DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds

Learning from 3D point-cloud data has rapidly gained momentum, motivated bythe success of deep learning on images and the increased availability of3D~data. In this paper, we aim to construct anisotropic convolution layers thatwork directly on the surface derived from a point cloud. This is challengingbecause of the lack of a global coordinate system for tangential directions onsurfaces. We introduce DeltaConv, a convolution layer that combines geometricoperators from vector calculus to enable the construction of anisotropicfilters on point clouds. Because these operators are defined on scalar- andvector-fields, we separate the network into a scalar- and a vector-stream,which are connected by the operators. The vector stream enables the network toexplicitly represent, evaluate, and process directional information. Ourconvolutions are robust and simple to implement and match or improve onstate-of-the-art approaches on several benchmarks, while also speeding uptraining and inference.