Parallel—and distance—alleys with moving points in the horizontal plane

Stimulus points were presented on the horizontal plane of eye level under both dark and illuminated homogeneous spaces. When two apparent movements towards the subject were generated and positions of points were so adjusted that the two movements appeared straight and parallel (P alley) or with a constant lateral distance (D alley), the D alley lay outside the P alley, as traditionally shown with stationary sets of points. The two alleys were constructed with various patterns and velocities of movement, and the Lüneburg formulas were used as experimental equations to describe the results. The equations have two parameters: K (curvature) and o (sensitivity in depth perception). Values of K and o obtained with stationary points in previous experiments are shown too. Predominantly, K < 0 (hyperbolic), and the same is true in the present study. No first-order effect of patterns and velocities of the movement upon K and o was found.     

Haptically straight lines

In this research, we set out to investigate haptically perceived space. Large deviations with respect to physical space have already been shown to exist. Here, research on haptic space is continued by investigating straight lines constructed by touch. In four experiments, subjects were asked to produce straight lines between two reference markers that were in the horizontal plane at a fixed distance from each other. Each experiment corresponded to a different task: two different interpolation tasks, an intersection task, and a pointing task. Straight lines had an orientation that was approximately frontoparallel. Subjects used both hands; manipulation was unrestricted. Although we found considerable differences between observers, the overall pattern of results showed that haptically straight lines were generally curved away from the observer. However, in one of the interpolation tasks they corresponded to physically straight lines. In addition, the pointing task generally produced larger deviations than the other three tasks. Taken together, the results show that there is no unique definition of the straight line, a conclusion that questions the viability of the concept of haptic space.     

The structure of frontoparallel haptic space is task dependent

In three experiments, we investigated the structure of frontoparallel haptic space. In the first experiment, we asked blindfolded participants to rotate a matching bar so that it felt parallel to the reference bar, the bars could be at various positions in the frontoparallel plane. Large systematic errors were observed, in which orientations that were perceived to be parallel were not physically parallel. In two subsequent experiments, we investigated the origin of these errors. In Experiment 2, we asked participants to verbally report the orientation of haptically presented bars. In this task, participants made errors that were considerably smaller than those made in Experiment 1. In Experiment 3, we asked participants to set bars in a verbally instructed orientation, and they also made errors significantly smaller than those observed in Experiment 1. The data suggest that the errors in the matching task originate from the transfer of the reference orientation to the matching-bar position.     

Haptic parallelity perception on the frontoparallel plane: the involvement of reference frames

It has been established that spatial representation in the haptic modality is subject to systematic distortions. In this study, the haptic perception of parallelity on the frontoparallel plane was investigated in a bimanual matching paradigm. Eight reference orientations and 23 combinations of stimulus locations were used. The current hypothesis from studies conducted on the horizontal and midsagittal planes presupposes that what is haptically perceived as parallel is a product of weighted contributions from both egocentric and allocentric reference frames. In our study, we assessed a correlation between deviations from the veridical and hand/arm postures and found support for the role of an intermediate frame of reference in modulating haptic parallelity on the frontoparallel plane as well. Moreover, a subject-dependent biasing influence of the egocentric reference frame determines both the reversal of the oblique effect and a scaling effect in deviations as a function of bar position.     

Proximal velocity change as a determinant of space perception

How and to what degree does proximal velocity change determine perceived translatory motion in depth? This question was studied with a stimulus consisting of a single dot, moving in a straight horizontal path in a frontoparallel plane. Its motion corresponded to distai depth motion with constant speed. Ss reported verbally what they perceived. The results show that proximal velocity changes of this kind are, within certain limits, utilized by the visual system for the perception of translatory motion in depth. The limits were found to be determined by the absolute rate of change in proximal velocity. Further, it was found that the perceived motion track was usually bent, although all stimuli simulated depth motions along straight paths.     

