This paper presents Point Convolutional Neural Networks (PCNN): a novel
framework for applying convolutional neural networks to point clouds. The
framework consists of two operators: extension and restriction, mapping point
cloud functions to volumetric functions and vise-versa. A point cloud
convolution is defined by pull-back of the Euclidean volumetric convolution via
an extension-restriction mechanism.
The point cloud convolution is computationally efficient, invariant to the
order of points in the point cloud, robust to different samplings and varying
densities, and translation invariant, that is the same convolution kernel is
used at all points. PCNN generalizes image CNNs and allows readily adapting
their architectures to the point cloud setting.
Evaluation of PCNN on three central point cloud learning benchmarks
convincingly outperform competing point cloud learning methods, and the vast
majority of methods working with more informative shape representations such as
surfaces and/or normals.

本文介绍了点卷积神经网络（PCNN）的框架和两个算子：扩展和限制。此外，还定义了点云卷积的概念，其具有高效性，不受各种因素的影响，并可将卷积核用于任何点云中。通过三项常见的点云学习基准测试，证明了 PCNN 方法的有效性。