The nonlinear structure of motion perception during smooth eye movements

To perceive object motion when the eyes themselves undergo smooth movement, we can either perceive motion directly-by extracting motion relative to a background presumed to be fixed-or through compensation, by correcting retinal motion by information about eye movement. To isolate compensation, we created stimuli in which, while the eye undergoes smooth movement due to inertia, only one object is visible-and the motion of this stimulus is decoupled from that of the eye. Using a wide variety of stimulus speeds and directions, we rule out a linear model of compensation, in which stimulus velocity is estimated as a linear combination of retinal and eye velocities multiplied by a constant gain. In fact, we find that when the stimulus moves in the same direction as the eyes, there is little compensation, but when movement is in the opposite direction, compensation grows in a nonlinear way with speed. We conclude that eye movement is estimated from a combination of extraretinal and retinal signals, the latter based on an assumption of stimulus stationarity. Two simple models, in which the direction of eye movement is computed from the extraretinal signal and the speed from the retinal signal, account well for our results.