  Magnetic Resonance Imaging (MRI) typically recruits multiple sequences
(defined here as "modalities"). As each modality is designed to offer different
anatomical and functional clinical information, there are evident disparities
in the imaging content across modalities. Inter- and intra-modality affine and
non-rigid image registration is an essential medical image analysis process in
clinical imaging, as for example before imaging biomarkers need to be derived
and clinically evaluated across different MRI modalities, time phases and
slices. Although commonly needed in real clinical scenarios, affine and
non-rigid image registration is not extensively investigated using a single
unsupervised model architecture. In our work, we present an un-supervised deep
learning registration methodology which can accurately model affine and
non-rigid trans-formations, simultaneously. Moreover, inverse-consistency is a
fundamental inter-modality registration property that is not considered in deep
learning registration algorithms. To address inverse-consistency, our
methodology performs bi-directional cross-modality image synthesis to learn
modality-invariant latent rep-resentations, while involves two factorised
transformation networks and an inverse-consistency loss to learn
topology-preserving anatomical transformations. Overall, our model (named
"FIRE") shows improved performances against the reference standard baseline
method on multi-modality brain 2D and 3D MRI and intra-modality cardiac 4D MRI
data experiments.
