基于双正交非均匀B样条小波的曲线逼近方法

Curve approximation method based on biorthogonal nonuniform B-spline wavelets

针对B样条曲线逼近有序数据点在应用最小二乘法时出现的计算量较大问题,提出一种基于双正交非均匀B样条小波的曲线逼近方法。其基本思想是:先用最小二乘法生成初始B样条逼近曲线,再用细节曲线逼近误差向量,接着将细节曲线叠加于原逼近曲线得到新的B样条曲线,这个过程是迭代的。细节曲线的基函数是双正交非均匀B样条小波。与传统最小二乘法相比,该方法仅需计算新增线性系统,避免重复计算原系统,降低了计算量,提高了运算效率;此外,给出了B样条逼近曲线的一种多分辨率表示形式。

For the large computional quantity caused by least square method in approximating ordered data points using B-spline curves, a curve approximation method based on biorthogonal nonuniform B-spline wavelets is proposed. The data points are approximated using a B-spline curve, which is generated by the least square method. The error vectors are fitted using a detail curve, whose basis functions are biorthogonal nonuniform B-spline wavelets. The new B-spline curve is generated by adding the detail curve onto the original B-spline curve, and the process is iterative. The approach only computes additional linear systems and avoids computing original systems repeatedly. It is more efficient compared with the traditional least square method. In addition, the method provides a kind of multiresolution representation for B-spline approximating curve.