双变量EMD分析的平面离散曲线光顺方法①-计算机系统应用.PDF

计 算 机 系 统 应 用 2011 年 第 20 卷 第 10 期 双变量EMD 分析的平面离散曲线光顺方法① 谭小俊，杜轶诚，秦绪佳 (浙江工业大学 计算机科学与技术系，杭州 310032) 摘 要：曲线的光顺在计算机辅助设计及其相关制造业中都有着重要作用。通过把平面离散曲线当作非平稳信 号来处理，提出了一种双变量经验模式分解(EMD)的平面数字曲线光顺方法。方法首先将平面数字曲线的各个变 量分离，参数化为两个一维信号；然后运用一维 EMD 方法对一维化的信号进行滤波处理，去除高频噪声；最后 对两个处理好的信号进行合成，得到光顺后曲线。采用端点对称延拓的方法消除分解过程中边界效应，从而得 到光顺的平面数字曲线。实验结果表明，该方法具有对二维双变量平面曲线有较好的平滑效果。 关键词：平面离散曲线；经验模式分解(EMD) ；光顺；双变量 Bivariate EMD Analysis Method for Discrete Plane Curve Smoothing TAN Xiao-Jun, DU Yi-Cheng, QIN Xu-Jia (School of Electronic Science and Technology, Zhejiang University of Technology, Hangzhou 310032, China) Abstract: Curve smoothing plays an important role in both Computer Aided Geometric Design and related manufacturing industries. In this paper, considering discrete digital curve is looked as non-stationary signal, a novel method of filtering discrete digital plane curves based on Bivariate Empirical Mode Decomposition (EMD) is presented. Firstly, separate the variables of the discrete plane curve, and parameterize them into two one-dimensional signals. Secondly, use the method of EMD to filter and remove the high-frequency noise of each one-dimensional signal. Finally, obtain the smoothing curve by combining these two processed one-dimensional signals. Meanwhile, in order to eliminate the boundary effect caused of the process of EMD, the method of symmetric extension of endpoints is proposed. The results of experiment show that the new method is effective while smoothing the bivariate discrete plane curve. Key words: discrete plane curve; empirical mode decomposition(EMD); smoothing; bivariate 1 引言 光顺法以每次修改型值点数量的不同可分为局部光顺 在计算机辅助几何设计（CAGD ）中，曲线曲面 法和整体光顺法。局部光顺法即为每次修改少量型值