HOW NORMAL FLOW CONSTRAINS RELATIVE DEPTH FOR AN ACTIVE OBSERVER

We present a set of constraints that relate the relative depth of (sta tionary or moving) objects in the field of view with the spatiotempora l derivatives of the time varying image intensity function. The constr aints are purposive in the sense that they can be used only for the re lative depth from motion problem and not in other problems related to motion (i.e. they lack generality). In addition, they show that relati ve depth could be obtained without having to go through the intermedia te step of fullly recovering 3D motion, as is commonly considered. Our analysis indicates that exact computation of retinal motion (optic fl ow or displacements) does not appear to be a necessary first step for some problems related to visual motion, contrary to conventional wisdo m. In addition, it is demonstrated that optic flow, whose computation is an ill-posed problem, is related to the motion of the scene only un der very restrictive assumptions. This paper is devoted to the discove ry of the mathematical constraints relating normal flow and relative d epth. The development of algorithms using these constraints and the st udy of stability issues of such algorithms, is not discussed here.