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Point cloud registration precision degrades when the scene contains symmetric structures or repeated patches. Also, the common operation of continuous downsampling in existing registration methods causes the loss of detailed information and leads to further registration precision degradation. In this paper, we propose a high precision point cloud registration network (HPNet) to learn discriminative features by considering both multi-scale information and position information. We first propose a multi-scale feature extraction module similar to the feature pyramid that allows the extracted features to contain multi-scale information. Then, an information interaction is performed on the features to learn global contextual information by using Transformer with a hybrid position encoding, which takes into account both absolute and relative positions of points. Finally, the features obtained from the information interaction module are directly used to predict the point correspondences. Comprehensive experiments on 3DMatch, 3DLoMatch, ModelNet, and ModelLoNet datasets demonstrate the state-of-the-art performance of the proposed method and the implementation of HPNet in SLAM shows its effectiveness in real application. [Display omitted] • Point cloud registration loses detail information during continuous downsampling. • Feature fusion of low-level detail information and high-level semantic information. • Hybrid position encoding consider both absolute and relative positions. positions. • Point cloud registration algorithms applied to SLAM. [ABSTRACT FROM AUTHOR]