  Introduction: In the realm of human-computer interaction and behavioral
research, accurate real-time gaze estimation is critical. Traditional methods
often rely on expensive equipment or large datasets, which are impractical in
many scenarios. This paper introduces a novel, geometry-based approach to
address these challenges, utilizing consumer-grade hardware for broader
applicability. Methods: We leverage novel face landmark detection neural
networks capable of fast inference on consumer-grade chips to generate accurate
and stable 3D landmarks of the face and iris. From these, we derive a small set
of geometry-based descriptors, forming an 8-dimensional manifold representing
the eye and head movements. These descriptors are then used to formulate linear
equations for predicting eye-gaze direction. Results: Our approach demonstrates
the ability to predict gaze with an angular error of less than 1.9 degrees,
rivaling state-of-the-art systems while operating in real-time and requiring
negligible computational resources. Conclusion: The developed method marks a
significant step forward in gaze estimation technology, offering a highly
accurate, efficient, and accessible alternative to traditional systems. It
opens up new possibilities for real-time applications in diverse fields, from
gaming to psychological research.
