A validation study on the accuracy and precision of gaze and vergence using stereoscopic eye-tracking technology

Abstract

Binocular video-based eye-tracking allows for gaze and vergence measurements, but the accuracy and precision of vergence are barely addressed. Here, we investigate the accuracy and precision of both gaze and vergence measurements using a stereoscopic eye-tracking system. Previous studies have evaluated stereoscopic eye-trackers for gaze eccentricities up to 16°. We validated a custom-built stereoscopic eye-tracker with two cameras and two infrared light sources for gaze eccentricities up to 21°. Additionally, we studied the impact of fixation distance and pupil size on vergence accuracy. Participants with normal binocular vision (N = 8) performed fixation tasks, enabling the assessment of both gaze and vergence errors. The stereoscopic system provided gaze estimates with a mean absolute error (MAE) of less than 1° within the central visual field. However, the accuracy decreased for peripheral angles larger than 14°. We found a MAE of 0.89 ± 0.58° in measuring vergence and a strong linear association between target vergence and measured vergence, with a slope of 0.99 ± 0.05. In contrast to previous studies using single-camera eye-trackers, we found no systematic influence of pupil size on the vergence measurements. Although there was high agreement between estimated and ground truth vergence in the central field, the system did struggle to maintain accuracy at larger eccentricities. This limitation arises primarily from the loss of reliable glints rather than technical constraints, indicating the need for alternative approaches to enhance accuracy in wider fields of view.

Keywords: Gaze accuracy; Gaze eccentricity; Pupil size; Stereoscopic eye-tracking; Vergence measurement.

Fig. 1

Stereoscopic eye-tracker hardware setup. Note. Two cameras with IR filters and two IR LED boards are mounted on an aluminum rail below a monitor. The cameras are positioned to capture both eyes for stereoscopic eye-tracking, with the LED boards producing glints on the subject’s eye and providing consistent illumination

Fig. 2

Visual representation of the eye’s optical and visual axis during calibration. Not drawn to scale. c: Center of corneal curvature. p_v: virtual pupil. $\kappa$: deviation angle. O_scs: origin of the screen coordinate system. s₀: fixation point

Fig. 3

Horizontal and vertical visual axis angles and the measured vergence over time for a single subject. Note. A, C, E Data measured with targets at 350 mm from the subject, B, D, F Data with targets at 610 mm. The dotted target vergence line for the right eye in plots C and D overlaps with the solid target vergence line for the left eye due to the absence of vertical target vergence

Fig. 4

Gaze angle estimations of one subject and mean absolute errors (MAEs) expressed as error bars. Note. A, B show gaze angle estimations of one subject from monocular and binocular measurements for the left and right eye, respectively. C MAE expressed in error bars for each stimulus location, plotted on the mean fixation location. Due to the right-handed coordinate system used in the setup, positive angles are to the left and down. In C, the error bars show the horizontal (MAE x) and vertical (MAE y) mean absolute error averaged across all eyes, subjects and viewing condition. The black crosses in the figure represent target locations

Fig. 5

Example of glints in eye images. Note. A Example of two well-detectable glints on the corneal surface. B Example where one glint remains well-detectable, while the other is near the cornea-sclera border, appearing smaller and more scattered due to optical distortion

Fig. 6

Horizontal and vertical gaze estimates against target position. Note. Each point is an averaged gaze estimation for each fixation trial. It shows data for each fixation, eye, viewing condition and subject. A, B The horizontal gaze angles versus de horizontal stimulus position. C, D The vertical gaze angles versus the vertical stimulus position. B, D Stimuli between – 14° and 14° horizontallyonly

Fig. 7

Box plots showing mean absolute error (MAE_gaze) accuracy of the eye-tracker in estimating gaze for the horizontal (x), vertical (y), and vectorial (r) components under monocular and binocular viewing conditions. Note. A Data including all stimuli positions. B Only stimuli positioned between – 14° and 14° horizontally. C The stimuli outside of – 14° and 14° horizontally. Dots represent individual subject data. MAE of each individual subject was calculated by averaging the MAEs of both eyes across all (selected) stimulus positions

Fig. 8

Box plots showing precision of the eye-tracker. Note. Precision is shown for the horizontal (SD x, S2S x) vertical (SD y, S2S y) and vectorial (S2S R) components and bivariate contour ellipse area (BCEA) vectorial precision for monocular and binocular measurements. A, D Data including all stimuli positions. B, E Only stimuli position between – 14° and 14° horizontally. C, F The stimuli outside of – 14° and 14° horizontally. For each subject, SD and BCEA precision measures are calculated by averaging the respective precision measure across all (selected) stimulus positions and both eyes. The left vertical axis shows the values for SD (in deg), where the right vertical axis shows the values for BCEA (in deg²)

Fig. 9

Mean absolute error of vergence for different stimulus locations, expressed with error bars. Note: Dots indicate stimulus positions. Error bars indicate the vergence MAE at these locations in degrees

Fig. 10

Scatter plot of the target vergence versus the measured vergence. Note. The regression line of the linear mixed effects model is plotted, as well as all the individual regression lines for each subject

Fig. 11

Average projected pupil area in pixels versus the measured vergence. Note. Mixed effects linear regression showed no significant influence of pupil area on estimated vergence. A projected pupil area of 5000 pixels, as captured by the camera, corresponded with an approximate pupil diameter of 7 mm