Maximum-likelihood circle-parameter estimation via convolution

Abstract

In this paper, we present an interpretation of the Maximum Likelihood Estimator (MLE) and the Delogne-K˚asa Estimator (DKE) for circle-parameter estimation via convolution. Under a certain model for theoretical images, this convolution is an exact description of the MLE. We use our convolution based MLE approach to find good starting estimates for the parameters of a circle, that is, the centre and radius. It is then possible to treat these estimates as preliminary estimates into the Newton-Raphson method which further refines these circle estimates and enables sub-pixel accuracy. We present closed form solutions to the Cram´er-Rao Lower Bound of each estimator and discuss fitting circles to noisy points along a full circle as well as along arcs. We compare our method to the DKE which uses a least squares approach to solve for the circle parameters.