  Graph convolutional neural networks (Graph-CNNs) extend traditional CNNs to
handle data that is supported on a graph. Major challenges when working with
data on graphs are that the support set (the vertices of the graph) do not
typically have a natural ordering, and in general, the topology of the graph is
not regular (i.e., vertices do not all have the same number of neighbors).
Thus, Graph-CNNs have huge potential to deal with 3D point cloud data which has
been obtained from sampling a manifold. In this paper, we develop a Graph-CNN
for classifying 3D point cloud data, called PointGCN. The architecture combines
localized graph convolutions with two types of graph downsampling operations
(also known as pooling). By the effective exploration of the point cloud local
structure using the Graph-CNN, the proposed architecture achieves competitive
performance on the 3D object classification benchmark ModelNet, and our
architecture is more stable than competing schemes.
