamic touch, just as was shown earlier for static touch. Using an apparatus specifically developed for this purpose, we tested this hypothesis by providing observers with two independently controlled sources of geometric information. The robotic-like apparatus could accurately control the position of a contact surface independently from its orientation in space, while allowing subjects to freely and actively explore virtual shapes in the lateral direction. In the first experiment, we measured discrimination thresholds for the two types of shape information and compared the discrimination of real shapes to that of virtual shapes. The results confirmed the dominance of local surface orientation. We propose a model that predicts cue dominance for different scales of exploration. In the second experiment, we investigated whether a virtual curved surface felt as curved as a real curved surface. We found that observers did not systematically judge either of the two kinds of stimuli to be more curved than the other. More importantly, we found that points of subjective curvedness were not influenced by the availability of height information.

Do reference surfaces influence exocentric pointing?

All elements of the visual field are known to influence the perception of the egocentric distances of objects. Not only the ground surface of a scene, but also the surface at the back or other objects in the scene can affect an observer's egocentric distance estimation of an object. We tested whether this is also true for exocentric direction estimations. We used an exocentric pointing task to test whether the presence of poster-boards in the visual scene would influence the perception of the exocentric direction between two test-objects. In this task the observer has to direct a pointer, with a remote control, to a target. We placed the poster-boards at various positions in the visual field to test whether these boards would affect the settings of the observer. We found that they only affected the settings when they directly served as a reference for orienting the pointer to the target.

Active haptic detection and discrimination of shape.

In previous research, we have shown that detection thresholds for Gaussian shapes increase with a power of 1.3 of spatial width. In the present three experiments, we generalized this finding to more complex shapes and to discrimination tasks. In Experiment 1, we found that the slope of the psychometric function for detection (i.e., distinguishing curved from flat surfaces) was independent of surface shape. In Experiment 3, we found the same result for discrimination of two different curved shapes. In Experiment 2, we found that detection and discrimination functions had the same dependence on spatial width, except that discrimination thresholds were two to four times larger. Possible neural mechanisms underlying these results are discussed.

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.

First-order structure induces the 3-D curvature contrast effect.

A 3-D curvature contrast effect has been reported in shading-and-texture-defined (Curran & Johnson (1996). Vision Research 36, 3641-3653) and in stereoscopically defined (te Pas, Rogers, & Ledgeway (2000). Current Psychology Letters: Brain, Behaviour and Cognition 1, 117-126) stimuli. Our experiments show that a clear 3-D curvature contrast effect also occurs in motion-defined stimuli. The magnitude of the effect is similar in motion-, stereo- and shading-and-texture defined stimuli, suggesting that the 3-D curvature contrast effect is shape-based. We find a distinct contrast effect that is similar in the case of inducers that contain second-order (curvature) information and in the case of inducers that contain only first-order (slant and tilt) information. The effect with inducers that contain only zeroth-order (depth) information is very small. We conclude that the first-order structure is sufficient to induce a 3-D contrast effect.

On the role of external reference frames on visual judgements of parallelity.

In a previous study we found large systematic errors (up to 40 degrees) when subjects adjusted the orientation of a horizontal test bar until it appeared parallel to a horizontal reference bar, both bars rotating about their vertical axes. The deviations increased linearly with the separation angle but vanished when the orientation of the reference bar was either parallel or perpendicular to the median line. In order to test the assumption that external references caused these deviations to vanish, the same task was repeated in four different conditions: in the normal condition the horizontal aperture, formed by a cabin, and the facing wall of the room were frontoparallel to the subject; in the other conditions either the room, the cabin or both were oriented 30 degrees to the right with respect to the subject. It was found that, depending on the subject, the occurrence of the vanishing deviations covaried with the orientation of the cabin or the room. Evidently, subjects are influenced by the external references provided by the walls of the room and the sides of the cabin. The results indicate that a description of visual space by a Riemannian metric of constant curvature is not valid in a visual environment containing external references.

Amplitude and spatial-period discrimination in sinusoidal gratings by dynamic touch.

We measured discrimination thresholds for sinusoidal gratings using active dynamic touch. In the first experiment we measured the thresholds for amplitude discrimination as a function of amplitude and spatial period. Thresholds ranged between 10.8%, and 15.8% of the standard amplitude. We showed that amplitude differences as small as 2 microm can be detected. We found that Weber fractions for amplitude discrimination are constant over a range of amplitudes, but are influenced by the spatial period of the grating; discrimination improved with increasing spatial period. In the second experiment we determined the thresholds for spatial-period discrimination. We used the same design as in the first experiment. Weber fractions ranged from 6.4% to 11.8%. Amplitude was found to have no effect on the Weber fractions for spatial-period discrimination. However, the spatial period had an effect on the Weber fractions: larger spatial periods yielded lower Weber fractions.

The combined influence of binocular disparity and shading on pictorial shape.

