基于EMD的四边域曲面光顺算法

曲面光顺在计算机辅助几何设计（CAGD）中有重要应用，带噪声离散曲面可视为一种非平稳离散几何信号。经验模式分解（EMD）方法是分析非线性、非平稳信号的有效方法。提出了一种空间任意曲线EMD光顺方法和基于2维可分离的EMD曲面光顺方法。针对四边域离散曲面可视为U和V离散曲线构成的网格，且U和V曲线呈现空间任意形态。空间曲线光顺中，首先对数字曲线进行1维参数化，将曲线展开成1维信号；然后采用EMD对展开信号进行多分辨率分解，得到不同尺度下的内蕴模式函数(IMF)，去除高频的IMF，重构信号；最后将重构信号逆映射回3维，得到光顺后的曲线。四边域曲面沿每条U，V线进行EMD光顺处理，得到光顺后曲面。实验结果表明，该方法可有效剔除曲面上的随机噪声，达到良好的曲面光顺效果。

EMD Based Smoothing Algorithm for Four-side Region Surfaces

Surfaces smoothing has been widely used in computer aided geometry design(CAGD). Digital surface with noise can be looked as non-stationary discrete geometry signal. Empirical mode decomposition (EMD) is a new method for non-stationary signal analyzing. In this paper, novel methods for spatial curves smoothing by EMD and four-side region surfaces smoothing with 2D separable EMD are presented.Four-side region digital surface can be represented as a mesh formed by U and V discrete curves. In spatial curve smoothing, we parameterize the digital curve to 1D, and transform the curve to 1D signal firstly. Then decompose the 1D signal into a collection of intrinsic mode functions (IMF) by using EMD. Thirdly, remove the high frequency IMFs and reconstructing the signal. Finally, mapping the reconstructed signal to 3D, and the smoothing curve is obtained. During the four-side region surface smoothing, smooth each U curve of the surface first and then each V curve with the spatial curve smoothing method. Experiments show that noises in the surface can be removed efficiently, and good results are obtained by using the smoothing method.