  We propose a deep autoencoder with graph topology inference and filtering to
achieve compact representations of unorganized 3D point clouds in an
unsupervised manner. Many previous works discretize 3D points to voxels and
then use lattice-based methods to process and learn 3D spatial information;
however, this leads to inevitable discretization errors. In this work, we
handle raw 3D points without such compromise. The proposed networks follow the
autoencoder framework with a focus on designing the decoder. The encoder adopts
similar architectures as in PointNet. The decoder involves three novel modules.
The folding module folds a canonical 2D lattice to the underlying surface of a
3D point cloud, achieving coarse reconstruction; the graph-topology-inference
module learns a graph topology to represent pairwise relationships between 3D
points, pushing the latent code to preserve both coordinates and pairwise
relationships of points in 3D point clouds; and the graph-filtering module
couples the above two modules, refining the coarse reconstruction through a
learnt graph topology to obtain the final reconstruction. The proposed decoder
leverages a learnable graph topology to push the codeword to preserve
representative features and further improve the unsupervised-learning
performance. We further provide theoretical analyses of the proposed
architecture. In the experiments, we validate the proposed networks in three
tasks, including 3D point cloud reconstruction, visualization, and transfer
classification. The experimental results show that (1) the proposed networks
outperform the state-of-the-art methods in various tasks; (2) a graph topology
can be inferred as auxiliary information without specific supervision on graph
topology inference; and (3) graph filtering refines the reconstruction, leading
to better performances.
