Mapping and Correcting Pupil Foreshortening Error (Hayes & Petrov, 2016)

What is Pupil Foreshortening Error (PFE)?

Changes in gaze position produce foreshortening of the pupillary image in image-based eye tracking because the camera is fixed but the eye rotates.  Specifically, as the eye rotates away from the camera, the pupil image becomes more elliptical and shrinks in apparent area.  It is important to understand pupil foreshortening error because use of image-based eye tracking cameras is widespread and the pupillary response is increasingly being used to study cognitive processing.

Foreshortening error occurs as the eye rotates away from the camera.

How much error is introduced by PFE?

To answer this question we mapped the pupil foreshortening error (PFE) using an artificial eye and socket model (See Hayes & Petrov, 2016).  Three artificial eyes with different fixed pupil sizes were used to systematically measure changes in pupil size as a function of gaze position and experimental layout of the camera, observer, and display.  The results revealed systematic PFE that is larger than the typical cognitive pupillary effect.  The PFE was invariant across the 3 different artificial eye diameters within a given experimental layout, which is critical because it establishes that the PFE surface is not affected by changes in pupil diameter that occur when measuring a dynamic, biological eye.

Observed deviation (PFE) in pupil diameter from the geometric mean.

Can PFE be corrected?

Yes!  We provide a geometric correction approach that virtually eliminates the pupil foreshortening error (Hayes & Petrov, 2016).  The geometric model expresses the foreshortening of the pupil area as a function of the cosine of the angle between the eye-to-camera axis and the eye-to-stimulus axis.  The model reduced the root mean squared error of the pupil measurements by 82.5% when the model parameters were pre-set to the physical layout dimensions, and by 97.5% when they were optimized to fit the empirical error surface.   Thus, very accurate PFE correction is possible and the corrected pupillometric data have the precision necessary to measure typical cognitive effects.

Optimized correction virtually eliminates pupil foreshortening error.