The combined influence of binocular disparity and shading on pictorial shape was studied. Stimuli were several pairs of stereo photographs of real objects. The stereo base was 0, 7, or 14 cm, and the location of the light source was varied over three positions (one from about the viewpoint of the camera, one about perpendicular to the line of sight, and one in between the two). Therefore, in total, nine different combinations were studied. Subjects had to perform surface attitude settings at about 300 positions in the image plane. From the settings, depth maps were calculated on which a principal components analysis was performed. It was found that three components were enough to account for at least 97.8% of the variance in the data. The first component accounted for shape constancy. The effects of the two cues could be isolated as a linear combination of the other two components. The effects of the disparity and the shading cue variation were found to combine in almost linear fashion.

On the affine structure of perceptual space.

Affine geometry is a generalization of Euclidean geometry in which distance can be scaled along parallel directions, though relative distances in different directions may be incommensurable. This article presents a new procedure for testing the intrinsic affine structure of a psychological space by having subjects perform bisection judgments over multiple directions. If those judgments are internally consistent with one another, they must satisfy a theorem first proved by Pierre Varignon around 300 years ago. In the experiment reported here, this procedure was employed to measure the perceived structure of a visual ground surface. The results revealed that observers' judgments were systematically distorted relative to the physical environment, but that the judged bisections in different directions had an internally consistent affine structure. Implications of these findings for other possible response tasks are considered.

Ambiguity and the 'mental eye' in pictorial relief.

Photographs of scenes do not determine scenes in the sense that infinitely many different scenes could have given rise to any given photograph. In psychophysical experiments, observers have (at least partially) to resolve these ambiguities. The ambiguities also allow them to vary their response within the space of 'veridical' responses. Such variations may well be called 'the beholder's share' since they do not depend causally on the available depth cues. We determined the pictorial relief for four observers, four stimuli, and four different tasks. In all cases we addressed issues of reliability (scatter on repeated trials) and consistency (how well the data can be explained via a smooth surface, any surface). All data were converted to depth maps which allows us to compare the relief from the different operationalisations. As expected, pictorial relief can differ greatly either between observers (same stimulus, same task) or between operationalisations (same observer, same stimulus). However, when we factor out the essential ambiguity, these differences almost completely vanish and excellent agreement over tasks and observers pertains. Thus, observers often resolve the ambiguity in idiosyncratic ways, but mutually agree--even over tasks--in so far as their responses are causally dependent on the depth cues. A change of task often induces a change in 'mental perspective'. In such cases, the observers switch the 'beholder's share', which resolves the essential ambiguity through a change in viewpoint of their 'mental eye'.

Haptic after-effect of successively touched curved surfaces.

A flat surface is more often judged to be convex after the touching of a concave surface than after the touching of a convex surface. This haptic after-effect increases with the time of contact with the curved surface till it saturates, and it decreases with the time-lapse between the touching of the first surface and the next one. In this paper, the haptic after-effect of two successively touched spherically curved surfaces is investigated. It is found that both surfaces contribute to the after-effect, but the after-effect is not additive. The time course of the after-effect of two successive surfaces can be described by a first-order integrator with a single time constant of about 7 s and an amplitude equal to the difference between the saturation levels of the after-effects of the two surfaces when measured in isolation. The new saturation level is therefore equal to that of the after-effect of the most recently touched surface.

Change in perceived spatial directions due to context.

We examined the influence of context on exocentric pointing. In a virtual three-dimensional set-up, we asked our subjects to aim a pointer toward a target in two conditions. The target and the pointer were visible alone, or they were visible with planes through each of them. The planes consisted of a regular grid of horizontal and vertical lines. The presence of the planes had a significant influence on the indicated direction. These changes in indicated direction depended systematically on the orientation of the planes relative to the subject and on the angle between the planes. When the orientation of the (perpendicular) planes varied from asymmetrical to symmetrical to the frontoparallel plane, the indicated direction varied over a range of 15 degrees--from a slightly larger slant to a smaller slant--as compared with the condition without the contextual planes. When the dihedral angle between the two planes varied from 90 degrees to 40 degrees, the indicated direction varied over a range of less than 5 degrees: A smaller angle led to a slightly larger slant. The standard deviations in the indicated directions (about 3 degrees) did not change systematically. The additional structure provided by the planes did not lead to more consistent pointing. The systematic changes in the indicated direction contradict all theories that assume that the perceived distance between any two given points is independent of whatever else is present in the visual field--that is, they contradict all theories of visual space that assume that its geometry is independent of its contents (e.g., Gilinsky, 1951; Luneburg, 1947; Wagner, 1985).

Haptic detection thresholds of Gaussian profiles over the whole range of spatial scales.

In the literature only a small subset of the broad range of scales of human haptic perception has been explored. In this experiment, haptic detection thresholds have been investigated over a wide range of spatial scales. Computer-controlled manufacturing techniques have made it possible to produce stimuli with sufficient accuracy to explore the gamut of haptic scales. We used stimuli with a convex or concave Gaussian-shaped profile running over the middle of a strip. The width of the Gaussian profile was varied between 150 microns and 240 mm. In this range of spatial scales a number of mechanisms, ranging from cutaneous mechanoreception to proprioception in fingers, arm and shoulder, contribute to haptic perception. The discrimination threshold between a flat surface and a Gaussian surface was investigated in a series of two alternative forced choice experiments on human subjects. The thresholds run from 1 micron for the narrowest Gaussian profiles to 8 mm for the broadest profile. The same thresholds were found for convex and concave shapes. Over the range of spatial scales, from 1 mm width on, the dependence of the detection threshold on the spatial width of the Gaussian profile was found to be a power function with an exponent of about 1.3.

