Saccadic Eye Movements and the Generalized Pareto Distribution
This work provides a novel statistical method for characterizing individual observers in eye-tracking studies, which is incremental in applying hyperbolic geometry to a known problem.
The authors analyzed eye movement transitions between fixations using hyperbolic geometry and found that step lengths follow a generalized Pareto distribution, with hyperbolic measurements being more robust than Euclidean ones, enabling individual observer identification.
We describe a statistical analysis of the eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. In contrast to the common approach of investigating the properties of the fixation points we analyze the properties of the transition phases between fixations. We introduce hyperbolic geometry as a tool to measure the step length between consecutive eye positions. We show that the step lengths, measured in hyperbolic and euclidean geometry, follow a generalized Pareto distribution. The results based on the hyperbolic distance are more robust than those based on euclidean geometry. We show how the structure of the space of generalized Pareto distributions can be used to characterize and identify individual observers.