High Order Mesh Denoising via <inline-formula> <tex-math notation="LaTeX">$\ell_{P}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\ell_{1}$ </tex-math></inline-formula> Minimization

Abstract

Mesh denoising is crucial for improving the quality of meshes required by scanning devices. The main challenge is to maximally preserve geometric features while removing different kinds of noise. In this paper, we propose a novel normal filtering model that incorporates a high order $\ell_{p}$ regularization term and an $\ell_{1}$ fidelity term. Then, vertex positions of the mesh can be reconstructed according to the filtered face normals. Thanking to the proposed $\ell_{p}$ - $\ell_{1}$ normal filtering model, our method has crucial advantage in preserving geometric features and simultaneously is robust against different kinds of noise. Numerically, we develop an efficient algorithm based on iteratively reweighted $\ell_{1}$ minimization and augmented Lagrangian method to solve the problem. We testify effectiveness of our mesh denoising method on synthetic meshes and a broad variety of scanning data produced by the laser scanner and Kinect sensors. We compare our method to state-of-the-art methods and demonstrate the superiority of our method in various cases.

Keywords

• Augmented lagrangian method
• ℓ₁ minimization%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> iteratively reweighted <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ℓ</italic>₁ minimization
• mesh denoising
• 3D geometry processing