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.
Highlights
In recent years, due to the rapid development of digital scanning devices (e.g., Microsoft Kinect, Xtion Pro, Google Project Tango, and Intel RealSense), more and more triangulated meshes can be acquired from the real world
This paper tries to overcome these limitations by using a novel normal filtering model including only two terms: a high order p regularization term for preserving geometric features without introducing unnatural artifacts, and an 1 fidelity term for encouraging the solution be less dependent on the exact value of outliers and noise
We propose an efficient minimization method based on iterative reweighted 1 minimization (IRL1) and augmented Lagrangian method (ALM) to solve the problem
Summary
Due to the rapid development of digital scanning devices (e.g., Microsoft Kinect, Xtion Pro, Google Project Tango, and Intel RealSense), more and more triangulated meshes can be acquired from the real world. Zheng et al [14] presented a global normal filtering model using bilateral weight function Their method works well for preserving fine details and smooth regions, but cannot recover sharp features well. Zhong et al [29] proposed a 1-based normal filtering model with three sparsity terms, which can recover both sharp features and smooth regions well This paper tries to overcome these limitations by using a novel normal filtering model including only two terms: a high order p regularization term for preserving geometric features (sharp features, fine details, and smoothly curved regions) without introducing unnatural artifacts, and an 1 fidelity term for encouraging the solution be less dependent on the exact value of outliers and noise. We introduce the 1 fidelity in mesh denoising to help the solution less dependent on the exact value of outliers and noise
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