Time-to-passage judgments in nonconstant optical flow fields

The time until an approaching object will pass an observer (time to passage, or TTP) is optically specified by a global flow field even in the absence of local expansion or size cues. Kaiser and Mowafy (1993) have demonstrated that observers are in fact sensitive to this global flow information. The present studies investigate two factors that are usually ignored in work related to TTP: (1) non-constant motion functions and (2) concomitant eye rotation. Non-constant velocities violate an assumption of some TTP derivations, and eye rotations may complicate heading extraction. Such factors have practical significance, for example, in the case of a pilot accelerating an aircraft or executing a roll. In our studies, a flow field of constant-sized stars was presented monocularly on a large screen. TTP judgments had to be made on the basis of one target star. The flow field varied in its acceleration pattern and its roll component. Observers did not appear to utilize acceleration information. In particular, TTPs with decelerating motion were consistently underestimated. TTP judgments were fairly robust with respect to roll, even when roll axis and track vector were decoupled. However, substantial decoupling between heading and track vector led to a decrement in performance, in both the presence and the absence of roll.     

Distance perception across spatial discontinuities

We investigated the use of nested contact relations in perceiving the relative distance of locations on discontinuous surfaces. Observers viewed computer-generated displays under monocular static conditions and adjusted a marker to match the perceived distance of a cube. The marker and cube were raised above the ground by two different platforms separated by a gap. The relative heights and distances of the platforms were varied. We found the following: (1) When spatially discontinuous surfaces are coplanar, locations of objects resting on these surfaces appear to be compared directly, bypassing relations with the underlying ground plane. (2) Spatial displacement between the platforms produces a bias, in the direction of the displacement, in the perceived relative locations of objects resting on the platforms. This suggests that local spatial relations between objects and their platforms are only partially integrated with more global spatial relations between the discontinuous surfaces of the platforms.     

Detection and discrimination of optical flow components

Observers viewed animation sequences consisting of random dots, some of which moved coherently in a given direction (signal dots) and the rest of which moved randomly (noise dots). Using forced-choice procedures, detectability of weak signals within noise was measured for translation, rotation, and expansion/contraction. Sensitivity to all motion types was approximately equal, with practiced observers reliably detecting coherent motion at signal levels as low as 4%. Observers were able to identify the motion structure presented on a given trial at signal levels corresponding to the detection threshold, implying that the neural signals supporting detection are labeled for motion type. Results are discussed in the context of hierarchical analysis of optic flow in which all motion types are registered as patterns of activity among neurons comprising a single mechanism.     

Heading backward: Perceived direction of movement in contracting and expanding optical flow fields

Two goals were pursued in an investigation of possible visual sources for directionality judgments of ego-motion. First, J. J. Gibson’s (1950) global radial outflow hypothesis was contrasted with a simple extrapolation strategy. Second, backing-direction judgments capitalizing on the informational equivalence of global radial outflow created during forward ego-motion and global radial inflow during backward ego-motion were explored. In comparing the accuracy of heading and backing judgments, new insights about global flow and extrapolation strategies were found. Consistent with the hypothesis of an extrapolation strategy, Experiment 1 demonstrated that backing judgments were more accurate than heading judgments when linear observer motion was simulated by means of a point-light flow field. In this case, accuracy was higher with two-point-light displays (extrapolation) than with more complex displays (global flow). Experiment 2 showed that in cases where extrapolation was not possible, such as circular motion, no advantage of backing judgments could be found and judgments were generally less accurate. We conclude that, whenever possible, observers use extrapolation to determine their heading/backing. Only when global flow is the only good source of information do they rely on it.     

Perceiving circular heading in noncanonical flow fields

Five experiments examined circular heading perception with optical flows that departed from the canonical form. Noncanonicity was achieved through nonrigidity of the environment (Experiments 1 and 2), oscillations of the point of observation (Experiment 3), and the bending of light (Experiments 4 and 5). In Experiments 1 and 2, perception was impaired more by nonrigidity of the ground plane than by nonrigidity of the medium. In Experiment 3, perception was unimpaired by noncanonical flows induced by the bounce and sway of observer locomotion. In Experiments 4 and 5, perception was not impaired when light paths were distorted by a spherical projection, but perception was impaired when they were distorted by a sine function. Results are discussed in relation to the hypothesis that the information for perceiving heading is the ordinal pattern of optical flow.     

