# Deep Ordinal Regression Network for Monocular Depth Estimation

arXiv: https://arxiv.org/abs/1806.02446 · HTML: https://mlsanity.com/paper/1806.02446/

## Key facts

- Cited by 723 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2018.

## Built on by (most cited first, 30 of 723)

- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depth](https://mlsanity.com/paper/2302.12288/) (2023)
- [BEVDepth: Acquisition of Reliable Depth for Multi-view 3D Object Detection](https://mlsanity.com/paper/2206.10092/) (2022)
- [Depth Pro: Sharp Monocular Metric Depth in Less Than a Second](https://mlsanity.com/paper/2410.02073/) (2024)
- [UniDepth: Universal Monocular Metric Depth Estimation](https://mlsanity.com/paper/2403.18913/) (2024)
- [Categorical Depth Distribution Network for Monocular 3D Object Detection](https://mlsanity.com/paper/2103.01100/) (2021)
- [Repurposing Diffusion-Based Image Generators for Monocular Depth Estimation](https://mlsanity.com/paper/2312.02145/) (2023)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [Cross-view Transformers for real-time Map-view Semantic Segmentation](https://mlsanity.com/paper/2205.02833/) (2022)
- [MoGe-2: Accurate Monocular Geometry with Metric Scale and Sharp Details](https://mlsanity.com/paper/2507.02546/) (2025)
- [Is Pseudo-Lidar needed for Monocular 3D Object detection?](https://mlsanity.com/paper/2108.06417/) (2021)
- [NoPe-NeRF: Optimising Neural Radiance Field with No Pose Prior](https://mlsanity.com/paper/2212.07388/) (2022)
- [Video Depth Anything: Consistent Depth Estimation for Super-Long Videos](https://mlsanity.com/paper/2501.12375/) (2025)
- [DepthCrafter: Generating Consistent Long Depth Sequences for Open-world Videos](https://mlsanity.com/paper/2409.02095/) (2024)
- [Probabilistic and Geometric Depth: Detecting Objects in Perspective](https://mlsanity.com/paper/2107.14160/) (2021)
- [The Temporal Opportunist: Self-Supervised Multi-Frame Monocular Depth](https://mlsanity.com/paper/2104.14540/) (2021)
- [Depth-Aware Generative Adversarial Network for Talking Head Video Generation](https://mlsanity.com/paper/2203.06605/) (2022)
- [Time Will Tell: New Outlooks and A Baseline for Temporal Multi-View 3D Object Detection](https://mlsanity.com/paper/2210.02443/) (2022)
- [UniDepthV2: Universal Monocular Metric Depth Estimation Made Simpler](https://mlsanity.com/paper/2502.20110/) (2025)
- [BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2204.00987/) (2022)
- [SAVi++: Towards End-to-End Object-Centric Learning from Real-World Videos](https://mlsanity.com/paper/2206.07764/) (2022)
- [Lotus: Diffusion-based Visual Foundation Model for High-quality Dense Prediction](https://mlsanity.com/paper/2409.18124/) (2024)
- [Omni3D: A Large Benchmark and Model for 3D Object Detection in the Wild](https://mlsanity.com/paper/2207.10660/) (2022)
- [NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](https://mlsanity.com/paper/2203.01502/) (2022)
- [Panoptic NeRF: 3D-to-2D Label Transfer for Panoptic Urban Scene Segmentation](https://mlsanity.com/paper/2203.15224/) (2022)
- [SpatialBot: Precise Spatial Understanding with Vision Language Models](https://mlsanity.com/paper/2406.13642/) (2024)
- [DDP: Diffusion Model for Dense Visual Prediction](https://mlsanity.com/paper/2303.17559/) (2023)
- [Delving into Localization Errors for Monocular 3D Object Detection](https://mlsanity.com/paper/2103.16237/) (2021)

## Abstract (arXiv)

Monocular depth estimation, which plays a crucial role in understanding 3D scene geometry, is an ill-posed problem. Recent methods have gained significant improvement by exploring image-level information and hierarchical features from deep convolutional neural networks (DCNNs). These methods model depth estimation as a regression problem and train the regression networks by minimizing mean squared error, which suffers from slow convergence and unsatisfactory local solutions. Besides, existing depth estimation networks employ repeated spatial pooling operations, resulting in undesirable low-resolution feature maps. To obtain high-resolution depth maps, skip-connections or multi-layer deconvolution networks are required, which complicates network training and consumes much more computations. To eliminate or at least largely reduce these problems, we introduce a spacing-increasing discretization (SID) strategy to discretize depth and recast depth network learning as an ordinal regression problem. By training the network using an ordinary regression loss, our method achieves much higher accuracy and ddfaster convergence in synch. Furthermore, we adopt a multi-scale network structure which avoids unnecessary spatial pooling and captures multi-scale information in parallel. The method described in this paper achieves state-of-the-art results on four challenging benchmarks, i.e., KITTI [17], ScanNet [9], Make3D [50], and NYU Depth v2 [42], and win the 1st prize in Robust Vision Challenge 2018. Code has been made available at: https://github.com/hufu6371/DORN.