Is the anisotropy of perceived 3-D shape invariant across scale?

A number of studies have resulted in the finding of a 3-D perceptual anisotropy, whereby spatial intervals oriented in depth are perceived to be smaller than physically equal intervals in the frontoparallel plane. In this experiment, we examined whether this anisotropy is scale invariant. The stimuli were L shapes created by two rods placed flat on a level grassy field, with one rod defining a frontoparallel interval, and the other, a depth interval. Observers monocularly and binocularly viewed L shapes at two scales such that they were projectively equivalent under monocular viewing. Observers judged the aspect ratio (depth/width) of each shape. Judged aspect ratio indicated a perceptual anisotropy that was invariant with scale for monocular viewing, but not for binocular viewing. When perspective is kept constant, monocular viewing results in perceptual anisotropy that is invariant across these two scales and presumably across still larger scales. This scale invariance indicates that the perception of shape under these conditions is determined independently of the perception of size.     

Visual perception of motion in depth: Application of a vector model to three-dot motion patterns

The aim of the present study was to identify spatial properties of three-dot motion patterns yielding perceived motion in depth. A proposed vector model analyzed each pattern in terms of common and relative motion components of the moving parts. The dots moved in straight paths in a frontoparallel plane. The Ss reported verbally what they perceived. The common motion did not affect the kénd of perceived event (translation or rotation in depth). Relative motions toward or away from a common point, i.e. concurrent motions, yielded perceived translatory motion in depth. Parallel relative motions toward or away from a common line generally yielded perceived rotation in depth. Complex motion patterns, consisting of concurrent and parallel relative motion components combined, evoked simultaneously perceived translation and rotation in depth under certain phase conditions of the components. Some limitations of the model were discussed and suggestions made to widen its generality.     

Errors in estimating the orientation of dot patterns

The error in estimating the orientation of a dot pattern was measured as the difference between the orientation of the least-squared-distances line (LS-line) of the pattern and the orientation of a line adjusted by the subject to match the perceived orientation of the pattern. Analysis of the mean errors (averaged over ten subjects) obtained for one hundred patterns confirmed that the orientation of the LS-line represents the orientation of elongated dot-patterns. It is shown that estimated orientation was systematically biased towards the nearest 45 degrees oblique meridian. This bias points to the importance of the +/-45 degrees directions as natural norms for left- and right-side tilt in the frontoparallel plane.     

Olp: An R package for optimal linear partitions of finite sets of points on the plane

Given a set of points on the plane and an assignment of values to them, an optimal linear partition is a division of the set into two subsets which are separated by a straight line and maximally contrast with each other in the values assigned to their points. We present a method for inspecting and rating all linear partitions of a finite set, and a package of three functions in the R language for executing the computations. One function is for finding the optimal linear partitions and corresponding separating lines, another for graphically representing the results, and a third for testing how well the data comply with the linear separability condition. We illustrate the method on possible data from a psychophysical experiment (concerning the size–weight illusion) and compare its performance with that of linear discriminant analysis and multiple logistic regression, adapted to dividing linearly a set of points on the plane.     

Multiple 3-D interpretations in a classic stereokinetic effect

It is known that a flat ellipse rotating in the frontoparallel plane sooner or later appears as a rigid circular disc tilting in 3-D space. An experiment is reported in which prolonged exposure to the same flat pattern produces a second previously unnoticed 3-D percept: an elongated egg slanted in 3-D space, which points towards the observer and the end parts of which describe a circular trajectory in the frontal plane. It is shown that the achievement of this alternative percept is not affected by the particular shape of the ellipse, although the time needed to reach it increases with an ellipse with a 2:3 axis ratio.     

