## 1 Introduction
The rationale was that invasive breast cancer spreads by degrading the tissue structure through proteolytic activity--the chronic inflammatory reaction to proteolysis causes the reduction of extra-cell water content, with a consequent reduction of ADC if compared to in situ tumors. In order to test the hypothesis, in [17], a dataset of 21 DCIS and 155 IDC was employed and a significant difference in ADC values between the two groups was found (\(p<0.001\) and AUC = 0.89). A Radiomics approach in DCE-MR images, using combined computer-extracted MR imaging kinetic and morphologic features, was tested by [PERSON] et al. [20] (in a dataset containing 32 benign, 71 DCIS, and 150 IDC cases), obtaining AUC = 0.83. Finally, deep learning was tried in [21], with the purpose of predicting invasive cancer after DCIS diagnosis. They used a transfer learning approach, in which a pre-trained GoogleNet was used to calculate features in 131 MRI images, then training a support vector machine (SVM). The result was AUC = 0.70. The Radiomics calculations to classify tumors as in situ or infiltrative must be performed in a region of interest (ROI) containing the tumor tissue [22]. For this reason, a necessary pre-processing step is manual or (semi)automatic segmentation (contouring) of the lesions, separating the tumor from normal tissue in the image. Breast tumor segmentation, especially in DCE-MRI images, is still a challenging task in the clinical setting, although it is necessary in some circumstances, e.g., when tumor-response prediction to chemotherapy is assessed [23; 24; 25]. Automating this procedure would help radiologists to reduce their manual workload on image analysis, as they normally perform tumor diagnosis by locating lesions layer-by-layer, and that is an arduous and time-consuming task [26]. Different image segmentation methods in MRIs were proposed in the past decades but no optimal method exists yet. The simplest pixel-based approaches generally rely on thresholding the image intensity and grouping individual pixels through appropriate classifiers. For example, [PERSON] et al. [27] determined the boundary of the suspected tumor on the assumption that the lesion intensity range was 110-140 on the 0-255 scale, so they simply applied a threshold for obtaining a binary image. The use of thresholding for breast tumor segmentation was also used by [PERSON] et al. [28] through the exploitation of intensity differences between the pixels, before and after providing contrast, followed by morphological post-processing steps. Fuzzy C Means (FCM) clustering [26] and its various versions [29; 30] is also one of the prevailing methods, due to its simplicity [26] in isolating suspicious lesions. Another popular method is the classic k-means used for segmenting the lesion [31; 32]. Other typical techniques used for lesion segmentation are region-based methods. [PERSON] and [PERSON] [33] proposed the algorithm of seeded region growing (SRG) and its advancement [34], which begins by determining the seed (or set of seeds) from which growth starts. Then, SRG grows these seeds into regions by successively adding surrounding pixels, until all pixels are assigned to one region. Other region-based methods exploit the watershed algorithm, followed by post-processing steps [35; 36]. Contour-based methods are also much used in the task of breast lesion segmentation, especially in case of active-contours of the lesion boundary. A recent work [37] describes an interactive segmentation method for BC lesions in DCE-MRI images, based on the active contour without edges (ACWE) algorithm and using parallel programming with general purpose computing on graphics processing units (GPGPU). The ACWE was able to segment objects with low gradient information in their boundaries. The performance of this algorithm was evaluated on a set of 32 breast DCE-MRI cases in terms of speed-up, and compared to non-GPU based approach. A high speed-up (40 or more) was obtained for high-resolution images, providing real-time outputs. [PERSON] et al.