  Generating a set of high-quality correspondences or matches is one of the
most critical steps in point cloud registration. This paper proposes a learning
framework COTReg by jointly considering the pointwise and structural matchings
to predict correspondences of 3D point cloud registration. Specifically, we
transform the two matchings into a Wasserstein distance-based and a
Gromov-Wasserstein distance-based optimizations, respectively. Thus the task of
establishing the correspondences can be naturally reshaped to a coupled optimal
transport problem. Furthermore, we design a network to predict the confidence
score of being an inlier for each point of the point clouds, which provides the
overlap region information to generate correspondences. Our correspondence
prediction pipeline can be easily integrated into either learning-based
features like FCGF or traditional descriptors like FPFH. We conducted
comprehensive experiments on 3DMatch, KITTI, 3DCSR, and ModelNet40 benchmarks,
showing the state-of-art performance of the proposed method.
