  In spite of the recent progresses on classifying 3D point cloud with deep
CNNs, large geometric transformations like rotation and translation remain
challenging problem and harm the final classification performance. To address
this challenge, we propose Geometry Sharing Network (GS-Net) which effectively
learns point descriptors with holistic context to enhance the robustness to
geometric transformations. Compared with previous 3D point CNNs which perform
convolution on nearby points, GS-Net can aggregate point features in a more
global way. Specially, GS-Net consists of Geometry Similarity Connection (GSC)
modules which exploit Eigen-Graph to group distant points with similar and
relevant geometric information, and aggregate features from nearest neighbors
in both Euclidean space and Eigenvalue space. This design allows GS-Net to
efficiently capture both local and holistic geometric features such as
symmetry, curvature, convexity and connectivity. Theoretically, we show the
nearest neighbors of each point in Eigenvalue space are invariant to rotation
and translation. We conduct extensive experiments on public datasets,
ModelNet40, ShapeNet Part. Experiments demonstrate that GS-Net achieves the
state-of-the-art performances on major datasets, 93.3% on ModelNet40, and are
more robust to geometric transformations.
