A novel anisotropic second order regularization for mesh denoising

• DOI: 10.1016/j.cagd.2019.04.013
• Publication Date: 2019-04-05T16:25:15Z
• Authors: Zheng Liu; Saishang Zhong; Zhong Xie; Weina Wang
• Keywords: Regularization; Laplacian smoothing; Augmented Lagrangian method

Abstract Mesh denoising is a fundamental, yet not well-solved problem in geometry processing. The main challenge is to remove noise while preserving geometric features and preventing unnatural effects, such as blurring of sharp features and staircase effects in smoothly curved regions. State-of-the-art mesh denoising methods still struggle with this issue. In the paper, we first propose a novel anisotropic second order regularization method to restore face normals of the noisy mesh, and then reconstruct vertex positions of the mesh according to the filtered face normals. The proposed anisotropic second order regularization can maximally recover the underlying surface from the noisy mesh without introducing the unnatural effects. Numerically, an efficient algorithm based on variable splitting and augmented Lagrangian method is proposed to solve the problem. Extensive experiments on a variety of meshes demonstrate that our mesh denoising method outperforms all the compared state-of-the-art methods visually and quantitatively.