Calibration Procedure

The calibration procedure is very simple and brief. Nine points are arranged in a $3\times3$ grid on the screen, and the user is asked to fixate his/her gaze on a certain target point, press a key, and move to a next target, until all the points are fixated. On each fixation, the vector from the center of the glint to the center of the pupil is saved, so that 9 corresponding points are obtained. The transformation from a glint-pupil vector ${\bf E} = (x_e, y_e)^t$, to a screen coordinate ${\bf S} = (x_s, y_s)^t$ is given by:

xe = a0 + a1 xs + a2 ys + a3 xs ys * a4 xs xs + a5 ys ys;
                                                                                                                (1)
ye = a6 + a7 xs + a8 ys + a9 xs ys + a10 xs xs + a11 ys ys;
 

where a_i are the coefficients of this second order polynomial. Each corresponding point gives 2 equations from (1), thus 18 equations are produced and an over determined linear system is obtained. The polynomial coefficients for x_e and y_e can be obtained independently, so that 2 simpler over determined systems are solved, using a least squares method.
 

1999-07-13