  Learning from 3D point-cloud data has rapidly gained momentum, motivated by
the success of deep learning on images and the increased availability of
3D~data. In this paper, we aim to construct anisotropic convolution layers that
work directly on the surface derived from a point cloud. This is challenging
because of the lack of a global coordinate system for tangential directions on
surfaces. We introduce DeltaConv, a convolution layer that combines geometric
operators from vector calculus to enable the construction of anisotropic
filters on point clouds. Because these operators are defined on scalar- and
vector-fields, we separate the network into a scalar- and a vector-stream,
which are connected by the operators. The vector stream enables the network to
explicitly represent, evaluate, and process directional information. Our
convolutions are robust and simple to implement and match or improve on
state-of-the-art approaches on several benchmarks, while also speeding up
training and inference.
