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：基于神经辐射场（NeRF）的现有方法显著缺乏量化预测不确定性的能力，尤其是在未见空间（包括被遮挡和场景外部内容）上。这一局限性阻碍了它们在机器人领域的广泛应用，因为在未知环境下进行机器人探索和规划等任务中，必须考虑模型预测的可靠性。为解决这一问题，我们提出了一种基于学习到的不完整场景几何来估计3D不确定性场的新方法，该方法能够明确识别这些未见区域。通过考虑每条相机射线的累积透射率，我们的不确定性场推断出2D像素级的不确定性，对于直接射向被遮挡或场景外部内容的射线，其值较高。为量化学习到的表面上的不确定性，我们对随机辐射场进行了建模。实验表明，与近期方法相比，我们的方法是唯一能够明确推理3D未见区域及其涉及的2D渲染像素高不确定性的方法。此外，我们展示了所设计的不确定性场非常适合实际机器人任务，例如最佳下一视角选择。