Orthogonal distance fitting of ellipses

Abstract

We are interested in the curve fitting problems in sucha way that the sum of the squares of the orthogonal distances tothe given data points is minimized. Especially, the fitting anellipse to the given data points is a problem that arises in manyapplication areas, e.g. computer graphics, coordinate metrology,etc. In [1] the problem of fitting ellipses was considered andnumerically solved with general purpose methods. In this paper wepresent another new ellipse fitting algorithm. Our algorithm ismainly based on the steepest descent procedure with the view ofensuring the convergence of the corresponding quadratic functionQ(u) to a local minimum. Numerical examples are given.