This paper presents a general theory for the remote estimation of the point-of-gaze (POG) from the coordinates of the centers of the pupil and corneal reflections. Corneal reflections are produced by light sources that illuminate the eye and the centers of the pupil and corneal reflections are estimated in video images from one or more cameras. The general theory covers the full range of possible system configurations. Using one camera and one light source, the POG can be estimated only if the head is completely stationary. Using one camera and multiple light sources, the POG can be estimated with free head movements, following the completion of a multiple-point calibration procedure. When multiple cameras and multiple light sources are used, the POG can be estimated following a simple one-point calibration procedure. Experimental and simulation results suggest that the main sources of gaze estimation errors are the discrepancy between the shape of real corneas and the spherical corneal shape assumed in the general theory, and the noise in the estimation of the centers of the pupil and corneal reflections. A detailed example of a system that uses the general theory to estimate the POG on a computer screen is presented.

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The cross-ratios method for point-of-gaze (PoG) estimation uses the invariance property of cross-ratios in projective transformations. The inherent causes of the subject-dependent PoG estimation bias exhibited by this method have not been well characterized in the literature. Using a model of the eye and the components of a system (camera, light sources) that estimates PoG, a theoretical framework for the cross-ratios method is developed. The analysis of the cross-ratios method within this framework shows that the subject-dependent estimation bias is caused mainly by: 1) the angular deviation of the visual axis from the optic axis and 2) the fact that the virtual image of the pupil center is not coplanar with the virtual images of the light sources that illuminate the eye (corneal reflections). The theoretical framework provides a closed-form analytical expression that predicts the estimation bias as a function of subject-specific eye parameters. The theoretical framework also provides a clear physical interpretation for an existing empirically derived two-step procedure that compensates for the estimation bias and shows that the first step of this procedure is equivalent to moving the corneal reflections to a new plane that minimizes the distance from this plane to the virtual image of the pupil center.

This paper describes a method for remote, non-contact point-of-gaze (POG) estimation that tolerates free head movements and requires a simple calibration procedure in which the subject has to fixate only on a single point. This method uses the centers of the pupil and at least two corneal reflections (virtual images of light sources) that are estimated from eye images captured by at least two cameras. Experimental results obtained with a prototype system that tolerates head movements in a volume of about 1 dm3, exhibited RMS POG estimation errors of approximately 0.6-1 degrees of visual angle. This system can enable applications with infants that, otherwise, would not be possible with existing POG estimation methods, which typically require multiple-point calibration procedures.

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