Direct Least Absolute Deviation Fitting of Ellipses. (11th July 2020)

• Record Type: Journal Article
• Authors: Zhou, Gang; Zhong, Kai; Li, Zhongwei; Shi, Yusheng
• Other Names: Schuster Thomas Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-07-11
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/1317349
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Scattered data from edge detection usually involve undesired noise which seriously affects the accuracy of ellipse fitting. In order to alleviate this kind of degradation, a method of direct least absolute deviation ellipse fitting by minimizing the ℓ 1 algebraic distance is presented. Unlike the conventional ℓ 2 estimators which tend to produce a satisfied performance on ideal and Gaussian noise data, while do a poor job for non-Gaussian outliers, the proposed method shows very competitive results for non-Gaussian noise. In addition, an efficient numerical algorithm based on the split Bregman iteration is developed to solve the resulting ℓ 1 optimization problem, according to which the computational burden is significantly reduced. Furthermore, two classes of ℓ 2 solutions are introduced as the initial guess, and the selection of algorithm parameters is studied in detail; thus, it does not suffer from the convergence issues due to poor initialization which is a common drawback existing in iterative-based approaches. Numerical experiments reveal that the proposed method is superior to its ℓ 2 counterpart and outperforms some of the state-of-the-art algorithms for both Gaussian and non-Gaussian artifacts.