  We tackle data-driven 3D point cloud registration. Given point
correspondences, the standard Kabsch algorithm provides an optimal rotation
estimate. This allows to train registration models in an end-to-end manner by
differentiating the SVD operation. However, given the initial rotation estimate
supplied by Kabsch, we show we can improve point correspondence learning during
model training by extending the original optimization problem. In particular,
we linearize the governing constraints of the rotation matrix and solve the
resulting linear system of equations. We then iteratively produce new solutions
by updating the initial estimate. Our experiments show that, by plugging our
differentiable layer to existing learning-based registration methods, we
improve the correspondence matching quality. This yields up to a 7% decrease in
rotation error for correspondence-based data-driven registration methods.
