## 1 Introduction
Despite the achievements obtained, automated segmentation of brain metastases and lesions, in general, remains an unsolved problem due to normal anatomical variations in brain morphology, variations in acquisition parameters of MRI scanners, the heterogeneous appearance of pathology. Recent BM segmentation studies propose the use of deep learning methods using different convolution neural network (CNN) architectures and different MRI sequences as input data. [PERSON] et al. have been among the first that investigated the use of deep networks to detect and segment BM [30]. Their work compares several types of spatial inputs and network topology to find performances comparable to conventional state-of-the-art models. The importance of database quality has also experimented. [PERSON] et al. propose the use of a CNN based on the GoogLeNet architecture for automatic BM detection and segmentation. The retrospective study focusses on 156 patients with brain metastases from several primary cancers and makes use of multi-sequence MR images, including pre- and post-gadolinium T1-weighted and FLAIR scans. Results obtained are good, but several limitations because of limited sample size and false-positive results near vascular structures, are highlighted. The use of multi-sequence MRI limits the applicability in the clinical domain. [PERSON] et al. [27] studied the influence of MRI modalities together with the impact of the number of segmented classes, both on the detection and segmentation of brain metastases in MRI imagery. To do this, they used a modified version of DeepMedic neural network proposed by [PERSON] et al. [31] and data augmentation strategies. The combined use of different MRI modalities outperformed the performances of the network when using single modalities. In single modality, best performances are obtained usingvolumetric T1c scans. [PERSON] et al. investigate the use of deep learning convolutional neural network (CNN) algorithm trained on both gliomas and BM [32] on T1c. In radiation therapy (RT), the workflow for BM treatment requires fast and accurate detection and delineation of tumour volume of small size on MRI scans. Contrast-enhanced T1 (T1c) magnetic resonance imaging (MRI) is generally the only imaging modality adopted. Segmentation accomplished through a complete manual tracing is still the standard routine although it has shown to be a time-consuming and labour-intensive process affected by high intra- and inter-observer variability. In this context, ML techniques would be very helpful, actively supporting human experts in tracing the boundaries of the pathological tissues with varying degrees of automation and improving the efficiency of the overall radiotherapy clinical workflow. Promising results obtained by recent studies in automated BM segmentation [4; 27; 28; 33] lead us to further investigate ML techniques derived from both conventional feature-based learning and deep learning approaches and measure and compare their capability to compute spatially accurate and stable results. Indeed, both approaches have their advantages and disadvantages. In the design of an automated segmentation procedure, the feature extraction phase plays a major role. Deep learning methods offer the advantage of automatically learn hierarchical image representations which often outperform the most effective features extracted by well-assessed procedures. However, good performances are obtained provided that a large annotated training sets are available. This requirement is especially critical in medical image analysis, in particular in BM segmentation where annotated consistent training data are difficult to collect and at best of our knowledge, no public datasets of diagnosed patients with metastatic brain tumours are available. Conventional ML models have shown excellent performances in MRI brain tumours segmentation studies even when using a much smaller training set.