Reduction of bias in maximum likelihood ellipse fitting

An improved maximum likelihood estimator for ellipse fitting based on the heteroscedastic errors-in-variables (HEIV) regression algorithm is proposed. The technique significantly reduces the bias of the parameter estimates present in the direct least squares method, while it is numerically more robust than renormalization, and requires less computations than minimizing the geometric distance with the Levenberg-Marquardt optimization procedure. The HEIV algorithm also provides closed-form expressions for the covariances of the ellipse parameters and corrected data points. The quality of the different solutions is assessed by defining confidence regions in the input domain, either analytically or by bootstrap. The latter approach is exclusively data driven and it is used whenever the expression of the covariance for the estimates is not available