## 1 Introduction  
Brain metastases (BMs) are one of the most common neurological neoplasms, and their incidence is increasing with the availability of advanced imaging techniques such as Magnetic Resonance Imaging (MRI) [1; 2]. By visual inspection of MR scans, physicians can accurately examine and identify pathological tissues thanks to the high spatial resolution and contrast and the enhanced signal differentiation. In the clinical practice, MRI has been confirmed as a significant approach supporting diagnosis, surgical planning, follow up and therapy. In order to exploit this potential, intelligent techniques should complement image acquisition and visualisation tools, addressing relevant issues such as cancer detection. Extensive research has already been developed to introduce computer-aided detection and segmentation methods in neuro-oncology clinical studies. Available methods include image-based methods and machine learning-based methods [3; 4]. The image-based methods use image data and image processing techniques to detect and delineate lesions. Exemplary techniques include tissue classification based on Raman spectroscopy [5], a colour-coded map from quantitative optical coherence tomography (OCT) for differentiating cancer from noncancer in human brain tissues [6], watershed segmentation algorithms [7], active contour algorithms [8], and region growing segmentation algorithms [9]. Supervised machine learning (ML) approaches have been successfully applied to circumvent the problem of explicitly and analytically describing the specific segmentation procedure and related parameters, lying to a learning stage the charge of inducing the classifier from supervised data available. The proposed techniques make use of a single image or multispectral pattern and are interactive or fully automatic [3; 10; 11; 12; 13; 14; 15; 16]. Among the most promising methods, we found the support vector machine (SVM) [17; 18], discriminative models based on Random Forest and logistic regression [19; 20]. [PERSON] et al. [21] and [PERSON] et al. [22] proposed classification methods based on SVM to classify brain neoplasms and their sub-components using multidimensional patterns obtained by a high number of MRI modalities. [PERSON] et al. [23] proposed SVM to segment lesions using a lower number of modalities. [PERSON] et al. [24] adopt a hybrid method, based on SVM and hierarchical regularisation, to segment tumour and healthy tissues, including sub-compartments. Random Forest-based methods are proposed by [PERSON] et al. [25] to identify brain tumour sub-compartments from multi-modal images and by [PERSON] et al. [26] that generate synthetic tumour images to train a discriminative regression forest algorithm using different groups of features. Although the problem of segmenting all or part of the brain in MRI imagery does continue to be investigated attempting to satisfy the high accuracy demand in diversified clinical and neuroimaging application, only a few studies have applied such ML approaches on BM detection and segmentation [27]. BM requires specific approaches given their small size and multiplicity and the stringent requirements of RT clinical practice in which usually segmentation procedures are inserted. In this application context, MRI T1c images are usually the only modality considered and fast segmentation is required for a rapid clinical workflow. In their review, [PERSON] et al. [28] describe methods that use hand-crafted templates or blob based complex procedures. These works report performances strongly affected by feature extraction methods, which becomes more and more complex to improve results. Machine learning algorithms such as SVM and Random Forest are proposed in combination with spatial regularisation procedures and Gaussian processes to refine patch-based segmentation [29].