## 3 Results
### Brain Dataset Results  
First all the architectures were evaluated on brain dataset. The considered architectures are Dense-U-Net, Residual-U-Net and basic U-Net network, all were tested in 2D and 3D mode, i.e., six neural network architectures. This phase verified, that 3D Dense-U-Net architecture performs better than the remaining architectures (see Table 4). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**3D Networks**} \\ \hline
**Metric** & **Dense-U-Net** & **Res-U-Net** & **U-Net** & **Human** & **FSL** \\ \hline P.A. & 0.99703 & 0.99662 & 0.99619 & 0.99489 & 0.94289 \\ Dice c. & 0.98843 & 0.98686 & 0.98514 & 0.98033 & 0.79698 \\ Lo.U. & 0.97713 & 0.97407 & 0.97072 & 0.96141 & 0.66248 \\ A.H.D. [voxel] & 0.01334 & 0.01911 & 0.02427 & 0.02479 & 4.58848 \\ A.u.R.C. & 0.99439 & 0.99353 & 0.99205 & 0.98325 & 0.96696 \\ \hline \multicolumn{6}{c}{**2D Networks**} \\ \hline
**Metric** & **Dense-U-Net** & **Res-U-Net** & **U-Net** & **Human** & **FSL** \\ \hline P.A. & 0.99576 & 0.99639 & 0.99636 & 0.99489 & 0.94289 \\ Dice c. & 0.98344 & 0.98357 & 0.98574 & 0.98033 & 0.79698 \\ Lo.U. & 0.96743 & 0.96768 & 0.97189 & 0.96141 & 0.66248 \\ A.H.D. [voxel] & 0.09477 & 0.09130 & 0.05632 & 0.02479 & 4.58848 \\ A.u.R.C. & 0.99647 & 0.99639 & 0.99663 & 0.98325 & 0.96696 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of tested U-Net versions on brain dataset in benchmark training phase versus Human expert and FMRIB’s Automated Segmentation Tool. Used metrics—pixel accuracy, Dice coefficient, intersection over union, average Hausdorff distance [voxel] and area under ROC curve. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Segmentation Algorithm** & **Prediction Time** & **Training Time [50 epochs]** \\ \hline U-Net—brain dataset & 8 s & 6 h \\ U-Net—spine dataset. & 23 s & 9 h \\ Res-U-Net—brain dataset & 12 s & 10 h \\ Res-U-Net—spine dataset & 32 s & 16 h \\ Dense-U-Net—brain dataset & 21 s & 12 h \\ Dense-U-Net—spine dataset & 43 s & 21 h \\ FSL—brain dataset & 3 s & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Segmentation alogorithms comparison based on their computation time when ran on gtx 1080 ti GPU. As stated in Section 2.1.5, the performance was evaluated on the last brain scan which was not used for training and therefore our results show reliability of our method on unseen data. We compared the predicted data to mask labelled by a human expert as in standard medical praxis, which are in Table 4 in column labelled \"Human\" and also to output of the FSL segmentation tool. Dense-U-Net network proved to give the best performance in all considered metrics in 3D processing mode. There should be stated, that even segmentation using basic U-Net network gave better accuracy than a human expert. When compared to other 2D networks, the Dense-U-Net had better results in all metrics except for average Hausdorff distance. This is most probably caused by the fact that 50 epochs of training was not enough for a network with so many parameters and therefore the network generated more artifacts in the output segmentation than the simpler versions. As can be seen in Figure 7 the methods had problems segmenting the area around nasal cartilage. FSL method results in this case were unusable for medical praxis. Dense-U-Net network had the best results also thanks to the fact, that it was able to successfully segment this area on the MRI scan. After the evaluation in the benchmark phase we trained the 3D Dense-U-Net again, now with 99 epochs, to get the final fine-tuned model. Obtained results are in Table 5.  
The Dense-U-Net network was trained in the fine-tuning phase (99 epochs) and validated using 3-folds cross-validation. In all five metrics the results are more accurate than a human expert. Output of the segmentation is visualised in Figure 8. It is clearly visible, that the proposed segmentation output overcame the human results and also results of older methods not based on deep neural networks such as the FSL.