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 latticebased methods to process and learn 3D spatial information; however, this leads to inevitable discretization errors. In this work, we try to handle raw 3D points without such compromise. The encoder of the proposed networks adopts similar architectures as in PointNet, which is a well-acknowledged method for supervised learning of 3D point clouds. The decoder of the proposed networks involves three novel modules: the folding module, the graph-topology-inference module, and the graphfiltering module. 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 designs graph filters based on the learnt graph topology and refines the coarse reconstruction to obtain the final reconstruction. We further provide theoretical analyses of the proposed architecture. We provide an upper bound for the reconstruction loss and further show the superiority of graph smoothness over spatial smoothness as a prior to model 3D point clouds. In the experiments, we validate the proposed networks in three tasks, including 3D point clouds reconstruction, visualization, and transfer classification. The experimental results show that (1) the proposed networks outperform the state-ofthe-art methods in various tasks, including reconstruction and transfer classification; (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.

We present a neural-network-based architecture for 3D point cloud denoising called neural projection denoising (NPD). In our previous work, we proposed a two-stage denoising algorithm, which first estimates reference planes and follows by projecting noisy points to estimated reference planes. Since the estimated reference planes are inevitably noisy, multiprojection is applied to stabilize the denoising performance. NPD algorithm uses a neural network to estimate reference planes for points in noisy point clouds. With more accurate estimations of reference planes, we are able to achieve better denoising performances with only one-time projection. To the best of our knowledge, NPD is the first work to denoise 3D point clouds with deep learning techniques. To conduct the experiments, we sample 40000 point clouds from the 3D data in ShapeNet to train a network and sample 350 point clouds from the 3D data in ModelNet10 to test. Experimental results show that our algorithm can estimate normal vectors of points in noisy point clouds. Comparing to five competitive methods, the proposed algorithm achieves better denoising performance and produces much smaller variances. Our code is available at https://github. com/chaojingduan/Neural-Projection.

As a collection of 3D points sampled from surfaces of objects, a 3D point cloud is widely used in robotics, autonomous driving and augmented reality. Due to the physical limitations of 3D sensing devices, 3D point clouds are usually noisy, which influences subsequent computations, such as surface reconstruction, recognition and many others. To denoise a 3D point cloud, we present a novel algorithm, called weighted multi-projection. Compared to many previous works on denoising, instead of directly smoothing the coordinates of 3D points, we use a two-fold smoothing: We first estimate a local tangent plane at each 3D point and then reconstruct each 3D point by weighted averaging of its projections on multiple tangent planes. We also provide the theoretical analysis for the surface normal estimation and achieve a tighter bound than in a previous work. We validate the empirical performance on the dataset of ShapeNetCore and show that weighted multi-projection outperforms its competitors in all nine classes.

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