Use of Level 1 and 2 driving automation on horizontal curves on interstates and freeways

Little is known about how the actual use of Level 1 and 2 driving automation systems may be affected by geometric road characteristics in naturalistic driving environments. This study examined the use of these systems on horizontal curves on interstates and freeways. It used travel data collected in a field operational test conducted with two 2016 Land Rover Range Rover Evoque vehicles equipped with adaptive cruise control (ACC) and two 2017 Volvo S90 vehicles equipped with ACC and Pilot Assist (PA). Logistic regression models estimated changes in the likelihood of ACC use associated with horizontal curvature in the Evoque vehicles, and of PA and ACC use in the S90 vehicles, while accounting for traffic conditions. Drivers were less likely to drive with ACC or PA on as horizontal curves became sharper. In the Evoque vehicles, the likelihood of using ACC was 71.6% lower on the sharpest category of horizontal curves (those with a degree of curvature>2.5 degrees per 100 feet of arc or a radius smaller than 2,292 feet), compared with straight road segments or the flattest horizontal curve category (those with a degree of curvature <= 1.5 degrees per 100 feet of arc or a radius no <3,820 feet). In the S90 vehicles, the likelihood of using PA and ACC declined 74.6 and 66.3%, respectively, on the sharpest curves. Many driving automation systems face challenges on horizontal curves, even within their operational design domain. Future implementations that improve functionality may enhance driver experience and boost drivers’ confidence in these systems, which should increase their use and maximize the safety benefits these systems might offer.     

Mirror vision: perceived size and perceived distance of virtual images

We investigated spatial perception of virtual images that were produced by convex and plane mirrors. In Experiment 1, 36 subjects reproduced both the perceived size and the perceived distance of virtual images for five targets that had been placed at a real distance of 10 or 20 m. In Experiment 2, 30 subjects verbally judged both the perceived size and the perceived distance of virtual images for five targets that were placed at each of five real distances of 2.5-45 m. In both experiments, the subjects received objective-size and objective-distance instructions. The results were that (1) size constancy was attained for a distance of up to 45 m, (2) distance was readily discriminated within this distance range, although virtual images produced by the mirror of strong curvature were judged to be farther away than those produced by the mirrors of less curvature, and (3) the ratio of perceived size to perceived distance was described as a power function of visual angle, and the ratio for the convex mirror was larger than that for the plane mirror. We compared the taking-into-account model and the direct perception model on the basis of a correlation analysis for proximal, virtual, and real levels of the stimuli. The taking-into-account model, which assumes that visual angle is transformed into perceived size by taking perceived distance into account, was supported by an analysis for the proximal level of stimuli. The direct perception model, which assumes that there is no inferential process between perceived size and perceived distance, was partially supported by an analysis for the distal level of the stimuli.     

Depth,size and distance in stereoscopic vision

Evidence is presented to show that in stereoscopic vision a constant ratio of perceived size to perceived distance corresponds to a constant visual angle (the size-distance invariance hypothesis). The functions relating the size/ distance ratio to visual angle and the depth/distance ratio to disparity are determined for three as using the methods of magnitude estimation and magnitude production. The results for each a may be represented by power functions, the depth/ distance function having the higher exponent. These scales are used to predict the outcome of an experiment in which depth is matched to size. The agreement of predictions with results is good for the combined data of the group, but significant deviations occur from curves predicted for individual as. An experiment in which an oblique line is matched to a frontal extent yields data consistent with Luneburg’s hypothesis that the intrinsic geometry of visual space is non-Euclidean. The indicated curvature is negative for two as and varying from positive to negative for the third.     

