# Optimisation of 2D U-Net Model Components for Automatic Prostate Segmentation on MRI
## 4 Results
### Implementation on the Private Dataset
#### 4.1.2 Results on the Private Dataset  
The performance difference between the optimised method and three traditional prostate segmentation methods [35; 37] is presented in this section. The three prostate segmentation methods that were used in previous studies are the multi-atlas [35], multi-object weighted and standard (unweighted) deformable model approaches [37].  
Five-fold cross-validation mean DSC, median DSC, average symmetric surface distance (ASD) and Hausdorff distance are used for the evaluation of the model performance to ensure that the segmentation errors are reasonable for the application, i.e., treatment planning.  
The ASD is the average Euclidean distance from all the points on the predicted region boundary, \(B_{P}\), to the ground truth region boundary, \(B_{GT}\), and from all the points on the \(B_{GT}\) to the \(B_{P}\)[55], given by  
\[ASD=\frac{\left(\sum_{x\in B_{P}}d(x,B_{GT})+\sum_{y\in B_{GT}}d(y,B_{P}) \right)}{|B_{P}|+|B_{GT}|}, \tag{5}\]  
where the Euclidean distance from a voxel \(x\) to a set of voxels \(A\) is given by  
\[d(x,A)=\min_{y\in A}d(x,y), \tag{6}\]  
with the Euclidean distance between 2 voxels (e.g., voxel \(x\) and \(y\)) denoted by \(d(x,y)\).  
The Hausdorff distance measures the maximum distance from a point in set A to the nearest point in set B [55], given by  
\[d_{H}(A,B)=\max_{x\in A}\min_{y\in B}d(x,y). \tag{7}\]Examining the score for the whole dataset, the optimised model gives a mean DSC of 87.38%, median DSC of 88.19%, median ASD of 0.72 mm and median Hausdorff of 4 mm. As shown in the Table 3, the optimised model outperforms the traditional methods by at least 7% and 6% in mean and median DSC respectively, 1.32 mm in median ASD and 5.6 mm in median Hausdorff distance.  
As can be seen in Figure 6, the optimised model performed well on all the cross-validation folds by having DSC scores in the range of 0.73 to 0.94, where the third quartile of the five folds are at least 0.9 and only 4 out of 40 predictions (2 in fold 1, 1 in fold 3, 1 in fold 5) get a DSC score below 0.81. All of the mean DSC scores are at least 0.86 and the median DSC scores are at least 0.87. Without the outliers, the minimum DSC scores of 4 cross-validation folds are all 0.84 and above (fold 2, 3, 4 and 5), which is above the mean and the median DSC scores achieved by the traditional methods.  
Excluding the obvious outliers in Figure 6, we present the best and worst predictions of the segmentation in Figure 7a,b respectively. These prediction volumes have DSC scores of 0.94 and 0.73. It is easily observed that the prediction volume with a DSC score of 0.94 is very similar to the ground truth segmented volume. We note that even for the worst case, the majority of the prediction volume still overlapped well with the ground truth segmented volume having a DSC score of 0.73.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Mean** & **Median** & **Median** & **Median** \\  & **DSC** & **DSC** & **ASD (mm)** & **Hausdorff (mm)** \\ \hline Multi-atlas & 0.80 & 0.82 & 2.04 & 13.3 \\ \hline Weighted & 0.79 & 0.81 & 2.08 & 9.6 \\ \hline Unweighted & - & 0.70 & 3.20 & 12.9 \\ \hline
**UNet\_S.2.0.1.1** & 0.87 & 0.88 & 0.72 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance comparison between the optimised model and traditional methods.  
Figure 6: Box-and-whisker plot of the optimised model five-fold cross-validation Dice’s ciliary coefficient (DSC) scores. All the mean and median DSC scores are at least 0.86 and 0.87 respectively (the best mean and median DSC scores achieved by the traditional method are 0.80 and 0.82 respectively in this dataset).