Identification of fixations and saccades in eye-tracking data using adaptive threshold-based method

TL;DR

This work addresses the problem of robustly classifying eye movements into fixations and saccades when standard fixed thresholds fail to generalize across tasks and individuals. It introduces an adaptive thresholding framework based on a Markovian approximation of gaze dynamics, using the $K$-ratio to minimize unnecessary state transitions and tune velocity, angular velocity, and dispersion thresholds for I-VT, I-AVT, and I-DT. Across two tasks and with Gaussian spatial noise, the approach yields the best baseline accuracy for I-VT (≈$90$–$93$ extbackslash%) and substantially improves robustness under noise for all algorithms, with adaptive dispersion thresholds showing the strongest resilience (≥$81$ extbackslash% at $\sigma=50$ px) albeit with a fixation-biased precision-recall trade-off. The findings offer practical guidance for selecting and tuning fixation-saccade classifiers based on data quality and analytical goals, and suggest directions for integrating $K$-ratio tuning with denoising or learning-based models.

Abstract

Properties of ocular fixations and saccades are highly stochastic during many experimental tasks, and their statistics are often used as proxies for various aspects of cognition. Although distinguishing saccades from fixations is not trivial, experimentalists generally use common ad-hoc thresholds in detection algorithms. This neglects inter-task and inter-individual variability in oculomotor dynamics, and potentially biases the resulting statistics. In this article, we introduce and evaluate an adaptive method based on a Markovian approximation of eye-gaze dynamics, using saccades and fixations as states such that the optimal threshold minimizes state transitions. Applying this to three common threshold-based algorithms (velocity, angular velocity, and dispersion), we evaluate the overall accuracy against a multi-threshold benchmark as well as robustness to noise. We find that a velocity threshold achieves the highest baseline accuracy (90-93\%) across both free-viewing and visual search tasks. However, velocity-based methods degrade rapidly under noise when thresholds remain fixed, with accuracy falling below 20% at high noise levels. Adaptive threshold optimization via K-ratio minimization substantially improves performance under noisy conditions for all algorithms. Adaptive dispersion thresholds demonstrate superior noise robustness, maintaining accuracy above 81% even at extreme noise levels (σ = 50 px), though a precision-recall trade-off emerges that favors fixation detection at the expense of saccade identification. In addition to demonstrating our parsimonious adaptive thresholding method, these findings provide practical guidance for selecting and tuning classification algorithms based on data quality and analytical priorities.

Figures (6)

• Figure 1: Example of scanpaths with overlaid classifications (orange = fixation, blue = saccade). Top row: Random Pixel task; bottom row: Waldo task. Columns (left to right): raw gaze points, I-VT, I-AVT, and I-DT results.
• Figure 2: $K$-ratio curves used for threshold optimization (top: Random Pixel; bottom: Waldo). Minima define the task-specific thresholds for I-VT, I-AVT, and I-DT. The respective $K$-ratio for each of the algorithms for both task are tabulated in a supplementary section at the end of the paper. See Appendix Tab. \ref{['tab:k_ratio_all']}. The $T_\mathrm{min}$ value used for I-DT is 50ms.
• Figure 3: Performance metrics at zero noise (left: Random Pixel; right: Waldo). Bars display overall accuracy, class-wise precision/recall/F1, and predicted fixation proportion for each algorithm.
• Figure 4: Robustness analysis of fixation classification algorithms under Gaussian spatial noise ($\sigma = 0$-$50$ pixels). Top row: Evolution of adaptive thresholds for I-VT, I-AVT, and I-DT algorithms across noise levels for Random Pixel and Waldo tasks. Bottom row: Classification accuracy comparing fixed thresholds (optimized at $\sigma = 0$) versus adaptive thresholds (re-optimized at each noise level). Solid lines represent original (fixed) thresholds; dashed lines represent adaptive thresholds.
• Figure S5: F1 scores for fixation and saccade classification across noise levels. Top row: F1-score for fixation detection. Bottom row: F1-score for saccade detection. Solid lines indicate original thresholds; dashed lines indicate adaptive thresholds.