The interpretation of a moving retinal image

It is shown that from a monocular view of a rigid, textured, curved surface it is possible, in principle, to determine the gradient of the surface at any point, and the motion of the eye relative to it, from the velocity field of the changing retinal image, and its first and second spatial derivatives. The relevant equations are redundant, thus providing a test of the rigidity assumption. They involve, among other observable quantities, the components of shear of the retinal velocity field, suggesting that the visual system may possess specialized channels for computing these components.