## 3 Results
### Accuracy Assessment for Rigid Registration  
As shown in Figure 5, the overall registration performance metrics, calculated after applying the rigid transformations at different learning rates and considering the 4 ROIs together, were acceptable for both the NM and the IM condition, aside from IM with learning rate 1. DSI, in particular, was generally higher than 0.75, and MSD smaller than 2 mm, regardless of the learning rate. Regarding the HD, the values exhibited a wider variability among subjects, but again IM and NM schemes were the best choice. In general, IM presented the lowest variability in all the accuracy indexes.  
As to the M condition, on the other hand, several cases showed a DSI \(<\) 0.6 and a MSD higher than 4 mm, and a much larger variation between observations was highlighted. Furthermore, in at least two cases, the registration failed to align the two images (DSI \(<\) 0.2). Considering its poor performance, M condition was not further considered for the non-rigid quantitative assessment.  
Considering the accuracy metrics of the four muscles separately, as shown in Figure 6, the same trend of the aggregated regions, with a larger value of DSI and smaller values of MSD for NM and IM groups was found. Registration performances, taking into account all schemes of the rigid transformation, were notably better for muscles with larger volumes (e.g., gluteus maximus and tensor fasciae latae).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & \multicolumn{4}{c}{**Muscle Volume (cm\({}^{3}\))**} \\
**Subject** & \multicolumn{2}{c}{**Sartorius**} & \multicolumn{2}{c}{**Gracilis**} & \multicolumn{2}{c}{**Gluteus Maximus**} & \multicolumn{2}{c}{**Tensor Fasciae Latae**} \\  & **t0** & **t1** & **t0** & **t1** & **t0** & **t1** & **t0** & **t1** \\ \hline
1 & 33.5 & 33.29 & 11.65 & 12.80 & 330.80 & 351.30 & 41.80 & 42.82 \\
2 & 30.66 & 30.34 & 15.83 & 15.90 & 306.80 & 309.50 & 31.39 & 37.79 \\
3 & 18.22 & 19.43 & 12.76 & 15.41 & 316.50 & 296.00 & 14.82 & 17.00 \\
4 & 15.40 & 18.71 & 11.15 & 13.98 & 351.50 & 346.30 & 40.96 & 37.85 \\
5 & 40.02 & 51.32 & 12.93 & 11.58 & 588.20 & 610.00 & 69.50 & 72.93 \\
6 & 23.32 & 26.21 & 21.83 & 28.94 & 326.60 & 353.10 & 26.48 & 30.07 \\
**mean** & 26.85 & 30.42 & 14.36 & 16.79 & 370.07 & 380.87 & 37.46 & 39.74 \\
**std. dev.** & 9.49 & 12.24 & 4.00 & 6.14 & 107.92 & 115.65 & 18.58 & 18.60 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Subjects’ muscle ROIs volumes as manually delineated on T1-w images.  
Figure 5: Dice similarity index (DSI), mean surface distance (MSD), and Hausdorff distance (HD) values of the isotropic voxels with mask (IM), native resolution with mask (M), native resolution without selecting a mask (NM) rigid registration schemes. The accuracy indexes were evaluated considering the 4 muscle ROIs together.  
Since no statistically significant differences were found between the schemes of any group with Kruskal-Wallis H tests (DSI: chi-squared = 15.10, df = 14, p-value = 0.37; MSD: chi-squared = 11.67, df = 14, p-value = 0.63; HD: chi-squared = 2.99, df = 14, \(p\)-value = 0.99), NM with learning rate 15 (DSI: 0.760 \(\pm\) 0.078; MSD: 1.582 \(\pm\) 0.586 mm; HD: 23.529 \(\pm\) 14.046 mm) and IM with learning rate 15 (DSI: 0.800 \(\pm\) 0.039; MSD: 1.289 \(\pm\) 0.39 mm; HD: 20.696 \(\pm\) 11.447 mm) were both chosen as the first steps of the registration pipeline, favoring a larger learning rate to speed up the alignment process.