Perceiving surface slant from deformation of optic flow

Perceived surface orientation and angular velocity were investigated for orthographic projections of 3-D rotating random-dot planes. It was found that (a) tilt was accurately perceived and (b) slant and angular velocity were systematically misperceived. It was hypothesized that these misperceptions are the product of a heuristic analysis based on the deformation, one of the differential invariants of the first-order optic flow. According to this heuristic, surface attitude and angular velocity are recovered by determining the magnitudes of these parameters that most likely produce the deformation of the velocity field, under the assumption that all slant and angular velocity magnitudes have the same a priori probability. The results of the present investigation support this hypothesis. Residual orientation anisotropies not accounted for by the proposed heuristic were also found.     

Velocity not acceleration of self-motion mediates vestibular-visual interaction

We investigated the influence of vestibular stimulation with different angular accelerations and velocities on the perception of visual motion direction. Constant accelerations resulting in different angular velocities and constant angular velocities obtained at different accelerations were combined in twenty healthy subjects. Random-dot kinematograms with coherently moving pixels and randomly moving pixels were used as visual stimuli during whole-body rotations. The smallest percentage of coherently moving pixels leading to a clear perception of motion direction was taken as the perception threshold. Perception thresholds significantly increased with increasing angular velocity. Increased acceleration, however, had no significant effect on the perception thresholds. We conclude that the achieved angular velocity, and not acceleration, is the predominant factor in the processing of vestibular-visual interaction.     

Smoothness of the velocity field and three-dimensional surface detection from optic flow

Five experiments were conducted to determine the importance of smoothness of the velocity field in detecting 3-D surfaces from optic flow. Subjects were presented with optic flow displays simulating either points positioned on a corrugated 3-D surface or points randomly positioned within a 3-D volume. The subject’s task was to indicate whether or not the display appeared to be a 3-D surface. Smoothness of the velocity field was examined by systematically varying the speed of individual velocities in the flow field according to a Gaussian distribution withM = 0 andSD = σ. Variations in frequency, amplitude, density, and surface complexity were also examined. Detection of the corrugated surfaces systematically declined with an increase in σ. An increase in frequency of the corrugation for simple (single-frequency corrugation) surfaces resulted in a decrease in surface detection accuracy. Accuracy increased with an increase in density and amplitude for both simple and complex (multiplefrequency corrugation) surfaces. An analysis of the deformation of the displays predicted performance on the basis of human observers, providing further support for the importance of deformation for 3-D surface detection.     

Binocular rivalry with rotary and radial motions

Binocular rivalry between a radially sectored and a concentrically circular pattern was investigated in three experiments. Motion of the circular pattern was either cyclical expansion and contraction with corresponding changes in spatial frequency (experiment 1), or outward motion with a constant linear velocity (experiment 2). When both patterns were static the circular pattern was visible for longer than the radial one. Motion of either pattern alone resulted in an increase in the predominance duration and the mean period for which the pattern was visible. This is at variance with Levelt's model of rivalry. In the third experiment, rivalry was between a static circular pattern and a radial pattern that could be rotated at different angular velocities. Again it was found that an increase in stimulus strength, as measured by predominance, led to an increase in the mean periods of visibility of the rotating pattern.     

Effects of optic flow on the kinematics of human gait: a comparison of young and older adults

This experiment studied the effect of imposed optic flow on human locomotion. Six young and 6 older adults were exposed to various patterns of optic flow while walking in a moving hallway. Results showed few cases of impaired postural control (staggers, parachute reactions). No falls were recorded. Kinematic patterns of gait were altered when vision was absent or inconsistent optic flow was presented: Ninety two percent of the subjects' mean step velocity differed from their step velocities under normal vision. Compared with imposed central flow, peripheral optic flow was not dominant in inducing kinematic changes. Characteristic gait profiles were obtained, depending on flow direction. Global backward flow tended to slow down step velocity, whereas subjects' step velocity increased during conditions of forward flow. The results suggest that subjects attempted to match their own walking speed to the velocity of the moving visual scenes. It is concluded that in an uncluttered environment, imposed optic flow has a modulating rather than a destabilizing effect on human locomotion.     

Visual orientation by motion-produced blur patterns: Detection of divergence

Blur patterns are physiological “streaks” of photochemical and neural activity that occur whenever an observer and his visual environment are in relative motion. When retinal velocities are high, the impression of visual “flow” gives way to one of a field of “blur lines” whose patterns are rich with information about the motions and the optical textures that produced them. Simulated blur patterns were produced and thresholds measured for the detection of divergence at nine retinal loci. Sensitivity was somewhat greater in the central retina. Thresh-olds remained the same despite variations in pattern velocity, number of elements, and the presence or absence of an internal velocity gradient. Observers were able to orient above-threshold patterns, but consistently underestimated the amount of slant.     

