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
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 <inline-formu...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8824104/ |
| _version_ | 1798001964511920128 |
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| author | Zheng Liu Mingqiang Guo Zhong Xie Jinqin Liu Bohong Zeng |
| author_facet | Zheng Liu Mingqiang Guo Zhong Xie Jinqin Liu Bohong Zeng |
| author_sort | Zheng Liu |
| collection | DOAJ |
| description | 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 <inline-formula> <tex-math notation="LaTeX">$\ell_{p}$ </tex-math></inline-formula> regularization term and an <inline-formula> <tex-math notation="LaTeX">$\ell_{1}$ </tex-math></inline-formula> fidelity term. Then, vertex positions of the mesh can be reconstructed according to the filtered face normals. Thanking to the proposed <inline-formula> <tex-math notation="LaTeX">$\ell_{p}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\ell_{1}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$\ell_{1}$ </tex-math></inline-formula> 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. |
| first_indexed | 2024-04-11T11:44:35Z |
| format | Article |
| id | doaj.art-8be56d687e044e7eb59223aa595ca47e |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T11:44:35Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-8be56d687e044e7eb59223aa595ca47e2022-12-22T04:25:42ZengIEEEIEEE Access2169-35362019-01-01714698914700010.1109/ACCESS.2019.29393628824104High 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> MinimizationZheng Liu0https://orcid.org/0000-0001-6713-6680Mingqiang Guo1Zhong Xie2Jinqin Liu3Bohong Zeng4School of Geography and Information Engineering, China University of Geosciences, Wuhan, ChinaSchool of Geography and Information Engineering, China University of Geosciences, Wuhan, ChinaSchool of Geography and Information Engineering, China University of Geosciences, Wuhan, ChinaSchool of Geography and Information Engineering, China University of Geosciences, Wuhan, ChinaSchool of Geography and Information Engineering, China University of Geosciences, Wuhan, ChinaMesh 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 <inline-formula> <tex-math notation="LaTeX">$\ell_{p}$ </tex-math></inline-formula> regularization term and an <inline-formula> <tex-math notation="LaTeX">$\ell_{1}$ </tex-math></inline-formula> fidelity term. Then, vertex positions of the mesh can be reconstructed according to the filtered face normals. Thanking to the proposed <inline-formula> <tex-math notation="LaTeX">$\ell_{p}$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\ell_{1}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$\ell_{1}$ </tex-math></inline-formula> 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.https://ieeexplore.ieee.org/document/8824104/Augmented lagrangian methoditeratively 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 minimizationmesh denoising3D geometry processing |
| spellingShingle | Zheng Liu Mingqiang Guo Zhong Xie Jinqin Liu Bohong Zeng 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 IEEE Access Augmented lagrangian method 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 |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | Augmented lagrangian method 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 |
| url | https://ieeexplore.ieee.org/document/8824104/ |
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