  We present an implementation of a new approach to diffeomorphic non-rigid
registration of medical images. The method is based on optical flow and warps
images via gradient flow with the standard $L^2$ inner product. To compute the
transformation, we rely on accelerated optimisation on the manifold of
diffeomorphisms. We achieve regularity properties of Sobolev gradient flows,
which are expensive to compute, owing to a novel method of averaging the
gradients in time rather than space. We successfully register brain MRI and
challenging abdominal CT scans at speeds orders of magnitude faster than
previous approaches. We make our code available in a public repository:
https://github.com/dgrzech/fastreg
