On Segmenting Pupil Contours in Terms of Elliptical Fourier Series

Accurate pupil segmentation is crucial for many videobased eye-tracking algorithms, often serving as a foundational step for downstream tasks such as gaze estimation and pupillometry. While it is typically assumed that unoccluded pupil contours are perfect ellipses, they often reveal significant deviations caused by corneal refraction and the inherent non-circularity of the iris's pupillary opening. To address these challenges, we introduce a novel deep-learning-based segmentation method that models pupil contours using low-order Elliptical Fourier Series. While providing a flexible representation capable of capturing realistic distortions, the chosen approach establishes a suitable inductive bias, effectively constraining the space of possible segmentations to smooth, closed, and non-intersecting curves. Our method achieves segmentation accuracy comparable to a state-of-the-art technique while offering additional benefits over pixel-wise segmentation approaches, including a compact representation and compatibility with temporal and spatial interpolation. Furthermore, we critically evaluate the limitations of the commonly used areabased Intersection over Union (IoU) metric, highlighting through theoretical modeling and experimental validation its susceptibility to biases from region size and label noise. To overcome these issues, we propose to use a contour-based evaluation metric instead that robustly assesses segmentation quality while addressing these shortcomings.