Circular Arcs Fitted on a Riemann Sphere

摘要

A method for fitting a circle to a set of points in two dimensions is presented. The method applies a stereographic projection to map the 2D points onto a cricle on a 3D Riemann sphere. Then, a plane is fitted to the transformed points, and the parameters of the sought circle are determined from the identified plane parameters. The method is direct, and it is shown that the estimator is unbiased to first-order accuracy. The best performance is obtained when the circle has unit radius and is centered at the origin. The method is unbiased to second order in this case, and experiments with synthetic data show that the method is practically unbiased. In addition, the simulations show that origin centering and unit radius requirements are not critical. Circular arcs down to 45° can be estimated at realistic noise levels. Comparisons with three alternative methods are done, and the accuracy and computational simplicity of this method compares favorably with the alternatives.