Planned Straight or Biased to Be So? The Influence of Visual Feedback on Reaching Movements

Abstract

Behavioral studies consistently find that subjects move their hand along straight paths despite considerations that suggest reaches should be curved. Literature on this topic makes it clear that the experimentally displayed feedback influences how subjects reach. Could the standard visual feedback, a displayed cursor, explain the lack of path curvature in experimental results? To address this question, we conducted three experiments to examine reach behavior in the absence of the standard visual feedback. In the first experiment, we found significant increases in curvature as visual feedback was progressively extinguished across groups. A second experiment revealed that practiced reaches became curved after the standard visual feedback was removed. A final experiment found that subjects’ reaches made before and after a brief display of visual feedback were similar, indicating a preference for specific curved trajectories. Our results suggest that the consistently straight reaches often observed could be due to a bias to move the displayed cursor straight, which when removed reveal subject-specific preferences for reaches that are often curved.     

Curved movement paths and the Hering illusion: Positions or directions?

When trying to move in a straight line to a target, participants produce movement paths that are slightly (but systematically) curved. Is this because perceived space is curved, or because the direction to the target is systematically misjudged? We used a simple model to investigate whether continuous use of an incorrect judgement of the direction to the target could explain the curvature. The model predicted the asymmetries that were found experimentally when moving across a background of radiating lines (the Hering illusion). The magnitude of the curvature in participants' movements was correlated with their sensitivity to the illusion when judging a moving dot's path, but not with their sensitivity when judging the straightness of a line. We conclude that a misjudgement of direction causes participants to perceive a straight path of a moving dot as curved and to produce curved movement paths.     

Heading and path information from retinal flow in naturalistic environments

In four experiments, we explored the heading and path information available to observers as we simulated their locomotion through a cluttered environment while they fixated an object off to the side. Previously, we presented a theory about the information available and used in such situations. For such a theory to be valid, one must be sure of eye position, but we had been unable to monitor gaze systematically; in Experiment 1, we monitored eye position and found performance best when observers fixated the designated object at the center of the display. In Experiment 2, when we masked portions of the display, we found that performance generally matched the amount of display visible when scaled to retinal sensitivity. In Experiments 3 and 4, we then explored the metric of information about heading (nominal vs. absolute) available and found good nominal information but increasingly poor and biased absolute information as observers looked farther from the aimpoint. Part of the cause for this appears to be that some observers perceive that they have traversed a curved path even when taking a linear one. In all cases, we compared our results with those in the literature.     

Processing time of contour integration: the role of colour, contrast, and curvature

We investigated the temporal properties of the red - green, blue-yellow, and luminance mechanisms in a contour-integration task which required the linking of orientation across space to detect a 'path'. Reaction times were obtained for simple detection of the stimulus regardless of the presence of a path, and for path detection measured by a yes/no procedure with path and no-path stimuli randomly presented. Additional processing times for contour integration were calculated as the difference between reaction times for simple stimulus detection and path detection, and were measured as a function of stimulus contrast for straight and curved paths. We found that processing time shows effects not apparent in choice reaction-time measurements. (i) Processing time for curved paths is longer than for straight paths. (ii) For straight paths, the achromatic mechanism is faster than the two chromatic ones, with no difference between the red-green and blue-yellow mechanisms. For curved paths there is no difference in processing time between mechanisms. (iii) The extra processing time required to detect curved compared to straight paths is longest for the achromatic mechanism, and similar for the red - green and blue-yellow mechanisms. (iv) Detection of the absence of a path requires at least 50 ms of additional time independently of chromaticity, contrast, and path curvature. The significance of these differences and similarities between postreceptoral mechanisms is discussed.     

Differential effects of shared attention on perception of heading and 3-D object motion

When a person moves in a straight line through a stationary environment, the images of object surfaces move in a radial pattern away from a single point. This point, known as the focus of expansion (FOE), corresponds to the person's direction of motion. People judge their heading from image motion quite well in this situation. They perform most accurately when they can see the region around the FOE, which contains the most useful information for this task. Furthermore, a large moving object in the scene has no effect on observer heading judgments unless it obscures the FOE. Therefore, observers may obtain the most accurate heading judgments by focusing their attention on the region around the FOE. However, in many situations (e.g., driving), the observer must pay attention to other moving objects in the scene (e.g., cars and pedestrians) to avoid collisions. These objects may be located far from the FOE in the visual field. We tested whether people can accurately judge their heading and the three-dimensional (3-D) motion of objects while paying attention to one or the other task. The results show that differential allocation of attention affects people's ability to judge 3-D object motion much more than it affects their ability to judge heading. This suggests that heading judgments are computed globally, whereas judgments about object motion may require more focused attention.     

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.     

