## 4 Discussion
The percentage of negatives \(p_{-}\) in the training data can have a strong implication on the segmentation quality. Experiments show that there are MRI records in the BraTS data sets that give the best segmentation accuracy at \(p_{-}=75\%\), others at \(p_{-}=95\%\), and many of them at various values between these two. It is very likely that the optimal value of \(p_{-}\) for a given MRI record strongly correlates with the true rate of negative pixels in the volume. However, this true rate is unknown, as we are not allowed to look at the ground truth while testing. The best accuracy at the ensemble output could be achieved if we had a precise estimation for each MRI record, which is the best choice for \(p_{-}\), only using the intensity values of the four observed data channels. Such an estimator would allow for 2-3% higher Dice similarity coefficients at the ensemble output. Without such an estimator, a dedicated constant value of \(p_{-}\) needs to be chosen for all MRI records in each data set. In this study, \(p_{-}\) was set to 91% for HGG data and 93% for LGG data, based on evaluations performed on OOB data. The number of trees in the ensemble (\(n_{T}\)) theoretically has an impact on the decision error, which should decrease with any additional tree included in the ensemble. Experiments show that the decision accuracy saturates at a certain level due to the noise that is present in the data. Further, the number of trees linearly affects the runtime of both the training and testing process. After several evaluation loops performed on OOB data, with various values of \(n_{T}\) ranging from five to 255, the size of the ensemble was chosen to be set to \(n_{T}=125\)[43; 64]. The use of the atlas caused up to a 3% improvement in the average Dice scores obtained at the output of the ensemble (see the difference between solutions \(S_{1}\) and \(S_{2}\) in Table 3), but this difference diminished to a maximum of 1% in the accuracy of the final segmentation. Even for this difference, we consider the use of the atlas beneficial, as it does not affect the execution time of the procedure much. The relatively high accuracy achieved by the proposed procedure is probably caused by the way it handles the imbalanced amounts of positive and negative data. Our BDTs are allowed to grow to unlimited depth during ensemble training, as deep as is found necessary by the entropy-based criterion applied in decision nodes. Unlike the random forest classifier, which limits its depth and sometimes assigns labels to mixtures of positives and negatives when the depth limit is reached, our binary trees has crisp labels assigned to their leaves. This allows for more precise classification unless the trees are over-trained. With the parameter settings we used, the decision trees did not show signs of being over-trained, which is supported by the accuracy indicators that improved as the training data size grew. The number of false positives was not high at the output of the ensemble, and it was still reduced by the twofold post-processing, which discarded those predicted positive structures that were too small or too flat to be reliably called tumors. The proposed procedure also has some limitations. In its current version, it is trained and tuned to segment the whole tumor only, not the parts of it. Using only a set of handcrafted features, it may not succeed in exploring the input data as thoroughly as a convolutional network can. Further, the approximately three million decision nodes contained by our most complex trained forest of binary decision trees is less than the number of parameters used in current CNN architectures by up to two orders of magnitude. This might become a visible limitation in accuracy if we increase the number of MRI records used for training and testing.