## 3 Materials and Methods
### The Proposed Analysis  
Clinical knowledge points out that breast lesions in DCE-MRI appear hyperintense compared to the adipose and muscle surrounding tissues. Furthermore, anatomical atlases and diagnosis reports also refer that breast lesions have the tendency to grow in an isotropic manner, preserving a pseudo-spherical shape [39]. Relying on these morphological features, in this study we decided to start the segmentation from the central slice, which should be the one with the largest area: adjacent slices were processed successively. The idea behind this choice is to segment initially the slice in which the lesion appears more evident, finding the centroid of the connected-component identifying the lesion. On slices different from the central one, the lesion ROI was found by identifying the connected-component with the centroid that has the minimum distance from the centroid found for the central slice. The whole segmentation process can be summarized as follows:  
* _dataset loading_: all DCE-MRI images (belonging to the selected patient) and its ground-truth are loaded;
* _ROI selection_: a bounding box containing the lesion is manually drawn in the central image: in this way, the algorithm analyzes only the pixels within the box, reducing computational times and avoiding classification mismatches;
* _pre-processing_: necessary to reduce noise and provide images with similar characteristics for the next processing steps;
* _lesion segmentation_: once the images are pre-processed, the MR image stack of each patient is segmented by all the analyzed methods (i.e., SMRG, k-means, FCM, and sFCM);
* _post-processing_: performed to refine the segmentation and to properly identify the ROI from each binary mask obtained in the previous step;  
Figure 1: Examples of DCE-MRI phases related to four breast cancer patients (one per row): malignant lesions are shown on rows 1 and 3, while benign lesions are shown on rows 2 and 4. Among phases, for segmentation purposes the clinician selected the strongest one. In particular, for these lesions, the 4 th, 3 rd, 4 th, and 3 rd phase was chosen, respectively.  
* _performance evaluation_: the final masks are stored and performance metrics (i.e., area-based and distance-based metrics) are calculated comparing the masks against the ground-truth.  
In addition to the well-known segmentation techniques, also the exploited pre- and post-processing operations are widely used by the international community in the field of medical imaging. In fact, the literature offers many works that use the same pre-processing [42, 43] and post-processing [44, 45] steps in the image analysis phases (before segmentation), as well as in the refinement phases (after segmentation), with excellent results.  
Figure 2 shows the flow diagram of the implemented and proposed analysis. Each processing block is described in the following subsections. All the methods were developed using the MatLab environment (Natick, MA, USA). The code is available via GitHub: [[https://github.com/carmilitello/UnsupervisedSegmentation.git](https://github.com/carmilitello/UnsupervisedSegmentation.git)]([https://github.com/carmilitello/UnsupervisedSegmentation.git](https://github.com/carmilitello/UnsupervisedSegmentation.git)) (accessed on 9 November 2021).