Constraints on quadratic-curved features under perspective projection

摘要

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 is known, along with its perspective projection in the image plane. In our approach, we decompose the 3D-location-estimation problem into a 3D-orientation-estimation problem and a 3D-position-estimation problem. 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 quadratic-curved 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 that, in general, 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 to obtain a unique solution to the 3D-location-estimation problem. The method developed and the results obtained for quadratic-curved features remove ambiguities that exist in a previously developed solution method. For experimentation purposes, two types of features are considered: circular and elliptical. A greylevel image of a set of circles is acquired, and subsequently processed according to a sequential distortion-compensation procedure; after which, the analytical method developed in this paper is applied and the features' 3D location are estimated. For elliptical features, a simulated example is presented. As an extra constraint, a second view of the same feature is utilized. It has been shown, through the application of a visual-computing procedure, that there exist a unique solution for the feature's 3D location under the given constraint.