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.
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