Structural salience and the nonaccidentality of a gestalt

We perceive structure through a process of perceptual organization. Here we report a new perceptual organization phenomenon-the facilitation of visual grouping by global curvature. Observers viewed patterns that they perceived as organized into collections of curves. The patterns were perceptually ambiguous such that the perceived orientation of the patterns varied from trial to trial. When patterns were sufficiently dense and proximity was equated for the predominant perceptual alternatives, observers tended to perceive the organization with the greatest curvature. This effect is tantamount to visual grouping by maximal curvature and thus demonstrates an unprecedented effect of global structure on perceptual organization. We account for this result with a model that predicts the perceived organization of a pattern as function of its nonaccidentality, which we define as the probability that it could have occurred by chance. Our findings demonstrate a novel relationship between the geometry of a pattern and the visual salience of global structure.     

Models of acceleration and deceleration rates on a complex two-lane rural highway: Results from a nighttime driving experiment

This study aimed to model driver’ deceleration or acceleration rates on a complex two-lane rural highway when approaching or departing horizontal curves under nighttime driving conditions. The data used in the study were from a field experiment conducted in Pennsylvania. Research participant speeds were continuously tracked along the experimental roadway. The deceleration and acceleration rate models when approaching and departing horizontal curves were treated as a uni-directional recursive system to account for the effects of upstream rates on deceleration and acceleration rates. This system was estimated using seemingly unrelated regression with random effects to account for the contemporaneous correlation across the two equations. Research participants were included in the model as random effects while several geometric roadway design features along the experimental roadway were included as fixed effects in the model. The results indicate that the explanatory variables associated with deceleration or acceleration rates when approaching or departing horizontal curves in the present experiment included several geometric design variables, such as curve direction, curve radius, horizontal curve length, and a vertical curve index. The deceleration and acceleration rates approaching and departing horizontal curves along the complex, two-lane rural highway included in this study have a larger range than those in past research studies of two-lane rural highways.     

Using motor tasks to quantitatively judge 3-D surface curvatures.

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects' sensitivity to the curvature of a curve lying on a surface and changes in the curvature as defined by Euler's formula, which relates maximum and minimum principal curvatures and their directions. Regardless of direction and surface shape (elliptic and hyperbolic), subjects could report the curvature of a curve lying on a surface through a drawing task. In addition, multiple curves drawn by subjects were used to reconstruct the surface. These reconstructed surfaces could be better accounted for by analysis that treated the drawing data as a set of curvatures rather than as a set of depths. A pointing task was utilized in Experiment 2, and subjects could report principal curvature directions of a surface rather precisely and consistently when the difference between principal curvatures was sufficiently large, but performance was poor for the direction of zero curvature (asymptotic direction) on a hyperbolic surface. In Experiment 3, it was discovered that sensitivity to the sign of curvature was different for perceptual judgments and motor responses, and there was also a difference for that of a curve itself and the same curve embedded in a surface. These findings suggest that humans are sensitive to relative changes in curvature and are able to comprehend quantitative surface curvature for some motor tasks.     

Visual curve tracing properties

Subjects decided whether 2 dots were on the same curve or 2 different curves, and the curvature of the curves or the proximity of other (distractor) curves to the target curve was varied. Response time increased as the arc length of the curve connecting the 2 dots increased, suggesting that the curve was traced to perform the task. Tracing rate was faster for low- than high-curvature contours and was increasingly slower as distractor contours were increasingly proximal to the traced curve. Proximity results were predicted by a model in which response time depends on the ratio of the distance between the dots and the distance between adjacent lines. Curve tracing operations used to integrate information along contours are sensitive to several properties of the contours. The implications of the sensitivity of tracing operations to these curve properties are discussed.     

Psychophysical judgment of curvatures

In this study we explored psychophysical judgments (magnitude estimation) of the curvature of visual lines. Prior research has lacked a rigorous definition of curvature, but here it was defined as the reverse of the ray of the osculating circle tangent to the curve in the given point. Four different functions were evaluated: hyperbole, sinusoid, parabola, and a cubic function. Using the method of magnitude estimation to judge 20 exemplar curves from each of the families, three respondents made a total of 1440 estimations each. Responses to all four families of curves were fit well by Stevens' power function with an exponent less than 1. One application of this research is the use of such curves as variables in assessing illusions of curvature.     

