Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Prediction
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Abstract (arXiv)
Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in terms of evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric constraints in the 3D space. In this work, we show the importance of the high-order 3D geometric constraints for depth prediction. By designing a loss term that enforces a simple geometric constraint, namely, virtual normal directions determined by randomly sampled three points in the reconstructed 3D space, we significantly improve the accuracy and robustness of monocular depth estimation. Significantly, the virtual normal loss can not only improve the performance of learning metric depth, but also disentangle the scale information and enrich the model with better shape information. Therefore, when not having access to absolute metric depth training data, we can use virtual normal to learn a robust affine-invariant depth generated on diverse scenes. In experiments, We show state-of-the-art results of learning metric depth on NYU Depth-V2 and KITTI. From the high-quality predicted depth, we are now able to recover good 3D structures of the scene such as the point cloud and surface normal directly, eliminating the necessity of relying on additional models as was previously done. To demonstrate the excellent generalizability of learning affine-invariant depth on diverse data with the virtual normal loss, we construct a large-scale and diverse dataset for training affine-invariant depth, termed Diverse Scene Depth dataset (DiverseDepth), and test on five datasets with the zero-shot test setting. Code is available at: https://git.io/Depth
Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). Builds on 44 of its 74 references that are in the map. First posted on arXiv 7 Mar 2021.
Builds on
44 of 74 references.
References · 44
- 2017ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenescited by 3,088
- 2019Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfercited by 1,484
- 2014Depth Map Prediction from a Single Image using a Multi-Scale Deep Networkcited by 1,264
- 2016FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networkscited by 780
- 2017Unsupervised Learning of Depth and Ego-Motion from Videocited by 778
- 2018MegaDepth: Learning Single-View Depth Prediction from Internet Photoscited by 731
- 2018Deep Ordinal Regression Network for Monocular Depth Estimationcited by 721
- 2018Taskonomy: Disentangling Task Transfer Learningcited by 631
- 2014Predicting Depth, Surface Normals and Semantic Labels with a Common Multi-Scale Convolutional Architecturecited by 483
- 2016Deeper Depth Prediction with Fully Convolutional Residual Networkscited by 402
- 2016Unsupervised CNN for Single View Depth Estimation: Geometry to the Rescuecited by 368
- 2019On The Power of Curriculum Learning in Training Deep Networkscited by 285
32 more
- 2019Unsupervised Scale-consistent Depth and Ego-motion Learning from Monocular Videocited by 244
- 2019DIODE: A Dense Indoor and Outdoor DEpth Datasetcited by 236
- 2019Enforcing geometric constraints of virtual normal for depth predictioncited by 233
- 2018Competitive Collaboration: Joint Unsupervised Learning of Depth, Camera Motion, Optical Flow and Motion Segmentationcited by 222
- 2020Learning to Recover 3D Scene Shape from a Single Imagecited by 214
- 2016Single-Image Depth Perception in the Wildcited by 179
- 2019Depth from Videos in the Wild: Unsupervised Monocular Depth Learning from Unknown Camerascited by 170
- 2015Learning Depth from Single Monocular Images Using Deep Convolutional Neural Fieldscited by 169
