  Point cloud, an efficient 3D object representation, has become popular with
the development of depth sensing and 3D laser scanning techniques. It has
attracted attention in various applications such as 3D tele-presence,
navigation for unmanned vehicles and heritage reconstruction. The understanding
of point clouds, such as point cloud segmentation, is crucial in exploiting the
informative value of point clouds for such applications. Due to the
irregularity of the data format, previous deep learning works often convert
point clouds to regular 3D voxel grids or collections of images before feeding
them into neural networks, which leads to voluminous data and quantization
artifacts. In this paper, we instead propose a regularized graph convolutional
neural network (RGCNN) that directly consumes point clouds. Leveraging on
spectral graph theory, we treat features of points in a point cloud as signals
on graph, and define the convolution over graph by Chebyshev polynomial
approximation. In particular, we update the graph Laplacian matrix that
describes the connectivity of features in each layer according to the
corresponding learned features, which adaptively captures the structure of
dynamic graphs. Further, we deploy a graph-signal smoothness prior in the loss
function, thus regularizing the learning process. Experimental results on the
ShapeNet part dataset show that the proposed approach significantly reduces the
computational complexity while achieving competitive performance with the state
of the art. Also, experiments show RGCNN is much more robust to both noise and
point cloud density in comparison with other methods. We further apply RGCNN to
point cloud classification and achieve competitive results on ModelNet40
dataset.
