## 2 Interactive BM Segmentation Based on Supervised Learning Models
### Supervised Classification of Pathological and Healthy Tissues  
In the second stage of the segmentation procedure, a supervised machine learning model is applied to the selected sub-image. The supervised learning task is aimed to perform a hard-binary categorisation, labelling voxels within the selected volume as Brain Metastasis (BM) and Healthy tissue (H). During the training phase, the classifier learns an approximation for the true input-output relationship based on a given training set of examples constituted by \(N\) input-output pairs \(\{(x_{i},y_{i})\}\), \(i=1,\ \ldots,\ N\) where \(x_{i}\) is the input vector and \(y_{i}\in\{BM,H\}\) is a supervised label denoting the membership in the metastasis or healthy class.  
Figure 1: **(a,b)** show two different source slices of T1c MR scans with the corresponding Volume slice perimeter bounding Brain metastases (BM) areas.  
We conceived and conducted two sets of experiments. The first used a conventional supervised classifier built on the top of a hand-crafted feature extraction procedure. In our previous works, we deal with MRI brain tumour segmentation using several methods selected from state-of-the-art classifiers in the field of MRI segmentation. In particular, we investigated the use of Fuzzy connectedness and Graph Cut for glial tumour segmentation [12] and SVM for meningioma and edema segmentation [13]. Fuzzy Connectedness and Graph Cut methods are interactive, asking experts to provide accurate initialisation information for each image processed. Results obtained by these methods were accurate but strongly influenced by the prior knowledge provided by the users or by ancillary methods. In the RT domain, where a large number of images are needed to be handled, they can be laborious and time-consuming. We have shown that trained SVM allows complete delineation of meningioma and edema tissues and accurate volume estimation by processing both volumetric and non-volumetric imagery in a few minutes, without requiring manual selection of example voxels or seeds. Performances obtained were good, confirming the results obtained in other studies [10]. Approaches based on Random Forest show similar characteristic and can also be suitable in the RT domain. [PERSON] et al. in their review [10] investigate the behaviour of SVM and Random Forest segmentation. The two methods showed comparable performances. It is worth to note, however, that evaluations were performed on different datasets and different evaluation metrics, making difficult the comparison. [PERSON] et al. [36] found that, both on average and in the majority of data used in the study, Random Forests exhibit larger classification error than SVM when processing microarray datasets. In the present work, the choice fell on SVM, not because the best that can be made but as it has been extensively used in MRI image segmentation and can be considered representative of the conventional learning approaches.  
The second experiment was conducted using the V-Net convolutional neural network model [34] selected among the deep learning models oriented to MRI volumetric images [37] and properly adapted for our application context. To make the work self-contained, we briefly outline the basic concepts of both learning models investigated.