Figure 1.
Near zone, far zone, tangent point (top), and the concept of optical flow lines (bottom).
Top. The tangent point (TP), the near zone (NZ), and the far zone (FZ) beyond the tangent point on a motorway on-ramp. Dotted blue line: future path. Here, we define the near zone as the visible road surface and edges up to the tangent point level and the far zone as road surface and road edges further away than the tangent point. We further divide the far zone into the far zone adjacent to the tangent point (FZa, the part of road surface visible in the top left quadrant), and the far zone beyond the tangent point (FZb, the part of road surface in the top right quadrant).
Middle. Potential target points on the future path. Target 1 (green): future path reference point of Boer’s model [3]. If the location at this point is fixated and tracked, this would create OKN to the left of TP (fixation Target 1, smooth pursuit of the corresponding point on the road, re-setting saccade to Target 1). Target 2 (blue): a hypothetical target point in the far zone beyond the tangent point. Targeting this point in the far zone beyond TP would create OKN above and to the right of TP. Gaze polling ( [18], see text for further explanation) could take the following form: (1) OKN around Target 1, (2) a polling (out) saccade to Target 2, (3) OKN around Target 2, (4) a polling (in) saccade to Target 1, (5) OKN around Target 1.
Bottom. Schematic illustration of optical flow in the road scene. Compared to the simple radial optic flow emanating from a focus of expansion (FOE) during linear translation in the direction of the visual axis (inset, top), or the homogenous horizontal optic flow during observer rotation at a stationary point of observation (inset, bottom) the optic flow pattern during curvilinear motion is rather complex. The main picture gives a schematic illustration of the flow pattern (for geometric analysis see 3). The tangent point falls on an imaginary circle (dotted white curve) from the current vantage point through the curve center, and inversion of the horizontal component of optical flow in the flow field occurs at this curve (at which optical flow is vertical). In the far zone adjacent to and beyond the tangent point, optic flow has a horizontal component opposite to the direction of the curve (to the left in right hand bends), and down; below the curve, below the tangent point, the flow has a horizontal component in the direction of the curve. Note that the TP is not a fixed physical point in the scene, and hence does not follow the local direction of flow – the physical point on the road edge corresponding to the tangent point travels forward as the vehicle moves into the bend.
Figure 2.
The motorway on-ramp used in the study (Kehä III - Lahdenväylä, N 60.274643; E25.086422).
Inset: the entry (dotted line) and cornering (solid line) phases of the curve, based on GPS data from an individual run. For explanation of sequencing the curve see main text. The cornering phase is 187 m in length. Image source: National Land Survey of Finland open Topographic Database. license version 1.0 -1 May 2012.
Figure 3.
Algorithimic tangent point identification during curve entry (left) and cornering (right).
The algorithm generally identifies the position of the tangent point to an accuracy of better than one degree. The green cross estimated the driver’s gaze position. Note also the lateral displacement of tangent point into the direction of the curve during entry phase (See also movie S1, S2 and S3).
Figure 4.
Example of raw gaze position signal and segmentation.
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. Yellow datapoints filtered out prior to analysis due to poor tracking/signal quality. Solid black line is the tangent point angular position as given by the lane edge detector algorithm.
Figure 5.
Top: 3 degree and 6 degree AOI cover much of the road surface, particularly in the entry phase. Bottom: Gaze catch percentage in different size AOI’s centered at the tangent point.
Each black dot and each red dot in the top picture represents per subject median AOI catch % in the entry and cornering phases, respectively. 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.
Figure 6.
Gaze displacement from tangent point during cornering.
Distribution of gaze displacement from the tangent point. Density estimate and marginal density distributions (horizontal and vertical). The tangent point lies at the origin, the near zone lies mainly in the lower left quadrant, and the far zone in the upper left quadrant (“adjacent to the tangent point”) and in the upper right quadrant (“beyond the tangent point”). Aggregate data for all subjects. The dashed contours in the main picture contain 25%, 50% and 75% of observations. Circles indicate mode of the gaze density distribution from individual subjects data. See Supplementary Results in Supporting Information S1 for individual subjects’ data.
Figure 7.
Individual trial gaze position time-series data.
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. The general pattern is orientation towards the curve apex / tangent point region, with clear optokinetic pursuit superimposed. 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.
Figure 8.
Orientation of OKN slow phases.
Histogram of the orientation of all identified pursuit eye movements in the data. 0° is up. For individual subjects’ data see Supplementary Results.
Figure 9.
Density estimates of eye-movements plotted to velocity-velocity phase space.
Density estimate and marginal density distributions (horizontal and vertical). Circles indicate individual mode values of individual subjects’ data. See Supplementary Results for individual subjects’ data.
Inset: Enlargement, individual modes only. The ellipses indicate Hotelling’s T-squared 95%, 99% and 99.9% confidence regions. The distribution is not centered at the origin (which would indicate stable fixation data), but clearly clustered to the left (indicating a horizontal eye-movement component) and below (indicating a vertical eye-movement component). This is the pattern that one would expect from gaze following regional optic flow in the far zone.