  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.
