## 1 Introduction
### Background on Segmentation
However to handle more complex tasks as medical image segmentation, different approaches have been introduced, such as Fuzzy C-means (FCM), allowing data points to partially belong to different clusters, which can improve segmentation performances [24]. These kinds of models can be trained easily without any knowledge of ground truth. However, this also means that the accuracy may be lower with respect to supervised approaches, as no feedback from the gold standard is used. Remarkable performance improvements have been achieved using deep learning models hold higher accuracy in different fields including medical imaging [25]. Deep neural networks (DNN) rely on the basic neuron unit, which performs a weighted sum of the input features and after a non-linear transformation (activation) produces a scalar output. DNN usually consist of multiple layers made of several neurons; the output of one layer is used as input for the subsequent one and so on for all the layers until the final layer producing the ultimate output is reached. The training procedure for a DNN involves the optimisation of all the parameters exploiting the gradient descent technique [22]. The number of parameters increases with the depth of the net, requiring a larger amount of training data to learn all the parameters. In particular, the architecture of convolutional neural networks (CNN) emerged for segmentation tasks due to its smaller number of parameters that come from sharing weights among neurons of the same layer [25]. CNN rely on different layer types: convolutional layers, in which a kernel of weights is convolved with the image producing a feature map; non-linear layers that apply the activation function to the produced feature map and lastly pooling layers that allow progressive downsampling of the initial image increasing the receptive field. These layers can be stacked and used to obtain features from progressively larger receptive fields, enabling the production of accurate segmentations [22]. Most of the commonly used models rely on fully convolutional networks using only convolutional layers and encoder-decoder networks. The latter consists of the encoder part exploiting convolutional and pooling layers to capture context and the decoder part for deconvolution and localization, finally producing pixelwise prediction on the image providing the segmentation mask [25]. In the last years with the improvements in computational capabilities especially of GPUs training complex models has become more and more feasible, marking the flourishing of DNN [22]. An overall perspective on DL approaches for general medical image segmentation can be found in [26]. To compare different models it is essential to define proper metrics, depending on the segmentation task different choices can be made, considering volume based, overlap and distance based metrics. Considering the segmentation of medical volumes, model performances are usually estimated using the Dice-Sorensen coefficient (DSC) to estimate the overlap between automatic segmentation and ground truth, but also to measure reproducibility [27]. Given two sets, \(S_{a}\) and \(S_{t}\) being respectively the automatic and the ground truth segmentation, the dice score is defined by twice the cardinality of the intersection divided by the sum of the cardinalities of each set \(DSC=\frac{2|S_{a}\cap S_{t}|}{|S_{a}|+|S_{t}|}\)[27]. The scope of this review is to explore the main results in terms of breast lesion segmentation on MR images with a particular accent on the evolution of DL, exploring results obtained with the most promising models and investigating their limits to guide new improvements of the models. The goal is to highlight the current state of the art in segmentation techniques, providing insights that could aid in the development of more effective models for automatic lesion delineation. The review addresses the advantages, limitations, and potential pitfalls of existing approaches.