Effectively measuring and modeling the reliability of a trained model is essential to the real-world deployment of monocular depth estimation (MDE) models. However, the intrinsic ill-posedness and ordinal-sensitive nature of MDE pose major challenges to the estimation of uncertainty degree of the trained models. On the one hand, utilizing current uncertainty modeling methods may increase memory consumption and are usually time-consuming. On the other hand, measuring the uncertainty based on model accuracy can also be problematic, where uncertainty reliability and prediction accuracy are not well decoupled. In this paper, we propose to model the uncertainty of MDE models from the perspective of the inherent probability distributions originating from the depth probability volume and its extensions, and to assess it more fairly with more comprehensive metrics. By simply introducing additional training regularization terms, our model, with surprisingly simple formations and without requiring extra modules or multiple inferences, can provide uncertainty estimations with state-of-the-art reliability, and can be further improved when combined with ensemble or sampling methods. A series of experiments demonstrate the effectiveness of our methods.

翻译：有效测量和建模训练模型的可靠性对于单目深度估计（MDE）模型在实际场景中的部署至关重要。然而，MDE固有的不适定性和序数敏感性给已训练模型不确定度的估计带来了重大挑战。一方面，现有不确定度建模方法可能增加内存消耗且通常耗时；另一方面，基于模型精度测量不确定度也存在问题——不确定度可靠性与预测精度未能充分解耦。本文提出从深度概率体积及其扩展所固有的概率分布视角对MDE模型的不确定度进行建模，并通过更全面的指标进行更公平的评估。通过仅引入额外的训练正则化项，本模型以出乎意料的简洁形式（无需额外模块或多重推理）即可提供具有最先进可靠性的不确定度估计，且在与集成或采样方法结合时性能可进一步提升。系列实验证明了我们方法的有效性。