Large sample bias in least squares estimators of a circular arc center and its radius

Abstract The statistical properties of a least squares algorithm for estimating the center and radius of noisy data along a circular arc, suggested in (Landau, Comput. Vision Graphics Image Process. 38 , 1987, 317–326), are discussed. In particular, it is pointed out that, when large data sets are generated from the simulation procedure used in op. cit. , the suggested algorithm will not converge to the true circle center and radius. Approximate formulae for the asymptotic biases of the estimators are given.