Various methods for fitting ellipses to data have been tested, although due to space limitations not all the results have been shown. The experiments suggest that in the presence of outliers the LMedS approach applied to either of the weighted algebraic or foci bisector distance approximations produces the best results. Both approximations result in robust and accurate fits. If the simpler but more biased algebraic distance approximation is used then the accuracy degrades significantly, and the robustness also suffers to a lesser extent. The LS method can produce excellent fits, but is not robust and therefore cannot be considered if the data may be contaminated by clutter or other outliers. The Theil-Sen method is markedly inferior to the LMedS residual method in terms of accuracy and robustness. Modifying the median operation of the Theil-Sen method and finding the LMedS estimates of the individual parameter values actually degrades the performance rather than improving it. Finally, both the Hilbert curve and MVE approaches were reasonably robust, but provided poor accuracy.
We discussed several issues concerning the sampling of points to form the minimal subsets. In order to avoid tuples with points separated by either too small or too large a gap a regular sampling of the points appeared advantageous. However, the experiments show that in fact no advantage for the LMedS method was gained by regular sampling, and that it actually caused the performance of the Theil-Sen method to deteriorate.
It should be noted that it is difficult to truly assess the performance of the fitting techniques. We have measured deviation in the parameter estimates from the underlying parameter set used to generate the contaminated data sets. However, many of the fits which produced low scores according to this criterion still represent the data quite adequately.
Paul L Rosin