ElliFit: An unconstrained, non-iterative, least squares based geometric Ellipse Fitting method

Abstract

A novel ellipse fitting method which is selective for digital and noisy elliptic curves is proposed in this paper. The method aims at fitting an ellipse only when the data points are highly likely belong to an ellipse. This is achieved using the geometric distances of the ellipse from the data points. The proposed method models the non-linear problem of ellipse fitting as a combination of two operators, with one being linear, numerically stable, and easily invertible, while the other being non-linear but unique and easily invertible operator. As a consequence, the proposed ellipse fitting method has several salient properties like unconstrained, stable, non-iterative, and computationally inexpensive. The efficacy of the method is compared against six contemporary and recent algorithms based on the least squares formulation using five experiments of diverse practical challenges, like digitization, incomplete ellipses, and Gaussian noise (up to 30%). Three of the experiments comprise of a total of 44,400 ellipses (positive test data) while the other two are tested on 320,000 non-elliptic conics (negative test data). The results show that the proposed method is quite selective to elliptic shapes only and provides accurate fitting results, indicating potential application in medical, robotics, object detection, and other image processing industrial applications.