# Deep Learning-Based Methods for Prostate Segmentation in Magnetic Resonance Imaging
## 3 Results  
Sensitivity, positive predictive value (PPV), DSC, volume overlap error (VOE), and volumetric difference (VD) were used for performance evaluation:  
\[\text{Sensitivity}=\frac{TP}{TN+FN} \tag{4}\]  
\[\text{PPV}=\frac{TP}{TP+FN} \tag{5}\]  
\[\text{DSC}=\frac{2 TP}{2 TP+FP+FN} \tag{6}\]  
\[\text{VOE}=1-\frac{TP}{TP+FP+FN} \tag{7}\]  
\[\text{DSC}=\frac{2 TP}{2 TP+FP+FN}\;\;DSC=\frac{2|P\cap G|}{|P|+|G|} \tag{8}\]  
Table 3 shows the performance obtained using ENet, UNet, and ERFNet methods. In particular, ENet showed a mean DSC of 90.89 \(\pm\) 3.87%, UNet of 90.14 \(\pm\) 4.69%, and ERFNet of 87.18 \(\pm\) 6.44%. Analysis of variance (ANOVA) based on DSC was calculated to test statistical differences (a _p_-value < 0.05 indicates a significant difference) between methods considering all patients (n = 85). Table 4 shows how though ENet and UNet minimized the difference between manual and automated segmentation. Despite the fact that they were statistically identical, they were computationally different. ENet is much faster than UNet. Specifically, Table 5 shows the comparison of computational complexity and performance of the three models. As both ENet and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**ANOVA** & **F Value** & **F Critic Value** & _p_**-Value** \\ \hline ENet vs. ERFNet & 20.70407668 & 3.897407169 & 0.000010236 \\ \hline ERFNet vs. UNet & 11.69135829 & 3.897407169 & 0.000788084 \\ \hline ENet vs. UNet & 1.301554482 & 3.897407169 & 0.255553164 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ANOVA on the DSC showed statistical differences between segmentation methods. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Sensitivity** & **PPV** & **DSC** & **VOE** & **VD** \\ \hline \multicolumn{5}{c}{ENet} \\ \hline Mean & 93.06\% & 89.25\% & 90.89\% & 16.50\% & 4.53\% \\ \hline \(\pm\)std & 6.37\% & 3.94\% & 3.87\% & 5.86\% & 9.43\% \\ \hline \(\pm\)CI (95\%) & 1.36\% & 0.84\% & 0.82\% & 1.24\% & 2.00\% \\ \hline \multicolumn{5}{c}{UNet} \\ \hline Mean & 88.89\% & 91.89\% & 90.14\% & 17.66\% & 3.16\% \\ \hline \(\pm\)std & 7.61\% & 3.31\% & 4.69\% & 6.91\% & 9.36\% \\ \hline \(\pm\)CI (95\%) & 1.62\% & 0.70\% & 1.00\% & 1.47\% & 1.99\% \\ \hline \multicolumn{5}{c}{ERFNet} \\ \hline Mean & 89.93\% & 85.44\% & 87.18\% & 22.18\% & 5.70\% \\ \hline \(\pm\)std & 10.92\% & 5.43\% & 6.44\% & 9.61\% & 14.72\% \\ \hline \(\pm\)CI (95\%) & 2.32\% & 1.16\% & 1.37\% & 2.04\% & 3.13\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance segmentation using the ENet, UNet, and ERFNet methods. ERFNet were developed for real-time applications, these are relatively smaller and faster than UNet. As shown in the table, the ENet model has an order of magnitude with fewer parameters than both ERFNet, and UNet while ERFNet has less than half the number of parameters compared to UNet. Consequently, the size of trained ENet is only 6 MB compared to 65 MB for the UNet model. To estimate the delineation time, we considered one of the trained models during the k-fold strategy for all three architectures and then computed the average. Using a fairly advanced GPU device (GEFORCE RTX 2080 Ti, 11 GB VRAM, 4352 CUDA Cores, NVIDIA), it takes only 1 s for ENet and about 1.5 s for UNet to generate segmentation on a 3D dataset (average 40 slices of 512 \(\times\) 512). However, when GPU hardware is not available then computation needs to be done on the CPU. In such a scenario, the size of a model can play a big role. On an AMD Ryzen 2950x processor, ENet only takes about 6 s while UNet takes about 40 s to delineate a study. Soon, this computational advantage of ENet may make it possible to use this model to segment cases on simple hardware like IPads or smartphones for faster clinical workflow. Finally, only the ENet model makes use of batch normalization layers, which have some parameters which are not trained, that is, gradients are not back-propagated during the training process. In Figure 3, we plot the training DSC and Tversky loss function for each DL network for one fold.