## 2 Materials and Methods
### Morphological MBI Image Post-Processing: Breast Lesion Detection Based on Persistence
This module may have a critical impact, especially in the case of small lesions, which are low contrasted against the background healthy breast tissue. 4. Spatial clustering of the ROIs which have been extracted on the set of X MBI images, formed with varying pc_fib search ranges, is performed. In the current implementation of the Wavelia QIF, the Euclidean distance between the centroids of two ROIs is required to be shorter than \(\mathrm{d_{R}}=1\) cm for the ROIs to be associated with the same lesion in the breast. 5. Persistence over varying pc-fib search range: Five pc-fib search ranges (2 wide and 3 narrow) are systematically used during the FiH clinical investigation of Wavelia to generate parametric 3D MBI images of each patient's breast, as earlier stated. Detection of a breast lesion in a minimum number of parametric images (3 out of the 5 pc_fib search ranges) is required for a ROI to be considered persistent and validated. Combination of 3D Shape Descriptors and Texture Features for Breast Lesion Characterization with Microwave Breast Imaging (MBI)  
Apart from using reflected microwave energy to reconstruct images of the breast, additional information on the size, shape, and surface texture can be extracted and potentially exploited for discrimination between benign and malignant breast lesions using microwaves [1]. Malignant tumors usually present the following characteristics: irregular and asymmetric shapes, blurred boundaries (lack of sharpness), rough and complex surfaces with spicules or micro-lobules, non-uniform permittivity, and irregular tissue density. Conversely, benign tumors tend to have the following characteristics: well-circumscribed contours, compactness, and a smooth surface. Previous research works on breast lesion characterization/classification with MBI [26; 27; 28; 29; 30] considered principally the MBI received signals as input to a classifier, with or without dimensionality reduction. These state-of-the-art research works [26; 27; 28; 29; 30] have been based on simulated datasets and/or simplified experimental setups; no evaluation of such methods on patient clinical datasets has been published to date. Among the state-of-the-art MBI prototypes which have been tested on clinical datasets, two of them published studies on breast lesion classification with MBI. Early concept work on the exploitation of the pattern of the frequency-domain Radio-Frequency (RF) responses of the ROIs representing the breast lesions in the MBI image was published in [31] for the MARIA M5 [4] MBI system. For the MammoWave MBI system, machine learning methods were employed with raw received signals in the frequency domain to classify them as healthy or non-healthy responses [32]. In the Wavelia QIF a module is integrated for the characterization of the ROIs which have been prior detected and validated based on morphological properties and their persistence, and thus associated with breast lesions. This module includes the following operations:  
* Breast Lesion sizing: by means of fitting an ellipsoid to the ROI associated with the persistent lesion detection, in the 3D MBI images that have been generated by applying either of the two wide pc_fib search ranges. The greatest linear dimension of the lesion is defined as the length of the longest axis of the fitted ellipsoid. This definition is compatible with the conventional method that is applied for sizing breast abnormalities based on 2D mammography and ultrasound images [24,33]. During the FiH clinical investigation, the Waelia MBI system showed promise for measuring lesion size with a more favorable linear trend between MBI and post-surgery histological lesion size, compared to the results obtained for conventional imaging [14]. Two challenging patient cases in terms of breast lesion sizing are indicatively discussed in Results Section 3.2, to better highlight the status of the MBI lesion sizing method, as integrated into the current version of the Waelia QIF.