  It has witnessed a growing demand for efficient representation learning on
point clouds in many 3D computer vision applications. Behind the success story
of convolutional neural networks (CNNs) is that the data (e.g., images) are
Euclidean structured. However, point clouds are irregular and unordered.
Various point neural networks have been developed with isotropic filters or
using weighting matrices to overcome the structure inconsistency on point
clouds. However, isotropic filters or weighting matrices limit the
representation power. In this paper, we propose a permutable anisotropic
convolutional operation (PAI-Conv) that calculates soft-permutation matrices
for each point using dot-product attention according to a set of evenly
distributed kernel points on a sphere's surface and performs shared anisotropic
filters. In fact, dot product with kernel points is by analogy with the
dot-product with keys in Transformer as widely used in natural language
processing (NLP). From this perspective, PAI-Conv can be regarded as the
transformer for point clouds, which is physically meaningful and is robust to
cooperate with the efficient random point sampling method. Comprehensive
experiments on point clouds demonstrate that PAI-Conv produces competitive
results in classification and semantic segmentation tasks compared to
state-of-the-art methods.
