Pursuit Eye-Movements in Curve Driving Differentiate between Future Path and Tangent Point Models

For nearly 20 years, looking at the tangent point on the road edge has been prominent in models of visual orientation in curve driving. It is the most common interpretation of the commonly observed pattern of car drivers looking through a bend, or at the apex of the curve. Indeed, in the visual science literature, visual orientation towards the inside of a bend has become known as “tangent point orientation”. Yet, it remains to be empirically established whether it is the tangent point the drivers are looking at, or whether some other reference point on the road surface, or several reference points, are being targeted in addition to, or instead of, the tangent point. Recently discovered optokinetic pursuit eye-movements during curve driving can provide complementary evidence over and above traditional gaze-position measures. This paper presents the first detailed quantitative analysis of pursuit eye movements elicited by curvilinear optic flow in real driving. The data implicates the far zone beyond the tangent point as an important gaze target area during steady-state cornering. This is in line with the future path steering models, but difficult to reconcile with any pure tangent point steering model. We conclude that the tangent point steering models do not provide a general explanation of eye movement and steering during a curve driving sequence and cannot be considered uncritically as the default interpretation when the gaze position distribution is observed to be situated in the region of the curve apex.


SUPPLEMENTARY FIGURE S2
Horizontal and vertical, gaze deviation (difference of median observed gaze position from designated target point) is under 2 o . Black dots: calibration datapoints from the current dataset. Open red circles: calibration datapoints from another simultaneously collected dataset.

Mathematical description of the segmentation algorithm
The system aims to maximize a fitness function, although it is not known if it actually reaches a (global) maximum: where is logarithm of the Poisson survival function for more than zero events with rate parameter for a new segment with being time between samples and 1, denotes the first sample index in the segment, is logarithm of the Gaussian probability density function with mean zero and (diagonal) covariance matrix , is the set of outliers and is a SUPPLEMENT SI for Lappi et al. (2013) Pursuit Eye-Movements in Curve Driving PLoS ONE doi: 10.1371/journal.pone.0068326 3 "penalty coefficient" for outliers, is the signal value of sample and is its estimate based on the segment's linear fit.
For the present analyses we used = 1/0.5 and = 0.6 based on tuning by hand.
was iteratively estimated similarly to the Expectation Maximization method by calculating the ML estimate based on a run of the algorithm and then running it again with the new estimate until the segmentation does not change. We used initial noise variances of 1.0 for both dimensions.

Driving behavior
The following figures and tables quantify physically driving behavior in the cornering phase in the present study. The Supplementary Figure S3 and S4 display group level and individual driving speeds as function of lap. Supplementary Tables T1 and T2 show individual participants' yaw-rate and the eccentricity in the visual scene.

SUPPLEMENTARY FIGURE S3
Boxplot showing average driving speed in the cornering phase as function of lap.

TP Hypothesis 0 (no OKN). Persistent fixation of the tangent point. Gaze is stable at the TP. Possibly observed in the TANG condition in Kandil et al. (2009) -although the presence or absence of OKN was not analysed in that study -but not in everyday driving.
That OKN is reliably elicited, however, shows that either the OKR is present while the TP is fixated (or that the drivers are not looking at the TP).
If the drivers' "attemp" to fixate the tangent point is hindered by OKR elicited by regional flow, gaze would move away from the fixation target and require re-setting saccades to restore fixation (hence OKN QP). QP characteristics may be therefore predicted if the dependence of SP on regional flow is known.
TP Hypothesis 1. Under the assumption that the OKR follows local flow, QP could reset gaze to the tangent point (assuming the SP has drawn gaze away from it), or to launch gaze "upstream" in the flow field, so that the slow phase pursuit OKR will bring gaze back to the TP.

TP Hypothesis 2.
If gaze is targeted at the tangent point, but is not stable at the tangent point because of OKR. But the as the SP does not follow local flow (it has a horizontal componens) the hypothesis needs to be adjusted.
The dependency of OKN SP on regional optic flow is not clear, and the assumptions of the TP hypotheses (above) do not give a specific prediction. Empirically, it is known that it is opposite to the direction of the curve and downwards. Thus, SUPPLEMENT SI for Lappi et al. (2013)  TP Hypothesis 3. Another possibility would be to launch gaze "upstream" in the flow field, so that the slow phase pursuit OKR will bring gaze back to the TP: TP Hypothesis 3. Gaze is cast "upstream" in the flow field. OKN following (regional) optic flow re-sets gaze to tangent point.
There are thus many ways in which targeting the TP and OKN could be combined.
Unless the size and shape of the relevant region assumed to determine the OKN SP need to be incorporated SP direction and magnitude is underspecified.  IN MAIN TEXT FOR EXPLANATION)