# Adaptive Surface Normal Constraint for Depth Estimation

arXiv: https://arxiv.org/abs/2103.15483 · HTML: https://mlsanity.com/paper/2103.15483/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Unsupervised Monocular Depth Estimation with Left-Right Consistency](https://mlsanity.com/paper/1609.03677/) (2016)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [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)
- [PAD-Net: Multi-Tasks Guided Prediction-and-Distillation Network for Simultaneous Depth Estimation and Scene Parsing](https://mlsanity.com/paper/1805.04409/) (2018)
- [Learning Depth from Single Monocular Images Using Deep Convolutional Neural Fields](https://mlsanity.com/paper/1502.07411/) (2015)
- [Revisiting Single Image Depth Estimation: Toward Higher Resolution Maps with Accurate Object Boundaries](https://mlsanity.com/paper/1803.08673/) (2018)
- [Pattern-Affinitive Propagation across Depth, Surface Normal and Semantic Segmentation](https://mlsanity.com/paper/1906.03525/) (2019)
- [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)
- [Pixel-Adaptive Convolutional Neural Networks](https://mlsanity.com/paper/1904.05373/) (2019)
- [Depth Completion from Sparse LiDAR Data with Depth-Normal Constraints](https://mlsanity.com/paper/1910.06727/) (2019)
- [EpicFlow: Edge-Preserving Interpolation of Correspondences for Optical Flow](https://mlsanity.com/paper/1501.02565/) (2015)
- [Multi-Scale Continuous CRFs as Sequential Deep Networks for Monocular Depth Estimation](https://mlsanity.com/paper/1704.02157/) (2017)
- [DepthTransfer: Depth Extraction from Video Using Non-parametric Sampling](https://mlsanity.com/paper/2001.00987/) (2019)
- [Designing Deep Networks for Surface Normal Estimation](https://mlsanity.com/paper/1411.4958/) (2014)
- [Normal Assisted Stereo Depth Estimation](https://mlsanity.com/paper/1911.10444/) (2019)
- [Occlusion-Aware Depth Estimation with Adaptive Normal Constraints](https://mlsanity.com/paper/2004.00845/) (2020)
- [GeoNet++: Iterative Geometric Neural Network with Edge-Aware Refinement for Joint Depth and Surface Normal Estimation](https://mlsanity.com/paper/2012.06980/) (2020)
- [EdgeStereo: A Context Integrated Residual Pyramid Network for Stereo Matching](https://mlsanity.com/paper/1803.05196/) (2018)
- [Depth from a Single Image by Harmonizing Overcomplete Local Network Predictions](https://mlsanity.com/paper/1605.07081/) (2016)

## Built on by (most cited first, 30 of 43)

- [Wonder3D: Single Image to 3D using Cross-Domain Diffusion](https://mlsanity.com/paper/2310.15008/) (2023)
- [Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation](https://mlsanity.com/paper/2404.15506/) (2024)
- [Triplane Meets Gaussian Splatting: Fast and Generalizable Single-View 3D Reconstruction with Transformers](https://mlsanity.com/paper/2312.09147/) (2023)
- [SparseNeuS: Fast Generalizable Neural Surface Reconstruction from Sparse Views](https://mlsanity.com/paper/2206.05737/) (2022)
- [NeuRIS: Neural Reconstruction of Indoor Scenes Using Normal Priors](https://mlsanity.com/paper/2206.13597/) (2022)
- [P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior](https://mlsanity.com/paper/2204.02091/) (2022)
- [iDisc: Internal Discretization for Monocular Depth Estimation](https://mlsanity.com/paper/2304.06334/) (2023)
- [NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2211.14173/) (2022)
- [VA-DepthNet: A Variational Approach to Single Image Depth Prediction](https://mlsanity.com/paper/2302.06556/) (2023)
- [IEBins: Iterative Elastic Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2309.14137/) (2023)
- [Domain Randomization-Enhanced Depth Simulation and Restoration for Perceiving and Grasping Specular and Transparent Objects](https://mlsanity.com/paper/2208.03792/) (2022)
- [NDDepth: Normal-Distance Assisted Monocular Depth Estimation](https://mlsanity.com/paper/2309.10592/) (2023)
- [Self-supervised Monocular Depth Estimation for All Day Images using Domain Separation](https://mlsanity.com/paper/2108.07628/) (2021)
- [WorDepth: Variational Language Prior for Monocular Depth Estimation](https://mlsanity.com/paper/2404.03635/) (2024)
- [IronDepth: Iterative Refinement of Single-View Depth using Surface Normal and its Uncertainty](https://mlsanity.com/paper/2210.03676/) (2022)
- [GEDepth: Ground Embedding for Monocular Depth Estimation](https://mlsanity.com/paper/2309.09975/) (2023)
- [OGNI-DC: Robust Depth Completion with Optimization-Guided Neural Iterations](https://mlsanity.com/paper/2406.11711/) (2024)
- [URCDC-Depth: Uncertainty Rectified Cross-Distillation with CutFlip for Monocular Depth Estimation](https://mlsanity.com/paper/2302.08149/) (2023)
- [Vision-Language Embodiment for Monocular Depth Estimation](https://mlsanity.com/paper/2503.16535/) (2025)
- [Single Image Depth Prediction Made Better: A Multivariate Gaussian Take](https://mlsanity.com/paper/2303.18164/) (2023)
- [PolyMaX: General Dense Prediction with Mask Transformer](https://mlsanity.com/paper/2311.05770/) (2023)
- [Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images](https://mlsanity.com/paper/2402.05869/) (2024)
- [PrimeDepth: Efficient Monocular Depth Estimation with a Stable Diffusion Preimage](https://mlsanity.com/paper/2409.09144/) (2024)
- [DCDepth: Progressive Monocular Depth Estimation in Discrete Cosine Domain](https://mlsanity.com/paper/2410.14980/) (2024)
- [Facial Depth and Normal Estimation using Single Dual-Pixel Camera](https://mlsanity.com/paper/2111.12928/) (2021)
- [NDDepth: Normal-Distance Assisted Monocular Depth Estimation and Completion](https://mlsanity.com/paper/2311.07166/) (2023)
- [Embodiment: Self-Supervised Depth Estimation Based on Camera Models](https://mlsanity.com/paper/2408.01565/) (2024)
- [PlaneRecNet: Multi-Task Learning with Cross-Task Consistency for Piece-Wise Plane Detection and Reconstruction from a Single RGB Image](https://mlsanity.com/paper/2110.11219/) (2021)
- [Multi-task learning with cross-task consistency for improved depth estimation in colonoscopy](https://mlsanity.com/paper/2311.18664/) (2023)
- [Wonder3D++: Cross-domain Diffusion for High-fidelity 3D Generation from a Single Image](https://mlsanity.com/paper/2511.01767/) (2025)

## Abstract (arXiv)

We present a novel method for single image depth estimation using surface normal constraints. Existing depth estimation methods either suffer from the lack of geometric constraints, or are limited to the difficulty of reliably capturing geometric context, which leads to a bottleneck of depth estimation quality. We therefore introduce a simple yet effective method, named Adaptive Surface Normal (ASN) constraint, to effectively correlate the depth estimation with geometric consistency. Our key idea is to adaptively determine the reliable local geometry from a set of randomly sampled candidates to derive surface normal constraint, for which we measure the consistency of the geometric contextual features. As a result, our method can faithfully reconstruct the 3D geometry and is robust to local shape variations, such as boundaries, sharp corners and noises. We conduct extensive evaluations and comparisons using public datasets. The experimental results demonstrate our method outperforms the state-of-the-art methods and has superior efficiency and robustness.