Recent advances in deep learning have improved 3D point cloud registration but increased graphics processing unit (GPU) memory usage, often requiring preliminary sampling that reduces accuracy. We propose an overlapping region sampling method to reduce memory usage while maintaining accuracy. Our approach estimates the overlapping region and intensively samples from it, using a k-nearest-neighbor (kNN) based point compression mechanism with multi layer perceptron (MLP) and transformer architectures. Evaluations on 3DMatch and 3DLoMatch datasets show our method outperforms other sampling methods in registration recall, especially at lower GPU memory levels. For 3DMatch, we achieve 94% recall with 33% reduced memory usage, with greater advantages in 3DLoMatch. Our method enables efficient large-scale point cloud registration in resource-constrained environments, maintaining high accuracy while significantly reducing memory requirements.