Data to 7 Oct 2026

Enforcing geometric constraints of virtual normal for depth prediction

arXiv 1907.12209 ↗First posted 29 Jul 2019cs.CVcited by 233

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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 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 one simple type of geometric constraints, namely, virtual normal directions determined by randomly sampled three points in the reconstructed 3D space, we can considerably improve the depth prediction accuracy. Significantly, the byproduct of this predicted depth being sufficiently accurate is that we are now able to recover good 3D structures of the scene such as the point cloud and surface normal directly from the depth, eliminating the necessity of training new sub-models as was previously done. Experiments on two benchmarks: NYU Depth-V2 and KITTI demonstrate the effectiveness of our method and state-of-the-art performance.

Key facts. Cited by 233 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jul 2019.

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Citing papers per year: 2021: 57; 2022: 57; 2023: 45; 2024: 40; 2025: 21; 2026: 13.

233 papers.

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2021Vision Transformers for Dense Predictioncited by 1,789
2024Depth Anything V2cited by 1,385
2024Depth Anything: Unleashing the Power of Large-Scale Unlabeled Datacited by 1,346
2023ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depthcited by 646
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
2025MoGe-2: Accurate Monocular Geometry with Metric Scale and Sharp Detailscited by 250
2022BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimationcited by 166
2022NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimationcited by 151
2023DDP: Diffusion Model for Dense Visual Predictioncited by 148
2021Transformer-Based Attention Networks for Continuous Pixel-Wise Predictioncited by 125

38 more

2022NeuRIS: Neural Reconstruction of Indoor Scenes Using Normal Priorscited by 125
2022Neural 3D Scene Reconstruction with the Manhattan-world Assumptioncited by 123
2022DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimationcited by 116
2022P3Depth: Monocular Depth Estimation with a Piecewise Planarity Priorcited by 106
2021Boosting Monocular Depth Estimation Models to High-Resolution via Content-Adaptive Multi-Resolution Mergingcited by 104
2022LocalBins: Improving Depth Estimation by Learning Local Distributionscited by 92
2022Attention Attention Everywhere: Monocular Depth Prediction with Skip Attentioncited by 92
2023Monocular Depth Estimation using Diffusion Modelscited by 87
2022SimpleRecon: 3D Reconstruction Without 3D Convolutionscited by 83
2021Deep Dense Multi-scale Network for Snow Removal Using Semantic and Geometric Priorscited by 82
2023DiffusionDepth: Diffusion Denoising Approach for Monocular Depth Estimationcited by 81
2023iDisc: Internal Discretization for Monocular Depth Estimationcited by 71
2021Unsupervised Scale-consistent Depth Learning from Videocited by 69
2021Ground-aware Monocular 3D Object Detection for Autonomous Drivingcited by 65
2022Multi-Frame Self-Supervised Depth with Transformerscited by 64
2022Global-Local Path Networks for Monocular Depth Estimation with Vertical CutDepthcited by 58
2021Regularizing Nighttime Weirdness: Efficient Self-supervised Monocular Depth Estimation in the Darkcited by 57
2024AffordanceLLM: Grounding Affordance from Vision Language Modelscited by 55
2023VA-DepthNet: A Variational Approach to Single Image Depth Predictioncited by 54
2023IEBins: Iterative Elastic Bins for Monocular Depth Estimationcited by 53
2023All in Tokens: Unifying Output Space of Visual Tasks via Soft Tokencited by 52
2022Hierarchical Normalization for Robust Monocular Depth Estimationcited by 51
2022SC-DepthV3: Robust Self-supervised Monocular Depth Estimation for Dynamic Scenescited by 50
2024VCR-GauS: View Consistent Depth-Normal Regularizer for Gaussian Surface Reconstructioncited by 50
2021Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Predictioncited by 48
2021Multi-View Depth Estimation by Fusing Single-View Depth Probability with Multi-View Geometrycited by 46
2023NDDepth: Normal-Distance Assisted Monocular Depth Estimationcited by 45
2021Adaptive Surface Normal Constraint for Depth Estimationcited by 43
2021MVS2D: Efficient Multi-view Stereo via Attention-Driven 2D Convolutionscited by 43
2021Toward Practical Monocular Indoor Depth Estimationcited by 42
2022Towards Accurate Reconstruction of 3D Scene Shape from A Single Monocular Imagecited by 42
2021Sparse Auxiliary Networks for Unified Monocular Depth Prediction and Completioncited by 39
2021Deep Two-View Structure-from-Motion Revisitedcited by 39
2021MonoIndoor: Towards Good Practice of Self-Supervised Monocular Depth Estimation for Indoor Environmentscited by 38
2021Pano3D: A Holistic Benchmark and a Solid Baseline for 360o Depth Estimationcited by 37
2021StructDepth: Leveraging the structural regularities for self-supervised indoor depth estimationcited by 36
2022RA-Depth: Resolution Adaptive Self-Supervised Monocular Depth Estimationcited by 36
2023Improving Depth Gradient Continuity in Transformers: A Comparative Study on Monocular Depth Estimation with CNNcited by 35

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