Investigation of visual space using an exocentric pointing task.

Classically, it has been assumed that visual space can be represented by a metric. This means that the distance between points and the angle between lines can be uniquely defined. However, this assumption has never been tested. Also, measurements outdoors, where monocular cues are abundant, conflict with this model. This paper reports on two experiments in which the structure of visual space was investigated, using an exocentric pointing task. In the first experiment, we measured the influence of the separation between pointer and target and of the orientation of the stimuli with respect to the observer. This was done both monocularly and binocularly. It was found that the deviation of the pointer settings depended linearly on the orientation, indicating that visual space is anisotropic. The deviations for configurations that were symmetrical in the median plane were approximately the same, indicating that left/right symmetry was maintained. The results for monocular and binocular conditions were very different, which indicates that stereopsis was an important cue. In both conditions, there were large deviations from the veridical. In the second experiment, the relative distance of the pointer and the target with respect to the observer was varied in both the monocular and the binocular conditions. The relative distance turned out to be the main parameter for the ranges used (1-5 m). Any distance function must have an expanding and a compressing part in order to describe the data. In the binocular case, the results were much more consistent than in the monocular case and had a smaller standard deviation. Nevertheless, the systematic mispointings remained large. It can therefore be concluded that stereopsis improves space perception but does not improve veridicality.

Large systematic deviations in visual parallelism.

The visual environment is distorted with respect to the physical environment. Luneburg [1947, Mathematical Analysis of Binocular Vision (Princeton, NJ: Princeton University Press)] assumed that visual space could be described by a Riemannian space of constant curvature. Such a space is described by a metric which defines the distance between any two points. It is uncertain, however, whether such a metric description is valid. Two experiments are reported in which subjects were asked to set two bars parallel to each other in a horizontal plane. The backdrop consisted of wrinkled black plastic sheeting, and the floor and ceiling were hidden by means of a horizontal aperture restricting the visual field of the subject vertically to 10 deg. We found that large deviations (of up to 40 degrees) occur and that the deviations are proportional to the separation angle: on average, the proportion is 30%. These deviations occur for 30 degrees, 60 degrees, 120 degrees, and 150 degrees reference orientations, but not for 0 degree and 90 degrees reference orientations; there the deviation is approximately 0 degree for most subjects. A Riemannian space of constant curvature, therefore, cannot be an adequate description. If it were, then the deviation between the orientation of the test and the reference bar would be independent of the reference orientation. Furthermore, we found that the results are independent of the distance of the bars from the subject, which suggests either that visual space has a zero mean curvature, or that the parallelity task is essentially a monocular task. The fact that the deviations vanish for a 0 degree and 90 degrees orientation is reminiscent of the oblique effect reported in the literature. However, the 'oblique effect' reported here takes place in a horizontal plane at eye height, not in a frontoparallel plane.

Optical properties (bidirectional reflectance distribution function) of shot fabric.

To study the optical properties of materials, one needs a complete set of the angular distribution functions of surface scattering from the materials. Here we present a convenient method for collecting a large set of bidirectional reflectance distribution function (BRDF) samples in the hemispherical scattering space. Material samples are wrapped around a right-circular cylinder and irradiated by a parallel light source, and the scattered radiance is collected by a digital camera. We tilted the cylinder around its center to collect the BRDF samples outside the plane of incidence. This method can be used with materials that have isotropic and anisotropic scattering properties. We demonstrate this method in a detailed investigation of shot fabrics. The warps and the fillings of shot fabrics are dyed different colors so that the fabric appears to change color at different viewing angles. These color-changing characteristics are found to be related to the physical and geometrical structure of shot fabric. Our study reveals that the color-changing property of shot fabrics is due mainly to an occlusion effect.

Similar mechanisms underlie curvature comparison by static and dynamic touch.

In four experiments, we tested whether haptic comparison of curvature ranging from -4/m to +4/m is qualitatively the same for static and for dynamic touch. In Experiments 1 and 3, we tested whether static and dynamic curvature discrimination are based on height differences, attitude (slope) differences, curvature differences, or a combination of these geometrical variables. It was found that both static and dynamic hepatic curvature discrimination are based on attitude differences. In Experiments 2 and 4, we tested whether this mechanism leads to errors in the comparison of stimuli with different lengths for static and dynamic touch, respectively. If the judgments are based on attitude differences, subjects will make systematic errors in these comparisons. In both experiments, we found that subjects compared the curvatures of strips of the same length vertically, whereas they made systematic errors if they were required to compare the curvatures of strips of different lengths. Longer stimuli were judged to be more curved than shorter stimuli with the same curvature. We conclude that similar mechanisms underlie static and dynamic haptic curvature comparison. Moreover, additional data comparison showed that static and dynamic curvature comparison is not only qualitatively, but also quantitatively similar.