- 2018Revisiting Single Image Depth Estimation: Toward Higher Resolution Maps with Accurate Object Boundariescited by 144
- 2020Feature-metric Loss for Self-supervised Learning of Depth and Egomotioncited by 140
- 2018Learning Depth with Convolutional Spatial Propagation Networkcited by 135
- 2018High Quality Monocular Depth Estimation via Transfer Learningcited by 133
- 2014Learning Rich Features from RGB-D Images for Object Detection and Segmentationcited by 124
- 2018Curriculum Learning by Transfer Learning: Theory and Experiments with Deep Networkscited by 113
- 2017Semi-Supervised Deep Learning for Monocular Depth Map Predictioncited by 109
- 2014Deep Convolutional Neural Fields for Depth Estimation from a Single Imagecited by 106
- 2016Estimating Depth from Monocular Images as Classification Using Deep Fully Convolutional Residual Networkscited by 91
- 2020Unsupervised Monocular Depth Learning in Dynamic Scenescited by 84
- 2019How do neural networks see depth in single images?cited by 82
- 2020Guiding Monocular Depth Estimation Using Depth-Attention Volumecited by 82
- 2019Web Stereo Video Supervision for Depth Prediction from Dynamic Scenescited by 73
- 2018Learning Monocular Depth by Distilling Cross-domain Stereo Networkscited by 64
- 2020OASIS: A Large-Scale Dataset for Single Image 3D in the Wildcited by 62
- 2019DepthTransfer: Depth Extraction from Video Using Non-parametric Samplingcited by 60
- 2020DiverseDepth: Affine-invariant Depth Prediction Using Diverse Datacited by 60
- 2014Designing Deep Networks for Surface Normal Estimationcited by 59
- 2019Structure-Aware Residual Pyramid Network for Monocular Depth Estimationcited by 49
- 2018Deep attention-based classification network for robust depth predictioncited by 36
- 2018Learning Single-Image Depth from Videos using Quality Assessment Networkscited by 25
- 2019A Large RGB-D Dataset for Semi-supervised Monocular Depth Estimationcited by 21
- 2020On Deep Learning Techniques to Boost Monocular Depth Estimation for Autonomous Navigationcited by 17
- 2016Depth from a Single Image by Harmonizing Overcomplete Local Network Predictionscited by 16
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Citing papers per year: 2021: 1; 2022: 10; 2023: 12; 2024: 15; 2025: 5; 2026: 5.
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- 2024Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimationcited by 389
- 2023Metric3D: Towards Zero-shot Metric 3D Prediction from A Single Imagecited by 357
- 2024GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Imagecited by 283
- 2024Lotus: Diffusion-based Visual Foundation Model for High-quality Dense Predictioncited by 163
- 2024Learning Temporally Consistent Video Depth from Video Diffusion Priorscited by 100
- 2024Fine-Tuning Image-Conditional Diffusion Models is Easier than You Thinkcited by 82
- 2022Hierarchical Normalization for Robust Monocular Depth Estimationcited by 51
- 20233D generation on ImageNetcited by 47
- 2022Towards Accurate Reconstruction of 3D Scene Shape from A Single Monocular Imagecited by 42
- 2021Image2Point: 3D Point-Cloud Understanding with 2D Image Pretrained Modelscited by 41
- 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translationcited by 36
- 2024Adaptive Fusion of Single-View and Multi-View Depth for Autonomous Drivingcited by 30
36 more
- 2023FreeReg: Image-to-Point Cloud Registration Leveraging Pretrained Diffusion Models and Monocular Depth Estimatorscited by 29
- 2022DELTAR: Depth Estimation from a Light-weight ToF Sensor and RGB Imagecited by 26
- 2023Learning to Fuse Monocular and Multi-view Cues for Multi-frame Depth Estimation in Dynamic Scenescited by 25
