Advanced Ellipse Fitting Algorithm Based on ADMM and Hybrid BFGS Method

Abstract

Quick and accurate ellipse detection is essential for computer vision, automatic manufacturing, and other fields. In order to obtain more accurate ellipse parameters, the least-squares support vector regression is employed to establish the objective function and further convert the ellipse fitting problem into an optimization problem. This article proposes a hybrid BFGS algorithm integrated with an alternating direction method of multipliers (ADMM) to reduce the number of iterations and improve the algorithm convergence speed. The effectiveness and accuracy of the proposed algorithm are then verified in a series of numerical simulations by using the actual data of crystal images taken by charge-coupled device (CCD) cameras within the Czochralski silicon growth. Finally, the effectiveness is verified by comparing Hough transform (HT), maximum correntropy criterion (MCC), sparsity-based method (SBM), and other methods.