Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representations

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.