Table 7.

Values for the determinant of the deformation gradient $det({\mathit{F}}_1^h)$ for exemplary results of the convergence study reported in Table 6. We report results for the Picard and the GN-PCG method. We refer to Table 6 and the text for details on the experimental setup. We report results for the Stokes regularization scheme (γ = 1; H¹-regularization). The regularization parameter is set to β = 1E–3. The grid size is n_x = (256, 256)^⊤. These results directly relate to those reported for the smooth registration problem (see section 5.3.2, in particular Table 5).

	$min(det({\mathit{F}}_1^h))$	$max(det({\mathit{F}}_1^h))$	$\text{mean}(det({\mathit{F}}_1^h))$	$\text{std}(det({\mathit{F}}_1^h))$
Picard	10.00E–1	1.00	1.00	2.03E–5
GN-PCG	10.00E–1	1.00	1.00	2.29E–5