## 2 Materials and Methods
### Morphological MBI Image Post-Processing: Breast Lesion Detection Based on Persistence  
Automated breast lesion detection is performed in the Wavelia QIF by means of morphological post-processing of the set of parametric radar images, which are formed with the employment of X = 5 search ranges for the pc_fib parameter. Automated segmentation of ROIs and association, or not, to a breast lesion is based on morphological properties (solidity and volume) of the ROI and its persistence on the set of parametric radar images, which is evaluated by means of spatial clustering. The persistent visibility of a ROI over multiple pc_fib search ranges is indicative of the association of the ROI with a physical object (breast lesion) in the MBI image. On the other hand, the presence of a ROI in the minority of the pc_fib search ranges under test is indicative of it being associated with an imaging artefact. This setting has been inspired by the \"breast mass\" definition for mammography, as the space-occupying a 3D lesion seen in two different projections [24]. To the authors' knowledge, no such breast lesion detection method, based on persistence in a set of parametric images carrying redundant information content, has ever been integrated into any of the state-of-the-art MBI systems before. A second novel element of the proposed method is the coupling of morphological properties (solidity) with the notion of persistence to validate a ROI detection. The automated breast lesion detection method, as designed and integrated into the Havelia QIF for the FiH clinical investigation of device prototype #1, is outlined below and in the block diagram in Figure 2.  
1. Iterative Image threshold setting: The following operation is first-of-all performed to set a threshold for the raw 3D MBI image, with no a priori available on how normal breast tissue is represented in this type of image: 1. Progressive increase in the image threshold, starting from the null threshold, 2. At each iteration, identification of the \"connected\" objects in the thresholded image, 3. Threshold setting based on the maximal accepted volumetric size of \"connected\" objects, potentially defining a breast mass in the image (default value 3 cm\({}^{3}\), in this implementation). 2. Semi-automated ROI extraction, based on morphological properties: The connected objects to be retained as ROIs, are defined based on a set of user-defined characteristics, including: 1. Volumetric size: all the small objects, of volume inferior to 1 cm\({}^{3}\), are removed from the FiH clinical data analysis, considering the status of the Havelia system prototype #1 in terms of minimum size of detectable lesions. 2. Solidity: this structural feature measures the density (or convexity) of an object. A measure of solidity can be obtained as a ratio of the volume of the object to the volume of a convex hull of the object. A value of 100% indicates a solid object,  
Figure 2: Havelia MBI: morphological image post-processing for breast lesion detection based on persistence. and a value less than 100% indicates an object having an irregular boundary or containing holes. All connected objects with solidity >30% have been ultimately retained, for the data analysis of the FiH clinical investigation of Wavelia. 3. Intensity Contrast: In case of ambiguity (i.e., multiple connected objects to be retained in a single 3D MBI image, based on the volume and solidity criteria), each connected object is retained as ROI, only if it is associated with the maximal intensity in the image and is minimally contrasted (by at least 5%) against the intensity of all the \"competing\" connected objects in the image. 3. Refinement of the ROI segmentation: An Active Contour segmentation module (Chan-Vese algorithm for segmentation without edges [25]) has been configured and employed to refine the contour of the extracted ROIs, in order to enable a more valid characterization of the lesions in terms of shape and texture, as defined in the following sub-section.