# Weakly Supervised Learning with Positive and Unlabeled Data for Automatic Brain Tumor Segmentation
## 4 Discussion  
We showed that the proposed approach allows for the training of an effective tumor segmentation algorithm from small and only positive samples. The approach dramatically reduces the labeling time when compared to the traditional workflow with training on complete segmentations. The results achieved by such a classifier are comparable or better than those achieved by learning from sparse positive and negative samples (SPN), while the required labeling time is further reduced--for our experiments, by nearly 50%. This will enable the creation and regular update of much larger training sets than previously employed, making it much easier to directly integrate the approach in a clinical workflow and to cover different scanner hardware, modalities, protocols, and even different clinical applications. Using a cost-based approach allows the combination of our method with most learning-based approaches, making it more general than previous methods such as [35]. Nevertheless, there are some difficulties in incorporating spacial priors from an atlas. However, instead of using a spacial prior, a tissue class prior can be derived for each voxel and a general tumor probability can be used for post-processing the segmentation. This allows the use of most information encoded within an atlas, although there are enough methods that obtain good results without using this information (for example, [17; 36]). For this paper, we purposely used simple features and classifiers in order to deflect attention to such details. However, given the flexibility of the proposed approach with the cost-based classifier as the only real requirement, the performance can be easily improved. For example, by using more advanced technology stacks, including the usage of deep learning. This could be by using learned features from a pretrained network [37], a combination of forest and deep learning [38], or a cost-sensitive deep segmentation network [39]. These changes will not affect the ability of the baseline approach proposed here to be trained from sparse and positive-only annotations and can improve the performance's results significantly. One benefit of PU-learning is that the estimation of the tissue ratios can be obtained with multiple approaches. The best approach depends on the use-case; for example, if the true tissue ratio is known from a previous study or a post-surgical histological measurement, those could be used without any additional overhead. However, even if such accurate measures are unavailable, PU-learning can still be used, as our experiments show that it  
Figure 7: Example axial and coronal (HG 006) slices from the validation set u(BraTS 2013 dataset) using the proposed PU-learning method. The colour coding is as follows: ‘yellow’: edema; ‘red’: enhancing tumour; ‘green’: non-enhancing tumour; ‘blue’: necrosis. The subject name is identical to the identifier within the original training dataset. is robust even with an estimation error of 20%, which allows the usage of quick but less accurate estimation methods for the reduction in annotation loads. The best manual estimation of tissue ratios depends on the actual task on hand. In our experiments, these measures showed a tendency to overestimate the tumor volume by 0.6 and 1.2 percentage points (cf. Table 1), which is in line with other findings suggesting a slight overestimation of tumors using simple measurements [40]. However, these approaches were shown to be sufficiently accurate and might already be assessed in clinical routines [41], thus offering a good alternative. However, there might be cases when manual estimations are unavailable and cannot simply be created, either because of time and cost restrictions or because it is simple not possible for the given task. In such settings, the heuristic estimation of the tumor volume is a possible alternative.