  We present a novel differential matching algorithm for 3D point cloud
registration. Instead of only optimizing the feature extractor for a matching
algorithm, we propose a learning-based matching module optimized to the
jointly-trained feature extractor. We focused on edge-wise feature-forwarding
architectures, which are memory-consuming but can avoid the over-smoothing
effect that GNNs suffer. We improve its memory efficiency to scale it for point
cloud registration while investigating the best way of connecting it to the
feature extractor. Experimental results show our matching module's significant
impact on performance improvement in rigid/non-rigid and whole/partial point
cloud registration datasets with multiple contemporary feature extractors. For
example, our module boosted the current SOTA method, RoITr, by +5.4%, and +7.2%
in the NFMR metric and +6.1% and +8.5% in the IR metric on the 4DMatch and
4DLoMatch datasets, respectively.
