Parameter estimation of Riccati motion based on perspective systems

Abstract

The problem we studied in this paper is to understand to what extent motion and shape parameters can be estimated from an optical flow generated on the image plane. The optical flow is generated by projecting the phase portrait of a class of motion of object in R3 onto the image plane in R2. Here, the class of motion of object we considered is a two-dimensional plane undergoing Riccati motion. The projection models are perspective and orthographic projections. Namely, in this paper, we show several results on the problem of parameter estimation of Riccati motion under the two projection models. One of results is that the parameters of Riccati motion can be estimated up to choice of a sign. Thus, for all practical purposes, when the relative position of the object undergoing Riccati motion is known, motion and shape parameters can be recovered uniquely. This fact is in sharp contrast with existing known result in the literature about affine motion under perspective projection where parameters can only be recovered up to a possible depth ambiguity.