Figure 10.

Exemplary illustration of the course of the parameter continuation in β for the quantitative results reported in Table 9. We refer to Table 9 and the text for details on the experimental setup. We report results for the brain images (top row) and the hand images (bottom row) for plain H²-regularization. For each experiment, we display (from left to right) (i) the trend of the minimal value of the determinant of the deformation gradient (the dashed line indicates the user-defined lower bound on $det({\mathit{F}}_1^h)$, (ii) the trend of the L²-distance (h_d is the grid cell volume and $\mathit{r}:=m_R^h-m_T^h$, r ∈ R^ñ, $\stackrel{\sim }{n}={\prod }_{i=1}^2{n}_x^i$) and (iii) the trend of β, all with respect to the parameter continuation step. We indicate our judgment on the results in color. That is, if a result is accepted (i.e., $min(det({\mathit{F}}_1^h))\ge {\epsilon }_F$) we plot the marker in green, and if a result is rejected (i.e., $min(det({\mathit{F}}_1^h))<{\epsilon }_F$) we plot the marker in red. The optimal value is plotted in blue. The plots correspond to the results reported in Table 9.