## 3 Results
We note that the hyperparameter optimization procedure provided by the SageMaker framework did not lead to considerably better results for the following reasons: 42 different parameter sets were tried, and out of these, only about 10 ran until the end, namely, 100 epochs, for about 48 h per training job of the 10 runs (200 h in total). In these 42 jobs, the batch size, learning rate, weight-decay, and momentum parameters were selected according to a random grid search. Out of the optimization functions, only AdaGrad and SGD were selected. The Sagemaker hyperparameter optimization process slightly modified the numerical parameters for each run of a different training job. The only parameter that was modified considerably on a logarithmic scale was the learning rate. The enormous resource requirements coupled with the small improvement achieved made us decide against running the hyperparameter optimization on the five other architectures studied. Figure 10: Segmentation Results of the 6 Architectures: visually, the segmentations are similar, and the difference on average for the whole dataset is about 1–3%. From Tables 4 and 5, we can see that the FCN with parameter optimization led to a barely observable Dice score improvement of 0.8% on average for all classes. Figure 11 shows a visual comparison of tumor tissue segmentation with and without hyperparameter optimization on the FCN-ResNet50 architecture. On average, there is an improvement of only about 1% to the detriment of the enormous computational complexity. The last group of experiments that were carried out was related to the combination of all six segmentation models in an attempt to obtain a so-called ensemble model from them. We obtained weighted segmentation maps from all six individual classifiers presented above. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Architecture** & **Background** & **Healthy Tissue** & **Whole Tumor** \\ \hline FCN-ResNet50 & 0.9965 & 0.9730 & 0.9068 \\ FCN-Parameter Optimization & 0.9982 & 0.9790 & 0.9100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dice for Background, Healthy Tissue, and Whole Tumor with Parameter Optimization. Figure 11: Comparison of FCN and Parameter-Optimized FCN: visually, the segmentations can barely be distinguished. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Architecture** & **Edema** & **Active Tumor** &
\begin{tabular}{c} **Necrosis/** \\ **Non-Enhanced Tumor** \\ \end{tabular} \\ \hline FCN-RN50 & 0.6963 & 0.6970 & 0.4617 \\ \hline FCN-Parameter Optimization & 0.7046 & 0.7104 & 0.4740 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Dice for Different Types of Tumor Tissues (Edema, Active Tumor, and Necrotic Tumor) with Parameter Optimization. Comparing Tables 2, 4, and 6, we can draw the following conclusions: The Dice score for the Whole Tumor is reduced by approximately 2-3% compared to the best method out of the six. On the other hand, the Dice scores for different tumor tissues of the ensemble model are better by about 4-10% (Tables 3, 5 and 7). This is a considerable improvement. The segmentation maps obtained by the ensemble model are depicted in Figure 12. It is obvious that the tissue contours and transitions from one tissue to the other are gradually colored from turquoise to yellow, and there is a slight green ring at the transition. This shows that the ensemble model obtains a probability map and does not make a final decision favoring any class for uncertain tissue voxels on the contour. These voxels are, in fact, the hard examples and are not clearly classifiable. The probabilistic heatmap of the ensemble model solves this problem through probabilistic voting. Overall, we propose the sequential application of the best DeepLabv3 model or the parameter-optimized FCN ResNet50 for obtaining the tumoral region, and after that, finetuning the results by obtaining the different tumor tissues through the use of the ensemble model. Finally, to highlight our results, we compare them to the best results from the BraTS Challenge 2020, published in 2021.