- 2024OGNI-DC: Robust Depth Completion with Optimization-Guided Neural Iterationscited by 23
- 2022Controllable Shadow Generation Using Pixel Height Mapscited by 22
- 2024SharpDepth: Sharpening Metric Depth Predictions Using Diffusion Distillationcited by 21
- 2025MonSter++: Unified Stereo Matching, Multi-view Stereo, and Real-time Stereo with Monodepth Priorscited by 19
- 2022Improving Monocular Visual Odometry Using Learned Depthcited by 17
- 2023FrozenRecon: Pose-free 3D Scene Reconstruction with Frozen Depth Modelscited by 17
- 2022Multi-Camera Collaborative Depth Prediction via Consistent Structure Estimationcited by 16
- 2023The Second Monocular Depth Estimation Challengecited by 12
- 2022Towards 3D Scene Reconstruction from Locally Scale-Aligned Monocular Video Depthcited by 11
- 2023Inverting the Imaging Process by Learning an Implicit Camera Modelcited by 10
- 2025PRISM: A Unified Framework for Photorealistic Reconstruction and Intrinsic Scene Modelingcited by 9
- 2025QuartDepth: Post-Training Quantization for Real-Time Depth Estimation on the Edgecited by 7
- 2022Scaling up Multi-domain Semantic Segmentation with Sentence Embeddingscited by 6
- 2023Robust Geometry-Preserving Depth Estimation Using Differentiable Renderingcited by 6
- 2024Stealing Stable Diffusion Prior for Robust Monocular Depth Estimationcited by 6
- 2022HALS: A Height-Aware Lidar Super-Resolution Framework for Autonomous Drivingcited by 4
- 2022Dense Depth Distillation with Out-of-Distribution Simulated Imagescited by 4
- 2024Scale-Invariant Monocular Depth Estimation via SSI Depthcited by 4
- 2024The Devil is in the Edges: Monocular Depth Estimation with Edge-aware Consistency Fusioncited by 3
- 2025SphereFusion: Efficient Panorama Depth Estimation via Gated Fusioncited by 2
- 2023Depth- and Semantics-aware Multi-modal Domain Translation: Generating 3D Panoramic Color Images from LiDAR Point Cloudscited by 1
- 2023MV-ROPE: Multi-view Constraints for Robust Category-level Object Pose and Size Estimationcited by 1
- 2023GSDC Transformer: An Efficient and Effective Cue Fusion for Monocular Multi-Frame Depth Estimationcited by 1
- 20243D WholeBody Pose Estimation based on Semantic Graph Attention Network and Distance Informationcited by 1
- 2024MetricDepth: Enhancing Monocular Depth Estimation with Deep Metric Learningcited by 1
- 2026DepthART: Scaling Foundation Monocular Depth to Tiny Modelscited by 1
- 2023Deep Planar Parallax for Monocular Depth Estimationcited by 0
- 2024FA-Depth: Toward Fast and Accurate Self-supervised Monocular Depth Estimationcited by 0
- 2024KineDepth: Utilizing Robot Kinematics for Online Metric Depth Estimationcited by 0
- 2026UniT: Unified Geometry Learning with Group Autoregressive Transformercited by 0
- 2026DepthMaster: Unified Monocular Depth Estimation for Perspective and Panoramic Imagescited by 0
- 2026SCOPE: Scale-Consistent One-Pass Estimation of 3D Geometrycited by 0
- 2026Monocular Depth Estimation from a Single Image: Progress and Opportunitiescited by 0
- 2026Monocular Depth Estimation from a Single Image: Progress and Opportunities1 Sep 2026
- 2026DepthART: Scaling Foundation Monocular Depth to Tiny Models19 Jul 2026
- 2026SCOPE: Scale-Consistent One-Pass Estimation of 3D Geometry19 Jun 2026
- 2026DepthMaster: Unified Monocular Depth Estimation for Perspective and Panoramic Images10 Jun 2026
- 2026UniT: Unified Geometry Learning with Group Autoregressive Transformer20 May 2026
- 2025PRISM: A Unified Framework for Photorealistic Reconstruction and Intrinsic Scene Modeling19 Apr 2025
