local-to-global point cloud registration is a critical task in computer vision that finds wide application in various fields such as 3D reconstruction, digitization of cultural heritage, robots. Despite extensive research in point cloud registration, existing methods face significant challenges when dealing with low-overlapping point clouds with a high proportion of outliers. In this paper, a local-to-global point cloud registration network IOPCNet that is based on inner and outer point classification is proposed. The main focus of IOPCNet is to transform the point cloud registration problem into a binary classification problem, effectively converting partial overlap registration into full overlap registration. Specifically, we first design a simple yet effective local reference framework to enhance the accuracy of coordinates of the correspondence points on both point clouds at an early stage. Then, we utilize edge convolution networks for feature extraction. Furthermore, we introduce a similarity matrix enhancement layer that corrects erroneous correspondences in the initial similarity matrix using external memory units. Subsequently, the corresponding features are decoded to distinguish the overlapping region point clouds, and finally the overlapping region point clouds are fed into the ICP-based registration channel to solve the transform matrix. IOPCNet exhibits robustness to noise, outliers, and low overlap rates, demonstrating effective registration even at just 10% overlap. We evaluated IOPCNet on point cloud datasets ModelNet40, KITTI and 3DMatch, and ETH and compared it to 12 benchmark methods. Extensive experiments confirm that our proposed method achieves state-of-the-art performance.