# Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields

**Authors:** Lily Goli, Cody Reading, Silvia Sellán, Alec Jacobson, Andrea Tagliasacchi  
**arXiv:** [2309.03185](https://arxiv.org/abs/2309.03185)  
**Date:** 2023-09-06  
**Summary page:** https://www.summarizepaper.com/en/paper/2309.03185v1/

## Key points

- Neural Radiance Fields (NeRFs) have shown potential in computer vision applications like view synthesis and depth estimation
- Bayes’ Rays is a post-hoc framework developed by researchers to quantify uncertainties in pre-trained NeRF models without modifying the training process
- Bayes’ Rays leverages spatial perturbations and a Bayesian Laplace approximation to establish a volumetric uncertainty field within NeRF models
- The framework outperforms previous methods in terms of correlation to reconstructed depth error and offers practical applications such as artifact removal and performance enhancement
- Bayes’ Rays provides a plug-and-play probabilistic method for uncertainty quantification, streamlining the assessment process for NeRF models

## Summary

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In the field of computer vision, Neural Radiance Fields (NeRFs) have demonstrated significant potential in applications such as view synthesis and depth estimation. However, learning from multiview images introduces inherent uncertainties that need to be quantified accurately. Existing methods for quantifying these uncertainties are either heuristic or computationally intensive. To address this challenge, a team of researchers led by Lily Goli, Cody Reading, Silvia Sellán, Alec Jacobson, and Andrea Tagliasacchi have introduced Bayes’ Rays: a novel post-hoc framework designed to evaluate uncertainty in any pre-trained NeRF without the need to modify the training process. Bayes’ Rays leverages spatial perturbations and a Bayesian Laplace approximation to establish a volumetric uncertainty field within the NeRF model. This approach allows for the accurate quantification of uncertainties associated with NeRF predictions. The researchers have statistically derived their algorithm and demonstrated its superior performance in key metrics and real-world applications. One notable aspect of Bayes’ Rays is its ability to provide meaningful uncertainties that outperform previous methods in terms of correlation to reconstructed depth error. Additionally, the framework offers practical applications such as removing artifacts from NeRF models and enhancing overall performance. By introducing a plug-and-play probabilistic method for uncertainty quantification independent of architecture and training data requirements, Bayes’ Rays streamlines the process of assessing uncertainties in NeRF models. Furthermore, the researchers highlight that Bayes’ Rays can compute a spatial uncertainty field in just over a minute, which can be rendered as an additional color channel for visualization purposes. They also propose thresholding the uncertainty field to facilitate interactive artifact removal from pre-trained NeRFs in real-time scenarios. In summary, Bayes’ Rays represents a significant advancement in uncertainty quantification for Neural Radiance Fields. By providing a robust framework for evaluating uncertainties without additional training data or computational overhead, this approach has the potential to enhance the reliability and performance of NeRF models across various applications in computer vision research.