mlsanityData to 7 Oct 2026

Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields

arXiv 2209.08718 ↗First posted 19 Sep 2022cs.CVcited by 58

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Abstract (arXiv)

We show that ensembling effectively quantifies model uncertainty in Neural Radiance Fields (NeRFs) if a density-aware epistemic uncertainty term is considered. The naive ensembles investigated in prior work simply average rendered RGB images to quantify the model uncertainty caused by conflicting explanations of the observed scene. In contrast, we additionally consider the termination probabilities along individual rays to identify epistemic model uncertainty due to a lack of knowledge about the parts of a scene unobserved during training. We achieve new state-of-the-art performance across established uncertainty quantification benchmarks for NeRFs, outperforming methods that require complex changes to the NeRF architecture and training regime. We furthermore demonstrate that NeRF uncertainty can be utilised for next-best view selection and model refinement.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). Builds on 25 of its 29 references that are in the map. First posted on arXiv 19 Sep 2022.

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25 of 29 references.

References · 25

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  3. 2022Instant Neural Graphics Primitives with a Multiresolution Hash Encodingcited by 3,698
  4. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  5. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  6. 2021Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fieldscited by 1,957
  7. 2021Plenoxels: Radiance Fields without Neural Networkscited by 1,607
  8. 2022TensoRF: Tensorial Radiance Fieldscited by 1,275
  9. 2020NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collectionscited by 1,230
  10. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  11. 2021NICE-SLAM: Neural Implicit Scalable Encoding for SLAMcited by 586
  12. 2021Neural Fields in Visual Computing and Beyondcited by 539
13 more
  1. 2021iMAP: Implicit Mapping and Positioning in Real-Timecited by 476
  2. 2016Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Agecited by 405
  3. 2021Vision-Only Robot Navigation in a Neural Radiance Worldcited by 153
  4. 2021Dex-NeRF: Using a Neural Radiance Field to Grasp Transparent Objectscited by 119
  5. 20213D Neural Scene Representations for Visuomotor Controlcited by 110
  6. 2018The Limits and Potentials of Deep Learning for Roboticscited by 104
  7. 2022NeRF-Supervision: Learning Dense Object Descriptors from Neural Radiance Fieldscited by 86
  8. 2021Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representationscited by 80
  9. 2022Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantificationcited by 71
  10. 2021Semantics for Robotic Mapping, Perception and Interaction: A Surveycited by 56
  11. 2020Neural Volume Rendering: NeRF And Beyondcited by 44
  12. 2022Reinforcement Learning with Neural Radiance Fieldscited by 43
  13. 2021Advances in Inference and Representation for Simultaneous Localization and Mappingcited by 16

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 8; 2024: 20; 2025: 15; 2026: 14.

58 papers.

