How normal flow constrains relative depth for an active observer

Abstract

We present a set of constraints that relate the relative depth of (stationary or moving) objects in the field of view with the spatiotemporal derivatives of the time varying image intensity function. The constraints are purposive in the sense that they can be used only for the relative depth from motion problem and not in other problems related to motion (i.e. they lack generality). In addition, they show that relative depth could be obtained without having to go through the intermediate step of fullly recovering 3D motion, as is commonly considered. Our analysis indicates that exact computation of retinal motion (optic flow or displacements) does not appear to be a necessary first step for some problems related to visual motion, contrary to conventional wisdom. In addition, it is demonstrated that optic flow, whose computation is an illposed problem, is related to the motion of the scene only under very restrictive assumptions. This paper is devoted to ihe discovery of the mathematical constraints relating normal flow and relative depth. The development of algorithms using these constraints and the study of stability issues of such algorithms, is not discussed here.