  We propose simple yet effective improvements in point representations and
local neighborhood graph construction within the general framework of graph
neural networks (GNNs) for 3D point cloud processing. As a first contribution,
we propose to augment the vertex representations with important local geometric
information of the points, followed by nonlinear projection using a MLP. As a
second contribution, we propose to improve the graph construction for GNNs for
3D point clouds. The existing methods work with a k-nn based approach for
constructing the local neighborhood graph. We argue that it might lead to
reduction in coverage in case of dense sampling by sensors in some regions of
the scene. The proposed methods aims to counter such problems and improve
coverage in such cases. As the traditional GNNs were designed to work with
general graphs, where vertices may have no geometric interpretations, we see
both our proposals as augmenting the general graphs to incorporate the
geometric nature of 3D point clouds. While being simple, we demonstrate with
multiple challenging benchmarks, with relatively clean CAD models, as well as
with real world noisy scans, that the proposed method achieves state of the art
results on benchmarks for 3D classification (ModelNet40) , part segmentation
(ShapeNet) and semantic segmentation (Stanford 3D Indoor Scenes Dataset). We
also show that the proposed network achieves faster training convergence, i.e.
~40% less epochs for classification. The project details are available at
https://siddharthsrivastava.github.io/publication/geomgcnn/
