Geometric framework for statistical analysis of eye tracking heat maps, with application to a tobacco waterpipe study

Health warning labels have been found to increase awareness of the harmful effects of tobacco products. An eye tracking study was conducted to determine the optimal placement and type of a health warning label on tobacco waterpipes. Participants viewed images that contained one of (1) four waterpipes, (2) three different types of warning labels, (3) placed in three locations. Typically, statistical analysis of eye tracking data is conducted based on summary statistics such as total dwell time, duration score, and number of visits to an area of interest. However, these summary statistics fail to capture the complete variability in a participant's eye movement. Instead, we propose to estimate heat maps defined on the entire image domain using the raw two-dimensional coordinates of eye movement via kernel density estimation. For statistical analysis of heat maps, we adopt the Fisher-Rao Riemannian geometric framework, which enables computationally efficient comparisons of heat maps, statistical summarization and exploration of variability in a sample of heat maps, and metric-based hierarchical clustering. We apply this framework to eye tracking data from the tobacco waterpipe study and comment on the results in the context of the optimal placement and type of health warning labels on tobacco waterpipes.