We introduce Primitive-based Representations of Uncertainty (PRIMU), a post-hoc uncertainty estimation (UE) framework for Gaussian Splatting (GS). Reliable UE is essential for deploying GS in safety-critical domains such as robotics and medicine. Existing approaches typically estimate Gaussian-primitive variances and rely on the rendering process to obtain pixel-wise uncertainties. In contrast, we construct primitive-level representations of error and visibility/coverage from training views, capturing interpretable uncertainty information. These representations are obtained by projecting view-dependent training errors and coverage statistics onto the primitives. Uncertainties for novel views are inferred by rendering these primitive-level representations, producing uncertainty feature maps, which are aggregate through pixel-wise regression on holdout data. We analyze combinations of uncertainty feature maps and regression models to understand how their interactions affect prediction accuracy and generalization. PRIMU also enables an effective active view selection strategy by directly leveraging these uncertainty feature maps. Additionally, we study the effect of separating splatting into foreground and background regions. Our estimates show strong correlations with true errors, outperforming state-of-the-art methods, especially for depth UE and foreground objects. Finally, our regression models show generalization capabilities to unseen scenes, enabling UE without additional holdout data.

翻译：本文提出基于基元的不确定性表示方法（PRIMU），一种面向高斯溅射（GS）的后验不确定性估计框架。可靠的不确定性估计对于在机器人、医疗等安全关键领域部署GS技术至关重要。现有方法通常通过估计高斯基元方差并依赖渲染过程获取逐像素不确定性。与之不同，我们基于训练视角构建误差与可见性/覆盖度的基元级表示，从而捕获可解释的不确定性信息。这些表示通过将视角相关的训练误差与覆盖度统计量投影至基元而获得。新视角的不确定性通过渲染这些基元级表示生成的 uncertainty feature maps 进行推断，并利用留出数据进行逐像素回归聚合。我们系统分析了不确定性特征图与回归模型的组合方式，探究其交互作用对预测精度与泛化能力的影响。PRIMU通过直接利用这些不确定性特征图，可实现高效的自适应视角选择策略。此外，我们研究了将溅射过程分离为前景与背景区域的影响。实验表明，我们的估计结果与真实误差具有强相关性，在深度不确定性估计及前景物体方面显著优于现有最优方法。最后，我们的回归模型展现出对未见过场景的泛化能力，可在无需额外留出数据的情况下实现不确定性估计。