End-to-end trained per-point embeddings are an essential ingredient of any state-of-the-art 3D point cloud processing such as detection or alignment. Methods like PointNet, or the more recent point cloud transformer -- and its variants -- all employ learned per-point embeddings. Despite impressive performance, such approaches are sensitive to out-of-distribution (OOD) noise and outliers. In this paper, we explore the role of an analytical per-point embedding based on the criterion of bandwidth. The concept of bandwidth enables us to draw connections with an alternate per-point embedding -- positional embedding, particularly random Fourier features. We present compelling robust results across downstream tasks such as point cloud classification and registration with several categories of OOD noise.

翻译：端到端训练的逐点嵌入是任何最先进的3D点云处理（如检测或配准）的核心组成部分。PointNet等经典方法以及近年提出的点云Transformer及其变体，均采用学习得到的逐点嵌入。尽管性能卓越，这类方法对分布外噪声和离群点较为敏感。本文基于带宽准则探索解析式逐点嵌入的作用：带宽概念使我们能够建立与另一种逐点嵌入方法（即位置嵌入，特别是随机傅里叶特征）的关联。我们展示了在点云分类与配准等下游任务中，针对多种分布外噪声类型获得的鲁棒性实验结果。