Saccadic Eye Movements and the Generalized Pareto Distribution

TL;DR

This paper analyzes eye movement transitions during free viewing, revealing that step lengths follow a generalized Pareto distribution, with hyperbolic geometry providing more robust measurements and enabling observer identification.

Contribution

It introduces hyperbolic geometry for measuring eye movement step lengths and demonstrates their distribution follows a generalized Pareto, improving robustness and individual identification.

Findings

Step lengths follow a generalized Pareto distribution.

Hyperbolic distance provides more robust measurements.

Distribution structure helps identify individual observers.

Abstract

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.