EMD Based Smoothing Algorithm for Four-side Region Surfaces
基于EMD的四边域曲面光顺算法

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.