# NDDepth: Normal-Distance Assisted Monocular Depth Estimation

arXiv: https://arxiv.org/abs/2309.10592 · HTML: https://mlsanity.com/paper/2309.10592/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 52 references that are in the map.
- First posted on arXiv 19 Sep 2023.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [AdaBins: Depth Estimation using Adaptive Bins](https://mlsanity.com/paper/2011.14141/) (2020)
- [Predicting Depth, Surface Normals and Semantic Labels with a Common Multi-Scale Convolutional Architecture](https://mlsanity.com/paper/1411.4734/) (2014)
- [Deeper Depth Prediction with Fully Convolutional Residual Networks](https://mlsanity.com/paper/1606.00373/) (2016)
- [From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimation](https://mlsanity.com/paper/1907.10326/) (2019)
- [Enforcing geometric constraints of virtual normal for depth prediction](https://mlsanity.com/paper/1907.12209/) (2019)
- [NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](https://mlsanity.com/paper/2203.01502/) (2022)
- [CNN-SLAM: Real-time dense monocular SLAM with learned depth prediction](https://mlsanity.com/paper/1704.03489/) (2017)
- [DeepLiDAR: Deep Surface Normal Guided Depth Prediction for Outdoor Scene from Sparse LiDAR Data and Single Color Image](https://mlsanity.com/paper/1812.00488/) (2018)
- [Transformer-Based Attention Networks for Continuous Pixel-Wise Prediction](https://mlsanity.com/paper/2103.12091/) (2021)
- [P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior](https://mlsanity.com/paper/2204.02091/) (2022)
- [PlaneRCNN: 3D Plane Detection and Reconstruction from a Single Image](https://mlsanity.com/paper/1812.04072/) (2018)
- [Estimating Depth from Monocular Images as Classification Using Deep Fully Convolutional Residual Networks](https://mlsanity.com/paper/1605.02305/) (2016)
- [Guiding Monocular Depth Estimation Using Depth-Attention Volume](https://mlsanity.com/paper/2004.02760/) (2020)
- [Structure-Aware Residual Pyramid Network for Monocular Depth Estimation](https://mlsanity.com/paper/1907.06023/) (2019)
- [Normal Assisted Stereo Depth Estimation](https://mlsanity.com/paper/1911.10444/) (2019)
- [Bidirectional Attention Network for Monocular Depth Estimation](https://mlsanity.com/paper/2009.00743/) (2020)
- [Adaptive Surface Normal Constraint for Depth Estimation](https://mlsanity.com/paper/2103.15483/) (2021)
- [P2Net: Patch-match and Plane-regularization for Unsupervised Indoor Depth Estimation](https://mlsanity.com/paper/2007.07696/) (2020)
- [Sparse Auxiliary Networks for Unified Monocular Depth Prediction and Completion](https://mlsanity.com/paper/2103.16690/) (2021)
- [StructDepth: Leveraging the structural regularities for self-supervised indoor depth estimation](https://mlsanity.com/paper/2108.08574/) (2021)
- [URCDC-Depth: Uncertainty Rectified Cross-Distillation with CutFlip for Monocular Depth Estimation](https://mlsanity.com/paper/2302.08149/) (2023)

