三次样条插值在变径内腔重建中的应用  

Application of Cubic Spline Interpolation to Variable-Diameter Lumen Surface Reconstruction

作　　者：王会峰[1] 刘上乾[1] 汪大宝[1] 卢泉[1] 

机构地区：[1]西安电子科技大学技术物理学院,陕西西安710071

出　　处：《中北大学学报（自然科学版）》2010年第1期65-70,共6页Journal of North University of China(Natural Science Edition)

摘　　要：结合变径内腔容积参数检测的特殊要求,在分析了内径-进深容积检测方法的基础上,提出了一种基于三次样条的内腔直径参数插值和基于插值后函数的内腔三维内表面高精度重建方法.该方法是在对内腔容积内径和进深间接测量的基础上,对测量中测头沿轴间歇移动时各进深直径值应用三次样条函数进行数值插值,通过建立M关系三对角方程组,并用"追赶法"实现插值函数稳定收敛求解,从而获得内径函数曲线的光滑高精度表达式,然后以插值后的内径函数曲线为母线进行内腔内表面的三维空间容积重建.实验和仿真结果证明:该方法能够克服直接累加和传统的分段低次线性插值方法由于函数本身的特性,在各次间歇测量点处产生的衔接不光滑性,满足了变径内腔内表面容积重建中的视觉需求;同时在不增加计算量的前提下使得插值后容积的测量精度得到了提高,且满足2‰测量误差的要求.Considering the special requirement of variable-diameter lumen volume measurement, and after analyzing the diameter-length volume detection method, we proposed a kind of high precision reconstruction method for variable-diameter 3D lumen surface, based on cubic spline inner radius parameter interpolation and the function after interpolation. In this method, a group of inner radius in various depths are measured and interpolated through a high precision cubic spline function. M-relation top-triangle diagonal equations are defined and solved in a stable and convergence way with a method named ＂pursue＂. Thus the method can obtain a precise inner radius function curve, and then the variable-diameter lumen volume 3D shape can be reconstructed with the interpolated inner radius curve. Test and simulation shows that the method can eliminate the unsmooth shortcoming caused by subsection low order interpolation with its inherent feature, and can meet the vision effect in inner capacity reconstruction. Further more the volume measurement error are reduced after interpolated by cubic spline without increasing any calculation, and the measurement relative error could reach 2‰ required by the system.

关 键 词：三次样条 变径内腔 M关系式 表面重建 光滑性 

分 类 号：TH741[机械工程—光学工程]