We present the Bayesian Neural Radiance Field (NeRF), which explicitly
quantifies uncertainty in geometric volume structures without the need for
additional networks, making it adept for challenging observations and
uncontrolled images. NeRF diverges from traditional geometric methods by
offering an enriched scene representation, rendering color and density in 3D
space from various viewpoints. However, NeRF encounters limitations in relaxing
uncertainties by using geometric structure information, leading to inaccuracies
in interpretation under insufficient real-world observations. Recent research
efforts aimed at addressing this issue have primarily relied on empirical
methods or auxiliary networks. To fundamentally address this issue, we propose
a series of formulational extensions to NeRF. By introducing generalized
approximations and defining density-related uncertainty, our method seamlessly
extends to manage uncertainty not only for RGB but also for depth, without the
need for additional networks or empirical assumptions. In experiments we show
that our method significantly enhances performance on RGB and depth images in
the comprehensive dataset, demonstrating the reliability of the Bayesian NeRF
approach to quantifying uncertainty based on the geometric structure.

我们提出了贝叶斯神经辐射场（NeRF），它能够在几何体积结构中明确量化不确定性，无需额外网络，使其适用于具有挑战性的观测和无控制的图像。NeRF 通过丰富的场景表示来区别于传统的几何方法，在三维空间中从不同视角呈现颜色和密度。然而，NeRF 在使用几何结构信息放松不确定性方面遇到限制，导致在不充分的真实观测下的解释不准确。为了从根本上解决这个问题，我们提出了一系列公式扩展 NeRF 的方法。通过引入广义近似和定义与密度相关的不确定性，我们的方法不仅无需额外网络或经验假设，还能无缝扩展来处理 RGB 和深度的不确定性。实验结果显示，我们的方法在全面的数据集上显著提升了 RGB 和深度图像的性能，展示了基于几何结构定量化不确定性的贝叶斯 NeRF 方法的可靠性。