The haptic perception of curvature

Ninety-two subjects, schoolchildren and undergraduate and postgraduate students, took part in a series of experiments on the haptic perception of curvature. A graded series of surfaces was produced using piano-convex lenses masked off to produce curved strips that could be explored without using arm movements. Thresholds were measured using the constant method and a staircase procedure. Experiments 1 and 2 yielded data on the absolute and difference thresholds for curvature. Experiment 3 demonstrated that the effective stimulus for curvature is represented by the overall gradient of a curved surface. Using this measure, it was shown that the present absolute thresholds for curvature are lower than those previously reported. In Experiment 4, absolute thresholds were compared using spherical and cylindrical curves: the results showed that, at least with the narrow strips used, the type of curvature does not exert a significant influence on performance. In Experiment 5, the subjective response to curvature was assessed using a rating procedure. Power functions are reported, although the relationship between stimuli and responses had a strong linear component. This suggests that haptically perceived curvature may be a metathetic rather than a prothetic continuum.     

Using motor tasks to quantitatively judge 3-D surface curvatures

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects’ sensitivity to the curvature of a curve lying on a surface and changes in the curvature as defined byEuler’s formula, which relates maximum and minimum principal curvatures and their directions. Regardless of direction and surface shape (elliptic and hyperbolic), subjects could report the curvature of a curve lying on a surface through a drawing task. In addition, multiple curves drawn by subjects were used to reconstruct the surface. These reconstructed surfaces could be better accounted for by analysis that treated the drawing data as a set of curvatures rather than as a set of depths. A pointing task was utilized in Experiment 2, and subjects could report principal curvature directions of a surface rather precisely and consistently when the difference between principal curvatures was sufficiently large, but performance was poor for the direction of zero curvature (asymptotic direction) on a hyperbolic surface. In Experiment 3, it was discovered that sensitivity to the sign of curvature was different for perceptual judgments and motor responses, and there was also a difference for that of a curve itself and the same curve embedded in a surface. These findings suggest that humans are sensitive to relative changes in curvature and are able to comprehend quantitative surface curvature for some motor tasks.     

Walking,looking to the side,and taking curved paths

In two experiments, viewers judged heading from displays simulating locomotion through tree-filled environments, with gaze off to the side. They marked their heading with a mouse-controlled probe at three different depths. When simulated eye or head rotation generally exceeded 0.5 deg/sec, there was reliable curvature in perceived paths toward the fixated object. This curvature, however, was slight even with rotation rates as great as 2.6 deg/sec. Best-fit paths to circular arcs had radii of 1.8 km or greater. In a third experiment, pedestrians walked with matched gaze to the side. Measured curvature in the direction of gaze corresponded to a circular radius of about 1.3 km. Thus, at minimum, vision scientists need not worry about perceived path curvature in this situation; real path curvatures are about the same. However, at present, we can make no claim that the same mechanisms necessarily govern the two results.     

Perception of curves.

In 4 experiments, in which 66 subjects participated, the perception of 6 types of curved contours in two-dimensional shapes was studied. Random polygons and their curvilinear transformations were presented for detection under low-luminance contrast conditions, oddity-type discrimination problem solving, tachistoscopic identification, and identification involving visual acuity in distance vision. In all experiments curvature affected perception at statistically significant levels, but the extent of this effect was a function of (1) the locus and direction of curvature, (2) the level of compactness-jaggedness of the figure, and (3) the nature of perceptual task. Shapes with acute corners were more easily perceived than shapes with curved corners. Within these two classes of shapes, those with convex sides were perceived as having greater curvedness than those with concave contours. However, the degree to which curvature affected response was determined primarily by the nature of the perceptual task.     

