Direct ellipse fitting by minimizing the L0 algebraic distance

Abstract

Given a set of 2D scattering points from an edge detection operator, the aim of ellipse fitting is to construct an elliptic equation that best fit the observations. For the data collected often contain noisy, uncertainty, and incompleteness which constitutes a considerable challenge for all algorithms. To address this issue, a method of direct ellipse fitting by minimizing the L0 algebraic distance is presented. Unlike its L2 counterparts that assumed the fitting error follows a Gaussian distribution, our method tried to model the outliers using the L0 norm of the algebraic distance between the ideal elliptic equation and its fitting data. In addition, an efficient numerical algorithm based on alternating optimization strategy with half-quadratic splitting is developed to solve the resulting L0 minimization problem and a detailed research of the selection of algorithm parameters is carried out benefit from which it does not suffer from the convergence issues due to poor initialization, which is an open question encountered in all iterative based approaches. Numerical experiments suggest that the proposed method achieves a very high precision and reliability to various bias especially for Non-Gaussian artifacts as well as easy to implement.