中文摘要：

针对点云数据的几何处理需要建立三角网格以及不能保护尖锐特征的问题，提出了基于局部彼得罗夫伽辽金（Petrov-Galerkin）法的完全无网格点采样曲面滤波方法．该方法不需要重建局部或全局三角形网格，也不需要全局参数化，而是通过在采样点处建立局部切空间，根据各项异性扩散方程在局部切空间中为每一采样点建立局部对称弱形式，然后根据局部对称弱形式组装质量矩阵和刚度矩阵，最后通过迭代方法解稀疏线性系统实现滤波．实验结果表明，基于无网格局部彼得罗夫伽辽金法的滤波方法在滤波的同时可以保护尖锐几何特征，取得的效果可以与传统的有限元方法相媲美．

英文摘要：

This paper presented a meshless approach for point-based surface filtering based on meshless lo- cal Petrov-Galerkin method. For the approach, there is neither need to construct local or global triangular meshes, nor need of global parameterization. By computing local tangent space, local symmetric weak form for every point is constructed in terms of anisotropic diffusion equation. Then PDE-specific mass and stiffness matrices are constructed. The corresponding sparse linear system is solved with an iterative sol- ver. The obtained results show that the approach can smooth noises on point-based surfaces while preser- ving geometric feature. Its efficiency is comparable with that of the traditional finite element method.