Image Based Estimation Problems in System Theory: Motion and Shape Estimation of a Planar Textured Surface Undergoing a Rigid Flow

In this paper we consider the problem of motion and shape estimation, of a planar textured surface undergoing a rigid flow, with the aid of a monocular camera. We show that the estimation problem reduces to a specific parameter estimation of a perspective dynamical system. Surprisingly, the above reduction is independent of whether or not the data measured is the brightness pattern which the object produces on the image plane or whether the data observed are points, lines or curves on the image plane produced as a result of discontinuities in the brightness pattern. The basic procedure introduced for parameter estimation is to subdivide the problem into two modules, one for spatial averaging and the other for time averaging. The estimation procedure is carried out with the aid of a new "Realization Theory" for perspective systems.