## 3 Experiments
### Experiments with SVM  
Performances of the SVM-based segmentation were evaluated by generating several segmentation procedures obtained by different SVM configurations and using different learning strategies. We used 25 reference data corresponding to those acquired and available in our clinical domain at the start of the study. We developed two preliminary tasks. First, we defined the optimal feature set that composes patterns in input to the SVM. For this task, the SVM has been configured as a soft-margin least square (LS) model with a linear kernel. Contextual and textural features have been analysed systematically in order to determine the combination that is most appropriate for the current classification task. In particular, several configurations of the segmentation procedure have been experimented initially providing in input only intensity values of central voxel and neighbour voxels. Different neighbourhoods have been considered including incrementally neighbours along with voxel faces, corners and edges up to a maximum of 26 voxels. In a second step, an enlarged feature set has been considered adding  
Figure 6: (**a–c**) Show three source slices of T1c MR Volumes with the delimitation of the lesion area. textural features to the best neighbourhood configuration. The following set of features has been finally selected (see Figure 7):  
* intensities from T1c scan
* first-order texture features: mean (\(\mu\)), variance (\(\sigma\)), skewness (\(\gamma\)), kurtosis (\(\beta\)) and entropy (\(H\))
* intensities in 26 neighbourhood voxels  
Feature values have been normalised to have zero mean and unit variance. The second step was to determine the value of the internal parameters of the model. Different types of kernels were tested, such as linear, quadratic, cubic, fine-medium-coarse gaussian. Given the results obtained, we confirmed the configuration of SVM as a soft-margin LS model with a linear kernel. With this optimised configuration, we conducted the first set of experiments by varying the modality for selecting training samples from the VoIs extracted from the available in-house dataset. In the first modality (M1) data are extracted from the reference masks selecting elements within the overall VoI under study. In the second modality (M2), the random selection was limited within a region built around the contour of the tumour reference masks. After trial and error procedures, the edge width was tuned to 8 pixels. These experiments have been conducted in intra-patient modality selecting training and test sets from the reference masks of the same VoI and built by randomly selecting elements in the proportion of 70% and 30% respectively. An equal number of elements labelled BM and H was extracted. In the M1 modality, before the random extraction of BM elements, contour elements of BM regions were reinserted. Table 1 shows the numerical results obtained in terms of mean values of \(DSC\), \(P\) and \(R\) indexes over 25 cases under study. SVM, trained according to M2 strategy, slightly prevails with a mean \(DSC\) value equal to 0.878. \(P\) and \(R\) values highlight a significant reduction of omission and commission errors. These results can be explained by the fact that metastases have little extensions and a high level of heterogeneity occurs in the internal part of the pathology due to the presence of necrosis and/or active parts (see Figure 6). This high level of heterogeneity is difficult to learn during training and, as seen in our experimental context, SVM shows better behaviour when trained on relatively homogeneous regions. Figure 7: Input pattern vector composed of contextual and textural features. Using the configuration described above and with the M2 voxel extraction strategy, we quantified segmentation performances by conducting a second set of experiments aimed to investigate the ability of the SVM to generalise under increasing levels of heterogeneity seen in training. First, 25 SVM models are trained from one case and tested on all the cases under study.