Synthetic and real-world registration problems. All images have been normalized to an intensity range of [0, 1]. The registration problems are referred to as sinusoidal images (top row, left), UT images (top row, right), hand images (bottom row, left), and brain images (bottom row, right). Each row displays the reference image mR, the template (deformable) image mT, and a map of their pointwise difference (from left to right as identified by the inset in the images). We provide an illustration of the deformation pattern y (overlaid onto mT) for the synthetic problems. This mapping is computed from v★ in (5.1) via (D.1).