mlsanityData to 14 Oct 2026

Estimating and Exploiting the Aleatoric Uncertainty in Surface Normal Estimation

arXiv 2109.09881 ↗First posted 20 Sep 2021cs.CVcited by 116

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Abstract (arXiv)

Surface normal estimation from a single image is an important task in 3D scene understanding. In this paper, we address two limitations shared by the existing methods: the inability to estimate the aleatoric uncertainty and lack of detail in the prediction. The proposed network estimates the per-pixel surface normal probability distribution. We introduce a new parameterization for the distribution, such that its negative log-likelihood is the angular loss with learned attenuation. The expected value of the angular error is then used as a measure of the aleatoric uncertainty. We also present a novel decoder framework where pixel-wise multi-layer perceptrons are trained on a subset of pixels sampled based on the estimated uncertainty. The proposed uncertainty-guided sampling prevents the bias in training towards large planar surfaces and improves the quality of prediction, especially near object boundaries and on small structures. Experimental results show that the proposed method outperforms the state-of-the-art in ScanNet and NYUv2, and that the estimated uncertainty correlates well with the prediction error. Code is available at https://github.com/baegwangbin/surface_normal_uncertainty.

Key facts. Cited by 116 papers in the map (data through 14 Oct 2026). Builds on 22 of its 43 references that are in the map. First posted on arXiv 20 Sep 2021.

Builds on

22 of 43 references.

References · 22

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  4. 2017ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenescited by 3,117
  5. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
  6. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  7. 2020AdaBins: Depth Estimation using Adaptive Binscited by 601
  8. 2014Predicting Depth, Surface Normals and Semantic Labels with a Common Multi-Scale Convolutional Architecturecited by 483
  9. 2019PointRend: Image Segmentation as Renderingcited by 440
  10. 2017Snapshot Ensembles: Train 1, get M for freecited by 350
  11. 2017Super-Convergence: Very Fast Training of Neural Networks Using Large Learning Ratescited by 199
  12. 2020On the uncertainty of self-supervised monocular depth estimationcited by 182
10 more
  1. 2019Pattern-Affinitive Propagation across Depth, Surface Normal and Semantic Segmentationcited by 142
  2. 2018Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flowcited by 135
  3. 2018Lightweight Probabilistic Deep Networkscited by 77
  4. 2014Designing Deep Networks for Surface Normal Estimationcited by 59
  5. 2019Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spherescited by 37
  6. 2020GeoNet++: Iterative Geometric Neural Network with Edge-Aware Refinement for Joint Depth and Surface Normal Estimationcited by 36
  7. 2016Marr Revisited: 2D-3D Alignment via Surface Normal Predictioncited by 34
  8. 2020Surface Normal Estimation of Tilted Images via Spatial Rectifiercited by 34
  9. 2019FrameNet: Learning Local Canonical Frames of 3D Surfaces from a Single RGB Imagecited by 26
  10. 2019Floors are Flat: Leveraging Semantics for Real-Time Surface Normal Predictioncited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 11; 2023: 30; 2024: 37; 2025: 20; 2026: 16.

116 papers.