- 2025QuartDepth: Post-Training Quantization for Real-Time Depth Estimation on the Edge20 Mar 2025
- 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translation10 Mar 2025
- 2025SphereFusion: Efficient Panorama Depth Estimation via Gated Fusion9 Feb 2025
- 2025MonSter++: Unified Stereo Matching, Multi-view Stereo, and Real-time Stereo with Monodepth Priors15 Jan 2025
- 2024MetricDepth: Enhancing Monocular Depth Estimation with Deep Metric Learning29 Dec 2024
- 2024SharpDepth: Sharpening Metric Depth Predictions Using Diffusion Distillation27 Nov 2024
36 more
- 2024KineDepth: Utilizing Robot Kinematics for Online Metric Depth Estimation29 Sep 2024
- 2024Lotus: Diffusion-based Visual Foundation Model for High-quality Dense Prediction26 Sep 2024
- 2024Fine-Tuning Image-Conditional Diffusion Models is Easier than You Think17 Sep 2024
- 2024OGNI-DC: Robust Depth Completion with Optimization-Guided Neural Iterations17 Jun 2024
- 2024Scale-Invariant Monocular Depth Estimation via SSI Depth13 Jun 2024
- 2024Learning Temporally Consistent Video Depth from Video Diffusion Priors3 Jun 2024
- 20243D WholeBody Pose Estimation based on Semantic Graph Attention Network and Distance Information3 Jun 2024
- 2024FA-Depth: Toward Fast and Accurate Self-supervised Monocular Depth Estimation17 May 2024
- 2024The Devil is in the Edges: Monocular Depth Estimation with Edge-aware Consistency Fusion30 Mar 2024
- 2024Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation22 Mar 2024
- 2024GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Image18 Mar 2024
- 2024Adaptive Fusion of Single-View and Multi-View Depth for Autonomous Driving12 Mar 2024
- 2024Stealing Stable Diffusion Prior for Robust Monocular Depth Estimation8 Mar 2024
- 2023FreeReg: Image-to-Point Cloud Registration Leveraging Pretrained Diffusion Models and Monocular Depth Estimators5 Oct 2023
- 2023GSDC Transformer: An Efficient and Effective Cue Fusion for Monocular Multi-Frame Depth Estimation29 Sep 2023
- 2023Robust Geometry-Preserving Depth Estimation Using Differentiable Rendering18 Sep 2023
- 2023MV-ROPE: Multi-view Constraints for Robust Category-level Object Pose and Size Estimation17 Aug 2023
- 2023FrozenRecon: Pose-free 3D Scene Reconstruction with Frozen Depth Models10 Aug 2023
- 2023Metric3D: Towards Zero-shot Metric 3D Prediction from A Single Image20 Jul 2023
- 2023Inverting the Imaging Process by Learning an Implicit Camera Model25 Apr 2023
- 2023Learning to Fuse Monocular and Multi-view Cues for Multi-frame Depth Estimation in Dynamic Scenes18 Apr 2023
- 2023The Second Monocular Depth Estimation Challenge14 Apr 2023
- 20233D generation on ImageNet2 Mar 2023
- 2023Depth- and Semantics-aware Multi-modal Domain Translation: Generating 3D Panoramic Color Images from LiDAR Point Clouds15 Feb 2023
- 2023Deep Planar Parallax for Monocular Depth Estimation9 Jan 2023
- 2022Hierarchical Normalization for Robust Monocular Depth Estimation18 Oct 2022
- 2022Multi-Camera Collaborative Depth Prediction via Consistent Structure Estimation5 Oct 2022
- 2022DELTAR: Depth Estimation from a Light-weight ToF Sensor and RGB Image27 Sep 2022
- 2022Towards Accurate Reconstruction of 3D Scene Shape from A Single Monocular Image28 Aug 2022
- 2022Dense Depth Distillation with Out-of-Distribution Simulated Images26 Aug 2022
- 2022Controllable Shadow Generation Using Pixel Height Maps12 Jul 2022
- 2022Improving Monocular Visual Odometry Using Learned Depth4 Apr 2022
- 2022HALS: A Height-Aware Lidar Super-Resolution Framework for Autonomous Driving8 Feb 2022
- 2022Scaling up Multi-domain Semantic Segmentation with Sentence Embeddings4 Feb 2022
