双变量EMD分析的平面离散曲线光顺方法

Bivariate EMD Analysis Method for Discrete Plane Curve Smoothing

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。

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.