## Built on by (most cited first, 30 of 45)

- [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)
- [UniDepth: Universal Monocular Metric Depth Estimation](https://mlsanity.com/paper/2403.18913/) (2024)
- [Flash3D: Feed-Forward Generalisable 3D Scene Reconstruction from a Single Image](https://mlsanity.com/paper/2406.04343/) (2024)
- [IEBins: Iterative Elastic Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2309.14137/) (2023)
- [Tri-Perspective View Decomposition for Geometry-Aware Depth Completion](https://mlsanity.com/paper/2403.15008/) (2024)
- [OGNI-DC: Robust Depth Completion with Optimization-Guided Neural Iterations](https://mlsanity.com/paper/2406.11711/) (2024)
- [DepthMaster: Taming Diffusion Models for Monocular Depth Estimation](https://mlsanity.com/paper/2501.02576/) (2025)
- [ScaleDepth: Decomposing Metric Depth Estimation into Scale Prediction and Relative Depth Estimation](https://mlsanity.com/paper/2407.08187/) (2024)
- [EVP: Enhanced Visual Perception using Inverse Multi-Attentive Feature Refinement and Regularized Image-Text Alignment](https://mlsanity.com/paper/2312.08548/) (2023)
- [MonoDiffusion: Self-Supervised Monocular Depth Estimation Using Diffusion Model](https://mlsanity.com/paper/2311.07198/) (2023)
- [AirPlanes: Accurate Plane Estimation via 3D-Consistent Embeddings](https://mlsanity.com/paper/2406.08960/) (2024)
- [LLaVA-SpaceSGG: Visual Instruct Tuning for Open-vocabulary Scene Graph Generation with Enhanced Spatial Relations](https://mlsanity.com/paper/2412.06322/) (2024)
- [DCDepth: Progressive Monocular Depth Estimation in Discrete Cosine Domain](https://mlsanity.com/paper/2410.14980/) (2024)
- [NDDepth: Normal-Distance Assisted Monocular Depth Estimation and Completion](https://mlsanity.com/paper/2311.07166/) (2023)
- [Scalable Autoregressive Monocular Depth Estimation](https://mlsanity.com/paper/2411.11361/) (2024)
- [SPIdepth: Strengthened Pose Information for Self-supervised Monocular Depth Estimation](https://mlsanity.com/paper/2404.12501/) (2024)
- [Metric-Solver: Sliding Anchored Metric Depth Estimation from a Single Image](https://mlsanity.com/paper/2504.12103/) (2025)
- [Event-Driven Dynamic Scene Depth Completion](https://mlsanity.com/paper/2505.13279/) (2025)
- [Structure-Aware Radar-Camera Depth Estimation](https://mlsanity.com/paper/2506.05008/) (2025)
- [Niagara: Normal-Integrated Geometric Affine Field for Scene Reconstruction from a Single View](https://mlsanity.com/paper/2503.12553/) (2025)
- [Floating No More: Object-Ground Reconstruction from a Single Image](https://mlsanity.com/paper/2407.18914/) (2024)
- [Region-aware Depth Scale Adaptation with Sparse Measurements](https://mlsanity.com/paper/2507.14879/) (2025)
- [GVDepth: Zero-Shot Monocular Depth Estimation for Ground Vehicles based on Probabilistic Cue Fusion](https://mlsanity.com/paper/2412.06080/) (2024)
- [FUSE: Label-Free Image-Event Joint Monocular Depth Estimation via Frequency-Decoupled Alignment and Degradation-Robust Fusion](https://mlsanity.com/paper/2503.19739/) (2025)
- [One Look is Enough: Seamless Patchwise Refinement for Zero-Shot Monocular Depth Estimation on High-Resolution Images](https://mlsanity.com/paper/2503.22351/) (2025)
- [Boosting Generalizability towards Zero-Shot Cross-Dataset Single-Image Indoor Depth by Meta-Initialization](https://mlsanity.com/paper/2409.02486/) (2024)
- [Occlusion Boundary and Depth: Mutual Enhancement via Multi-Task Learning](https://mlsanity.com/paper/2505.21231/) (2025)
- [TR2M: Transferring Monocular Relative Depth to Metric Depth with Language Descriptions and Dual-Level Scale-Oriented Contrast](https://mlsanity.com/paper/2506.13387/) (2025)
- [Into the Fog: Evaluating Robustness of Multiple Object Tracking](https://mlsanity.com/paper/2404.10534/) (2024)

## Abstract (arXiv)

Monocular depth estimation has drawn widespread attention from the vision community due to its broad applications. In this paper, we propose a novel physics (geometry)-driven deep learning framework for monocular depth estimation by assuming that 3D scenes are constituted by piece-wise planes. Particularly, we introduce a new normal-distance head that outputs pixel-level surface normal and plane-to-origin distance for deriving depth at each position. Meanwhile, the normal and distance are regularized by a developed plane-aware consistency constraint. We further integrate an additional depth head to improve the robustness of the proposed framework. To fully exploit the strengths of these two heads, we develop an effective contrastive iterative refinement module that refines depth in a complementary manner according to the depth uncertainty. Extensive experiments indicate that the proposed method exceeds previous state-of-the-art competitors on the NYU-Depth-v2, KITTI and SUN RGB-D datasets. Notably, it ranks 1st among all submissions on the KITTI depth prediction online benchmark at the submission time.