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

arXiv: https://arxiv.org/abs/2604.24328 · HTML: https://mlsanity.com/paper/2604.24328/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 25 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 22 of 22)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Unsupervised Learning of Depth and Ego-Motion from Video](https://mlsanity.com/paper/1704.07813/) (2017)
- [AdaBins: Depth Estimation using Adaptive Bins](https://mlsanity.com/paper/2011.14141/) (2020)
- [Depth Pro: Sharp Monocular Metric Depth in Less Than a Second](https://mlsanity.com/paper/2410.02073/) (2024)
- [Unsupervised CNN for Single View Depth Estimation: Geometry to the Rescue](https://mlsanity.com/paper/1603.04992/) (2016)
- [Omnidata: A Scalable Pipeline for Making Multi-Task Mid-Level Vision Datasets from 3D Scans](https://mlsanity.com/paper/2110.04994/) (2021)
- [MiDaS v3.1 -- A Model Zoo for Robust Monocular Relative Depth Estimation](https://mlsanity.com/paper/2307.14460/) (2023)
- [Learning Depth from Single Monocular Images Using Deep Convolutional Neural Fields](https://mlsanity.com/paper/1502.07411/) (2015)
- [BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2204.00987/) (2022)
- [Marigold: Affordable Adaptation of Diffusion-Based Image Generators for Image Analysis](https://mlsanity.com/paper/2505.09358/) (2025)
- [What Matters When Repurposing Diffusion Models for General Dense Perception Tasks?](https://mlsanity.com/paper/2403.06090/) (2024)
- [DiverseDepth: Affine-invariant Depth Prediction Using Diverse Data](https://mlsanity.com/paper/2002.00569/) (2020)
- [Hierarchical Normalization for Robust Monocular Depth Estimation](https://mlsanity.com/paper/2210.09670/) (2022)
- [Bidirectional Attention Network for Monocular Depth Estimation](https://mlsanity.com/paper/2009.00743/) (2020)
- [Attention meets Geometry: Geometry Guided Spatial-Temporal Attention for Consistent Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/2110.08192/) (2021)
- [Deep Digging into the Generalization of Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/2205.11083/) (2022)
- [GANVO: Unsupervised Deep Monocular Visual Odometry and Depth Estimation with Generative Adversarial Networks](https://mlsanity.com/paper/1809.05786/) (2018)
- [Distill Any Depth: Distillation Creates a Stronger Monocular Depth Estimator](https://mlsanity.com/paper/2502.19204/) (2025)

## Abstract (arXiv)

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 vCech 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.