  In contrast to the literature where local patterns in 3D point clouds are
captured by customized convolutional operators, in this paper we study the
problem of how to effectively and efficiently project such point clouds into a
2D image space so that traditional 2D convolutional neural networks (CNNs) such
as U-Net can be applied for segmentation. To this end, we are motivated by
graph drawing and reformulate it as an integer programming problem to learn the
topology-preserving graph-to-grid mapping for each individual point cloud. To
accelerate the computation in practice, we further propose a novel hierarchical
approximate algorithm. With the help of the Delaunay triangulation for graph
construction from point clouds and a multi-scale U-Net for segmentation, we
manage to demonstrate the state-of-the-art performance on ShapeNet and PartNet,
respectively, with significant improvement over the literature. Code is
available at https://github.com/Zhang-VISLab.
