## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Year** & **Classifier** & **Data** & **Dice Scores** \\ \hline [PERSON] et al. [11] & 2015 & RF, MRF & BraTS 2013 & \(\overline{\text{DSC}}=0.87\) \\ [PERSON] et al. [29] & 2016 & CNN & BraTS 2013 & \(\overline{\text{DSC}}=0.88\) \\ [PERSON] et al. [58] & 2017 & RF & BraTS 2013 & \(\overline{\text{DSC}}=0.868\) \\ [PERSON] et al. [59] & 2017 & deep CNN & BraTS 2013 & \(\overline{\text{DSC}}=0.88\) \\ [PERSON] et al. [12] & 2018 & ERT & BraTS 2013 & \(\overline{\text{DSC}}=0.85\) \\ [PERSON] et al. [60] & 2019 & FCNN & BraTS 2013 & \(\overline{\text{DSC}}=0.86\) \\ \hline [PERSON] et al. [29] & 2016 & CNN & BraTS 2015 & \(\overline{\text{DSC}}=0.78\) \\ [PERSON] et al. [32] & 2017 & deep CNN & BraTS 2015 & \(\overline{\text{DSC}}=0.849\) \\ [PERSON] et al. [34] & 2018 & CNN, GAN & BraTS 2015 & \(\overline{\text{DSC}}=0.85\) \\ [PERSON] et al. [30] & 2018 & FCNN, CRF & BraTS 2015 & \(\overline{\text{DSC}}=0.84\) \\ [PERSON] et al. [61] & 2018 & deep CNN & BraTS 2015 & \(\overline{\text{DSC}}=0.86\) \\ [PERSON] et al. [35] & 2019 & CNN & BraTS 2015 & \(\overline{\text{DSC}}=0.85\) \\ [PERSON] et al. [33] & 2019 & deep residual network & BraTS 2015 & \(\overline{\text{DSC}}=0.86\) \\ [PERSON] et al. [62] & 2020 & RF, boosting & BraTS 2015 & \(\overline{\text{DSC}}=0.850\) \\ [PERSON] et al. [31] & 2020 & CNN & BraTS 2015 & \(\overline{\text{DSC}}=0.83\) \\ \hline \multirow{3}{*}{Proposed method} & \multirow{3}{*}{2020} & \multirow{3}{*}{ensembles of} & BraTS 2015 & \(\overline{\text{DSC}}=0.8564\), \(\overline{\text{DSC}}=0.8696\) (LGG) \\  & & & \(\overline{\text{DSC}}=0.8355\), \(\overline{\text{DSC}}=0.8625\) (HGG) \\ \cline{1-1}  & & \multirow{2}{*}{binary decision trees} & \multirow{2}{*}{BraTS 2019} & \(\overline{\text{DSC}}=0.8479\), \(\overline{\text{DSC}}=0.8691\) (LGG) \\ \cline{1-1}  & & & \(\overline{\text{DSC}}=0.8516\), \(\overline{\text{DSC}}=0.8775\) (HGG) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Accuracy comparison with state-of-the-art methods using BraTS 2013 and BraTS 2015 data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Year** & **CPU** & **GPU** & **Runtime (s)** \\ \hline [PERSON] et al. [29] & 2016 & i7 3.5 GHz & GTX 980 & 480 \\ [PERSON] et al. [59] & 2017 & unspecified & unspecified & 90–180 \\ [PERSON] et al. [32] & 2017 & unspecified & GTX TitanX 12 GB & 210 \\ [PERSON] et al. [30] & 2018 & unspecified & shared GPU server & 120–240 \\ [PERSON] et al. [35] & 2019 & unspecified & GTX TitanX 12 GB & 187 \\ [PERSON] et al. [63] & 2019 & unspecified & unspecified & 90–180 \\ [PERSON] et al. [15] & 2019 & i7 3.2 GHz & no GPU involved & 335 \\ Proposed method & 2020 & i7 1.8 GHz & no GPU involved & 58 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Efficiency comparison with state-of-the-art methods. Runtime is expressed in seconds, and it represents the total time needed for the whole processing of a multi-spectral BraTS record, averaged over one or more BraTS data sets. The main parameters of the proposed brain tumor segmentation procedure are: (1) the size of training data, or in other words, the number of feature vectors used to train each BDT in the ensemble, \(n_{F}\); (2) the percentage of negatives \(p_{-}\) and positives \(p_{+}\) in the set of feature vectors used to train the BDTs; (3) the number of trees in the ensemble \(n_{T}\); (4) the presence or absence of the atlas enhanced pre-processing within the pipeline of the procedure. The decision on the training data size has to take into account its twofold implications. Larger training data sets enable the procedure to achieve slightly better accuracy in all tested cases. On the other hand, changing \(n_{F}\) from \(100k\) to \(1000k\) raises the training time of an ensemble from 2 to 40 min, but the total duration of a segmentation after having the ensemble trained only increases by 4-5 s. Once the large ensembles are trained, they can perform the segmentation quickly enough without prohibitive computational load.