  Point cloud registration has seen recent success with several learning-based
methods that focus on correspondence matching and, as such, optimize only for
this objective. Following the learning step of correspondence matching, they
evaluate the estimated rigid transformation with a RANSAC-like framework. While
it is an indispensable component of these methods, it prevents a fully
end-to-end training, leaving the objective to minimize the pose error
nonserved. We present a novel solution, Q-REG, which utilizes rich geometric
information to estimate the rigid pose from a single correspondence. Q-REG
allows to formalize the robust estimation as an exhaustive search, hence
enabling end-to-end training that optimizes over both objectives of
correspondence matching and rigid pose estimation. We demonstrate in the
experiments that Q-REG is agnostic to the correspondence matching method and
provides consistent improvement both when used only in inference and in
end-to-end training. It sets a new state-of-the-art on the 3DMatch, KITTI, and
ModelNet benchmarks.
