Topological and geometrical joint learning for 3D graph data

Traditional convolutional neural networks (CNNs) are limited to be directly applied to 3D graph data due to their inherent grid structure. And most of graph-based learning methods use local-to-global hierarchical structure learning, and often ignore the global context. To overcome these issues, we propose two strategies: one is topological learning with 3D offset convolution, which provides learnable parameters in local graph construction, effectively expands the sampling space and improves the perception ability of diverse local structures. The other is geometrical learning with an adaptive spec-graph convolution network (AsGCN), which establishes a joint learning mechanism of local geometry in spatial domain and global structure in feature domain, and generates informative deep features through spectral filtering and weighting. Extensive experiments demonstrate that our deep features have strong discerning ability and robustness to non-rigid transformed graph data, incomplete mesh data, and better performance can be obtained compared to state-of-the-art methods.