表面测量中高斯滤波器的B样条函数实现方法

Implementation Approach for Gaussian Filter in Surface Measurement Applying B-spline Function

提出一种新的高斯滤波器B样条函数实现方法。在B样条函数理论基础上,通过对变分原则引入约束条件的方法,并结合小尺度高斯滤波器级联的特性,得出了高斯滤波器的逼近滤波器。其与高斯滤波器的最大幅度偏差小于1%,并且也具有零相移的特性。在相应的滤波算法中,包括了一级零相移滤波和一级加权滤波,只进行二次循环,算法结构简单,计算效率高。对实际表面测量数据进行应用试验,能够满足高斯滤波器实现方法高精度、高效率的要求。

A new implementation approach for Gaussian filter is presented. Based on the theory of B-spline function, the variational principle with constraint condition and the cascade characteristic of small-scale Gaussian filter, the approximation filter of Gaussian filter is obtained, and its maximum amplitude deviation from Gaussian filter is less than 1%, and it also has the zero-phase-shift characteristic. The algorithm for the approximation filter consists of the zero-phase-shift filtering and the weighing filtering, and only carries out two times of cycle. The algorithm teatures simple structure and high calculation efficiency. The approximation filter is also efficient and accurate for the implementation of Gaussian filter in the application of surface roughness measurement.