Motion fields are hardly ever ambiguous

摘要

There has been much concern with ambiguity in the recovery of motion and structure from time-varying images. I show here that the class of surfaces leading to ambiguous motion fields is extremely restricted—only certain hyperboloids of one sheet (and some degenerate forms) qualify. Furthermore, the viewer must be on the surface for it to lead to a potentially ambiguous motion field. Thus the motion field over an appreciable image region almost always uniquely defines the instantaneous translational and rotational velocities, as well as the shape of the surface (up to a scale factor).