Monocular Depth Estimation via Neural Network with Learnable Algebraic Group and Ring Structures

arXiv:2604.24328v1 Announce Type: new Abstract: 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 Cech 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.

Related

• Attention Is not Everything: Efficient Alternatives for Vision
• Analytical Modeling and Correction of Distance Error in Homography-Based Ground-Plane Mapping
• Location Is All You Need: Continuous Spatiotemporal Neural Representations of Earth Observation Data
• Training-free Spatially Grounded Geometric Shape Encoding (Technical Report)

Source: arXiv cs.CV | 2026-04-28