  The majority of deep learning (DL) based deformable image registration
methods use convolutional neural networks (CNNs) to estimate displacement
fields from pairs of moving and fixed images. This, however, requires the
convolutional kernels in the CNN to not only extract intensity features from
the inputs but also understand image coordinate systems. We argue that the
latter task is challenging for traditional CNNs, limiting their performance in
registration tasks. To tackle this problem, we first introduce Coordinate
Translator, a differentiable module that identifies matched features between
the fixed and moving image and outputs their coordinate correspondences without
the need for training. It unloads the burden of understanding image coordinate
systems for CNNs, allowing them to focus on feature extraction. We then propose
a novel deformable registration network, im2grid, that uses multiple Coordinate
Translator's with the hierarchical features extracted from a CNN encoder and
outputs a deformation field in a coarse-to-fine fashion. We compared im2grid
with the state-of-the-art DL and non-DL methods for unsupervised 3D magnetic
resonance image registration. Our experiments show that im2grid outperforms
these methods both qualitatively and quantitatively.