Curved apparent motion induced by amodal completion

We investigated whether amodal completion can bias apparent motion (AM) to deviate from its default straight path toward a longer curved path, which would violate the well-established principle that AM follows the shortest possible path. Observers viewed motion sequences of two alternating rectangular tokens positioned at the ends of a semicircular occluder, with varying interstimulus intervals (ISIs; 100-500?ms). At short ISIs, observers tended to report simple straight-path motion-that is, outside the occluder. But at long ISIs, they became increasingly likely to report a curved-path motion behind the occluder. This tendency toward reporting curved-path motion was influenced by the shape of tokens, display orientation, the gap between tokens and the occluder, and binocular depth cues. Our results suggest that the visual system tends to minimize unexplained absence of a moving object, as well as its path length, such that AM deviates from the shortest path when amodal integration of motion trajectory behind the curved occluder can account for the objective invisibility of the object during the ISI.     

Differential effects of shared attention on perception of heading and 3-D object motion

When a person moves in a straight line through a stationary environment, the images of object surfaces move in a radial pattern away from a single point. This point, known as thefocus of expansion (FOE), corresponds to the person’s direction of motion. People judge their heading from image motion quite well in this situation. They perform most accurately when they can see the region around the FOE, which contains the most useful information for this task. Furthermore, a large moving object in the scene has no effect on observer heading judgments unless it obscures the FOE. Therefore, observers may obtain the most accurate heading judgments by focusing their attention on the region around the FOE. However, in many situations (e.g., driving), the observer must pay attention to other moving objects in the scene (e.g., cars and pedestrians) to avoid collisions. These objects may be located far from the FOE in the visual field. We tested whether people can accurately judge their heading and the three-dimensional (3-D) motion of objects while paying attention to one or the other task. The results show that differential allocation of attention affects people’s ability to judge 3-D object motion much more than it affects their ability to judge heading. This suggests that heading judgments are computed globally, whereas judgments about object motion may require more focused attention.     

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.     

Retinal flow is sufficient for steering during observer rotation

How do people control locomotion while their eyes are simultaneously rotating? A previous study found that during simulated rotation, they can perceive a straight path of self-motion from the retinal flow pattern, despite conflicting extraretinal information, on the basis of dense motion parallax and reference objects. Here we report that the same information is sufficient for active control ofjoystick steering. Participants steered toward a target in displays that simulated a pursuit eye movement. Steering was highly inaccurate with a textured ground plane (motion parallax alone), but quite accurate when an array of posts was added (motion parallax plus reference objects). This result is consistent with the theory that instantaneous heading is determined from motion parallax, and the path of self-motion is determined by updating heading relative to environmental objects. Retinal flow is thus sufficient for both perceiving self-motion and controlling self-motion with a joystick; extraretinal and positional information can also contribute, but are not necessary.     

Dissociating position and heading estimations: Rotated visual orientation cues perceived after walking reset headings but not positions

This project examined the roles of idiothetic cues due to individuals’ movement and allothetic cues independent of individuals’ movement in individuals’ estimations of their position and heading during locomotion. In an immersive virtual environment, participants learned the locations of five objects and then moved along two legs of a path before positioning the origin and the objects. Participants’ estimations of their test position and their test heading were calculated based on the responded objects’ locations, using a method of dissociating position estimation and heading estimation developed in this project. Results showed that when a conflicting visual orientation cue was presented after walking, participants relied on the allothetic cues (i.e., the visual orientation cue) for their heading estimation, but on idiothetic cues for their position estimation. These results indicate that after participants updated their position in terms the origin of the path (homing vector) via path integration, they estimated their heading. These results are inconsistent with the theoretical models stipulating that homing vectors are specified in terms of participants’ body coordinate systems, but are consistent with the models stipulating that both homing vectors and participants’ heading are specified in terms of a fixed reference direction in the environment.     

The discrimination of heading from optic flow is not retinally invariant.

Three experiments were conducted to determine whether the discrimination of heading from optic flow is retinally invariant and to determine the importance of acuity in accounting for heading eccentricity effects. In the first experiment, observers were presented with radial flow fields simulating forward translation through a three-dimensional volume of dots. The flow fields subtended 10 degrees of visual angle and were presented at 0 degree, 10 degrees, 20 degrees, and 40 degrees of retinal eccentricity. The observers were asked to indicate whether the simulated movement was to the right or the left of a target that appeared at the end of the display sequence. Eye movements were monitored with an electrooculogram apparatus. In a second experiment, static acuity thresholds were derived for each of the observers at the same retinal eccentricities. There was a significant increase in heading detection thresholds with retinal eccentricity (from 0.92 degree at 0 degree retinal eccentricity to 3.47 degrees at 40 degrees). An analysis of covariance indicated that the variation in sensitivity to radial flow, as a function of retinal eccentricity, is independent of acuity. Similar results were obtained when the Vernier acuity of observers was measured. These results suggest that the discrimination of heading from radial flow is not retinally invariant.     

Perception of circular heading from optical flow

Observers viewed random-dot optical flow displays that simulated self-motion on a circular path and judged whether they would pass to the right or left of a target at 16 m. Two dots in two frames are theoretically sufficient to specify circular heading if the orientation of the rotation axis is known. Heading accuracies were better than 1.5 degrees with a ground surface, wall surface, and 3D cloud of dots, and were constant over densities down to 2 dots, consistent with the theory. However, there was an inverse relation between the radius of the observer's path and constant heading error, such that at small radii observers reported heading 3 degrees to the outside of the actual path with the ground and to the inside with the wall and cloud. This may be an artifact of a small display screen.     