Judging distance across texture discontinuities

Sinai et al (1998 Nature 395 497-500) showed that less distance is perceived along a ground surface that spans two differently textured regions than along a surface that is uniformly textured. We examined the effect of texture continuity on judged distance using computer-generated displays of simulated surfaces in five experiments. Discontinuities were produced by using different textures, the same texture reversed in contrast, or the same texture shifted horizontally. The simulated surface was either a ground plane or a frontoparallel plane. For all textures and both orientations, less distance was judged in the discontinuous conditions than in continuous conditions. We propose that when a surface contains a texture discontinuity, a small area adjacent to the perceived boundary is excluded from judged distances.     

Exocentric pointing in three-dimensional space

A study is reported of an exocentric pointing task in all three dimensions, in near space, with only two visible luminous objects--a pointer and a target. The task of the subject was to aim a pointer at a target. The results clearly show that visual space is not isotropic, since every set direction appeared to consist of two independent components--one in the projection onto a frontoparallel plane (tilt), the other in depth (slant). The tilt component shows a general trend across subjects, an oblique effect, and can be judged monocularly. The slant component is symmetrical in the mid-sagittal plane, requires the use of binocular information, and shows considerable differences between subjects. These differences seem to depend on the amount of binocular information used by each subject. There was a remarkably high level of consistency in the exocentric pointing, despite the absence of environmental cues. The within-subject consistency in the settings of the pointer corresponds to a consistency of about 1 min of arc in disparity of its tip, even though the pointer and target are separated by more than 5 deg.     

Dissociation between visual perception of allocentric distance and visually directed walking of its extent

Walking without vision to previously viewed targets was compared with visual perception of allocentric distance in two experiments. Experimental evidence had shown that physically equal distances in a sagittal plane on the ground were perceptually underestimated as compared with those in a frontoparallel plane, even under full-cue conditions. In spite of this perceptual anisotropy of space, Loomis et al (1992 Journal of Experimental Psychology. Human Perception and Performance 18 906-921) found that subjects could match both types of distances in a blind-walking task. In experiment 1 of the present study, subjects were required to reproduce the extent of allocentric distance between two targets by either walking towards the targets, or by walking in a direction incompatible with the locations of the targets. The latter condition required subjects to derive an accurate allocentric distance from information based on the perceived locations of the two targets. The walked distance in the two conditions was almost identical whether the two targets were presented in depth (depth-presentation condition) or in the frontoparallel plane (width-presentation condition). The results of a perceptual-matching task showed that the depth distances had to be much greater than the width distances in order to be judged to be equal in length (depth compression). In experiment 2, subjects were required to reproduce the extent of allocentric distance from the viewing point by blindly walking in a direction other than toward the targets. The walked distance in the depth-presentation condition was shorter than that in the width-presentation condition. This anisotropy in motor responses, however, was mainly caused by apparent overestimation of length oriented in width, not by depth compression. In addition, the walked distances were much better scaled than those in experiment 1. These results suggest that the perceptual and motor systems share a common representation of the location of targets, whereas a dissociation in allocentric distance exists between the two systems in full-cue conditions.     

Mobility of normal observers under conditions of reduced visual input.

The importance in mobility performance of the rate of presentation of visual information, binocular versus monocular vision, the use of multiple rather than single reference points, and local motion parallax was investigated in two experiments. In each experiment ten subjects walked a triangular mobility course in a totally darkened room; the only visible targets were light emitting diodes (LEDs), mounted on poles, at the apices of the triangle. The LEDs were mounted so that one or two could be used in a trial; if two were used the distance between them was varied horizontally (in experiment 1) and vertically (in experiment 2). The subjects walked around the course under a range of conditions, including two 'optimal trials' in full light. The LEDs were flashed for 1 ms at frequencies of 0.5, 1 and 5 Hz in experiment 1 and at 1 and 5 Hz in experiment 2. Mobility was measured with the use of an ultrasonic locator system which measured the subject's position on the course 10 times per second. The mean velocity of the subject in traversing the course was significantly reduced when the flash rate was slower, when the subject had one eye occluded, or when there was only one LED on the pole; when the spacing between the LEDs was varied, either vertically or horizontally performance was unaffected. These results imply that the frequency of updating of visual information is important in determining mobility performance, as are binocular cues, but that local motion parallax is not important. The number of LEDs on each pole had a significant effect on mobility performance an 'object' (two lights) gave more information than a point reference.     

