Ellipse fitting by spatial averaging of random ensembles

Abstract

Earlier ellipse fitting methods often consider the algebraic and geometric forms of the ellipse. The work presented here makes use of an ensemble to provide better results. The method proposes a new ellipse parametrization based on the coordinates of both foci, and the distance between them and each point of the ellipse where the Euclidean norm is applied. Besides, a certain number of subsets are uniformly drawn without replacement from the overall training set which allows estimating the center of the distribution robustly by employing the L1 median of each estimated focus. An additional postprocessing stage is proposed to filter out the effect of bad fits. In order to evaluate the performance of this method, four different error measures were considered. Results show that our proposal outperforms all its competitors, especially when higher levels of outliers are presented. Several synthetic and real data tests were developed and confirmed such finding.