Seeking one’s heading through eye movements

A study of eye movements during simulated travel toward a grove of four stationary trees revealed that observers looked most at pairs of trees that converged or decelerated apart. Such pairs specify that one’s direction of travel, calledheading, is to the outside of the near member of the pair. Observers looked at these trees more than those that accelerated apart; such pairs do not offer trustworthy heading information. Observers also looked at gaps between trees less often when they converged or diverged apart, and heading can never be between such pairs. Heading responses were in accord with eye movements. In general, if observers responded accurately, they had looked at trees that converged or decelerated apart; if they were inaccurate, they had not. Results support the notion that observers seek out their heading through eye movements, saccading to and fixating on the most informative locations in the field of view.     

Variability in stepping direction explains the veering behavior of blind walkers

Walking without vision results in veering, an inability to maintain a straight path that has important consequences for blind pedestrians. In this study, the authors addressed whether the source of veering in the absence of visual and auditory feedback is better attributed to errors in perceptual encoding or undetected motor error. Three experiments had the following results: No significant differences in the shapes of veering trajectories were found between blind and blindfolded participants; accuracy in detecting curved walking paths was not correlated with simple measures of veering behavior; and explicit perceptual cues to initial walking direction did not reduce veering. The authors present a model that accounts for the major characteristics of participants' veering behavior by postulating 3 independent sources of undetected motor error: initial orientation, consistent biases in step direction, and, most important, variable error in individual steps.     

Optic-flow-based perception of two-dimensional trajectories and the effects of a single landmark

Human observers can detect their heading direction on a short time scale on the basis of optic flow. We investigated the visual perception and reconstruction of visually travelled two-dimensional (2-D) trajectories from optic flow, with and without a landmark. As in our previous study, seated, stationary subjects wore a head-mounted display in which optic-flow stimuli were shown that simulated various manoeuvres: linear or curvilinear 2-D trajectories over a horizontal plane, with observer orientation either fixed in space, fixed relative to the path, or changing relative to both. Afterwards, they reproduced the perceived manoeuvre with a model vehicle, whose position and orientation were recorded. Previous results had suggested that our stimuli can induce illusory percepts when translation and yaw are unyoked. We tested that hypothesis and investigated how perception of the travelled trajectory depends on the amount of yaw and the average path-relative orientation. Using a structured visual environment instead of only dots, or making available additional extra-retinal information, can improve perception of ambiguous optic-flow stimuli. We investigated the amount of necessary structuring, specifically the effect of additional visual and/or extra-retinal information provided by a single landmark in conditions where illusory percepts occur. While yaw was perceived correctly, the travelled path was less accurately perceived, but still adequately when the simulated orientation was fixed in space or relative to the trajectory. When the amount of yaw was not equal to the rotation of the path, or in the opposite direction, subjects still perceived orientation as fixed relative to the trajectory. This caused trajectory misperception because yaw was wrongly attributed to a rotation of the path: path perception is governed by the amount of yaw in the manoeuvre. Trajectory misperception also occurs when orientation is fixed relative to a curvilinear path, but not tangential to it. A single landmark could improve perception. Our results confirm and extend previous findings that, for unambiguous perception of ego-motion from optic flow, additional information is required in many cases, which can take the form of fairly minimal, visual information.     

Controlling steering and judging heading: retinal flow,visual direction,and extraretinal information

The contribution of retinal flow (RF), extraretinal (ER), and egocentric visual direction (VD) information in locomotor control was explored. First, the recovery of heading from RF was examined when ER information was manipulated; results confirmed that ER signals affect heading judgments. Then the task was translated to steering curved paths, and the availability and veracity of VD were manipulated with either degraded or systematically biased RF. Large steering errors resulted from selective manipulation of RF and VD, providing strong evidence for the combination of RF, ER, and VD. The relative weighting applied to RF and VD was estimated. A point-attractor model is proposed that combines redundant sources of information for robust locomotor control with flexible trajectory planning through active gaze.     

Straight lines, 'uncurved lines', and Helmholtz's 'great circles on the celestial sphere'

Helmholtz's famous pincushioned chessboard figure has been used to make the point that straight lines in the world are not always perceived as straight and, conversely, that curved lines in the world can sometimes be seen as straight. However, there is little agreement as to the cause of these perceptual errors. Some authors have attributed the errors to the shape of the retina, or the amount of cortex devoted to the processing of images falling on different parts of the retina, while others have taken the effects to indicate that visual space itself is curved. Helmholtz himself claimed that the 'uncurved lines on the visual globe' corresponded to 'direction circles' defined as those arcs described by the line of fixation when the eye moves according to Listing's law. Careful re-reading of Helmholtz together with some additional observations lead us to the conclusion that two other factors are also involved in the effect: (i) a lack of information about the distance of peripherally viewed objects and (ii) the preference of the visual system for seeing the pincushion squares as similar in size.     

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.