Haptic underestimation of angular extent

To what extent can individuals accurately estimate the angle between two surfaces through touch alone, and how does tactile judgment compare to visual judgment? Subjects' ability to estimate angle size for a variety of haptic and visual stimuli was examined in a series of nine experiments. Triangular wooden blocks and raised contour outlines comprising different angles and radii of curvature at the apex were used in experiments 1-4 and it was found that subjects consistently underestimated angular extent relative to visual baselines and that the degree of underestimation was inversely related to the actual size of the angle. Angle estimates also increased with increasing radius of curvature when actual angle size was held constant. In contrast, experiments 5-8 showed that subjects did not underestimate angular extent when asked to perform a haptic-visual match to a computerized visual image; this outcome suggests that visual input may 'recalibrate' the haptic system's internal metric for estimating angle. The basis of this cross-modal interaction was investigated in experiment 9 by varying the nature and extent of visual cues available in haptic estimation tasks. The addition of visual-spatial cues did not significantly reduce the magnitude of haptic underestimation. The experiments as a whole indicate that haptic underestimations of angle occur in a number of different stimulus contexts, but leave open the question of exactly what type of visual information may serve to recalibrate touch in this regard.     

Biological movements look uniform: evidence of motor-perceptual interactions.

Six experiments demonstrate a visual dynamic illusion. Previous work has shown that in 2-dimensional (2D) drawing movements, tangential velocity and radius of curvature covary in a constrained manner. The velocity of point stimuli is perceived as uniform if and only if this biological constraint is satisfied. The illusion is conspicuous: The variations of velocity in the stimuli exceed 200%. Yet movements are perceived as uniform. Conversely, 2D stimuli moving at constant velocity are perceived as strongly nonuniform. The illusion is robust: Exposure to true constant velocity fails to suppress it. Results cannot be explained entirely by the kinetic depth effect. The illusion is evidence of a coupling between motor and perceptual processes: Even in the absence of any intention to perform a movement, certain properties of the motor system implicitly influence perceptual interpretation of the visual stimulus.     

Curvature biases in stereoscopic vision: a nasotemporal asymmetry

The reliability of curvature judgments for linear elements was studied, with stereograms that contained a binocular arc with curvature in depth, and either a binocular frontoparallel arc or a monocular one, on a background representing a hemiellipsoid. The subjects made about 15% errors on binocular arcs with curvature in depth, and 60%-80% of these occurred when both the hemiellipsoid and the arc were convex, the arc being perceived as concave, by transparency through the hemiellipsoid. There were also about 15%-30% errors on frontoparallel arcs, but spread among all situations, with a small prevalence of concave judgments. Curvature in depth was assigned to the monocular stimuli in more than 60% of the cases. There was a curvature bias when the monocular arcs were on the nasal side, and were viewed against a concave background. Assuming parallel viewing, nasal ingoing arcs were usually perceived as concave, and nasal outgoing arcs usually perceived as convex, in agreement with geometrical likelihood. Nasal-side elements captured by one eye are, in general, those with the highest likelihood of having matching elements in the other eye. Then the observed nasal bias effect suggests that the matching process in stereopsis could be driven from the nasal sides of the projections in the two cerebral hemispheres.     

The effects of curvature on haptic judgments of extent in sighted and blind people

A series of experiments was carried out to examine the effect of curvature on haptic judgments of extent in sighted and blind individuals. Experiment 1 showed that diameters connecting the endpoints of semicircular lines were underestimated with respect to straight lines, but failed to show an effect of visual experience on length judgments. In experiment 2 we tested are lengths. The effects of curvature on perceived path length were weaker, but were still present in this experiment. Visual experience had no effect on path length judgments. Another experiment was performed to examine the effect of repeated tracing (1, 5, 9, or unlimited number of traces) on judgments of the lengths of straight lines and diameters of semicircles. Judgments of extent were more accurate when subjects engaged in larger numbers of traces. There was no effect of number of traces on curve-height judgments, suggesting that subjects were not using height estimates to judge diameters of semicircles. In a further experiment we tested the effect of number of traces on curves that varied in height. Restricting subjects to a single trace magnified the effect of path length on judgments of the distance between the endpoints of curves. Additional experiments showed that curvature effects on diameter judgments were not eliminated when stimuli were in the frontal plane or when the curves were explored with the use of two hands. Arm support had no effect on judged length in experiment 7. A final experiment showed a robust horizontal vertical illusion in haptic perception of convex curves, with overestimation of the heights of the curves compared with their widths. The practical and theoretical implications of the results are discussed.     

