# Focal Dice Loss-Based V-Net for Liver Segments Classification
## 1 Introduction  
Computed Tomography (CT) is one of the most adopted imaging methodologies to accomplish different medical tasks. If combined with intelligent systems based on artificial intelligence, its range of applicability includes, but is not limited to, Computer-Aided Diagnosis (CAD) systems and intelligent applications supporting surgical procedures [1, 2].  
Liver segmentation is a pivotal task in abdominal radiology, as it is essential for several clinical tasks, including surgery, radiotherapy, and objective quantification [3]. In addition, several pieces of clinical evidence over the last few decades have demonstrated the necessity to go beyond the conception of the liver as a single object (from a morphological perspective), but rather to consider the liver as formed by functional segments [4]. [PERSON]'s classification [5] of liver segments is the most widely adopted system for this purpose, since it is especially useful in surgery setups. The separation of these anatomical areas can be exploited for tumor resections in Computer-Assisted Surgery (CAS) systems [6], allowingsurgeons to focus on different segments. In this way, a surgeon can avoid removing healthy liver parenchyma, by performing a segmentectomy, also reducing the risk of complications for the patient [7].  
However, different other tissues and organs, such as the kidney and spleen, are in the abdominal area. Since the tissues in such an area are characterized by similar intensity levels when acquired by CT or other imaging systems in general, their segmentation with automatic methods is not a simple task. In fact, the segmentation of organs in the abdominal area is mostly tackled by employing manual or semi-automatic approaches [8; 9]. To do this, there is a multitude of traditional image processing algorithms for biomedical image segmentation, including thresholding algorithms, Region-Growing (RG) algorithms, level sets, and graph cuts.  
Deep Learning (DL) is an emerging paradigm that is changing the world of medical imaging. DL consists of the application of hierarchical computational models that can directly learn from data, creating representations with multiple levels of abstraction [10]. Thanks to the natural proneness of DL architectures to process grid-like data, such as images or multi-dimensional signals, they are extensively investigated in image classification and segmentation tasks; in fact, several works have already demonstrated their capabilities to outperform the state-of-the-art in such tasks, making them valid systems to be applied also in the medical domain [11; 12; 13; 14].  
DL architectures may be employed for both classification and segmentation tasks, i.e., the delineation of areas or Regions of Interest (ROIs) within images or volumes. In this regard, it is necessary to distinguish between semantic segmentation [15; 16] and object detection [17; 18] approaches implemented using DL methodologies. The first aims at producing a dense, pixel- (or voxel-) level segmentation mask, whereas the latter aims at individuating the bounding boxes of the regions of interest [19; 20]. In many contexts, precise segmentation masks are more useful than bounding boxes, especially in the medical domain, but they require more human effort for labeling the ground-truth dataset required to train and validate the models (since a domain expert must manually produce precise voxel-level masks to create the dataset themselves).  
In this work, we performed the segmentation of the liver segments. This task may be performed directly or by performing a prior segmentation of the liver parenchyma. Although literature exists for both approaches, our experiments revealed that liver parenchyma segmentation is not needed to train a multi-class classification DL model on liver segments, since applying liver masks to the volumes reduces the context. Nonetheless, other authors found this step useful [21].