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  1. 2022Unified-IO: A Unified Model for Vision, Language, and Multi-Modal Taskscited by 421
  2. 2024Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimationcited by 395
  3. 2023Unified-IO 2: Scaling Autoregressive Multimodal Models with Vision, Language, Audio, and Actioncited by 302
  4. 2024GeoWizard: Unleashing the Diffusion Priors for 3D Geometry Estimation from a Single Imagecited by 286
  5. 2023Sequential Modeling Enables Scalable Learning for Large Vision Modelscited by 212
  6. 2024Probing the 3D Awareness of Visual Foundation Modelscited by 177
  7. 2023RichDreamer: A Generalizable Normal-Depth Diffusion Model for Detail Richness in Text-to-3Dcited by 168
  8. 2024StableNormal: Reducing Diffusion Variance for Stable and Sharp Normalcited by 154
  9. 2022NeuRIS: Neural Reconstruction of Indoor Scenes Using Normal Priorscited by 125
  10. 2024Rethinking Inductive Biases for Surface Normal Estimationcited by 124
  11. 2025Hi3DGen: High-fidelity 3D Geometry Generation from Images via Normal Bridgingcited by 99
  12. 2023Bayes' Rays: Uncertainty Quantification for Neural Radiance Fieldscited by 91
38 more
  1. 2024Fine-Tuning Image-Conditional Diffusion Models is Easier than You Thinkcited by 83
  2. 2025Marigold: Affordable Adaptation of Diffusion-Based Image Generators for Image Analysiscited by 78
  3. 2022Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantificationcited by 73
  4. 2023iDisc: Internal Discretization for Monocular Depth Estimationcited by 73
  5. 2025WorldMirror: Universal 3D World Reconstruction with Any-Prior Promptingcited by 67
  6. 2024PhyRecon: Physically Plausible Neural Scene Reconstructioncited by 45
  7. 2026HY-World 2.0: A Multi-Modal World Model for Reconstructing, Generating, and Simulating 3D Worldscited by 44
  8. 2023Unbiased Scene Graph Generation in Videoscited by 39
  9. 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translationcited by 36
  10. 2023Tame a Wild Camera: In-the-Wild Monocular Camera Calibrationcited by 34
  11. 2024GaussianRoom: Improving 3D Gaussian Splatting with SDF Guidance and Monocular Cues for Indoor Scene Reconstructioncited by 31
  12. 2024PixWizard: Versatile Image-to-Image Visual Assistant with Open-Language Instructionscited by 31
  13. 2022IronDepth: Iterative Refinement of Single-View Depth using Surface Normal and its Uncertaintycited by 30
  14. 2023Prismer: A Vision-Language Model with Multi-Task Expertscited by 28
  15. 2022GRIT: General Robust Image Task Benchmarkcited by 26
  16. 2024HI-SLAM2: Geometry-Aware Gaussian SLAM for Fast Monocular Scene Reconstructioncited by 25
  17. 2025NormalCrafter: Learning Temporally Consistent Normals from Video Diffusion Priorscited by 25
  18. 2022MonoGraspNet: 6-DoF Grasping with a Single RGB Imagecited by 24
  19. 2022BayesCap: Bayesian Identity Cap for Calibrated Uncertainty in Frozen Neural Networkscited by 23
  20. 2024From Specific-MLLMs to Omni-MLLMs: A Survey on MLLMs Aligned with Multi-modalitiescited by 22
  21. 2022SPARC: Sparse Render-and-Compare for CAD model alignment in a single RGB imagecited by 19
  22. 2023UncLe-SLAM: Uncertainty Learning for Dense Neural SLAMcited by 19
  23. 2024Neural LightRig: Unlocking Accurate Object Normal and Material Estimation with Multi-Light Diffusioncited by 19
  24. 2023DebSDF: Delving into the Details and Bias of Neural Indoor Scene Reconstructioncited by 17
  25. 2024CREMA: Generalizable and Efficient Video-Language Reasoning via Multimodal Modular Fusioncited by 17
  26. 2024ImOV3D: Learning Open-Vocabulary Point Clouds 3D Object Detection from Only 2D Imagescited by 17
  27. 2023Measured Albedo in the Wild: Filling the Gap in Intrinsics Evaluationcited by 16
  28. 2024PCF-Lift: Panoptic Lifting by Probabilistic Contrastive Fusioncited by 16
  29. 2023Blowing in the Wind: CycleNet for Human Cinemagraphs from Still Imagescited by 14
  30. 2023PolyMaX: General Dense Prediction with Mask Transformercited by 14
  31. 2023Heteroscedastic Uncertainty Estimation Framework for Unsupervised Registrationcited by 14
  32. 2025UncAD: Towards Safe End-to-end Autonomous Driving via Online Map Uncertaintycited by 14
  33. 2025Uncertainty Quantification for Machine Learning in Healthcare: A Surveycited by 14
  34. 2022DAG: Depth-Aware Guidance with Denoising Diffusion Probabilistic Modelscited by 12
  35. 2023SuperPrimitive: Scene Reconstruction at a Primitive Levelcited by 11
  36. 2024Buffer Anytime: Zero-Shot Video Depth and Normal from Image Priorscited by 11
  37. 2025GLaD: Geometric Latent Distillation for Vision-Language-Action Modelscited by 11
  38. 2024Sources of Uncertainty in 3D Scene Reconstructioncited by 10

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