# Density Uncertainty Quantification with NeRF-Ensembles: Impact of Data and Scene Constraints

arXiv: https://arxiv.org/abs/2312.14664 · HTML: https://mlsanity.com/paper/2312.14664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 30 of 34)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [NoPe-NeRF: Optimising Neural Radiance Field with No Pose Prior](https://mlsanity.com/paper/2212.07388/) (2022)
- [GNeRF: GAN-based Neural Radiance Field without Posed Camera](https://mlsanity.com/paper/2103.15606/) (2021)
- [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)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimation](https://mlsanity.com/paper/2204.05735/) (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)
- [AdaNeRF: Adaptive Sampling for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2207.10312/) (2022)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [Parallel Inversion of Neural Radiance Fields for Robust Pose Estimation](https://mlsanity.com/paper/2210.10108/) (2022)
- [ViP-NeRF: Visibility Prior for Sparse Input Neural Radiance Fields](https://mlsanity.com/paper/2305.00041/) (2023)
- [DUDES: Deep Uncertainty Distillation using Ensembles for Semantic Segmentation](https://mlsanity.com/paper/2303.09843/) (2023)
- [CBARF: Cascaded Bundle-Adjusting Neural Radiance Fields from Imperfect Camera Poses](https://mlsanity.com/paper/2310.09776/) (2023)

## Built on by (most cited first, 1 of 1)

- [FeatureGS: Eigenvalue-Feature Optimization in 3D Gaussian Splatting for Geometrically Accurate and Artifact-Reduced Reconstruction](https://mlsanity.com/paper/2501.17655/) (2025)

## Abstract (arXiv)

In the fields of computer graphics, computer vision and photogrammetry, Neural Radiance Fields (NeRFs) are a major topic driving current research and development. However, the quality of NeRF-generated 3D scene reconstructions and subsequent surface reconstructions, heavily relies on the network output, particularly the density. Regarding this critical aspect, we propose to utilize NeRF-Ensembles that provide a density uncertainty estimate alongside the mean density. We demonstrate that data constraints such as low-quality images and poses lead to a degradation of the training process, increased density uncertainty and decreased predicted density. Even with high-quality input data, the density uncertainty varies based on scene constraints such as acquisition constellations, occlusions and material properties. NeRF-Ensembles not only provide a tool for quantifying the uncertainty but exhibit two promising advantages: Enhanced robustness and artifact removal. Through the utilization of NeRF-Ensembles instead of single NeRFs, small outliers are removed, yielding a smoother output with improved completeness of structures. Furthermore, applying percentile-based thresholds on density uncertainty outliers proves to be effective for the removal of large (foggy) artifacts in post-processing. We conduct our methodology on 3 different datasets: (i) synthetic benchmark dataset, (ii) real benchmark dataset, (iii) real data under realistic recording conditions and sensors.