  Inverse consistency is a desirable property for image registration. We
propose a simple technique to make a neural registration network inverse
consistent by construction, as a consequence of its structure, as long as it
parameterizes its output transform by a Lie group. We extend this technique to
multi-step neural registration by composing many such networks in a way that
preserves inverse consistency. This multi-step approach also allows for
inverse-consistent coarse to fine registration. We evaluate our technique on
synthetic 2-D data and four 3-D medical image registration tasks and obtain
excellent registration accuracy while assuring inverse consistency.
