基于高斯逼近的广义B样条平滑滤波快速算法  

The Fast Algorithm of Generalized B- spline Smooth Filter Based on the Gaussian Filter Approximation

作　　者：申丁[1] 高诚辉[1,2] 任志英[1,2] 

机构地区：[1]福州大学机械工程及自动化学院,福建福州350108 [2]福州大学摩擦学研究所,福建福州350002

出　　处：《机械设计与制造工程》2014年第4期6-10,共5页Machine Design and Manufacturing Engineering

基　　金：国家自然科学基金资助项目(51175085);福建省教育厅A类资助项目(JA13059);福州大学科技发展基金资助项目(600907)

摘　　要：将添加了速度项s(xi)xi的平滑变分公式引入广义B样条滤波器,通过速度项αs(xi)αxi来增加数字滤波器传输特性对参数t1,t2的敏感性,推导出一个小尺度且能够快速逼近高斯滤波的平滑数字滤波器,并且讨论在不同截止角频率ωc下文中算法与标准高斯滤波器的逼近程度。最后对一个长度为19 000的实测轮廓数据进行滤波,实验结果表明:该滤波器一定程度上抑制了传统高斯滤波边界畸变的缺陷,且响应时间短,整个过程耗时1.6ms,仅为传统高斯滤波的1/40,为工程表面滤波提供了一种新方法。It introduces the smooth variational formula with speed item э s（xi）э xi into the Generalized B-spline fil-ter, so as to increase the sensitivity of the parameter of generalized B -spline t1 ,t2 to the transmission characteris-tic of the final digital filter , and deduce a fast smooth digital filter which is the approximation to the Gaussian fil-ter with small scale .It discusses the amplitude -deviation between the introduced algorithm and standard Gauss-ian filter in different cut -off angle frequencyωc .Appling the smooth digital filter to a measured profile contained 19000 data points , it obtains the result .The data show that the filter restrains the boundary distortion to some ex-tent which always happens in traditional Gaussian filtering .The whole procedure is merely 1.6ms, which means it has a fast response time .The conclusion provides a new method for the practical engineering surface filtering .

关 键 词：广义B样条 高斯滤波 边界畸变 

分 类 号：TH161.14[机械工程—机械制造及自动化]