  3D point cloud registration is a fundamental problem in computer vision and
robotics. Recently, learning-based point cloud registration methods have made
great progress. However, these methods are sensitive to outliers, which lead to
more incorrect correspondences. In this paper, we propose a novel deep graph
matching-based framework for point cloud registration. Specifically, we first
transform point clouds into graphs and extract deep features for each point.
Then, we develop a module based on deep graph matching to calculate a soft
correspondence matrix. By using graph matching, not only the local geometry of
each point but also its structure and topology in a larger range are considered
in establishing correspondences, so that more correct correspondences are
found. We train the network with a loss directly defined on the
correspondences, and in the test stage the soft correspondences are transformed
into hard one-to-one correspondences so that registration can be performed by a
correspondence-based solver. Furthermore, we introduce a transformer-based
method to generate edges for graph construction, which further improves the
quality of the correspondences. Extensive experiments on object-level and
scene-level benchmark datasets show that the proposed method achieves
state-of-the-art performance. The code is available at:
\href{https://github.com/fukexue/RGM}{https://github.com/fukexue/RGM}.
