{"title":"An Approximate Maximum Likelihood Linear Estimator of Circle Parameters","authors":"Y.T. Chan , S.M. Thomas","doi":"10.1006/gmip.1997.0424","DOIUrl":null,"url":null,"abstract":"<div><p>The problem of estimating the center and radius of a circle from a given set of noisy coordinate measurements has many applications. Even though the estimation process is inherently nonlinear, it is possible to obtain linear estimators, which are attractive because of their simplicity. This paper presents an approximate maximum likelihood estimator of circle parameters. It is linear. Simulation results showed that under conditions of small arc length and high noise, which occur often in practice, the new estimator outperforms the linear estimator of S. Thomas and Y. T. Chan (<em>Comput. Vision Graph. Image Process.</em>45 (1989), 362–370).</p></div>","PeriodicalId":100591,"journal":{"name":"Graphical Models and Image Processing","volume":"59 3","pages":"Pages 173-178"},"PeriodicalIF":0.0000,"publicationDate":"1997-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/gmip.1997.0424","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S107731699790424X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
The problem of estimating the center and radius of a circle from a given set of noisy coordinate measurements has many applications. Even though the estimation process is inherently nonlinear, it is possible to obtain linear estimators, which are attractive because of their simplicity. This paper presents an approximate maximum likelihood estimator of circle parameters. It is linear. Simulation results showed that under conditions of small arc length and high noise, which occur often in practice, the new estimator outperforms the linear estimator of S. Thomas and Y. T. Chan (Comput. Vision Graph. Image Process.45 (1989), 362–370).
从一组给定的噪声坐标测量中估计圆的圆心和半径的问题有许多应用。尽管估计过程本质上是非线性的，但也有可能得到线性估计量，线性估计量因其简单而具有吸引力。本文给出了圆参数的近似极大似然估计。它是线性的。仿真结果表明，在实际应用中经常出现的小弧长和高噪声条件下，该估计器优于S. Thomas和Y. T. Chan (Comput)的线性估计器。远景图。图像处理。45(1989)，362-370)。
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