Visual search asymmetries in motion and optic flow fields

In visual search, items defined by a unique feature are found easily and efficiently. Search for a moving target among stationary distractors is one such efficient search. Search for a stationary target among moving distractors is markedly more difficult. In the experiments reported here, we confirm this finding and further show that searches for a stationary target within a structured flow field are more efficient than searches for stationary targets among distractors moving in random directions. The structured motion fields tested included uniform direction of motion, a radial flow field simulating observer forward motion, and a deformation flow field inconsistent with observer motion. The results using optic flow stimuli were not significantly different from the results obtained with other structured fields of distractors. The results suggest that the local properties of the flow fields rather than global optic flow properties are important for determining the efficiency of search for a stationary target.     

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.     

Perception of translational heading from optical flow

Radial patterns of optical flow produced by observer translation could be used to perceive the direction of self-movement during locomotion, and a number of formal analyses of such patterns have recently appeared. However, there is comparatively little empirical research on the perception of heading from optical flow, and what data there are indicate surprisingly poor performance, with heading errors on the order of 5 degrees-10 degrees. We examined heading judgments during translation parallel, perpendicular, and at oblique angles to a random-dot plane, varying observer speed and dot density. Using a discrimination task, we found that heading accuracy improved by an order of magnitude, with 75%-correct thresholds of 0.66 degrees in the highest speed and density condition and 1.2 degrees generally. Performance remained high with displays of 63-10 dots, but it dropped significantly with only 2 dots; there was no consistent speed effect and no effect of angle of approach to the surface. The results are inconsistent with theories based on the local focus of outflow, local motion parallax, multiple fixations, differential motion parallax, and the local maximum of divergence. But they are consistent with Gibson's (1950) original global radial outflow hypothesis for perception of heading during translation.     

Detection of spatial cues in linear and logarithmic frequency-modulated sweeps

Frequency- and amplitude-modulated (FM and AM) sounds are the building blocks of complex sounds. In the present study, we investigated the ability of human observers to process spatial information in an important class of FM sounds: broadband directional sweeps common in natural communication signals such as speech. The stimuli consisted of linear or logarithmic unidirectional FM pulses that swept either up or down in frequency at various rates. Spatial localization thresholds monotonically improved as sweep duration decreased and as sweep rate increased, but no difference in performance was observed between logarithmic and linear or between upand down-frequency sweeps. Counterintuitive reversals in localization were observed which suggested that the localization of high-frequency sweeps may be strongly dominated by amplitude information even in situations in which one might consider timing cues to be critical. Implications of these findings for the localization of complex sounds are discussed.     

Visual search asymmetries in motion and optic flow fields.

In visual search, items defined by a unique feature are found easily and efficiently. Search for a moving target among stationary distractors is one such efficient search. Search for a stationary target among moving distractors is markedly more difficult. In the experiments reported here, we confirm this finding and further show that searches for a stationary target within a structured flow field are more efficient than searches for stationary targets among distractors moving in random directions. The structured motion fields tested included uniform direction of motion, a radial flow field simulating observer forward motion, and a deformation flow field inconsistent with observer motion. The results using optic flow stimuli were not significantly different from the results obtained with other structured fields of distractors. The results suggest that the local properties of the flow fields rather than global optic flow properties are important for determining the efficiency of search for a stationary target.     

The visual perception of rigid motion from constant flow fields

Four experiments investigated observers’ judgments of rigidity for different types of optical motion. The depicted structural deformations were of two types: (1) those with nonparallel image trajectories that are detectable from the first-order spatiotemporal relations between pairs of views; and (2) those with parallel image trajectories that can only be detected from higher order relations among three or more views. Patterns were composed of smooth flow fields in Experiments 1 and 3, and of wire frame figures in Experiments 2 and 4. For both types of display, the nonrigidity detectable from the first-order spatiotemporal structure of the motion sequence was much more salient than the deformation detectable only from the higher order spatiotemporal structure. These results indicate that observers’ judgments of rigidity are based primarily on a two-view analysis, but that some useful information can be obtained under appropriate circumstances from higher order spatiotemporal relations among three or more views.     

