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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11876 |
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| _version_ | 1866910792159330304 |
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| author | Leng, Jiaqi Ju, Yakun Duan, Yuanxu Zhang, Jiangnan Lv, Qingxuan Wu, Zuxuan Fan, Hao |
| author_facet | Leng, Jiaqi Ju, Yakun Duan, Yuanxu Zhang, Jiangnan Lv, Qingxuan Wu, Zuxuan Fan, Hao |
| contents | Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients. Traditional methods encounter significant challenges in achieving high accuracy and handling high-resolution inputs, particularly facing the complex nature of discontinuities and the inefficiencies associated with large-scale linear solvers. Although recent advances in deep learning, such as photometric stereo, have enhanced normal estimation accuracy, they do not fully address the intricacies of gradient-based surface reconstruction. To overcome these limitations, we propose a Fourier neural operator-based Numerical Integration Network (FNIN) within a two-stage optimization framework. In the first stage, our approach employs an iterative architecture for numerical integration, harnessing an advanced Fourier neural operator to approximate the solution operator in Fourier space. Additionally, a self-learning attention mechanism is incorporated to effectively detect and handle discontinuities. In the second stage, we refine the surface reconstruction by formulating a weighted least squares problem, addressing the identified discontinuities rationally. Extensive experiments demonstrate that our method achieves significant improvements in both accuracy and efficiency compared to current state-of-the-art solvers. This is particularly evident in handling high-resolution images with complex data, achieving errors of fewer than 0.1 mm on tested objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FNIN: A Fourier Neural Operator-based Numerical Integration Network for Surface-form-gradients Leng, Jiaqi Ju, Yakun Duan, Yuanxu Zhang, Jiangnan Lv, Qingxuan Wu, Zuxuan Fan, Hao Computer Vision and Pattern Recognition Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients. Traditional methods encounter significant challenges in achieving high accuracy and handling high-resolution inputs, particularly facing the complex nature of discontinuities and the inefficiencies associated with large-scale linear solvers. Although recent advances in deep learning, such as photometric stereo, have enhanced normal estimation accuracy, they do not fully address the intricacies of gradient-based surface reconstruction. To overcome these limitations, we propose a Fourier neural operator-based Numerical Integration Network (FNIN) within a two-stage optimization framework. In the first stage, our approach employs an iterative architecture for numerical integration, harnessing an advanced Fourier neural operator to approximate the solution operator in Fourier space. Additionally, a self-learning attention mechanism is incorporated to effectively detect and handle discontinuities. In the second stage, we refine the surface reconstruction by formulating a weighted least squares problem, addressing the identified discontinuities rationally. Extensive experiments demonstrate that our method achieves significant improvements in both accuracy and efficiency compared to current state-of-the-art solvers. This is particularly evident in handling high-resolution images with complex data, achieving errors of fewer than 0.1 mm on tested objects. |
| title | FNIN: A Fourier Neural Operator-based Numerical Integration Network for Surface-form-gradients |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2501.11876 |