# 3D Liver and Tumor Segmentation with CNNs Based on Region and Distance Metrics
## 1 Introduction  
Liver together with related lesion automatic segmentation represents a vital link to obtain quantitative biomarkers for the support systems to accurately diagnose in the clinic and make decisions based on the computer [1]. Nonetheless, liver segmentation remains a challenge in the medical image processing field, which is due to the anatomical complexity of the liver and the poor demarcation between the liver and other neighboring organs [2]. Accurate measurements based on the computed tomography (CT) image, such as location, shape, and the volume of the tumor, together with the functional liver volume, helps physicians evaluate hepatocellular carcinoma (HCC) and plan treatment [3]. However, manually outlining the target organ on every slice can be greatly demanding and effort-consuming; besides, the obtained results are subjective [1]. Two grand challenges benchmarks were carried out with the coordination of the MICCAI (Medical Image Computing and Computer-Assisted Intervention Society) conference to segment the liver and related lesions in 2007 and 2008, respectively [4; 5]. Several approaches based on artificial design features were proposed for liver and related lesion segmentation base on CT images. Recently, thresholding [6, 7], graph cut and level set techniques [8, 9, 10], region growing, and deformable model-based methods [11, 12] have been applied in research to segment the liver and related lesions. However, those methods require substantial human intervention, which may cause bias and mistakes. Therefore, it is necessary to develop automatic and end-to-end approaches to segment tumors on CT images [13]. The scientific community has paid great attention to deep Convolutional Neural Networks (CNN) to solve tasks in computer vision, including recognizing, classifying, and segmenting objects [14, 15, 16, 17]. Similarly, novel deep learning-based segmentation approaches have been put forward to analyze medical images, which achieve greatly competitive findings in comparison with state-of-the-art methods [18, 19, 20, 21, 22]. End-to-end CNN-based approaches have been verified to be sound for analyzing image appearance, and this has motivated researchers to employ them for fully automatic segmentation of the liver and related lesions within the CT volumes. The existing deep learning-based liver and tumor segmentation studies are roughly divided into two classes--(1) 2D Fully Convolutional Networks (FCN), like U-Net [23], multi-channel FCN [24], as well as VGG (Oxford Visual Geometry Group) based FCN [25]; (2) 3D FCN, in which 2D convolutions are substituted with the 3D convolutions in the presence of volumetric input data [26, 27]. The 2D FCN-based methods use 2D slices from 3D volumes for the segmentation task. Specifically, singular or three neighboring slices cropped based on volumetric images are incorporated into the 2D FCNs [24, 25], and then 2D segmentation maps are stacked to produce a segmentation volume. [PERSON] et al. [24] designed a multi-channel fully convolutional network (MC-FCN) to segment liver tumors from multi-phase contrast-enhanced CT images. Since each stage of the contrast-enhanced data provided information about pathological features, it is possible to generate fusion feature maps through merging features from different channels. However, the spatial structural organizations of organs are not considered, and the volumetric information is not fully explored. It remains insufficient to explore spatial data even though neighboring slices are used, which may degrade the performance of the segmentation [3]. The 3D FCN-based method can avoid discontinuities between adjacent slices. For instance, [PERSON] et al. introduced a 3D U-Net network for volumetric segmentation that learns from sparsely annotated volumetric images [28]. The network extended the previous U-Net [18] architecture by replacing all 2D operations with their 3D counterparts. The implementation performed on-the-fly elastic deformations for efficient data augmentation during training. [PERSON] et al.