Point cloud analysis is very challenging, as the shape implied in irregular points is difficult to capture. In this paper, we propose RS-CNN, namely, Relation-Shape Convolutional Neural Network, which extends regular grid CNN to irregular configuration for point cloud analysis. The key to RS-CNN is learning from relation, i.e., the geometric topology constraint among points. Specifically, the convolutional weight for local point set is forced to learn a high-level relation expression from predefined geometric priors, between a sampled point from this point set and the others. In this way, an inductive local representation with explicit reasoning about the spatial layout of points can be obtained, which leads to much shape awareness and robustness. With this convolution as a basic operator, RS-CNN, a hierarchical architecture can be developed to achieve contextual shape-aware learning for point cloud analysis. Extensive experiments on challenging benchmarks across three tasks verify RS-CNN achieves the state of the arts.
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