## 2 Materials and Methods
### Morphological MBI Image Post-Processing: Breast Lesion Detection Based on Persistence
* Malignant-to-benign Breast Lesion labelling is performed in the Waelia QIF using a combination of 3 features, extracted from morphologically validated ROIs in the MBI images. The selected features include: a shape descriptor [34], a Gray-Level Co-occurrence Matrix (GLCM) texture feature [35] and a Neighborhood Gray Tone Difference Matrix (NGTDM) texture feature [36]. The 3 features which were selected in the Waelia QIF implementation for the FiH study of the investigational device are more specifically the following: \(\bigcirc\) Shape descriptors--Solidity: This feature measures the density, or the convexity, of an object. It is computed as the ratio of the volume of the object to the volume of the convex hull of the object, as illustrated in Figure 3. Breast lesion scoring, in terms of risk for malignancy, is routinely based on visual inspection and evaluation of the shape and margins of the imaged breast lesion, as per BIRADS [24,33]. Shape descriptors have been earlier considered for breast lesion classification with mammography [34,37] and ultrasound [38]. \(\bigcirc\) GLCM texture--Correlation: The GLCM texture features measure the spatial relationship between pixels per specific directions, thus highlighting the properties of uniformity, homogeneity, randomness, and linear dependency of the image [35]. More specifically, the \"correlation\" feature varies between 0 (uncorrelated) and 1 (perfectly correlated), showing the linear dependency of gray level values to their respective voxels, as graphically illustrated in Figure 3. \(\bigcirc\) NGTDM texture--Busyness: The NGTDM texture features measure the spatial relationship among three or more pixels neighborhood, closely approaching the human perception of the image [36], as graphically illustrated in Figure 3 More specifically, for the \"busyness\" feature, a high value indicates a \"busy\" image, with rapid changes of intensity between pixels and its neighborhood. Texture-based features have been earlier considered in Radiomics Research for cancerous lesions identification on CT, PET and MRI images [39, 40, 41]. Breast lesion classification, employing texture features on multi-parametric breast MRI images has also been introduced in the state-of-the-art [42]. Figure 3: The 3-d feature vector employed in Waelia for malignant-to-benign breast lesion discrimination. In contrast to the Radiomics Research studies, which suggest the employment of high-dimensional feature vectors (typical size > 30) [39; 40; 41], appropriate feature selection has been considered in the Wavelia QIF, to achieve malignant-to-benign lesion separability in a feature space of low dimensionality. To the authors' knowledge, no shape-based or texture-based feature extraction from Microwave Breast Images (MBI) has ever been considered in the past. The 3-dimensional (3-d) lesion feature vector data [Solidity; Correlation; Busyness] is exploited in a malignant-to-benign breast lesion classification framework in the Wavelia QIF. A 2-class discrimination problem is defined, with: (i) Class #1: Malignant breast lesions, and (ii) Class #2: Benign breast lesions. Two classifiers have been trained in this 3-d feature space. The two classifiers, i.e., a Naive Bayesian (NB) classifier and a Quadratic Discriminant Analysis (QDA) classifier, were selected such that their decision hypersurface partitions the 3-d feature space in two disjoint and continuous manifolds (malignant lesions subspace vs. benign lesions subspace). In the Wavelia FiH clinical investigation [12], female patients were recruited from the symptomatic unit to one of three groups: Biopsy-proven breast cancers (Group-1), unaspirated cysts (Group-2) and biopsy-proven benign breast lesions (Group-3). For the training of the 2 classifiers:  
* The Group-1 patient datasets were labelled as Class #1. * The Group-2 and Group-3 patient datasets were labelled as Class #2. A total of 25 patients underwent MBI in this FiH study. Of these, 24 were included in the final data analysis (11 Group-1, 8 Group-2 and 5 Group-3 patients).