# Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images

arXiv: https://arxiv.org/abs/2402.05869 · HTML: https://mlsanity.com/paper/2402.05869/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 76 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 30 of 39)

- [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)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [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)
- [DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://mlsanity.com/paper/2108.10869/) (2021)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (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)
- [CNN-SLAM: Real-time dense monocular SLAM with learned depth prediction](https://mlsanity.com/paper/1704.03489/) (2017)
- [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)
- [Gen6D: Generalizable Model-Free 6-DoF Object Pose Estimation from RGB Images](https://mlsanity.com/paper/2204.10776/) (2022)
- [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)
- [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)
- [FCFR-Net: Feature Fusion based Coarse-to-Fine Residual Learning for Depth Completion](https://mlsanity.com/paper/2012.08270/) (2020)
- [VolumeFusion: Deep Depth Fusion for 3D Scene Reconstruction](https://mlsanity.com/paper/2108.08623/) (2021)
- [Adaptive Surface Normal Constraint for Depth Estimation](https://mlsanity.com/paper/2103.15483/) (2021)
- [Occlusion-Aware Depth Estimation with Adaptive Normal Constraints](https://mlsanity.com/paper/2004.00845/) (2020)
- [STEPS: Joint Self-supervised Nighttime Image Enhancement and Depth Estimation](https://mlsanity.com/paper/2302.01334/) (2023)

## Built on by (most cited first, 14 of 14)

- [Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation](https://mlsanity.com/paper/2404.15506/) (2024)
- [GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Image](https://mlsanity.com/paper/2403.12013/) (2024)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [GaussianGrasper: 3D Language Gaussian Splatting for Open-vocabulary Robotic Grasping](https://mlsanity.com/paper/2403.09637/) (2024)
- [Tri-Perspective View Decomposition for Geometry-Aware Depth Completion](https://mlsanity.com/paper/2403.15008/) (2024)
- [Training-Free Model Merging for Multi-target Domain Adaptation](https://mlsanity.com/paper/2407.13771/) (2024)
- [UncAD: Towards Safe End-to-end Autonomous Driving via Online Map Uncertainty](https://mlsanity.com/paper/2504.12826/) (2025)
- [Wonder3D++: Cross-domain Diffusion for High-fidelity 3D Generation from a Single Image](https://mlsanity.com/paper/2511.01767/) (2025)
- [PanoNormal: Monocular Indoor 360deg Surface Normal Estimation](https://mlsanity.com/paper/2405.18745/) (2024)
- [Multi-view Surface Reconstruction Using Normal and Reflectance Cues](https://mlsanity.com/paper/2506.04115/) (2025)
- [Multi-task Geometric Estimation of Depth and Surface Normal from Monocular 360deg Images](https://mlsanity.com/paper/2411.01749/) (2024)
- [Propagating Sparse Depth via Depth Foundation Model for Out-of-Distribution Depth Completion](https://mlsanity.com/paper/2508.04984/) (2025)
- [Locate n' Rotate: Two-stage Openable Part Detection with Foundation Model Priors](https://mlsanity.com/paper/2412.13173/) (2024)
- [Cross360: 360deg Monocular Depth Estimation via Cross Projections Across Scales](https://mlsanity.com/paper/2601.17271/) (2026)

## Abstract (arXiv)

We introduce a novel approach to learn geometries such as depth and surface normal from images while incorporating geometric context. The difficulty of reliably capturing geometric context in existing methods impedes their ability to accurately enforce the consistency between the different geometric properties, thereby leading to a bottleneck of geometric estimation quality. We therefore propose the Adaptive Surface Normal (ASN) constraint, a simple yet efficient method. Our approach extracts geometric context that encodes the geometric variations present in the input image and correlates depth estimation with geometric constraints. By dynamically determining reliable local geometry from randomly sampled candidates, we establish a surface normal constraint, where the validity of these candidates is evaluated using the geometric context. Furthermore, our normal estimation leverages the geometric context to prioritize regions that exhibit significant geometric variations, which makes the predicted normals accurately capture intricate and detailed geometric information. Through the integration of geometric context, our method unifies depth and surface normal estimations within a cohesive framework, which enables the generation of high-quality 3D geometry from images. We validate the superiority of our approach over state-of-the-art methods through extensive evaluations and comparisons on diverse indoor and outdoor datasets, showcasing its efficiency and robustness.