  We study the problem of extracting accurate correspondences for point cloud
registration. Recent keypoint-free methods bypass the detection of repeatable
keypoints which is difficult in low-overlap scenarios, showing great potential
in registration. They seek correspondences over downsampled superpoints, which
are then propagated to dense points. Superpoints are matched based on whether
their neighboring patches overlap. Such sparse and loose matching requires
contextual features capturing the geometric structure of the point clouds. We
propose Geometric Transformer to learn geometric feature for robust superpoint
matching. It encodes pair-wise distances and triplet-wise angles, making it
robust in low-overlap cases and invariant to rigid transformation. The
simplistic design attains surprisingly high matching accuracy such that no
RANSAC is required in the estimation of alignment transformation, leading to
$100$ times acceleration. Our method improves the inlier ratio by $17{\sim}30$
percentage points and the registration recall by over $7$ points on the
challenging 3DLoMatch benchmark. Our code and models are available at
https://github.com/qinzheng93/GeoTransformer.
