A Note on Parameter Identifiability of Riccati Dynamics under Perspective Projection

抄録

In thisp aper, we consider the problem of estimating the parameters of a Riccati equation under perspective observation. We consider a plane in R³ undergoing a general Riccati dynamics and assume that feature points on the plane are observed via perspective projection. Projection of each of the points generate an optical flow on the image plane. The problem we investigate is the extent to which the optical flow dynamics identifies the parameters of the motion dynamics and the initial position of the plane. The paper concludes with the claim that the initial depth and orientation of the plane is totally arbitrary and that for a given depth and orientation of the plane, there is a one parameter

ambiguity on the motion parameters. This paper, therefore, sheds new insight to the problem of parameter identification assuming that the motion dynamics is non-rigid, in particular a Riccati dynamics Our conclusion reported in this paper should be contrasted with the problem of parameter identification in the case when the motion dynamics is rigid, wherein the only parameter ambiguity, generically, is restricted to the depth.