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 accounting for eye-movement-induced rotation. We propose an alternative: the visual system utilizes mean retinal curl from fixations as a surrogate signal for heading, rendering the explicit recovery of the FoE unnecessary. Stationary participants viewed simulated walking paths on a large screen while fixating on points on the projected ground texture at varying eccentricities —a natural behavior inducing sustained retinal curl. Participants continuously reported perceived heading in 3D scene coordinates. To isolate the role of retinal curl, we employed a real-time manipulation that kept translational flow constant while the foveal curl component was either unaltered, cancelled, or overcancelled. Under natural conditions (unaltered), participants exhibited systematic heading biases opposite the direction of gaze. Crucially, these biases vanished when we cancelled the expected curl, and flipped when we overcancelled it, 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.