Evaluating Harker and O’Leary’s distance approximation for ellipse fitting

Harker and O’Leary’s [Harker, M., O’Leary, P., 2006. First order geometric distance (the myth of Sampsonus). British Machine Vision Conf., 87–96] recently proposed a new distance measure for conics. This paper compares its accuracy and effectiveness against several other error of fits (EOFs) for ellipses using: (1) visualisations of the distortions with respect to the Euclidean distance; (2) a set of evaluation measures specifically designed for assessing ellipse EOFs [Rosin, P.L., 1996a. Analysing error of fit functions for ellipses. Pattern Recognition Lett. 17, 1461–1470; Rosin, P.L., 1996b. Assessing error of fit functions for ellipses. Graphical Models Image Process. 58, 494–502]; (3) the accuracy of LMedS ellipse fitting using the various EOFs.