A theoretical analysis of three-dimensional eye position measurement using polar cross-correlation

Polar cross-correlation is a commonly used technique for determination of torsional eye position from video images. At eccentric eye positions, the projection of the sampling window onto the image plane of the camera is translated and deformed due to the spherical shape of the eyeball. In this paper, we extend the polar cross-correlation technique by developing the formulas required to determine the correct location and shape of the sampling window at all eye positions. These formulas also allow the representation of three-dimensional eye position in Fick-angles, which are commonly used in oculomotor research. A numerical simulation shows the size of the errors in ocular torsion if the spherical geometry of the eye is not considered. Other effects which can affect the accuracy of video-based eye position measurements are also discussed.