  Video-based glint-free eye tracking commonly estimates gaze direction based
on the pupil center. The boundary of the pupil is fitted with an ellipse and
the euclidean center of the ellipse in the image is taken as the center of the
pupil. However, the center of the pupil is generally not mapped to the center
of the ellipse by the projective camera transformation. This error resulting
from using a point that is not the true center of the pupil directly affects
eye tracking accuracy. We investigate the underlying geometric problem of
determining the center of a circular object based on its projective image. The
main idea is to exploit two concentric circles -- in the application scenario
these are the pupil and the iris. We show that it is possible to computed the
center and the ratio of the radii from the mapped concentric circles with a
direct method that is fast and robust in practice. We evaluate our method on
synthetically generated data and find that it improves systematically over
using the center of the fitted ellipse. Apart from applications of eye tracking
we estimate that our approach will be useful in other tracking applications.
