Curve of Pursuit


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In their simulator study, a bi-ocularly viewed screen image was partitioned into flow fields of different sizes — circular fields of 1 degree to 7 degrees radius, and a 49 degrees x 40 degrees rectangular field representing the whole simulator screen — but none of these resulted in a good match between OKN SP orientation and flow orientation. Instead, they found that the difference between the direction of motion of the flow field and OKN SP, a. The lowest value was in fact obtained for the whole screen for which a coherent flow field does not exist.

We would point out that in binocular viewing, smooth pursuit follows flow of scene elements at the plane of fixation [ 20 , 21 ]. This would suggest that the local flow field in real 3D environment may also incorporate depth information by tracking retinal image elements with zero disparity. Based on this analysis of how these different hypotheses of visual orientation during curve driving can be related to different eye-movement patterns as well as different gaze target locations , we can se how a more detailed understanding of optokinetic pursuit movements can be employed as a complementary methodology for differentiating between predictions of the tangent point vs.

This is the task we set ourselves upon in this study. A convenience sample of 21 subjects participated in the study 11 M, 10 F, age 22 y y, mean 27 y. In the end, data from four subjects were omitted due to poor signal quality, leaving a sample of 17 participants. Participants were recruited through personal contacts and university mailing lists. The subjects reported no medical conditions that might affect eye movements, and had normal or corrected to normal eye-sight The participants with corrected eyesight wore contact lenses in the experiment. The study was covered by a written approval from the ethics committee of the Faculty of Behavioural Sciences, University of Helsinki, for the use of human subjects in real traffic conditions.

Written informed consent to participate in this study was obtained from each participant. This was done, in accordance with the approval of the ethics committee, in the form of a fixed-format consent form explaining the purpose of the study, the procedure, and intended use of the data for scientific purposes only. Paper copies of the consent forms were archived.

The instrumented car was a model year Toyota, Corolla 1. The passenger side was equipped with brake pedals and extra mirrors, as well as a computer display that allowed the experimenter to monitor vehicle speed, the operation of the eye-tracker and the data-logging systems. The car was equipped with a two-camera eye tracker operating at 60 Hz Smart Eye Pro version 5. Vehicle telemetry speed, steering, throttle, braking and horizontal rotational velocity, i. Gaze position accuracy during calibration can be seen to be about 1—2 degrees; on the move, however, a more conservative estimate of 2—3 degrees accuracy is more appropriate See Supplementary Methods in Supporting Information S1 for more details on calibration.

All signals were synchronized and time stamped on-line, and stored on a computer. All data preparation, visualization and analysis was done using custom-made scripts written in Python, and using the NumPy, SciPy and matplotlib packages.

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The ramp was chosen because of its ideal curve geometry from the point of view of the present investigation: the projection of the road surface in the visual scene allows us to better resolve the tangent point from the road surface beyond it the elevation produces differentiation of the vertical angle of the tangent point and the road , and, also, the curve has a distinct cornering phase where the curve radius remains relatively constant for a significant period of time, as the theoretical analyses of tangent point orientation [ 1 — 3 ] use the idealizing assumption of locally constant radius.

The length of the curve the car rotates o and relatively large radius mean that the duration of the curve — and the cornering phase in particular — is therefore sufficient to provide abundant data on eye-movement patterns during cornering over five minutes of pure cornering phase data per subject. Here, the road geometry also allowed us most reliably to identify the tangent point algorithmically. Theoretically, we also reasoned that given the reliable observation of high concentration of fixations near the tangent point immediately before and after the turn point [ 1 ], if there are indeed other gaze strategies at work during curve driving, we would have the best opportunity to observe them by looking at a later part of the bend.

The location was 15 km from the university campus, and the participant drove the car to the site in order to familiarize him with the vehicle. The ramp was driven 16 times, and the eye cameras calibrated on arrival and after the 5th and 11th run to maintain good calibration throughout the session. All drives were carried out in daylight, sometimes in varying weather conditions overcast or light rain.

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The participants drove at their own pace, and were instructed to observe traffic laws and safety. In addition to the participant, a member of the research team TI acted as experimenter. He was seated on the front passenger seat, giving route directions, ensuring safety, monitoring the recording and performing the calibrations.

The data was segmented into discrete curve-driving events based on GPS coordinates and vehicle telemetry. The curve entry phase begins when the driver begins to rotate the vehicle by turning the steering wheel at her chosen turn point. Both the steering wheel angle and vehicle yaw rate increase progressively throughout the entry phase in normal everyday driving, assuming no rear wheel skid.

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In very long curves which is what the turns analyzed here are , the entry phase is followed by a steady cornering phase where the steering wheel angle and vehicle rate of rotation remain relatively constant. The exit phase of a turn begins when the driver begins to steer out of the bend to unwind the steering lock, the yaw rate beginning to reduce having reached a local maximum. The driver can be considered to have completely exited the corner, and having completed the entire cornering sequence, when he reaches an exit point where the vehicle is no longer in yaw.

Curves where the exit point is visible during approach and turn-in before the end of the entry phase are considered sighted , curves where the exit point only becomes visible during the curve after turning in are considered blind. The on-ramp is a blind curve, the exit only becoming visible towards the very end of the cornering phase. To render trials comparable, the data was given a location-based representation.

The vehicle trajectory in an allocentric xy plane GPS latitude and longitude coordinates was computed by interpolating the GPS signal.

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This interpolated trajectory would then be used as the template of a route-location value meters from the beginning of the leg , with which all other signals could be associated. The transition points of entry, cornering and exit phases were established manually, based on median yaw rate. To determine the presence of tangent point orientation, the tangent point was identified algorithmically from forward looking VGA video from the SmartEye Scene camera , using an in-house developed lane detection algorithm designed specifically for finding the edgeline and tangent point in curves Figure 3 see also movie S1-S3.