Factors influencing perceived angular velocity.

The assumption that humans are able to perceive and process angular kinematics is critical to many structure-from-motion and optical flow models. The current studies investigate this sensitivity, and examine several factors likely to influence angular velocity perception. In particular, three factors are considered: (1) the extent to which perceived angular velocity is determined by edge transitions of surface elements, (2) the extent to which angular velocity estimates are influenced by instantaneous linear velocities of surface elements, and (3) whether element-velocity effects are related to three-dimensional (3-D) tangential velocities or to two-dimensional (2-D) image velocities. Edge-transition rate biased angular velocity estimates only when edges were highly salient. Element velocities influenced perceived angular velocity; this bias was related to 2-D image velocity rather than 3-D tangential velocity. Despite these biases, however, judgments were most strongly determined by the true angular velocity. Sensitivity to this higher order motion parameter was surprisingly good, for rotations both in depth (y-axis) and parallel to the line of sight (z-axis).     

Factors influencing perceived angular velocity

The assumption that humans are able to perceive and process-angular kinematics is critical to many structure-from-motion and optical flow models. The current studies investigate this sensitivity, and examine several factors likely to influence angular velocity perception. In particular, three factors are considered: (1) the extent to which perceived angular velocity is determined by edge transitions of surface elements, (2) the extent to which angular velocity estimates are influenced by instantaneous linear velocities of surface elements, and (3) whether element-velocity effects are related to three-dimensional (3-D) tangential velocities or to two-dimensional (2-D) image velocities. Edge-transition rate biased angular velocity estimates only when edges were highly salient. Element velocities influenced perceived angular velocity; this bias was related to 2-D image velocity rather than 3-D tangential velocity. Despite these biases, however, judgments were most strongly determined by the true angular velocity. Sensitivity to this higher order motion parameter was surprisingly good, for rotations both in depth (y-axis) and parallel to the line of sight (z-axis).     

Effects of circular motion on judgment of rotation direction and depth order in visual motion

Abstract:  The rotation direction and depth order of a rotating sphere consisting of random dots often reverses while it is viewed under orthographic projection. However, if a short viewing distance is simulated under perspective projection, the correct rotation direction can be perceived. There are two motion cues for the rotation direction and depth order. One is the speed cue; points with higher velocities are closer to the observer. The other is the vertical motion cue; vertical motion is induced when the dots recede from or approach the observer. It was examined whether circular motion, which does not have any depth information but induces vertical velocities, masks the vertical motion cue. In Experiment 1, the effects of circular motion on the judgment of the rotation direction of a rotating sphere were examined. The magnitude of the two cues (the speed cue and the vertical velocity cue) as well as the angular speed of circular motion was varied. It was found that the performance improved as the vertical velocity increased and that the speed cue had slight effects on the judgment of the rotation direction. It was also found that the performance worsened as the angular speed of the circular motion was increased. In Experiment 2, the effects of circular motion on depth judgment of a rotating half sphere were investigated. The performance worsened as the angular speed of the circular motion increased, as in Experiment 1. These results suggest that the visual system cannot compensate perfectly for circular motion for the judgment of the rotation direction and depth order.     

Detection of three-dimensional surfaces from optic flow: The effects of noise

Previous research (Andersen, 1989) has suggested that the recovery of 3-D shape from nonsmooth optic flow (motion transparency) can be performed by segregating surfaces according to the distributions of velocities present in the flow field. Five experiments were conducted to examine this hypothesis in a surface detection paradigm and to determine the limitations of human observers to detect 3-D surfaces in the presence of noise. Two display types were examined: a flow field that simulateda surface corrugated in depth and a flow field-that simulated a random volume. In addition, two types of noise were examined: a distribution of noise velocities that overlapped or did not overlap the velocity distribution that defined the -surface. Corrugation frequency and surface density were also examined. Detection performance increased with decreasing corrugation frequency, decreasing noise density, and decreasing surface density. Overall, the subjects demonstrated remarkable tolerance to the presence of noise and, for some conditions, could discriminate surface from random conditions when noise density was twice the-surface density. Discrimination accuracy was greater for the nonoverlapping than for the overlapping noise, providing support for an analysis based on the distribution of velocities.     

