  Image registration is an essential step in many medical image analysis tasks.
Traditional methods for image registration are primarily optimization-driven,
finding the optimal deformations that maximize the similarity between two
images. Recent learning-based methods, trained to directly predict
transformations between two images, run much faster, but suffer from
performance deficiencies due to model generalization and the inefficiency in
handling individual image specific deformations. Here we present a new neural
net based image registration framework, called NIR (Neural Image Registration),
which is based on optimization but utilizes deep neural nets to model
deformations between image pairs. NIR represents the transformation between two
images with a continuous function implemented via neural fields, receiving a 3D
coordinate as input and outputting the corresponding deformation vector. NIR
provides two ways of generating deformation field: directly output a
displacement vector field for general deformable registration, or output a
velocity vector field and integrate the velocity field to derive the
deformation field for diffeomorphic image registration. The optimal
registration is discovered by updating the parameters of the neural field via
stochastic gradient descent. We describe several design choices that facilitate
model optimization, including coordinate encoding, sinusoidal activation,
coordinate sampling, and intensity sampling. Experiments on two 3D MR brain
scan datasets demonstrate that NIR yields state-of-the-art performance in terms
of both registration accuracy and regularity, while running significantly
faster than traditional optimization-based methods.
