Dense prediction tasks are common for 3D point clouds, but the uncertainties inherent in massive points and their embeddings have long been ignored. In this work, we present CUE, a novel uncertainty estimation method for dense prediction tasks in 3D point clouds. Inspired by metric learning, the key idea of CUE is to explore cross-point embeddings upon a conventional 3D dense prediction pipeline. Specifically, CUE involves building a probabilistic embedding model and then enforcing metric alignments of massive points in the embedding space. We also propose CUE+, which enhances CUE by explicitly modeling crosspoint dependencies in the covariance matrix. We demonstrate that both CUE and CUE+ are generic and effective for uncertainty estimation in 3D point clouds with two different tasks: (1) in 3D geometric feature learning we for the first time obtain wellcalibrated uncertainty, and (2) in semantic segmentation we reduce uncertainty's Expected Calibration Error of the state-of-the-arts by 16.5%. All uncertainties are estimated without compromising predictive performance.

翻译：密集预测任务在三维点云中常见，但大量点及其嵌入中的不确定性长期以来被忽视。本文提出CUE，一种针对三维点云密集预测任务的新型不确定性估计方法。受度量学习启发，CUE的核心思想是在常规三维密集预测流程中探索交叉点嵌入。具体而言，CUE构建概率嵌入模型，并在嵌入空间中实施大量点的度量对齐。我们还提出CUE+，通过显式建模协方差矩阵中的交叉点依赖关系来增强CUE。我们证明CUE和CUE+在三维点云中具有通用性和有效性，涵盖两项不同任务：（1）在三维几何特征学习中，我们首次获得校准良好的不确定性；（2）在语义分割中，我们将最先进方法的期望校准误差降低16.5%。所有不确定性估计均在不牺牲预测性能的前提下完成。