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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.24328 |
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| _version_ | 1866918469907251200 |
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| author | Wang, Qianlei Chen, Kexun Zhang, Shaolin Gao, Hongli Zhang, Chaoning Qin, Xiaolin |
| author_facet | Wang, Qianlei Chen, Kexun Zhang, Shaolin Gao, Hongli Zhang, Chaoning Qin, Xiaolin |
| contents | Monocular depth estimation (MDE) has witnessed remarkable progress driven by Convolutional Neural Networks and transformer-based architectures. However, these approaches typically treat the problem as a generic image-to-image regression on Euclidean grids, thereby overlooking the intrinsic algebraic and geometric structures induced by perspective projection. To address this limitation, we propose LAGRNet, a novel framework that fundamentally grounds MDE in algebraic geometry by explicitly embedding learnable group, ring, and sheaf structures into the deep learning pipeline. Modeling feature maps as sections of a sheaf over an approximated image manifold, our method first establishes a Group-defined Feature Manifold (GFM) parameterized by a learned algebraic group action to enforce projective equivariance and robustness against view changes. To facilitate algebraically consistent cross-scale interactions, we subsequently introduce a Ring Convolution Layer (RCL) that formulates feature fusion as a graded ring homomorphism. Furthermore, to ensure global topological consistency, a Sheaf-based Module (SM) aggregates local depth cues via Čech nerve on the image topology. Extensive zero-shot evaluations across the KITTI, NYU-Depth V2, and ETH3D benchmarks demonstrate that LAGRNet significantly outperforms state-of-the-art methods in both accuracy and generalization capabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24328 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monocular Depth Estimation via Neural Network with Learnable Algebraic Group and Ring Structures Wang, Qianlei Chen, Kexun Zhang, Shaolin Gao, Hongli Zhang, Chaoning Qin, Xiaolin Computer Vision and Pattern Recognition Monocular depth estimation (MDE) has witnessed remarkable progress driven by Convolutional Neural Networks and transformer-based architectures. However, these approaches typically treat the problem as a generic image-to-image regression on Euclidean grids, thereby overlooking the intrinsic algebraic and geometric structures induced by perspective projection. To address this limitation, we propose LAGRNet, a novel framework that fundamentally grounds MDE in algebraic geometry by explicitly embedding learnable group, ring, and sheaf structures into the deep learning pipeline. Modeling feature maps as sections of a sheaf over an approximated image manifold, our method first establishes a Group-defined Feature Manifold (GFM) parameterized by a learned algebraic group action to enforce projective equivariance and robustness against view changes. To facilitate algebraically consistent cross-scale interactions, we subsequently introduce a Ring Convolution Layer (RCL) that formulates feature fusion as a graded ring homomorphism. Furthermore, to ensure global topological consistency, a Sheaf-based Module (SM) aggregates local depth cues via Čech nerve on the image topology. Extensive zero-shot evaluations across the KITTI, NYU-Depth V2, and ETH3D benchmarks demonstrate that LAGRNet significantly outperforms state-of-the-art methods in both accuracy and generalization capabilities. |
| title | Monocular Depth Estimation via Neural Network with Learnable Algebraic Group and Ring Structures |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2604.24328 |