Constraints on Quadratic Curves Under Perspective Projection

In this paper we address the problem of 3D-location estimation based on quadratic-curved features. It is assumed that the true size and true shape of a feature in object space are known, along with its perspective projection in the image plane. In our approach, we decompose the 3D-location-estimation problem into a concatenated process of SD-orientation estimation and 3D-position estimation. In order to simplify the analysis, we have adopted the concepts of "standard rotation" and "canonical position", introduced by Kanatani. In this context we present a new analytical method for determining the shapes of all quadraticcurved features (whether elliptical, circular, parabolic or hyperbolic). viewed at their "canonical positions". A set of geometrical constraints on the 3D location for each type of quadratic feature is derived, as the main contribution of this research. We prove, in general, that knowledge of the true size and shape does not yield a sufficient number of constraints to determine uniquely 3D orientation and position. As a result, extra constraints must be acquired from other sources and fused with these constraints in order to obtain a unique solution to the 3Dlocationestimation problem. The method developed and the results obtained for quadratic-curved features remove ambiguities that exist in a previously developed solution method.