Gauss-Seidel最小二乘渐进迭代逼近  

Gauss-Seidel Progressive and Iterative Approximation for Least Squares Fitting

作　　者：Yusuf Fatihu Hamza 蒋旖旎 蔺宏伟[1,2] Yusuf Fatihu Hamza;Jiang Yini;Lin Hongwei(School of Mathematical Sciences,Zhejiang University,Hangzhou 310027;State Key Laboratory of CAD&CG,Zhejiang University,Hangzhou 310058)

机构地区：[1]浙江大学数学科学学院,杭州310027 [2]浙江大学CAD&CG国家重点实验室,杭州310058

出　　处：《计算机辅助设计与图形学学报》2021年第1期1-10,共10页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61872316,61932018)。

摘　　要：几何迭代法,即渐进迭代逼近(progressive-iterativeapproximation,PIA),作为一种有效的数据拟合方法,吸引了众多研究者的关注,并获得广泛的应用.针对经典LSPIA算法收敛速度较慢的问题,提出一种基于Gauss-Seidel迭代方法的快速PIA算法,称为GS-LSPIA.首先,从给定的数据点中选取拟合曲线的控制点;然后,采用累加弦长法参数化给定数据点;最后,GS-LSPIA通过迭代地调整控制点来生成一系列拟合曲线(曲面),并且保证了生成的曲线(曲面)的极限是对于给定数据点的最小二乘拟合结果.在多个曲线曲面拟合上的实验结果表明,为达到相同的拟合精度,GS-LSPIA算法比LSPIA算法需要更少的步骤和更短的运算时间.因此,GS-LSPIA是有效的,而且具有比LSPIA算法更快的收敛速度.Progressive-iterative approximation(PIA)is an efficient method for data fitting that attracts the attention of many researchers and has a wide range of applications.However,the convergence rate of LSPIA is prolonged.In this study,we design a fast PIA format based on the Gauss-Seidel iterative method named Gauss-Seidel progressive and iterative approximation for least squares curve and surface fitting(GS-LSPIA).Firstly,the control points of the fitting curve(surface)are selected from the given data points.Then,the chord length method is used to assign the parameters of the given data points.GS-LSPIA generates a series of fitting curves(surfaces)by refining the control points iteratively,and the limit of the generated curve(surface)is the least square fitting result to the given data points.Several experimental results presented in this paper demonstrate that,to achieve the same accuracy for GS-LSPIA and LSPIA,GS-LSPIA required fewer steps and shorter running time compared with LSPIA.Thus,the proposed GS-LSPIA is efficient and has a faster convergence rate compared with the LSPIA algorithm.

关 键 词：渐进迭代逼近 GAUSS-SEIDEL迭代法 数据拟合 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]