Modelling the psychophysics of eye movements in a large corpus of binocular reading behaviours

The position and shape of the pupil entrance of the eye plays a central role in video-based eye-tracking. As a result, any unexpected translation and deformation of the pupil image on camera may introduce systematic errors to eye-tracking. In this thesis we explored and corrected the spatial and temporal errors in the process of eye-tracking by means of various geometric models that involve the pupil. The main focus of this thesis is on how the properties of the pupil mediate the generation and correction of errors. There are two groups of experiments and simulations that emphasise the movement of the eyeball itself and the experiment setting, respectively. 1) For the movement of the eyeball, 1a) firstly we constructed a geometric model of the eyeball and deduced an analytical description for the eyeball, pupil, and pupil-CR trajectory during saccades and fixations. We used the model to explain the relationship between the properties of the Post Saccadic Oscillation (PSO) and other variables such as age, binocularity, saccade direction, pupil size deformation, and corneal bulge. We found that the abruptness of braking at the saccade end mediates the effects on PSO amplitude of age, binocularity, saccade size and direction. We also found that the effect of pupil-CR processing on the shape and size of PSO is big and highly dependent on the abruptness of saccade braking. 1b) Secondly, we constructed an event detection algorithm by incorporating our eye model into the Scaled Unscented Kalman filter. The algorithm can make an informed correction of the glissade artefact created by the default Eyelink event detection algorithm. Also, the algorithm is able to detect boundaries and different phases of PSO. We found that pupil size at the first peak of PSO is smaller than pupil size at the following first resting point of PSO. 2) For the experiment settings in eye-tracking, 2a) first, we used a geometric model and the differentiation among Pupil Foreshortening Error (PFE), saccadic non-PFE, and fixational non-PFE to improve the performance of pupil size correction across the page by a large margin. The performance of pupil size correction was improved by using the pupil size measured at the first resting point of PSO instead of those at the highest peak of PSO. The process of pupil size correction also produced estimates of the camera positions during eye tracking. 2b) Second, we constructed a geometric model to calculate the error in eye-tracking brought about by the movement of the head. A solution was offered to the fixation disparity problem by analysing the effect of head movement during monocular calibration on the direction of fixation disparity, as opposed to the pupil artefact solution. 2c) Third, we used a ray traced simulation to differentiate between anatomical pupil artefact and refraction pupil artefact. The simulation results show that the size of the refraction pupil artefact is about one-third the size of the anatomical pupil artefact at a camera viewing angle of 30°. In conclusion, this thesis offers a model-based approach to explore and explain various effects and errors in eye-tracking by emphasizing the role of the pupil. This approach is ready to be generalized to other data sets and offers methods of post-hoc correction to errors in pupil size and gaze position