基于正则渐进迭代逼近的自适应B样条曲线拟合  

Adaptive B-spline Curve Fitting Based on Regularized Progressive Iterative Approximation

作　　者：刘明增 郭庆杰 王思奇 LIU Mingzeng;GUO Qingjie;WANG Siqi(School of Mathematics and Physics Science,Dalian University of Technology,Panjin Liaoning 124221,China)

机构地区：[1]大连理工大学盘锦校区基础教学部,辽宁盘锦124221

出　　处：《图学学报》2018年第2期287-294,共8页Journal of Graphics

基　　金：国家自然科学基金项目(11601064);中央高校基本科研业务专项资金项目(DUT14RC(3)024;DUT16RC(4)67;DUT17LK09)

摘　　要：基于渐进迭代逼近(PIA)的数据拟合方法以其简单和灵活的特性获得了广泛的关注。为了获得高保真度的拟合曲线,提出了一种基于主导点选取和正则渐进迭代逼近(RPIA)的自适应B样条曲线拟合算法。首先根据数据点的曲率估计选取初始主导点并生成初始PIA曲线。然后,借助于拟合误差和数据点集的曲率分布选取加细的主导点及实现PIA曲线的更新。得益于基于曲率分布的主导点选取,使得拟合曲线在复杂区域分布较多的控制顶点,而在平坦区域则较少。通过正则参数的引入构造了一种RPIA格式,提升了渐进迭代控制的灵活性。最后,数值算例表明相比于传统最小二乘曲线拟合该算法在使用较少数量的控制顶点时可实现较高的拟合精度。The use of progressive iterative approximation(PIA)to fit data points has received a deal of attention benefitting from its simplicity and flexibility.To obtain a fitting curve satisfying the shape high fidelity,we present an adaptive B-spline curve fitting algorithm based on regularized progressive iterative approximation(RPIA)and the selection of dominant points.Firstly,the initial dominant points are selected from the given points in terms of curvature estimates and an initial progressive iterative approximation curve is constructed.Then the fitting curve based on RPIA is updated by means of the fitting error and the selection of refinement dominant points according to the curvature distribution of given points.The fitting curve possesses fewer control points at flat regions but more at complex regions.By the use of a regular parameter,progressive iterative approximation is generalized and the flexibility of PIA is promoted.Finally,numerical examples are provided to demonstrate that compared with the conventional least square approaches the proposed method can achieve a higher fitting precision with far fewer control points.

关 键 词：B样条曲线拟合 正则渐进迭代逼近 自适应加细 曲率估计 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]