  Registration of distant outdoor LiDAR point clouds is crucial to extending
the 3D vision of collaborative autonomous vehicles, and yet is challenging due
to small overlapping area and a huge disparity between observed point
densities. In this paper, we propose Group-wise Contrastive Learning (GCL)
scheme to extract density-invariant geometric features to register distant
outdoor LiDAR point clouds. We mark through theoretical analysis and
experiments that, contrastive positives should be independent and identically
distributed (i.i.d.), in order to train densityinvariant feature extractors. We
propose upon the conclusion a simple yet effective training scheme to force the
feature of multiple point clouds in the same spatial location (referred to as
positive groups) to be similar, which naturally avoids the sampling bias
introduced by a pair of point clouds to conform with the i.i.d. principle. The
resulting fully-convolutional feature extractor is more powerful and
density-invariant than state-of-the-art methods, improving the registration
recall of distant scenarios on KITTI and nuScenes benchmarks by 40.9% and
26.9%, respectively. Code is available at https://github.com/liuQuan98/GCL.