Use of central and peripheral optical flow in stance and locomotion in young walkers

Young walkers (up to 5 years of age) were presented with optical flow in a moving room. Flow was global or was restricted to either the center or the periphery of the visible optic array. On standing trials the response rate was greatest when peripheral flow was available. The availability of central flow had a smaller effect on standing, and the younger children showed greater response rates to frontal flow than did the older ones. There was a strong negative correlation between age and response rate for all conditions. Flow also affected stability during locomotion. Response rate was again related to the location of the available flow. It is concluded that children show the same relative sensitivity for flow in the periphery of the dynamic structure of the optic array as has been observed in adults, but that this differentiation of different areas of optical structure is not yet fully developed when children learn to stand.     

The role of discontinuities in the perception of subjective figures

Recently we proposed a theory of visual interpolation (Kellman & Shipley, in press) that addresses a variety of unit formation phenomena, including the perception of partly occluded objects and subjective figures. A basic notion of the theory is that discontinuities in the first derivative of projected edges are the initiating conditions for interpolation of boundaries that are not physically specified. In this paper, we report four experiments in which this claim was tested in the domain of subjective figures. Experiments 1 and 2 demonstrate that discontinuities in the first derivative of the edges of inducing elements have a clear effect on the frequency of report and the perceived clarity of simple subjective figures. Similar effects are found when unfamiliar subjective figures and inducing elements are used (Experiment 3). Experiment 4 rules out the possibility that the discontinuities in the first derivative merely add to the clarity of subjective figures. These experiments suggest that first-order discontinuities play a central role in unit formation.     

The perception of an optical flow projected on the ground surface

In most experiments in which the importance of visual control on postural stability is studied, optical stimuli attached to vertical surfaces are used. Analyses of long-term standing readjustments generally involve back-and-forth movements of a visual scene or its projection on vertical circular screens. In a natural environment, however, visual information is largely available from the ground. The aim of the experiment reported was to assess the effect of a flow pattern simulating an open outdoor setting on motion perception and postural control. Subjects were presented with an optical texture projected onto the ground. Periods of motionless texture alternated with equivalent durations of unidirectional flows. The change of position of the subject's centre of gravity over time was recorded on a force platform. Results show that the direction of body sway corresponded with that of texture motion. Important aftereffects, as shown in linear vection experiments, were also observed. However, the latency of postural responses was much shorter than with prolonged unidirectional flows produced in other locations of the visual environment. The hypothesis of an ecological specificity of the flows perceived on the ground during terrestrial displacements is discussed.     

Role of optical flow field asymmetry in the perception of heading during linear motion

During linear translation through a stationary environment, the pattern of optical flow generated on each retina is symmetrical when the head is aligned with the heading, but during lateral gaze the optical flow is asymmetric. We assessed whether human subjects could use the magnitude of this asymmetry to determine the direction of heading during passive translation through a 3-D environment. When allowed to move their heads in order to look in the direction of self-motion, subjects indicated their heading precisely and accurately. When the head was locked in alignment with the misaligned body, and gaze adjustments were not allowed, responses were quite precise, but showed a large bias which increased with increasing heading angle.     

Wayfinding on foot from information in retinal, not optical, flow.

People find their way through cluttered environments with ease and without injury. How do they do it? Two approaches to wayfinding are considered: Differential motion parallax (DMP) is a retinal motion invariant of near and far objects moving against fixation; the information in optical flow (IOF) is a radial pattern of vectors, relying on decomposition of retinal flow. Evidence is presented that DMP guides wayfinding during natural gait, accounting for errors as well as correct responses. Evidence against IOF is also presented, and a space-time aliasing artifact that can contaminate IOF displays is explored. Finally, DMP and IOF are separated, showing they can yield different results in different environments. Thus, it is concluded that (a) DMP and IOF are different, (b) DMP and not IOF is used for wayfinding, (c) moving observers do not usually decompose retinal flow, and (d) optical flow may be a mathematical fiction with no psychological reality.     

Reasoning about actions and obligations in first-order logic

We describe a new way in which theories about the deontic status of actions can be represented in terms of the standard two-sorted first-order extensional predicate calculus. Some of the resulting formal theories are easy to implement in Prolog; one prototype implementation—R. M. Lee's deontic expert shell DX—is briefly described.This research was partially supported by the Esprit III Basic Research Working Group No. 8319 ModelAge.