A study of the restitution coefficient in elastic-plastic impact

The aim of this work is to provide useful quantitative support for theories of the restitution coefficient for normal impacts involving plastic deformation, especially in the region close to the threshold at which plastic deformation begins. The impacts were from spheres of 5 mm diameter of aluminium oxide (which deformed elastically), dropped on to thick plates of mild steel or aluminium alloy. Very accurate measurements of impact and rebound velocities were made for drop heights from 1.75 m down to 0.6 mm, covering a range of velocities down to the yield threshold. Most of these results are in the elastic-plastic velocity range over which the indentation pressure varies from its value at initial yield of about 1.1sigma_y to the value when full plasticity is established of about 2.8sigma_y. The variation in the restitution coefficient with velocity in this range closely fits the rebound model of Tabor, which allows the indentation pressure to vary through the Meyer index n. The fitted values of n take into account these elastic-plastic effects as well as work hardening, demonstrating that a power-law compliance relationship is a very good model for the increase in indentation pressure as plasticity develops. Full plasticity only becomes established at impact velocities which are of the order of 100 times the velocity at which initial yield takes place. Models which assume a constant indentation pressure (perfect plasticity) are not a good match for the data in the elastic-plastic regime.     

Response Timing Accuracy as a Function of Movement Velocity and Distance

In two experiments, patterns of response error during a timing accuracy task were investigated. In Experiment 1, these patterns were examined across a full range of movement velocities, which provided a test of the hypothesis that as movement velocity increases, constant error (CE) shifts from a negative to a positive response bias, with the zero CE point occurring at approximately 50% of maximum movement velocity (Hancock & Newell, 1985). Additionally, by examining variable error (VE), timing error variability patterns over a full range of movement velocities were established. Subjects (N = 6) performed a series of forearm flexion movements requiring 19 different movement velocities. Results corroborated previous observations that variability of timing error primarily decreased as movement velocity increased from 6 to 42% of maximum velocity. Additionally, CE data across the velocity spectrum did not support the proposed timing error function. In Experiment 2, the effect(s) of responding at 3 movement distances with 6 movement velocities on response timing error were investigated. VE was significantly lower for the 3 high-velocity movements than for the 3 low-velocity movements. Additionally, when MT was mathematically factored out, VE was less at the long movement distance than at the short distance. As in Experiment 1, CE was unaffected by distance or velocity effects and the predicted CE timing error function was not evident.     

“Center-of-gravity” Tendencies for fixations and flow patterns

Fixation positions were measured for a variety of simple patterns. Generally, the spontaneous fixation tendencies hovered near the “center-of-gravity” of the pattern, providing that the overall dimensions of the figure were less than about 5 deg. “Open” figures such as angles were found to be roughly equivalent to their “enclosed” counterparts, such as triangles. The constraints imposed by the pattern upon the fixation tendencies occur at a level where the binocular inputs are processed. Of further importance was the fact that the fixation points approximate the foci observed in the same patterns when they are seen against a background of visual noise. It is suggested that the two results may be functionally related..     

Implied velocity and acceleration induce transformations of visual memory

In this study, the phenomenon of representational momentum (Freyd & Finke, 1984) is investigated in cases where visual memories are distorted by implied motions of the elements of a pattern. Our theory predicts that these memory distortions should be sensitive not only to the direction of the implied motions but also to changes in the implied velocity. Subjects observed a sequence of dot-pattern displays that implied that the dots were moving at either a constant velocity or constant acceleration, but in separate directions. Discrimination functions for recognizing the final pattern in the sequence revealed that subjects' memories had shifted forward, corresponding to small continuations of the implied motions. The induced memory shifts increased in size as the implied velocity and acceleration of the dots increased, but were eliminated when the display sequence implied a deceleration of the dots to a final velocity of zero. These findings suggest that mentally extrapolated motion may have some of the same inertial properties as actual physical motion.     

Kinetic attraction during bimanual coordination

Two experiments examined the effects of independent variations in kinetic and kinematic requirements on interlimb coupling during a bimanual task. The goal of the investigation was to provide preliminary evidence regarding one general class of physical variables that constrains discrete bimanual movements. Subjects attempted to execute a smooth unidirectional movement with the left arm, along with a three-segment reversal movement with the right arm. The first experiment manipulated the torque required to produce the reversal action, while movement duration and average angular velocity were held constant for both limbs. Several indications of increased interlimb coupling, due to the kinetic variation, were evident. The converse manipulation was used in the second experiment, with movement time and kinematics (velocity, acceleration) changed independently of joint torque requirements for the reversal limb. No clear effect of kinematics on coupling strength was noted. The results suggest that one variable influencing interlimb attraction toward common spatiotemporal trajectories may be kinetic in nature.     

