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.

翻译：我们提出贝叶斯神经辐射场，其无需额外网络即可显式量化几何体积结构中的不确定性，适用于具有挑战性的观测场景和非受控图像。神经辐射场区别于传统几何方法，通过从不同视角在三维空间中渲染颜色与密度，提供更丰富的场景表征。然而，现有神经辐射场在利用几何结构信息松弛不确定性方面存在局限，导致在真实观测数据不足时解释不准确。近期针对该问题的研究主要依赖经验方法或辅助网络。为从根本上解决此问题，我们提出一系列神经辐射场公式化扩展。通过引入广义近似并定义密度相关不确定性，本方法可无缝扩展至RGB和深度不确定性的联合管理，无需额外网络或经验假设。实验表明，本方法在综合数据集的RGB与深度图像上显著提升性能，验证了基于几何结构的贝叶斯神经辐射场不确定性量化方法的可靠性。