Identification of Riccati dynamics under perspective and orthographic observations

In this paper, the problem of identifying motion and shape parameters of a planar object undergoing a Riccati motion, from the associated optical flow generated on the image plane of a single CCD camera, has been studied. The optical flow is generated by projecting feature points on the object onto the image plane via perspective and orthographic projections. Riccati dynam ics is to be viewed as a natural extension of the well-known affine dynamic s that has been the subject of parameter estimation research for many years . An important result we show is that, under perspective projection, the pa rameters of a specific Riccati dynamics that extend the well-known "rigid m otion" can he identified up to choice of a sign. This fact is in sharp cont rast to many other results in the literature, where under perspective proje ction, parameters are recovered up to a possible depth ambiguity. The paper also discusses other Riccati equations obtained from quadratic extension o f a rigid motion and affine motion. For each of the various motion models c onsidered and for each of the two projection models, we show that the exten t to which motion and shape parameters can he recovered from optical flow r an in fact be recovered from the linear approximation of the optical flow. The quadratic part of the optical flow carries no additional information fo r the class of parameter identification problems considered. We also extend our analysis to a pair of cameras.