  Point clouds are an increasingly relevant data type but they are often
corrupted by noise. We propose a deep neural network based on
graph-convolutional layers that can elegantly deal with the
permutation-invariance problem encountered by learning-based point cloud
processing methods. The network is fully-convolutional and can build complex
hierarchies of features by dynamically constructing neighborhood graphs from
similarity among the high-dimensional feature representations of the points.
When coupled with a loss promoting proximity to the ideal surface, the proposed
approach significantly outperforms state-of-the-art methods on a variety of
metrics. In particular, it is able to improve in terms of Chamfer measure and
of quality of the surface normals that can be estimated from the denoised data.
We also show that it is especially robust both at high noise levels and in
presence of structured noise such as the one encountered in real LiDAR scans.
