A model of the appearance of the moving human eye

The entrance pupil and first Purkinje reflection ("glint") in an image of the human eye serve as important features in 3D, model-based eye tracking applications. Here I present a physically and biologically accurate, ray-traced model that supplies the appearance of the pupil and glint of a moving eye. Once biometrically calibrated for a subject under study, simultaneous fitting of the pupil and glint features by the model supplies eye rotation, radius of the aperture stop, and the translation of the eye relative to the initial camera position. The biometric parameters of the model, including corneal curvature and the depth of the centers of rotation, are obtained by model-based fitting of images of the eye posed at known gaze angles. This approach was applied to eye recordings from 30 people obtained during gaze calibration, and while head position was recorded simultaneously using echoplanar magnetic resonance imaging. The refractive and reflective effects of spectacle and contact lenses worn by some subjects were incorporated into the model. The fitted parameters reveal that the center of rotation for horizontal eye movements is deeper (13.8 mm) than that for vertical eye movements (12.1) mm, consistent with prior studies. Individual differences in the depth of the rotation centers, and in corneal curvature, were well related to biometric measures obtained from these subjects using clinical ophthalmologic instruments. Once biometrically calibrated for each subject, gaze position was modeled with a cross-validated, median (across subject) absolute error of 0.58{degrees}, and image-plane translation of the head was estimated with sub-millimeter accuracy. The open-source model described here produces biologically accurate simulations of the appearance of the eye in motion, and may be used in model-based search to derive eye pose and biometric properties from empirical data.