Tracking facilitates 3-D motion estimation

The recently emerging paradigm of Active Vision advocates studying visual problems in form of modules that are directly related to a visual task for observers that are active. Along these lines, we are arguing that in many cases when an object is moving in an unrestricted manner (translation and rotation) in the 3D world, we are just interested in the motion's translational components. For a monocular observer, using only the normal flow — the spatio-temporal derivatives of the image intensity function — we solve the problem of computing the direction of translation and the time to collision. We do not use optical flow since its computation is an ill-posed problem, and in the general case it is not the same as the motion field — the projection of 3D motion on the image plane. The basic idea of our motion parameter estimation strategy lies in the employment of fixation and tracking. Fixation simplifies much of the computation by placing the object at the center of the visual field, and the main advantage of tracking is the accumulation of information over time. We show how tracking is accomplished using normal flow measurements and use it for two different tasks in the solution process. First it serves as a tool to compensate for the lack of existence of an optical flow field and thus to estimate the translation parallel to the image plane; and second it gathers information about the motion component perpendicular to the image plane.