Point clouds smoothing and enhancing based on empirical mode decomposition

In applications of computer aided design and reverse engineering, for the data of point clouds without any topology information, we propose an effective smoothing and enhancing algorithm for point clouds based on empirical mode decomposition (EMD). First, the input signal of EMD is computed via the inner product of Laplacian vector and point's normal. For the input signal, the extreme points are extracted, and then the upper and lower envelopes are calculated by considering the extreme points as interpolating points. Second, in order to achieve feature preserving EMD signal decomposition, the sharp feature points are detected and considered as constrains in envelope computing. In this way, the over smoothing effect of traditional EMD algorithm can be effectively overcome. Finally, we can obtain the intrinsic mode function (IMF) and the residue by iteratively subtracting the mean of upper and lower envelops from the input signal in each iteration. Based on the multi-scale decomposition, different filter operators are designed to achieve point clouds smoothing and enhancing. Experimental results show that satisfactory smoothing and enhancing results of point clouds are obtained by the proposed novel EMD-based algorithm and EMD can be effectively extended to point clouds, which expands the application range of EMD in three-dimensional geometry processing.