Improved ellipse fitting by considering the eccentricity of data point sets

Ellipse and conic fitting is a highly researched and mature topic in image processing and computer vision. Surprisingly, however, none of the methods have thus far considered eccentricity of data point sets in the fitting of an ellipse. In this paper we show that irrespective of the method used to fit ellipses, the root mean square error (RMSE) of an algorithm increases with the eccentricity of the data point set. We propose a novel way of weighting data points based on their eccentricity to improve the results of ellipse fitting. Data points with higher weights are repeated and data points with insignificant weights are dropped. We empirically demonstrate that the proposed method improves the accuracy of ellipse fitting. Almost all methods of ellipse fitting irrespective of whether they minimize algebraic error or geometric error will benefit by the proposed method of pre-processing the data points.