  Point cloud registration is a crucial problem in computer vision and
robotics. Existing methods either rely on matching local geometric features,
which are sensitive to the pose differences, or leverage global shapes, which
leads to inconsistency when facing distribution variances such as partial
overlapping. Combining the advantages of both types of methods, we adopt a
coarse-to-fine pipeline that concurrently handles both issues. We first reduce
the pose differences between input point clouds by aligning global features;
then we match the local features to further refine the inaccurate alignments
resulting from distribution variances. As global feature alignment requires the
features to preserve the poses of input point clouds and local feature matching
expects the features to be invariant to these poses, we propose an
SE(3)-equivariant feature extractor to simultaneously generate two types of
features. In this feature extractor, representations that preserve the poses
are first encoded by our novel SE(3)-equivariant network and then converted
into pose-invariant ones by a pose-detaching module. Experiments demonstrate
that our proposed method increases the recall rate by 20% compared to
state-of-the-art methods when facing both pose differences and distribution
variances.
