  Standard convolutional neural networks assume a grid structured input is
available and exploit discrete convolutions as their fundamental building
blocks. This limits their applicability to many real-world applications. In
this paper we propose Parametric Continuous Convolution, a new learnable
operator that operates over non-grid structured data. The key idea is to
exploit parameterized kernel functions that span the full continuous vector
space. This generalization allows us to learn over arbitrary data structures as
long as their support relationship is computable. Our experiments show
significant improvement over the state-of-the-art in point cloud segmentation
of indoor and outdoor scenes, and lidar motion estimation of driving scenes.
