三维几何模型的L0去噪算法

A L_0 Denoising Algorithm for 3D Shapes

三维几何模型(例如网格、点云等)的去噪是计算机图形学领域的一个重要研究问题.对于一个无噪声的模型,其局部区域要么是光滑的,要么包含几何特征.为此,提出一种基于L0稀疏优化的几何数据去噪算法.针对网格模型,首先结合顶点位置和顶点法向给出一种L0稀疏约束来衡量几何特征的稀疏性,从而有效地区分出噪声和特征;其次,给出一个改进的求解框架来处理L0优化问题,在大尺度噪声和复杂模型上表现出更好的收敛性.上述方法具有良好的延拓性,能够被扩展至点云模型的去噪.大量的实验结果表明,文中算法能够处理大尺度噪声,鲁棒地恢复出模型的几何特征,获得令人满意的去噪结果.

It is a fundamental problem to denoise 3D shapes(e.g.,triangular meshes and point clouds)in computer graphics.For a noisy mesh,its local region is smooth,or contains geometric features.This paper introduces a shape denoising algorithm based on L0 sparse optimization.First,we present a L0 sparse constraint with respect to position and normal of mesh vertices,which can distinguish features from noises effectively.Second,we deal with L0 optimization problem using an improved optimization scheme,which exhibits better convergence.Furthermore,we extend the above algorithm to denoise point clouds.Massive experiments show that our algorithm can handle high noises,recover geometric features,and obtain satisfactory results.