  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.
