基于小波框架的非局部曲面去噪

摘要

This paper proposes a wavelet frame based variational model for surface fairing. We extend nonlocal smoothing techniques for image regularization to surface smoothing or fairing, with surfaces represented by triangular meshes. Our method is able to smooth the surfaces and preserve features due to geometric similarities using a mean curvature based local geometric descriptor. We present an efficient two step approach that first smoothes the mean curvature normal map, and then corrects the surface to fit the smoothed normal field. This leads to a fast implementation of a feature preserving fourth order geometric flow. We demonstrate the efficacy of the model with several surface fairing examples.%提出了一种基于小波框架的非局部曲面去噪方法.该方法首先平滑了曲面法线方向上的平均曲率,然后根据基于小波紧框架的变分模型校正了含噪声曲面.变分模型由正则项和保真项构成.其中,正则项为包含小波框架的L1范数项,保真项为离散曲面的平均曲率和点坐标的最小二乘项之和.最后,进行了数值实验验证了所提出模型和算法的有效性和实用性.