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  1. 2023Bayes' Rays: Uncertainty Quantification for Neural Radiance Fieldscited by 90
  2. 2024PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splattingcited by 85
  3. 2023FisherRF: Active View Selection and Uncertainty Quantification for Radiance Fields using Fisher Informationcited by 63
  4. 2024CountGD: Multi-Modal Open-World Countingcited by 59
  5. 2023Deceptive-NeRF/3DGS: Diffusion-Generated Pseudo-Observations for High-Quality Sparse-View Reconstructioncited by 39
  6. 2023Active Neural Mappingcited by 30
  7. 20244D Gaussian Splatting in the Wild with Uncertainty-Aware Regularizationcited by 28
  8. 2024Neural Visibility Field for Uncertainty-Driven Active Mappingcited by 25
  9. 2024Modeling uncertainty for Gaussian Splattingcited by 17
  10. 2023Estimating 3D Uncertainty Field: Quantifying Uncertainty for Neural Radiance Fieldscited by 14
  11. 2024NeRF Director: Revisiting View Selection in Neural Volume Renderingcited by 14
  12. 2025Free360: Layered Gaussian Splatting for Unbounded 360-Degree View Synthesis from Extremely Sparse and Unposed Viewscited by 11
38 more
  1. 2024Bayesian NeRF: Quantifying Uncertainty with Volume Density for Neural Implicit Fieldscited by 9
  2. 2024Sources of Uncertainty in 3D Scene Reconstructioncited by 9
  3. 2024Multimodal LLM Guided Exploration and Active Mapping using Fisher Informationcited by 9
  4. 2024Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Networkcited by 6
  5. 2025These Magic Moments: Differentiable Uncertainty Quantification of Radiance Field Modelscited by 6
  6. 2025ExploreGS: Explorable 3D Scene Reconstruction with Virtual Camera Samplings and Diffusion Priorscited by 6
  7. 2025View-Dependent Uncertainty Estimation of 3D Gaussian Splattingcited by 5
  8. 2025Uncertainty Matters in Dynamic Gaussian Splatting for Monocular 4D Reconstructioncited by 5
  9. 2026Predictive Photometric Uncertainty in Gaussian Splatting for Novel View Synthesiscited by 5
  10. 2024Exploiting Priors from 3D Diffusion Models for RGB-Based One-Shot View Planningcited by 4
  11. 2024Uncertainty-aware Active Learning of NeRF-based Object Models for Robot Manipulators using Visual and Re-orientation Actionscited by 4
  12. 2025Peering into the Unknown: Active View Selection with Neural Uncertainty Maps for 3D Reconstructioncited by 4
  13. 2025PRIMU: Uncertainty Estimation for Novel Views in Gaussian Splatting from Primitive-Based Representations of Error and Coveragecited by 4
  14. 2025Auto3R: Automated 3D Reconstruction and Scanning via Data-driven Uncertainty Quantificationcited by 4
  15. 2026Uncertainty-driven 3D Gaussian Splatting Active Mapping via Anisotropic Visibility Fieldcited by 4
  16. 2023Indoor Scene Reconstruction with Fine-Grained Details Using Hybrid Representation and Normal Prior Enhancementcited by 3
  17. 2023Instant Uncertainty Calibration of NeRFs Using a Meta-Calibratorcited by 3
  18. 2024ProvNeRF: Modeling per Point Provenance in NeRFs as a Stochastic Fieldcited by 3
  19. 2024Metric-Guided Conformal Bounds for Probabilistic Image Reconstructioncited by 3
  20. 2024Uni-SLAM: Uncertainty-Aware Neural Implicit SLAM for Real-Time Dense Indoor Scene Reconstructioncited by 3
  21. 2026Evidential Neural Radiance Fieldscited by 3
  22. 2025DNRSelect: Active Best View Selection for Deferred Neural Renderingcited by 2
  23. 2025WarpRF: Multi-View Consistency for Training-Free Uncertainty Quantification and Applications in Radiance Fieldscited by 2
  24. 2026SA-ResGS: Self-Augmented Residual 3D Gaussian Splatting for Next Best View Selectioncited by 2
  25. 2023Density Uncertainty Quantification with NeRF-Ensembles: Impact of Data and Scene Constraintscited by 1
  26. 2024STAIR: Semantic-Targeted Active Implicit Reconstructioncited by 1
  27. 2024VF-NeRF: Viewshed Fields for Rigid NeRF Registrationcited by 1
  28. 2025Hestia: Voxel-Face-Aware Hierarchical Next-Best-View Acquisition for Efficient 3D Reconstructioncited by 1
  29. 2026Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstructioncited by 1
  30. 2026Predicting 3D structure by latent posterior samplingcited by 1
  31. 2026Uncertainty-Aware Gaussian Map for Vision-Language Navigationcited by 1
  32. 2026When Variance Is Not an Error Map: Calibrated Uncertainty for Radiative Gaussian Splatting in Sparse-View CTcited by 1
  33. 2026GO-PRE: Goal-Oriented Next-Best-View Selection via Predictive Rendering Entropy for Active 3D Reconstructioncited by 1
  34. 2022A Review of Scene Representations for Robot Manipulatorscited by 0
  35. 2024Active Scout: Multi-Target Tracking Using Neural Radiance Fields in Dense Urban Environmentscited by 0
  36. 2024IOVS4NeRF:Incremental Optimal View Selection for Large-Scale NeRFscited by 0
  37. 2024PH-Dropout: Practical Epistemic Uncertainty Quantification for View Synthesiscited by 0
  38. 2025Data Augmentation for NeRFs in the Low Data Limitcited by 0

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