Jaeseon Song¹ (), Kimberly Meier¹; ¹University of Houston College of Optometry

The stability of fixational eye movements is commonly quantified using the bivariate contour ellipse area (BCEA), which assumes a unimodal Gaussian distribution. While sufficient for simple fixation patterns, this assumption fails when fixation produces multimodal or irregular spatial structures. Isoline-based metrics using kernel density estimation (KDE) have recently been adopted to address these limitations, providing greater flexibility in representing the spatial distribution of gaze. However, KDE models gaze samples as independent, ignoring the temporal autocorrelation inherent in natural gaze behavior. We introduce Autocorrelated KDE (AKDE), adapting a method from ecology used for estimating animal ranges to quantify fixation stability. AKDE incorporates temporal dependencies through effective sample size estimation, which adjusts for information redundancy, and locally-adaptive bandwidths that capture underlying spatiotemporal structure. We compared area estimates from AKDE with BCEA and standard KDE using gaze recordings from the GazeBase dataset (N = 298 of 322; Griffith et al., Scientific Data 2021;8:184). AKDE showed a strong correlation with BCEA (r = 0.84), yet Bland-Altman analysis revealed systematic differences, with BCEA consistently estimating larger areas (mean difference = 0.16 log deg², p < .0001). AKDE correlated moderately with KDE (r = 0.55), which estimated smaller areas (difference = 0.42 log deg², p < .0001). KDE and BCEA showed the weakest correlation (r = 0.29) and largest disagreement (difference = −0.58 log deg², p < .0001). These findings demonstrate that AKDE captures structure missed by both BCEA’s normality assumption and KDE’s independence assumption. By addressing multimodality and temporal dependence, AKDE provides a flexible, distribution-free metric that combines spatial precision with temporal realism. This method offers a principled alternative to traditional approaches: while BCEA may suffice for controls with tightly clustered, near-Gaussian fixation patterns, AKDE provides greater flexibility for populations with unstable or multimodal fixation, making it well-suited for diverse clinical applications.

Acknowledgements: This work was supported by NIH grant EY007551 to the University of Houston College of Optometry.