A Method for Accurate 3-D Gaze Estimation With a Single Camera and Two Collinear Light Sources

The simplest configuration for estimating 3-D line-of-sight (LoS) based on corneal reflection and pupil refraction uses a single camera and two noncollinear light sources. The corneal radius and 3-D corneal center can be determined by solving a system of six equations with six unknowns. However, when two light sources are collinear with the camera, the reflection planes of the two light sources are coplanar. In this case, the estimation of the 3-D corneal center is underdetermined in the absence of any preknown eyeball parameters (e.g., corneal radius). To solve this issue, this article proposes to calibrate the corneal radius with corneal reflections from two light sources combined with an iris imaging model so that the 3-D corneal center is estimated with a known corneal radius. Then, the pupil features or iris features can be selected to estimate the 3-D pupil center or 3-D iris center, which uses an optimization solution for only the center parameters to avoid unnecessary errors. Thus, the optical axis of the eyeball is constructed with two spatial centers, and the kappa angle calculated in real time is used to convert the optical axis of the eyeball to the 3-D LoS. We simulated this gaze estimation process using pupil and iris features, and performed error analysis on the proposed method. In practical experiments, the proposed method was verified using iris features, and the gaze accuracy was 1.22° and 1.13° in the
$x$
- and
$y$
-directions, respectively, which is comparable to that of more sophisticated systems. A single-camera-two-collinear-light-source system is the most typical and common system configuration, and the realization of 3-D gaze estimation under such a system configuration can effectively promote the wide application of eye-tracking interaction.