Euclidean Distance Fit of Ellipses with a Genetic Algorithm

Abstract

We use a genetic algorithm to solve the problem, widely treated in the specialized literature, of fitting an ellipse to a set of given points. Our proposal uses as the objective function the minimization of the sum of orthogonal Euclidean distances from the given points to the curve; this is a non-linear problem which is usually solved using the minimization of the quadratic distances that allows to use the gradient and the numerical methods based on it, such as Gauss-Newton. The novelty of the proposed approach is that as we are using a GA, our algorithm does not need initialization, and uses the Euclidean distance as the objective function. We will also show that in our experiments, we are able to obtain better results than those previously reported. Additionally our solutions have a very low variance, which indicates the robustness of our approach.