Fitting Ellipses and General Second-Order Curves

摘要

Many methods exist for fitting ellipses and other second-order curves to sets of points on the plane. Different methods use different measures for the goodness of fit of a given curve to a set of points. The method most frequently used, minimization based on the general quadratic form, has serious deficiencies. Two alternative methods are proposed: the first, based on an error measure divided by its average gradient, uses an eigenvalue solution; the second is based on an error measure divided by individual gradients, and requires hill climbing for its solution. As a corollary, a new method for fitting straight lines to data points on the plane is presented. (Author)