  Many organisms, from flies to humans, use visual signals to estimate their
motion through the world. To explore 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.
