Reduction of Bias in Maximum Likelihood Ellipse Fitting

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ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Year:
2000

Citing 0
Cited 3

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Abstract

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 fewer computations than minimizing the geometric distance with Levenberg-Marquardt optimization procedure. Closed-form expressions for the covariances of the ellipse parameters and the corrected data points are also provided for the HEIV algorithm. Defining confidence regions in the input domain, either analytically, or by bootstrap, assesses the quality of the different solutions. The latter approach is exclusively data driven and it is used whenever the expression of the covariance for the estimates is not available.