Inferring local surface orientation from motion fields.

The problem of inferring local surface orientation from changing images is studied computationally by deriving conditions under which the motion information is sufficient for an information processing system, biological or otherwise, to infer unique descriptions of the local surface orientation. The analysis is based on shape-from-motion proposition, which states, that given the first spatial derivatives of the orthographically projected velocity and acceleration fields of a rigidly rotating regular surface, then the angular velocity and the surface normal at each visible point on that surface are uniquely determined up to a reflection. The proof proceeds in two steps. First it is shown that surface tilt and one component of the angular velocity are uniquely determined by the first spatial derivatives of the velocity field. Then it is shown that surface slant and the remaining two components of the angular velocity are uniquely determined if the first spatial derivatives of the acceleration field are also available.