ABSTRACT Partial-to-partial point cloud registration is a fundamental and challenging task in the three-dimensional computer vision. In this letter, we propose a novel Hierarchical Channel-Spatial Interaction Network (HCSINet), which can hierarchically explore information interaction in terms of the channel and spatial dimensions, enabling well partial point cloud perception for partial-to-partial registration. Specifically, the Channel-wise Feature Interaction (CFI) module is regarded as the basic unit of the encoder sub-network, which achieves feature hierarchical interaction to learn the overlapping scores and intuitively improve the importance of overlapping areas. Furthermore, to improve the discrimination of the overlapping points, the Co-Attention-based Spatial Association (CA-SA) module progressively excavates multi-scale spatial correlation of overlapping points by conjointly computing collaborative attention. Experimental results verify the validity of our HCSINet, which achieves competitive partial-to-partial registration performances compared to existing traditional and deep learning-based methods. The source code is publicly available https://github.com/lxnudt/HCSINet.