Direct least absolute deviation fitting of ellipses
type: Item
instance of: scholarly article
title: Direct least absolute deviation fitting of ellipses
zbMATH Open document ID: 1459.65025
DOI: 10.1155/2020/1317349
author: Gang Zhou
author: Kai Zhong
author: Zhongwei Li
author: Yusheng Shi
published in: Mathematical Problems in Engineering
publication date: 2020-07-23T00:00:00Z
review text: Summary: 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 \(\ell_1\) algebraic distance is presented. Unlike the conventional \(\ell_2\) 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 \(\ell_1\) optimization problem, according to which the computational burden is significantly reduced. Furthermore, two classes of \(\ell_2\) 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 \(\ell_2\) counterpart and outperforms some of the state-of-the-art algorithms for both Gaussian and non-Gaussian artifacts.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 7224338
describes a project that uses: RecPF
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/1317349
OpenAlex ID: W3041142395
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description: scientific article; zbMATH DE number 7224338