A second look at the least-squares algorithm for recovering information from optical flow

The changes in an image arising from the motion of the environment have been intensively studied over the past few years. These changes, termed optical flow, depend on both the motion and the shape of the environment. The central problem in the study of optical flow is to find the best way of recovering information about the motion and shape of the environment from the associated optical flow field. The author has previously shown (1986, 1987) that some parameters of the motion can be recovered with greater accuracy than the remaining parameters, provided the optical flow field arises from an irregular moving rigid surface. A surface is classed as irregular if the set of inverse distances to points on the surface do not possess a good linear approximation. The algorithm in question is based on a least-square error function, ε(ν_). In the case of an optical flow field arising from an irregular moving rigid surface, there in a simple approximation to ε(ν_) which can be used to predict the performance of the algorithm in situations of practical interest. Experimental results show that the approximation to ε(ν_) is astonishingly accurate. In this paper the approximation to ε(ν_) is given and some experiments to check this approximation are described