- 2022Towards 3D Scene Reconstruction from Locally Scale-Aligned Monocular Video Depth3 Feb 2022
- 2021Image2Point: 3D Point-Cloud Understanding with 2D Image Pretrained Models8 Jun 2021
- 2024GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Imagecited by 283
- 2024Lotus: Diffusion-based Visual Foundation Model for High-quality Dense Predictioncited by 163
- 2024Learning Temporally Consistent Video Depth from Video Diffusion Priorscited by 100
- 2024Fine-Tuning Image-Conditional Diffusion Models is Easier than You Thinkcited by 82
- 2023FreeReg: Image-to-Point Cloud Registration Leveraging Pretrained Diffusion Models and Monocular Depth Estimatorscited by 29
- 2024SharpDepth: Sharpening Metric Depth Predictions Using Diffusion Distillationcited by 21
- 2024Stealing Stable Diffusion Prior for Robust Monocular Depth Estimationcited by 6
- 2024SharpDepth: Sharpening Metric Depth Predictions Using Diffusion Distillation27 Nov 2024
- 2024Lotus: Diffusion-based Visual Foundation Model for High-quality Dense Prediction26 Sep 2024
- 2024Fine-Tuning Image-Conditional Diffusion Models is Easier than You Think17 Sep 2024
- 2024Learning Temporally Consistent Video Depth from Video Diffusion Priors3 Jun 2024
- 2024GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Image18 Mar 2024
- 2024Stealing Stable Diffusion Prior for Robust Monocular Depth Estimation8 Mar 2024
- 2023FreeReg: Image-to-Point Cloud Registration Leveraging Pretrained Diffusion Models and Monocular Depth Estimators5 Oct 2023
- 2024Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimationcited by 389
- 2023Metric3D: Towards Zero-shot Metric 3D Prediction from A Single Imagecited by 357
- 2022Hierarchical Normalization for Robust Monocular Depth Estimationcited by 51
- 20233D generation on ImageNetcited by 47
- 2022Towards Accurate Reconstruction of 3D Scene Shape from A Single Monocular Imagecited by 42
- 2021Image2Point: 3D Point-Cloud Understanding with 2D Image Pretrained Modelscited by 41
- 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translationcited by 36
- 2024Adaptive Fusion of Single-View and Multi-View Depth for Autonomous Drivingcited by 30
- 2022DELTAR: Depth Estimation from a Light-weight ToF Sensor and RGB Imagecited by 26
- 2023Learning to Fuse Monocular and Multi-view Cues for Multi-frame Depth Estimation in Dynamic Scenescited by 25
- 2024OGNI-DC: Robust Depth Completion with Optimization-Guided Neural Iterationscited by 23
- 2022Controllable Shadow Generation Using Pixel Height Mapscited by 22
12 most cited of 41 All 41 (JSON)
- 2026Monocular Depth Estimation from a Single Image: Progress and Opportunities1 Sep 2026
- 2026DepthART: Scaling Foundation Monocular Depth to Tiny Models19 Jul 2026
- 2026SCOPE: Scale-Consistent One-Pass Estimation of 3D Geometry19 Jun 2026
- 2026DepthMaster: Unified Monocular Depth Estimation for Perspective and Panoramic Images10 Jun 2026
- 2026UniT: Unified Geometry Learning with Group Autoregressive Transformer20 May 2026
- 2025PRISM: A Unified Framework for Photorealistic Reconstruction and Intrinsic Scene Modeling19 Apr 2025
- 2025QuartDepth: Post-Training Quantization for Real-Time Depth Estimation on the Edge20 Mar 2025
- 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translation10 Mar 2025
- 2025SphereFusion: Efficient Panorama Depth Estimation via Gated Fusion9 Feb 2025
- 2025MonSter++: Unified Stereo Matching, Multi-view Stereo, and Real-time Stereo with Monodepth Priors15 Jan 2025
- 2024MetricDepth: Enhancing Monocular Depth Estimation with Deep Metric Learning29 Dec 2024
- 2024KineDepth: Utilizing Robot Kinematics for Online Metric Depth Estimation29 Sep 2024
12 newest of 41 All 41 (JSON)