UNBIASED LEAST-SQUARES FITTING OF CIRCULAR ARCS

Previous solutions to the problem of obtaining a least squares fit to a circular arc are discussed. The existence of severe bias in closed f orm solutions and non-convergence in iterative solutions for shallow a rcs is noted. A straightforward and economical iterative procedure is developed which is shown to be stable and have rapid convergence to an unbiased least squares fit on a wide range of synthetic data. The ran dom error in the parameters of these fits is measured and compared wit h theoretical predictions. The procedure is shown to operate up to the limit of the validity of circular arc fitting. The term well-defined is introduced to describe arcs within this limit. Example applications to image data show the utility of the method, and the inadequacy of p revious solutions, in real image analysis tasks. (C) 1994 Academic Pre ss, Inc.