Mesh smoothing method based on local wave analysis

Abstract

As the mesh models usually contain noise data, it is necessary to eliminate the noises and smooth the mesh. But existed methods always lose geometric features during the smoothing process. Hence, the noise is considered as a kind of random signal with high frequency, and then the mesh model smoothing is operated with signal processing theory. Local wave analysis is used to deal with geometric signal, and then a novel mesh smoothing method based on the local wave is proposed. The proposed method includes following steps: Firstly, analyze the principle of local wave decomposition for 1D signal, and expand it to 2D signal and 3D spherical surface signal processing; Secondly, map the mesh to the spherical surface with parameterization, resample the spherical mesh and decompose the spherical signals by local wave analysis; Thirdly, propose the coordinate smoothing and radical radius smoothing methods, the former filters the mesh points’ coordinates by local wave, and the latter filters the radical radius from their geometric center to mesh points by local wave; Finally, remove the high-frequency component of spherical signal, and obtain the smooth mesh model with inversely mapping from the spherical signal. Several mesh models with Gaussian noise are processed by local wave based method and other compared methods. The results show that local wave based method can obtain better smoothing performance, and reserve more original geometric features at the same time.