Abstract: To improve accuracy, robustness, and generalization of point cloud registration and address the problem of the Iterative Closest Point (ICP) algorithm easily falling into local optimal solutions, a point cloud registration method (GSDCP) based on coordinate geometric sampling was proposed. Firstly, central point curvature was estimated using coordinates of surrounding points, and points that preserve geometric features of point clouds were selected based on their curvature size. After downsampling the point cloud, a Dynamic Graph Convolutional Network (DGCNN) was employed in conjunction with the downsampled point cloud to learn integrated point cloud features that incorporate local geometry information. Contextual information is captured using a Transformer, and soft Pointers facilitate approximate combination and matching between two feature embedders. A differentiable Single Value Decomposition (SVD) layer is utilized to estimate the final rigid transformation. Point cloud registration experiments were conducted on the ModelNet40 dataset. Comparisons were made with ICP, Globally Optimal ICP (Go-ICP), PointNetLK, Fast Global Registration (FGR), Attention Dynamic Graph Convolutional Neural Network Lucas-Kanade (ADGCNNLK), Deep Closest Point (DCP), and Multi-Features Guidance Network (MFGNet), revealing that GSDCP achieves superior registration accuracy and robustness in scenarios involving noise, as well as when the point cloud category is invisible. In noise-free scenarios, GSDCP reduces rotational mean square error by 31.3% and translational mean square error by 58.3% compared to MFGNet. In noisy scenarios, GSDCP reduces rotational mean square error by 33.9% and translational mean square error by 73.4% compared to MFGNet. When the point cloud category is invisible, GSDCP reduces rotational mean square error by 57.7% and translational mean square error by 77.9% compared to MFGNet. Additionally, when dealing with incomplete point cloud data (including random occlusion and point cloud fragmentation), GSDCP exhibits a reduction of 35.1% in rotational mean square error and 39.8% in translational mean square error compared to MFGNet when point cloud integrity is below 75%.