Fig 1. Calculation of the center of eye rotation in a two-dimensional image plane.

(A) Pupil ellipses and the minor axis of the pupil ellipse obtained during circular eye movement induced by swirling the mouse around manually. (B) Point of intersection of multiple minor axes of a pupil ellipse. Ideally, multiple minor axes of a pupil ellipse would intersect at a single point, but they did not. The point of intersection of multiple minor axes of a pupil ellipse were determined as a point of the sum of the squares of the minimum distances between the point and the minor axes (black lines). (C) Center of eye rotation in the image calculated from the six minor axes shown in (A). The six minor axes shown in (A) are drawn here. The white small circle was the point where the sum of the squares of the distance between the point and the minor axis was minimum. After calculating the coordinates of the center of eye rotation in the image plane, a three-dimensional coordinate frame of XYZ was determined, as shown in the Inset.