Size invariance in curve tracing

Subjects decided whether two dots were on the same curve or on different curves in patterns consisting of two curves and two dots in displays that had an exposure duration of 200 msec or that remained in view until the subjects' response. The overall size of the patterns was varied by a factor of two. Furthermore, across experiments, we manipulated the predictability of the size of the pattern on a particular trial. On half of the trials, the two dots were on the same curve; across these trials, the distance between the dots, along the curve, was manipulated systematically while the Euclidean distance between the dots was held constant. On the other half of the trials, the two dots were on different curves. The time to respond same increased monotonically as curve distance between the dots increased, suggesting that subjects mentally traced the curve in order to perform the task. The absolute size of the pattern had little or no effect on the response times, indicating that it was curve distance relative to the overall pattern size, rather than absolute distance, that controlled response times. Furthermore, expectancies about pattern size had essentially no effect on performance. Taken together, the results suggest that the rate of tracing is determined by various stimulus properties that covary with the overall size of the pattern on which tracing takes place, such as the distance between the traced curve and nearby distractor curves, or the curvature of the traced curve.     

Curve tracing: A possible basic operation in the perception of spatial relations

The two experiments in this study suggest that fast internal tracing of curves is employed by the visual system in the perception of certain shape properties and spatial relations. The experimental task in the first experiment was to determine, as rapidly as possible, whether two Xs lay on the same curve or on different curves in a visual display. Mean response time for “same” responses increased monotonically with increasing distance along the curve between the Xs. The task in the second experiment was to decide either that a curve joining two Xs was unbroken or that the curve had a gap. Decision times again increased as the length of the curve joining the Xs was increased. The results of both experiments suggest that people can trace curves in a visual display internally at high speed (the average rate of tracing was about 40° of visual angle per second). Curve tracing may be an important visual process used to integrate information from different parts of a visual display.     

Do observers like curvature or do they dislike angularity?

Humans have a preference for curved over angular shapes, an effect noted by artists as well as scientists. It may be that people like smooth curves or that people dislike angles, or both. We investigated this phenomenon in four experiments. Using abstract shapes differing in type of contour (angular vs. curved) and complexity, Experiment 1 confirmed a preference for curvature not linked to perceived complexity. Experiment 2 tested whether the effect was modulated by distance. If angular shapes are associated with a threat, the effect may be stronger when they are presented within peripersonal space. This hypothesis was not supported. Experiment 3 tested whether preference for curves occurs when curved lines are compared to straight lines without angles. Sets of coloured lines (angular vs. curved vs. straight) were seen through a circular or square aperture. Curved lines were liked more than either angular or straight lines. Therefore, angles are not necessary to generate a preference for curved shapes. Finally, Experiment 4 used an implicit measure of preference, the manikin task, to measure approach/avoidance behaviour. Results did not confirm a pattern of avoidance for angularity but only a pattern of approach for curvature. Our experiments suggest that the threat association hypothesis cannot fully explain the curvature effect and that curved shapes are, per se, visually pleasant.     

The Three-Dimensional Curvature of Straight-Ahead Movements

Three-dimensional curvature of point-to-point hand movements in the forward direction was examined. Subjects (N = 4) moved their hand from a position above the start point to a forward position above targets of different size and distance. Paths were curved as a result of an initial lateral and downward movement that was compensated for in the second half of the movement. The downward component of motion had a bell-shaped velocity profile and was temporally coupled to the forward motion. Curvature was greater for movements to near targets. Examination of the relation between kinematics and geometry revealed that velocity was related to radius of curvature by a power law with an exponent of 0.59. Simulations of the component of motion in the vertical plane reproduced the qualitative behavior of curvature and fit a power law relationship between velocity and radius of curvature