Simplifying the Cross-ratios Method of Point-of-gaze Estimation

Point-of-gaze estimation systems estimate the point within the visual field that is imaged on the highest acuity region of the retina known as the fovea. A new method has been introduced that estimates point-of-gaze by exploiting the invariance property of cross-ratios in projective transformations [1]. The projective transformation is formed by two perspective projections. The first projection has a projective center at the center of corneal curvature, and projects four light sources placed around a plane to their corneal reflections in the eye. These corneal reflections are virtual images formed when light from the sources reflects off of the outer corneal surface, which acts as a convex mirror. The second projection is a camera projection, centered at the nodal point of a camera that images the eye, and projects the corneal reflections to their images on the camera’s imaging plane. These two perspective projections form a single projective transformation relating the plane defined by the four light sources (the scene plane) to the camera’s imaging plane. The same two perspective projections also project the point-of-gaze on the scene plane to the image of the pupil center on the imaging plane.