Perceptual inequality between two physically equal constant velocities

When an object moves with an equal constant velocity before and after passing through a tunnel (or before and after a sudden acceleration--or deceleration--in the central part of its trajectory), the two velocities (the one preceding and the one following the tunnel or the sudden acceleration or deceleration) are perceived as different even if actually physically equal. Four experiments were carried out to underestimation of the second velocity (i.e., the one following the tunnel) when the first one (i.e., the one preceding the tunnel) is low, and an overestimation of the second one when the values of the first velocity are higher. An interpretation of the results is proposed, suggesting that an appearance effect (i.e., an apparent higher velocity at the beginning of the movement) could be for the perceptual inequality between the two physically equal constant velocities.     

Kinetic Attraction During Bimanual Coordination

Two experiments examined the effects of independent variations in kinetic and kinematic requirements on interlimb coupling during a bimanual task. The goal of the investigation was to provide preliminary evidence regarding one general class of physical variables that constrains discrete bimanual movements. Subjects attempted to execute a smooth unidirectional movement with the left arm, along with a three-segment reversal movement with the right arm. The first experiment manipulated the torque required to produce the reversal action, while movement duration and average angular velocity were held constant for both limbs. Several indications of increased interlimb coupling, due to the kinetic variation, were evident. The converse manipulation was used in the second experiment, with movement time and kinematics (velocity, acceleration) changed independently of joint torque requirements for the reversal limb. No clear effect of kinematics on coupling strength was noted. The results suggest that one variable influencing interlimb attraction toward common spatiotemporal trajectories may be kinetic in nature.     

Response Timing Accuracy as a Function of Movement Velocity and Distance

In two experiments, patterns of response error during a timing accuracy task were investigated. In Experiment 1. these patterns were examined across a full range of movement velocities, which provided a test of the hypothesis that as movement velocity increases, constant error (CE) shifts from a negative to a positive response bias, with the zero CE point occurring at approximately 50% of maximum movement velocity (Hancock & Newell, 1985). Additionally, by examining variable error (VE), timing error variability patterns over a full range of movement velocities were established. Subjects (N = 6) performed a series of forearm flexion movements requiring 19 different movement velocities. Results corroborated previous observations that variability of timing error primarily decreased as movement velocity increased from 6 to 42% of maximum velocity. Additionally, CE data across the velocity spectrum did not support the proposed timing error function. In Experiment 2, the effect(s) of responding at 3 movement distances with 6 movement velocities on response timing error were investigated. VE was significantly lower for the 3 high-velocity movements than for the 3 low-velocity movements. Additionally, when MT was mathematically factored out. VE was less at the long movement distance than at the short distance. As in Experiment 1, CE was unaffected by distance or velocity effects and the predicted CE timing error function was not evident.     

Mental rotation of random two-dimensional shapes

Two experiments are reported in which Ss were required to determine whether a random, angular form, presented at any of a number of picture-plane orientations, was a “standard” or “reflected” version. Average time required to make this determination increased linearly with the angular departure of the form from a previously learned orientation. The slope and intercept of the reaction-time (RT) function were virtually constant, regardless of the perceptual complexity of the test form and the orientation selected for initial learning.When Ss were informed in advance as to the identity and the orientation of the upcoming test form and, further, were permitted to indicate when they were prepared for its external presentation, RT for determining the version of the form was constant for all test-form orientations. However, the time needed to prepare for the test-form presentation increased linearly with the angular departure of the form from the learned orientation.It is argued that the processes both of preparing for and of responding to a disoriented test form consist of the mental rotation of an image, and that both sorts of mental rotation (pre-stimulus and post-stimulus) are carried out at essentially the same constant rate.     

Perceiving shape from profiles

Four experiments related human perception of shape from profiles to current theoretical predictions. In Experiment 1, judgments of structure and motion were obtained for single- and dualellipsoid displays rotating about various axes. Ratings were highest when the axis of rotation was in the image plane and were influenced by the number of ellipsoids and the orientation of a single ellipsoid. The subsequent experiments explored the effect of orientation on shape judgments of a single ellipsoid. The results of Experiments 2 and 3 suggested that the effect of orientation found in Experiment 1 was not due to either the inability of certain orientations to be perceived as three-dimensional objects or to two-dimensional artifacts. It was thus argued that this effect of orientation was due to points of correspondence in relative motion that arise when the major axis is not perpendicular to the axis of rotation. In Experiment 4, subjects provided judgments of both shape and angular velocity. The elevated ellipsoids that were judged as larger were also judged as rotating more slowly. The inverse relationship between size and angular velocity is consistent with current theories. The connection between theory and data was further demonstrated by applying a shape-recovery algorithm to the stimuli used in Experiment 4 and finding a similar tradeoff between angular velocity and shape.