Abstract
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-ofthe-art in point cloud segmentation of indoor and outdoor
scenes, and lidar motion estimation of driving scenes