## 4 Results
### Three-Dimensional Model  
To evaluate the quality of the 3D model derived from the proposed workflow, the models were compared using two pixel-based metrics, the DC and JI, and one distance-based metric, the Hausdorff distance. Specifically, the mesh derived from U-Net with MPT segmentation was compared to those obtained using other methods, including SegNet with MPT, thresholded bone segmentation, and with a graph cut algorithm proposed by [PERSON] et al. (2018) and implemented as described by [PERSON] et al. (2018)  
The results in term of the Jaccard index and Dice coefficient are presented in Table 2.  
The Hausdorff distance was computed between the mesh produced by each segmentation method and the corresponding ground truth mesh. The Hausdorff distance provides  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Axial Training**} & \multicolumn{2}{c}{**Multiplanar Training**} & \multicolumn{2}{c}{**Majority Voting**} \\ \hline \multirow{3}{*}{Axial} & JI & 0.904 \(\pm\) 0.019 & 0.917 \(\pm\) 0.029 & 0.939 \(\pm\) 0.010 & 0.939 \(\pm\) 0.014 & \multirow{3}{*}{0.933 \(\pm\) 0.018 1} \\  & DC & 0.949 \(\pm\) 0.011 & 0.957 \(\pm\) 0.015 & 0.969 \(\pm\) 0.005 & 0.968 \(\pm\) 0.008 & \\ \hline \multirow{3}{*}{Sagittal} & JI & 0.861 \(\pm\) 0.014 & 0.901 \(\pm\) 0.021 & 0.936 \(\pm\) 0.002 & 0.931 \(\pm\) 0.020 & 0.927 \(\pm\) 0.010 1 & 0.933 \(\pm\) 0.018 1 \\  & DC & 0.899 \(\pm\) 0.03 & 0.948 \(\pm\) 0.011 & 0.967 \(\pm\) 0.001 & 0.964 \(\pm\) 0.012 & 0.962 \(\pm\) 0.004 1 & 0.965 \(\pm\) 0.009 1 \\ \hline \multirow{3}{*}{Frontal} & JI & 0.899 \(\pm\) 0.006 & 0.897 \(\pm\) 0.011 & 0.933 \(\pm\) 0.010 & 0.937 \(\pm\) 0.013 & \multirow{3}{*}{0.937 \(\pm\) 0.013 1} \\  & DC & 0.946 \(\pm\) 0.012 & 0.946 \(\pm\) 0.006 & 0.965 \(\pm\) 0.007 & 0.968 \(\pm\) 0.009 & \\ \hline \hline \end{tabular}  
* Results obtained through a majority voting scheme, which uses axial, sagittal, and frontal views.  
\end{table}
Table 1: Results in terms of Jaccard index and Dice coefficient.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Threshold** & **Graph Cut** & **SegNet** & **U-Net** \\ \hline JI & 0.74 & 0.77 & 0.83 & 0.85 \\ DC & 0.85 & 0.87 & 0.91 & 0.92 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Jaccard index and Dice coefficient of the 3D model of a human talus, obtained with the proposed workflow.  
a measure of the maximum discrepancy between two point sets on the surfaces of the meshes, thus allowing assessing the accuracy and precision of the segmentation methods.  
The results of this comparative analysis are presented in Table 3. This table highlights the max, mean, and standard deviation of the Hausdorff distances for each segmentation method on the target bone, thereby allowing us to determine which method produces the most accurate and reliable 3D models. By analyzing these distances, the effectiveness of each segmentation technique can be objectively evaluated. The proposed method, U-Net with MPT segmentation, demonstrated the lowest mean in terms of the Hausdorff distance. Figure 5 depicts a visualization of the Hausdorff distances for the target bone across the evaluated methods. In this context, blue areas on the models indicate minimal differences from the ground truth, while red areas signify substantial discrepancies. The model obtained via threshold-based segmentation shows high Hausdorff distances across the entire surface, indicating poor accuracy. The graph cut segmentation model has high distances in specific regions, reflecting localized segmentation errors. The U-Net and SegNet methods exhibit lower Hausdorff distances, with the U-Net model demonstrating the best overall performance, closely aligning with the ground truth. The color bar at the bottom provides a visual reference for the distance values, emphasizing the superiority of the U-Net segmentation approach.