Cross-Validated Locally Polynomial Modeling for 2-D/3-D Gaze Tracking with Head-Worn Devices

In the context of wearable gaze tracking techniques, the problems of two-dimensional (2-D) and three-dimensional (3-D) gaze estimation can be viewed as inferring 2-D epipolar lines and 3-D visual axes from eye monitoring cameras. To this end, in this article, a simple local polynomial model is proposed to back-project a pupil center onto its corresponding visual axis. Based on this approximation, a homographylike relation is derived in a local manner, and via the Leave-One-Out cross-validation criterion, training gaze samples at one certain depth is leveraged to partition entire input space into multiple overlapping subregions. Then, the gaze data at another depth are utilized to recover the epipolar point, i.e., the image eyeball center. Thus, given a pupil image, the corresponding epipolar line can be determined by the resolved homographylike mapping and the epipolar point. By using the same partition structure, 3-D gaze prediction model can be inferred by solving a nonlinear optimization problem, which aims to minimize the angular disparities between training visual directions and prediction ones. Meanwhile, it is necessary to form a good starting point and suitable constraints for the optimization problem. Otherwise, it may end up with trivial solutions, i.e., faraway eye positions. To facilitate the practical implementation of our proposed method, we also analyze how the spatial distribution of calibration points impacts the model learning accuracy. The experiment results justify the effectiveness of our proposed gaze estimation method for both the normal vision and eyewear users.