  Deformable image registration, estimating the spatial transformation between
different images, is an important task in medical imaging. Many previous
studies have used learning-based methods for multi-stage registration to
perform 3D image registration to improve performance. The performance of the
multi-stage approach, however, is limited by the size of the receptive field
where complex motion does not occur at a single spatial scale. We propose a new
registration network combining recursive network architecture and mutual
attention mechanism to overcome these limitations. Compared with the
state-of-the-art deep learning methods, our network based on the recursive
structure achieves the highest accuracy in lung Computed Tomography (CT) data
set (Dice score of 92\% and average surface distance of 3.8mm for lungs) and
one of the most accurate results in abdominal CT data set with 9 organs of
various sizes (Dice score of 55\% and average surface distance of 7.8mm). We
also showed that adding 3 recursive networks is sufficient to achieve the
state-of-the-art results without a significant increase in the inference time.
