  We study the problem of extracting accurate correspondences for point cloud
registration. Recent keypoint-free methods have shown great potential through
bypassing the detection of repeatable keypoints which is difficult to do
especially in low-overlap scenarios. 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, or GeoTransformer for short, to
learn geometric feature for robust superpoint matching. It encodes pair-wise
distances and triplet-wise angles, making it invariant to rigid transformation
and robust in low-overlap cases. 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. Extensive
experiments on rich benchmarks encompassing indoor, outdoor, synthetic,
multiway and non-rigid demonstrate the efficacy of GeoTransformer. Notably, our
method improves the inlier ratio by $18{\sim}31$ percentage points and the
registration recall by over $7$ points on the challenging 3DLoMatch benchmark.
Our code and models are available at
\url{https://github.com/qinzheng93/GeoTransformer}.