This yielded time-stamped image coordinates, for each time point, which could be assigned a GPS location coordinate. The image coordinate system was physically calibrated to the angular coordinate system of the eye-tracker, so that horizontal and vertical angular displacement of gaze from the TP could be computed. After this, all gaze position data could be referenced to the vehicle frame of reference or a tangent point centered frame of reference, as required by a particular analysis. The algorithm generally identifies the position of the tangent point to an accuracy of better than one degree.


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Note also the lateral displacement of tangent point into the direction of the curve during entry phase See also movie S1, S2 and S3. This signal also has the advantage that it is not sensitive to small measurement errors in gaze position, such as may arise from linear calibration bias these afflict especially AOI based measurements, particularly when the putative targets are theoretically expected to lie within a few degrees adjacent to each other.

Ideally, a gaze velocity signal is, of course, the first time derivative of the gaze position signal, or, with discrete sampling, a time difference signal. In practice, differentiating or taking the difference from a noisy signal with a relatively low sampling rate is problematic. On the other hand, fixation detection algorithms suitable for on-road data with a low sampling rate rate and high noise levels e.

Shahzia Sikander: Pursuit Curve (2004)

The basis for the method is based on Optimal Partitioning described by Jackson et al. However, due to outliers in the data also assumed Poisson distributed , we expanded the method in a manner inspired by the Multiple Hypothesis Tracking method [ 25 ]; For details of the algorithm see the supplementary methods in Supporting Information S1. Samples categorized as outliers are left out from the local linear fit and its residuals. The data is thus partitioned by fitting to the data points line segments representing pursuit movements.

Curves of Pursuit

Free parameters are the expected segment length, noise and outlier frequency. The segmentation of raw data can be seen in Figure 4 where the linear segments are drawn superimposed on the raw signal. Each segment red is a linear regression to the raw horizontal top and vertical bottom gaze position datapoints gray between the initiation and termination points of the segment, where the initiation and termination points are computed by a robust segmentation algorithm approximating a maximum likelihood linear segmentation.

Blue datapoints indicate outliers not included in the regression. Solid black line is the tangent point angular position as given by the lane edge detector algorithm. For gaze position we used the segmentation signal at the time coordinate of each valid gaze position observation rather than the noisy raw gaze position observation and computed for each datapoint its displacement from the tangent point position giving us gaze displacement from the TP for each point. The gaze velocity horizontal and vertical components at each point in time was likewise defined by the horizontal and vertical slopes of the linear segment associated to the datapoint.

For statistical analysis of the gaze pattern, density estimates were made of the gaze position horizontal and vertical displacement from the tangent point as well as change in gaze position horizontal and vertical velocity components of gaze movement. Modes were estimated from the density estimates by first finding an approximation by discretizing the density estimate and numerically optimizing the density estimate function bounded in the discretization bin.

The participants drove at a moderate pace. During the cornering phase the vehicle yaw rate remained quite stable indicating steady-state cornering Mean The tangent point eccentricity depends on the driving line of the participant, but is quite stable during steady-state cornering and repeatable across runs. We see that the gaze catch percentages are higher for larger AOIs which is logical as each smaller AOI is a proper subset of the larger one.

Also, it appears that the catch percentages tend to be higher in the entry phase than the approach phase. The maximum average difference is Dotted black line entry phase and solid red line cornering phase indicate their averages, by phase. The bottom figures illustrate the problem of AOI overlap: AOIs centered on the tangent point also cover much of the future path in the far zone.

Due to the projection geometry, this overlap is greater in the entry phase which may in part account for the higher gaze catch. It is important to note, however, that this result arises in the context of another important feature, illustrated in Figure 5 top : large AOIs more than 4 degrees are completely ambiguous as to what gaze targets within the AOI are actually used, because there is considerable overlap between the TP AOI, and almost any AOI one might place on the future path.

The apex of the bend — i. The AOI result as such does not tell us what gaze targets — let alone what steering strategies — the drivers might be using. Especially once they are well set into the bend, the drivers sample the road ahead. This data is gathered during the constant radius cornering phase. The figure represents some 60 minutes of data. Distribution of gaze displacement from the tangent point.

Density estimate and marginal density distributions horizontal and vertical. Aggregate data for all subjects. Circles indicate mode of the gaze density distribution from individual subjects data.

We see that the distribution is elongated, roughly following the visual shape of the road surface. In particular, we note that there is quite a lot of mass as far as 10 degrees to the right and to the left of the tangent point. Vertically, the mass is well above the tangent point level, especially on the right beyond the tangent point , where the uphill bend rises above the horizon. The typical gaze position during cornering represented by the mode does not coincide with the tangent point, and is also variable across individuals.

But while there is variability in "typical" gaze position among the subjects - but consistently the overall pattern, both at the aggregate and individual level, shows gaze position to be concentrated in the far zone, above and often beyond the tangent point. Horizontal gaze position in relation to vehicle centerline degrees plotted against time from three individual trials of representative subjects see Supplementary Videos. Zero angle corresponds to vehicle centerline approximately equal to instantaneous heading , positive is to the right in the direction of the curve.

Dashed line is TP.


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  7. Vertical angle indicates gaze to be in the far zone. For the subject in the first image top horizontal angle indicates that gaze is in the far zone beyond the tangent point, in the bottom image adjacent to the tangent point. On average gaze is offset by some small constant from the tangent point a few degrees , but this offset does not arise from a small constant deviation of measured gaze position from the tangent point. Instead, it is generated by a process where the gaze moves in a systematic manner rather than being located at the tangent point or some point offset by a constant angle.

    Clearly the typical gaze position does not characterize the eye movements of that individual.

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