Non‐Local Low‐Rank Normal Filtering for Mesh Denoising

Abstract

AbstractThis paper presents a non‐local low‐rank normal filtering method for mesh denoising. By exploring the geometric similarity between local surface patches on 3D meshes in the form of normal fields, we devise a low‐rank recovery model that filters normal vectors by means of patch groups. In summary, our method has the following key contributions. First, we present the guided normal patch covariance descriptor to analyze the similarity between patches. Second, we pack normal vectors on similar patches into the normal‐field patch‐group (NPG) matrix for rank analysis. Third, we formulate mesh denoising as a low‐rank matrix recovery problem based on the prior that the rank of the NPG matrix is high for raw meshes with noise, but can be significantly reduced for denoised meshes, whose normal vectors across similar patches should be more strongly correlated. Furthermore, we devise an objective function based on an improved truncated γ norm, and derive an optimization procedure using the alternative direction method of multipliers and iteratively re‐weighted least squares techniques. We conducted several experiments to evaluate our method using various 3D models, and compared our results against several state‐of‐the‐art methods. Experimental results show that our method consistently outperforms other methods and better preserves the fine details.