Optimal visual motion estimation in a natural environment*

Many organisms, from flies to humans, use visual signals to estimate their motion through the world. In flies we know that the precision of motion estimation is close to the limits set by photon shot noise and diffraction blur, yet the actual estimates suffer from systematic errors, some of which are shared by human perception. To explore the structure of the motion estimation problem, we have constructed a camera/gyroscope system that allows us to sample, at high temporal resolution, the joint distribution of input images and rotational motions during a long walk in the woods. From these data we construct the optimal estimator of velocity based on spatial and temporal derivatives of image intensity in small patches of the visual world. Over the bulk of the naturally occurring dynamic range, the optimal estimator exhibits the same systematic errors seen in neural and behavioral responses, including the confounding of velocity and contrast. These results suggest that apparent errors of sensory processing may reflect an optimal response to the physical signals in the environment.