LightConvPoint: convolution for points

Recent state-of-the-art methods for point cloud semantic segmentation are based on convolution defined for point clouds. In this paper, we propose a formulation of the convolution for point cloud directly designed from the discrete convolution in image processing. The resulting formulation underlines the separation between the discrete kernel space and the geometric space where the points lies. The link between the two space is done by a change space matrix $\mathbf{A}$ which distributes the input features on the convolution kernel. Several existing methods fall under this formulation. We show that the matrix $\mathbf{A}$ can be easily estimated with neural networks. Finally, we show competitive results on several semantic segmentation benchmarks while being efficient both in computation time and memory.