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Point cloud registration is a critical research area in computer vision with extensive applications. Recent studies have unveiled the significant potential of graph neural networks (GNNs) for point cloud registration. One key approach is to leverage the smoothness of graph convolutions to extract similarity information between points. However, as the number of convolution layers increases, the features between points tend to become consistent, and distinctiveness is always neglected, which contradicts point cloud registration. To this end, this paper presents a new GNN framework with 3D graph smoothing-sharpening convolution (GNN-GSSC) for point cloud registration. It includes two new convolutional strategies: graph smoothing convolution (SmoothGConv) and graph sharpening convolution (SharpGConv). The former utilizes Laplacian smoothing to aggregate similar information from neighbouring nodes, whereas the latter encourages each node to move away from its neighbours to obtain more discriminative information. Specifically, we calculate the difference information between the central node and neighbouring nodes to supplement the node feature information while aggregating the similarity information of the nodes. In addition, we devise a Transformer-based overlapping point scoring module, enhancing the emphasis on overlapping areas while weakening the focus on non-overlapping areas by scoring each point. Experiments reveal that the proposed method is optimal compared to other existing methods. More importantly, SharpGConv is a plug-and-play graph convolution module that is particularly advantageous for extracting distinctive information in point cloud registration.

Graph convolutional neural networks can effectively process geometric data and thus have been successfully used in point cloud data representation. However, existing graph-based methods usually adopt the K-nearest neighbor (KNN) algorithm to construct graphs, which may not be optimal for point cloud analysis tasks, owning to the solution of KNN is independent of network training. In this paper, we propose a novel graph structure learning convolutional neural network (GSLCN) for multiple point cloud analysis tasks. The fundamental concept is to propose a general graph structure learning architecture (GSL) that builds long-range and short-range dependency graphs. To learn optimal graphs that best serve to extract local features and investigate global contextual information, respectively, we integrated the GSL with the designed graph convolution operator under a unified framework. Furthermore, we design the graph structure losses with some prior knowledge to guide graph learning during network training. The main benefit is that given labels and prior knowledge are taken into account in GSLCN, providing useful supervised information to build graphs and thus facilitating the graph convolution operation for the point cloud. Experimental results on challenging benchmarks demonstrate that the proposed framework achieves excellent performance for point cloud classification, part segmentation, and semantic segmentation.