# Estimating 3D Uncertainty Field: Quantifying Uncertainty for Neural Radiance Fields

arXiv: https://arxiv.org/abs/2311.01815 · HTML: https://mlsanity.com/paper/2311.01815/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 39 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 30 of 37)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [AD-NeRF: Audio Driven Neural Radiance Fields for Talking Head Synthesis](https://mlsanity.com/paper/2103.11078/) (2021)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [Modelling Uncertainty in Deep Learning for Camera Relocalization](https://mlsanity.com/paper/1509.05909/) (2015)
- [ActiveNeRF: Learning where to See with Uncertainty Estimation](https://mlsanity.com/paper/2209.08546/) (2022)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [Dex-NeRF: Using a Neural Radiance Field to Grasp Transparent Objects](https://mlsanity.com/paper/2110.14217/) (2021)
- [NeRF-Supervision: Learning Dense Object Descriptors from Neural Radiance Fields](https://mlsanity.com/paper/2203.01913/) (2022)
- [Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representations](https://mlsanity.com/paper/2109.02123/) (2021)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [Loc-NeRF: Monte Carlo Localization using Neural Radiance Fields](https://mlsanity.com/paper/2209.09050/) (2022)

## Built on by (most cited first, 15 of 15)

- [NeRF On-the-go: Exploiting Uncertainty for Distractor-free NeRFs in the Wild](https://mlsanity.com/paper/2405.18715/) (2024)
- [Drone-assisted Road Gaussian Splatting with Cross-view Uncertainty](https://mlsanity.com/paper/2408.15242/) (2024)
- [Toward Real-world BEV Perception: Depth Uncertainty Estimation via Gaussian Splatting](https://mlsanity.com/paper/2504.01957/) (2025)
- [Modeling uncertainty for Gaussian Splatting](https://mlsanity.com/paper/2403.18476/) (2024)
- [Next Best Sense: Guiding Vision and Touch with FisherRF for 3D Gaussian Splatting](https://mlsanity.com/paper/2410.04680/) (2024)
- [Uncertainty-Aware Normal-Guided Gaussian Splatting for Surface Reconstruction from Sparse Image Sequences](https://mlsanity.com/paper/2503.11172/) (2025)
- [Uncertainty-driven 3D Gaussian Splatting Active Mapping via Anisotropic Visibility Field](https://mlsanity.com/paper/2605.30342/) (2026)
- [Evidential Neural Radiance Fields](https://mlsanity.com/paper/2602.23574/) (2026)
- [WarpRF: Multi-View Consistency for Training-Free Uncertainty Quantification and Applications in Radiance Fields](https://mlsanity.com/paper/2506.22433/) (2025)
- [DAV-GSWT: Diffusion-Active-View Sampling for Data-Efficient Gaussian Splatting Wang Tiles](https://mlsanity.com/paper/2602.15355/) (2026)
- [PH-Dropout: Practical Epistemic Uncertainty Quantification for View Synthesis](https://mlsanity.com/paper/2410.05468/) (2024)
- [OCSplats: Observation Completeness Quantification and Label Noise Separation in 3DGS](https://mlsanity.com/paper/2508.01239/) (2025)
- [HAD: Hallucination-Aware Diffusion Priors for 3D Reconstruction](https://mlsanity.com/paper/2605.16873/) (2026)
- [Data Augmentation for NeRFs in the Low Data Limit](https://mlsanity.com/paper/2503.02092/) (2025)
- [VCURF: Virtual Camera-based Uncertainty of Radiance Fields](https://mlsanity.com/paper/2610.04076/) (2026)

## Abstract (arXiv)

Current methods based on Neural Radiance Fields (NeRF) significantly lack the capacity to quantify uncertainty in their predictions, particularly on the unseen space including the occluded and outside scene content. This limitation hinders their extensive applications in robotics, where the reliability of model predictions has to be considered for tasks such as robotic exploration and planning in unknown environments. To address this, we propose a novel approach to estimate a 3D Uncertainty Field based on the learned incomplete scene geometry, which explicitly identifies these unseen regions. By considering the accumulated transmittance along each camera ray, our Uncertainty Field infers 2D pixel-wise uncertainty, exhibiting high values for rays directly casting towards occluded or outside the scene content. To quantify the uncertainty on the learned surface, we model a stochastic radiance field. Our experiments demonstrate that our approach is the only one that can explicitly reason about high uncertainty both on 3D unseen regions and its involved 2D rendered pixels, compared with recent methods. Furthermore, we illustrate that our designed uncertainty field is ideally suited for real-world robotics tasks, such as next-best-view selection.