Current methods based on Neural Radiance Fields (NeRF) significantly lack the capacity to quantify uncertainty in their predictions, particularly on the unseen space including the occluded and outside scene content. This limitation hinders their extensive applications in robotics, where the reliability of model predictions has to be considered for tasks such as robotic exploration and planning in unknown environments. To address this, we propose a novel approach to estimate a 3D Uncertainty Field based on the learned incomplete scene geometry, which explicitly identifies these unseen regions. By considering the accumulated transmittance along each camera ray, our Uncertainty Field infers 2D pixel-wise uncertainty, exhibiting high values for rays directly casting towards occluded or outside the scene content. To quantify the uncertainty on the learned surface, we model a stochastic radiance field. Our experiments demonstrate that our approach is the only one that can explicitly reason about high uncertainty both on 3D unseen regions and its involved 2D rendered pixels, compared with recent methods. Furthermore, we illustrate that our designed uncertainty field is ideally suited for real-world robotics tasks, such as next-best-view selection.

翻译：当前基于神经辐射场（NeRF）的方法在预测不确定性量化能力上存在显著不足，尤其是在处理遮挡区域和场景外部内容等未观测空间时。这一缺陷限制了其在机器人领域的广泛应用——例如未知环境中的机器人探索与规划任务，必须考虑模型预测的可靠性。针对此问题，我们提出一种基于学习的不完整场景几何估计3D不确定场的新方法，能够显式识别上述未观测区域。通过分析每条相机光线的累积透射率，我们的不确定场可推断出二维像素级不确定性，对直接射向遮挡区域或场景外部内容的光线赋予高不确定值。为量化已学习表面的不确定性，我们构建了一个随机辐射场。实验表明，与近期方法相比，本方法是唯一能在三维未观测区域及其关联二维渲染像素上显式推理高不确定性的方案。此外，我们证明了所设计的不确定场能完美适配真实世界的机器人任务，例如最优视角选择。