Frequency implementation of the Euler-Lagrange equations for variational image registration

In this letter, a novel theoretical framework defined in the frequency domain for variational nonparametric image registration is proposed. It provides more efficient implementations than existing theoretical approaches for the most common registration techniques. The presented frequency domain analysis adds simplicity to the variational image registration implementations and allows for an easy extension to higher dimensions by using the multidimensional Fourier transform of multidimensional signals.