Bayesian NeRF: Quantifying Uncertainty with Volume Density for Neural Implicit Fields
Sibaek Lee, Kyeongsu Kang, Seongbo Ha, Hyeonwoo Yu
AI summary
Problem
Standard NeRF models struggle to quantify uncertainty in unobserved views and sensor noise, while existing Bayesian extensions either ignore density uncertainty or rely on inefficient auxiliary networks.
Approach
The method integrates Bayesian probability directly into NeRF’s rendering equations by modeling volume density and occupancy as Gaussian distributions, enabling uncertainty quantification without adding extra network parameters.
Key results
- Significant PSNR and SSIM improvements on synthetic and real-world datasets with limited training images
- Accurate depth uncertainty estimation compatible with non-RGB sensors like LiDAR
- Notable improvements in mapping and tracking performance when integrated into NICE SLAM
- Elimination of auxiliary networks while maintaining real-time rendering feasibility
Why it matters
Provides a lightweight, uncertainty-aware 3D representation crucial for safe navigation and robust scene understanding in robotics and autonomous systems operating in uncontrolled environments.
Abstract
We present a Bayesian Neural Radiance Field (NeRF), which explicitly quantifies uncertainty in the volume density by modeling uncertainty in the occupancy, without the need for ad- ditional networks, making it particularly suited for challenging observations and uncontrolled image environments. NeRF diverges from traditional geometric methods by providing an enriched scene representation, rendering color and density in 3D space from various viewpoints. However, NeRF encounters limitations in addressing uncertainties solely through geometric structure in- formation, leading to inaccuracies when interpreting scenes with insufficient real-world observations. While previous efforts have relied on auxiliary networks, we propose a series of formulation extensions to NeRF that manage uncertainties in density, both color and density, and occupancy, all without the need for addi- tional networks. In experiments, we show that our method signif- icantly enhances performance on RGB and depth images in the comprehensive dataset. Given that uncertainty modeling aligns well with the inherently uncertain environments of Simultaneous Localization and Mapping (SLAM), we applied our approach to SLAM systems and observed notable improvements in mapping and tracking performance. These results confirm the effectiveness of our Bayesian NeRF approach in quantifying uncertainty based on geometric structure, making it a robust solution for challenging real-world scenarios.