Effects of different motion characteristics on perceived motion in depth

Abstract.— The effect of different velocity characteristics on type of perceived motion were tested with three different stimulus patterns, each representing a certain case of relative motion vectors derived from a vector model for perceived motion in space. The oscilloscope generated patterns, displayed onto a translucent screen, consisted of two dots moving back and forth in their motion paths. The subjects described the perceived motion verbally. The reports were classified into four response categories, i.e. perceived translation in depth, rotation in depth, translation and rotation in depth, and finally, perceived motion in a frontoparallel plane. It was found, first, that no type of relative motion vectors consistently yielded the same distribution of responses for the different velocity conditions. Second, there were no main effects of type of velocity functions (sinusoidal, hyperbolical, and constant) on perceived motion. Third, the position of maximum velocity of the dots affected perceived motion, maximum velocity at the center of the motion path favoring perceived rotation in depth and maximum velocity at the end points of the paths favoring perceived translation in depth. Finally, patterns with continuously repeated motion cycles favored perceived rotation in depth. When the continuity was broken down by pauses at the center and the end points of the motion paths and a small spatial gap at the center of the path, perceived translation in depth was favored.     

The representation of uniform motion in vision

For veridical detection of object motion any moving detecting system must allocate motion appropriately between itself and objects in space. A model for such allocation is developed for simplified situations (points of light in uniform motion in a frontoparallel plane). It is proposed that motion of objects is registered and represented successively at four levels within frames of reference that are defined by the detectors themselves or by their movements. The four levels are referred to as retinocentric, orbitocentric, egocentric, and geocentric. Thus the retinocentric signal is combined with that for eye rotation to give an orbitocentric signal, and the left and right orbitocentric signals are combined to give an egocentric representation. Up to the egocentric level, motion representation is angular rather than three-dimensional. The egocentric signal is combined with signals for head and body movement and for egocentric distance to give a geocentric representation. It is argued that although motion perception is always geocentric, relevant registrations also occur at the three earlier levels. The model is applied to various veridical and nonveridical motion phenomena.     

Perceptual unit formation in simple motion patterns

The present study investigated the proximal constraints that determine perceptual unit formation under minimal stimulus conditions. Projections of three moving dots, which could form two possible two-dot configurations, were presented to naive observers. In a forced-choice situation, their task was to report which two-dot configuration was perceived as a distinct perceptual unit. The results showed that common motions (arbitrary translations and rigid rotations in the frontoparallel plane) have stronger grouping power as compared to different relative motions (expansions/contractions, or simultaneous expansions/contractions and deformations in the frontoparallel plane). It was found that proximal changes of distances between elements in two-dot structures reduce grouping power. Changes of proximal directions, however, did not affect unit formation in two-dot structures at all. The effect of vector algebraic combinations on grouping power in three-dot strutures was also investigated. Evidently, visual vector analysis splits up motion combinations into their constituents, and in come cases this contributes to additive effects.     

Perceived bending and stretching motions from a line of points

Abstract.— The aim of this investigation was to study to what extent bending and stretching motions can be accurately perceived. The (imaginary) "distal" stimuli were lines of points, either in bending motion with constant distances between adjacent points or in stretching motion with the same distances equal at each moment (thus making the relations between the distances constant). The proximal stimuli were produced by a computer, and the subject indicated the slant and curvature of the turning positions of the perceived motion. The result for the stimuli with motion towards the subject was that a majority of the percepts were rather close to the accurate value. That was not true, however, for the stimuli with motion away from the subject. All stimuli were ambiguous demonstrating that more information must be added to get unambiguity.