  We present VoxelMorph, a fast learning-based framework for deformable,
pairwise medical image registration. Traditional registration methods optimize
an objective function for each pair of images, which can be time-consuming for
large datasets or rich deformation models. In contrast to this approach, and
building on recent learning-based methods, we formulate registration as a
function that maps an input image pair to a deformation field that aligns these
images. We parameterize the function via a convolutional neural network (CNN),
and optimize the parameters of the neural network on a set of images. Given a
new pair of scans, VoxelMorph rapidly computes a deformation field by directly
evaluating the function. In this work, we explore two different training
strategies. In the first (unsupervised) setting, we train the model to maximize
standard image matching objective functions that are based on the image
intensities. In the second setting, we leverage auxiliary segmentations
available in the training data. We demonstrate that the unsupervised model's
accuracy is comparable to state-of-the-art methods, while operating orders of
magnitude faster. We also show that VoxelMorph trained with auxiliary data
improves registration accuracy at test time, and evaluate the effect of
training set size on registration. Our method promises to speed up medical
image analysis and processing pipelines, while facilitating novel directions in
learning-based registration and its applications. Our code is freely available
at voxelmorph.csail.mit.edu.
