Approximate maximum-likelihood estimation of circle parameters using a Phase-Coded Kernel

The accurate fitting of a circle to noisy measurements of points on its circumference is an important and much-studied problem in statistics. ATHERTON & KERBYSON (Image and Vision Computing 17, 1999, 795-803) have proposed a complex convolutional circle parameter estimator. One of the estimators proposed is a `Phase-Coded Annulus´ to estimate for the centre and radius. ZELNIKER & CLARKSON (Digital Image Computing: Tech. and Appl. 2003, 509-518) have shown that it is possible to exactly describe the Maximum Likelihood Estimator (MLE) in terms of convolution under a certain model for ideal images formed from noisy circle points. In this paper, we investigate the relationship between the convolution of an ideal image with a Phase-Coded Kernel and the MLE. We compare our approximate MLE (AMLE) method to the DELOGNE-KÅ SA Estimator which uses a least squares approach to solve for the circle parameters, the MLE as well as the theoretical CRAMÉR-RAO Lower Bound.