Beyond the Focus of Expansion: Retinal curl as a functional signal for heading estimation

Prevailing models aiming at explaining heading assume that humans need to recover the Focus of Expansion (FOE) while filtering out rotational flow (curl) caused by eye movements. We propose an alternative: the visual system utilizes retinal curl directly to estimate heading, rendering the explicit recovery of the FOE unnecessary. Stationary participants viewed simulated walking paths on a large screen while fixating on ground targets at varying eccentricities--a natural behavior inducing sustained retinal curl. Participants continuously reported perceived heading. To isolate the role of rotational flow, we employed a real-time manipulation that kept translational flow constant while the foveal curl component was either intact, cancelled, or overcancelled. Under natural conditions, participants exhibited systematic heading biases opposite the direction of gaze. Crucially, these biases vanished in the cancelled curl condition, identifying retinal curl as the specific driver of perceptual bias. We modeled these results using a simple feedback controller and a ring-attractor neural network featuring gaze-contingent inhibition and a straight-ahead prior. These findings suggest the brain exploits the geometry of gaze stabilization to simplify navigation, treating retinal curl as a functional signal rather than noise to be filtered.