An Automatic Calibration Method for Kappa Angle Based on a Binocular Gaze Constraint

Kappa-angle calibration shows its importance in gaze tracking due to the special structure of the eyeball. In a 3D gaze-tracking system, after the optical axis of the eyeball is reconstructed, the kappa angle is needed to convert the optical axis of the eyeball to the real gaze direction. At present, most of the kappa-angle-calibration methods use explicit user calibration. Before eye-gaze tracking, the user needs to look at some pre-defined calibration points on the screen, thereby providing some corresponding optical and visual axes of the eyeball with which to calculate the kappa angle. Especially when multi-point user calibration is required, the calibration process is relatively complicated. In this paper, a method that can automatically calibrate the kappa angle during screen browsing is proposed. Based on the 3D corneal centers and optical axes of both eyes, the optimal objective function of the kappa angle is established according to the coplanar constraint of the visual axes of the left and right eyes, and the differential evolution algorithm is used to iterate through kappa angles according to the theoretical angular constraint of the kappa angle. The experiments show that the proposed method can make the gaze accuracy reach 1.3 [Formula: see text] in the horizontal plane and 1.34 [Formula: see text] in the vertical plane, both of which are within the acceptable margins of gaze-estimation error. The demonstration of explicit kappa-angle calibration is of great significance to the realization of the instant use of gaze-tracking systems.