Reduction of Bias in Maximum Likelihood Ellipse Fitting
Bogdan Matei and Peter Meer
Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08854-8058, USA
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
15th International Conference on Computer Vision and
Pattern Recognition , September 2000, Barcelona, Spain,
vol. III, 802-806.
Return to Research: Estimation under heteroscedasticity