A Method of Ellipse Fitting Based on Total Least Squares

XIONG Feng-guang; LI Xi; HAN Xie

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A Method of Ellipse Fitting Based on Total Least Squares

更新时间：2026-09-04

- A Method of Ellipse Fitting Based on Total Least Squares
- Vol. 34, Issue 1, Pages: 102-105(2017)
- 作者机构：
  
  中北大学机构计算机与控制工程学院,山西,太原,030051
- 作者简介：
- 基金信息：
- DOI：
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- Published：2017
- 稿件说明：
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熊风光, 李希, 韩燮. 基于整体最小二乘的椭圆拟合方法[J]. 微电子学与计算机, 2017, 34(1): 102-105.

XIONG Feng-guang, LI Xi, HAN Xie. A Method of Ellipse Fitting Based on Total Least Squares[J]. 2017, 34(1): 102-105.
熊风光, 李希, 韩燮. 基于整体最小二乘的椭圆拟合方法[J]. 微电子学与计算机, 2017, 34(1): 102-105. DOI：

XIONG Feng-guang, LI Xi, HAN Xie. A Method of Ellipse Fitting Based on Total Least Squares[J]. 2017, 34(1): 102-105. DOI：

摘要

针对传统椭圆拟合方法中存在的无法剔除噪声点并且参数误差较大的缺陷

提出了一种基于随机采样一致性、约束条件及整体最小二乘的椭圆拟合改进算法.该方法首先根据椭圆的性质

利用随机采样一致性剔除噪声点

再利用基于约束条件的整体最小二乘法

对去噪之后的数据进行椭圆拟合.实验证明

随机采样一致算法能很好地去除噪声

并且跟传统最小二乘法的拟合结果相比较可以看出

改进之后的拟合方法拟合出的椭圆参数精度更高.

Abstract

Considering the fact that the defects of failing to eliminate the noise and large errors existed in traditional ellipse fitting method

the improved method with the foundation of Random Sample Consensus(RANSAC)

constraint condition and total least squares was proposed.The new method first use the Random Sample Consensus to eliminate the noise based on the property of ellipse

then the ellipse is fitted by the total least squares with constraint condition.The experimental results show that the RANSAC algorithm can effectively remove the noise of data.The new method has a higher precision on parameter of ellipse compared with the traditional least squares method.

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references

Wang Jun, Yu Zeyun. Quadratic curve and surface fitting via squared distance minimization[J]. Computer % amp; amp; Graphics, 2011(35): 1035-1050. DOI: 1035

Lmre Evren, Hilton Adrian. Order statistics of RANSAC and their practical application[J]. International Journaln of Computer Vision, 2015, 111(3): 276-297. DOI: 276

杨仕平. 整体最小二乘理论及其在变形监测中的应用研究[D]. 成都: 西南交通大学, 2013.

Kurt O, ArslanO. Geometric Interpretation and precision analysis of algebraic ellipse fitting using least squares method[J]. Acta Geod. Geoph. Hung, 2012, 47(4): 430-440. DOI: 430

Yang Dingli, Bai Qiuchan, Zhang Yulin, et al. Eye location based on hough transform and direct least square ellipse fitting[J]. Journal of Software, 2014, 9(2): 319-323. DOI: 319

Levente Hunyadi·István Vajk. Constrained quadratic errors-in-variables fitting[J]. Visual Computer, 2014, 30: 1347-1358. DOI: 1347

Zhang C, Sun C, Vallotton P, et al. Automatic nuclear bud detection using ellipse fitting, moving sticks or top-hat transformation[J]. Journal of Microscopy, 2013, 252(2): 122-134. DOI: 122

Mitchell D R G, Berg J A Van den. Development of an ellipse fitting method with which to analyse selected area electron diffraction patterns[J]. Ultramicroscopy, 2016, 160: 140-145. DOI: 140

马向南, 李航, 刘丽丽, 等. 最小二乘改进算法及其在椭圆拟合中的应用[J]. 河南科技大学学报(自然科学版), 2014, 35(3): 18-21. DOI: 18

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