Polyaffine parametrization of image registration based on geodesic flows

Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which is very similar to existing methods, we show that we can find an analytical solution.

This solution converges exponentially to the true solution, and the gradients may be determined similarly. We compare to existing prominent methods; the log-euclidean polyaffine framework, and the DARTEL implementation of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether.