Bayesian NeRF: Quantifying Uncertainty with Volume Density for Neural Implicit Fields

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 additional 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 information, 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 additional networks. In experiments, we show that our method significantly 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.