To address the limited capability of edge convolution in extracting neighborhood features under varying sampling densities, this paper proposes a point cloud registration network based on an improved edge convolution. First, a Progressive Interval Sampling (PIS) strategy is designed to enhance the spatial coverage of neighborhoods. Then, a Coordinated Attention-Pooling Module (CAPM) is incorporated into the PISEdgeConv to improve the edge feature extraction ability. Finally, a feature-weighted fusion module is employed to mine feature information extracted from multiple neighborhood scales. The network achieves root mean square errors (RMSE) of 0.893275 for rotation matrices and 0.002647 for translation vectors on the ModelNet40 dataset, demonstrating the effectiveness of the proposed method.