Torsion in motion: the visual system as a three-axis gimbal

Rigorously tracking eye and head behavior in space is key to building realistic models of the stimulus that reaches our retina. The motion structure of this stimulus or retinal flow is created by the relative movement of the eyes with respect to the world. Characterizing this stimulus requires tracking the eye's three degrees of freedom in the head and the head's six degrees of freedom in the world. While vertical and horizontal eye rotations have been described during locomotion in the context of gaze stabilization, the component around the line of sight - torsion - has remained difficult to quantify, and how all three rotational components jointly contribute to retinal flow during self-motion remains largely unexplored. Here, we leveraged head-mounted technology to estimate eye torsion in ten subjects as they walked towards a distant target. More specifically, we combined automatic feature tracking with gaze-constrained simulations of eye rotations and camera projection to recover torsion from image data. We then estimated the curl present in the optic-flow field in head and retina centered frames in two scenarios: torsion as estimated from our data and with no torsion. We show that the eye's torsional component compensates for the roll component of head's angular displacement, altering the incoming visual flow in ways that are relevant for the extraction of self-motion parameters from retinal flow.