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.