# NDDepth: Normal-Distance Assisted Monocular Depth Estimation and Completion

arXiv: https://arxiv.org/abs/2311.07166 · HTML: https://mlsanity.com/paper/2311.07166/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 95 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 30 of 64)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (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)
- [Deep Mutual Learning](https://mlsanity.com/paper/1706.00384/) (2017)
- [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)
- [Non-Local Spatial Propagation Network for Depth Completion](https://mlsanity.com/paper/2007.10042/) (2020)
- [BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2204.00987/) (2022)
- [Sparse-to-Dense: Depth Prediction from Sparse Depth Samples and a Single Image](https://mlsanity.com/paper/1709.07492/) (2017)
- [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)
- [PENet: Towards Precise and Efficient Image Guided Depth Completion](https://mlsanity.com/paper/2103.00783/) (2021)
- [Pattern-Affinitive Propagation across Depth, Surface Normal and Semantic Segmentation](https://mlsanity.com/paper/1906.03525/) (2019)
- [Self-supervised Sparse-to-Dense: Self-supervised Depth Completion from LiDAR and Monocular Camera](https://mlsanity.com/paper/1807.00275/) (2018)
- [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)
- [DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimation](https://mlsanity.com/paper/2203.14211/) (2022)
- [Learning Guided Convolutional Network for Depth Completion](https://mlsanity.com/paper/1908.01238/) (2019)

## Built on by (most cited first, 9 of 9)

- [Jasmine: Harnessing Diffusion Prior for Self-supervised Depth Estimation](https://mlsanity.com/paper/2503.15905/) (2025)
- [Scene Prior Filtering for Depth Super-Resolution](https://mlsanity.com/paper/2402.13876/) (2024)
- [Uncertainty-Aware Normal-Guided Gaussian Splatting for Surface Reconstruction from Sparse Image Sequences](https://mlsanity.com/paper/2503.11172/) (2025)
- [DVP-MVS++: Synergize Depth-Normal-Edge and Harmonized Visibility Prior for Multi-View Stereo](https://mlsanity.com/paper/2506.13215/) (2025)
- [FUSE: Label-Free Image-Event Joint Monocular Depth Estimation via Frequency-Decoupled Alignment and Degradation-Robust Fusion](https://mlsanity.com/paper/2503.19739/) (2025)
- [Discriminately Treating Motion Components Evolves Joint Depth and Ego-Motion Learning](https://mlsanity.com/paper/2511.01502/) (2025)
- [Need for Speed: Zero-Shot Depth Completion with Single-Step Diffusion](https://mlsanity.com/paper/2603.10584/) (2026)
- [Spectral Rectification for Parameter-Efficient Adaptation of Foundation Models in Colonoscopy Depth Estimation](https://mlsanity.com/paper/2603.15374/) (2026)
- [The Midas Touch for Metric Depth: Interpretable Metricization for Generalizable Depth Perception](https://mlsanity.com/paper/2610.16749/) (2026)

## Abstract (arXiv)

Over the past few years, monocular depth estimation and completion have been paid more and more attention from the computer vision community because of their widespread applications. In this paper, we introduce novel physics (geometry)-driven deep learning frameworks for these two tasks by assuming that 3D scenes are constituted with piece-wise planes. Instead of directly estimating the depth map or completing the sparse depth map, we propose to estimate the surface normal and plane-to-origin distance maps or complete the sparse surface normal and distance maps as intermediate outputs. To this end, we develop a normal-distance head that outputs pixel-level surface normal and distance. Meanwhile, the surface normal and distance maps are regularized by a developed plane-aware consistency constraint, which are then transformed into depth maps. Furthermore, we integrate an additional depth head to strengthen the robustness of the proposed frameworks. Extensive experiments on the NYU-Depth-v2, KITTI and SUN RGB-D datasets demonstrate that our method exceeds in performance prior state-of-the-art monocular depth estimation and completion competitors. The source code will be available at https://github.com/ShuweiShao/NDDepth.