  We present a simple and general framework for feature learning from point
clouds. The key to the success of CNNs is the convolution operator that is
capable of leveraging spatially-local correlation in data represented densely
in grids (e.g. images). However, point clouds are irregular and unordered, thus
directly convolving kernels against features associated with the points, will
result in desertion of shape information and variance to point ordering. To
address these problems, we propose to learn an $\mathcal{X}$-transformation
from the input points, to simultaneously promote two causes. The first is the
weighting of the input features associated with the points, and the second is
the permutation of the points into a latent and potentially canonical order.
Element-wise product and sum operations of the typical convolution operator are
subsequently applied on the $\mathcal{X}$-transformed features. The proposed
method is a generalization of typical CNNs to feature learning from point
clouds, thus we call it PointCNN. Experiments show that PointCNN achieves on
par or better performance than state-of-the-art methods on multiple challenging
benchmark datasets and tasks.
