摘要
椭圆拟合在数据处理领域应用广泛,具有重要意义。为此,首先建立了椭圆拟合问题的数学模型,分析了最小二乘拟合与最小一乘拟合的几何意义;然后,基于代数距离,选用椭圆拟合的最小一乘模型,采用正弦余弦算法确定模型参数;最后,将算法应用于无异常值的椭圆拟合以及含有异常值的椭圆拟合问题,进行数值实验。结果表明:最小二乘模型易受异常值的影响,而最小一乘模型对少量的异常值不敏感,稳健性较强。
Elliptical fitting is widely applied in the field of data processing and holds significant importance.Firstly,a mathematical model of ellipse fitting problem was established,and the geometric significance of least square fitting and least absolute deviation fitting was analyzed.Then,based on algebraic distance,the least absolute deviation model of ellipse fitting was selected,whose parameters were determined by sine cosine algorithm.Finally,the algorithm was applied to the ellipse fitting both without outliers and with outliers.Numerical experiments were conducted.The results show that least squares model is easily affected by outliers,while the least absolute deviation model is of strong robustness,not sensitive to a small number of outliers.
作者
雍龙泉
YONG Longquan(Shaanxi Univ.of Technology,Hanzhong 723001,China)
出处
《海军工程大学学报》
北大核心
2025年第5期23-28,共6页
Journal of Naval University of Engineering
基金
国家自然科学基金资助项目(11401357)
陕西省自然科学基础研究计划项目(2024JC-YBMS-014)
陕西理工大学科研项目(SLGNL202409)。
关键词
椭圆拟合
最小二乘
最小一乘
正弦余弦算法
异常值
ellipse fitting
least squares
least absolute deviation
sine cosine algorithm
outliers
