A LFramework with Anisotropic Sparsity and Fairness for 3D Denoising

Jinfeng Qian, Ling Li, Xin Si, Yong Zhao, Jingliang Zhang

Abstract: Triangular mesh is a very popular representation for 3D objects, which is mainly acquired via laser scanning. Mesh denoising is very important for subsequent 3D geometry processing and understanding. It is challenging to distinguish features from noises because both of them belong to high frequency part. Although data-driven methods are popular, their performance relies on the number of mesh pairs for training, which are very tedious to collect in practice. Inspired by sparse signal recovery theory, this paper develops a novel L0 framework to deal with mesh denoising problem. First, an anisotropic L0 constraint is developed to reflect the sparsity of shape features, thus achieving noise removal and feature preservation effectively. The anisotropy is expressed by a weighting scheme which is calculated via region covariances. And then, we derive a new fairness constraint from the thin-plate energy to improve the quality of local surface significantly. Numerous experimental results have demonstrated that our approach successfully eliminates high noises while preserving shape features and outperforms existing state-of-the-art methods.