# Spider U-Net: Incorporating Inter-Slice Connectivity Using LSTM for 3D Blood Vessel Segmentation
## 1 Introduction  
Blood vessel segmentation (BVS) is a prerequisite step that aids in a wide range of clinical procedures such as surgery planning and disease diagnosis. In the radiology field, it is done on images from various imaging modalities such as computed tomography (CT), magnetic resonance imaging (MRI), and magnetic resonance angiography (MRA). For example, there is a study in which coronary arteries are segmented with CT angiography to assess and diagnose coronary heart diseases [1]. Intracranial artery segmentation with MRA images can help radiologists diagnose serious cerebrovascular diseases such as ischemic stroke by displaying areas with stenosis or occlusion [2]. The automation of BVS is an important subject because the manual segmentation of blood vessels is challenging and laborious. The anatomical complexity of the blood vessel structure is generally higher than other organs of the human body, thus it is time consuming for trained technicians to perform. There are various traditional methods for automatic BVS, such as the vessel enhancing model, the deformable model, and the tracking model. The tracking model [3, 4] increases vessel contrast compared with the non-vessel area by applying adequate filters to the image. Binarization with a pre-defined threshold value is done to produce the final segmentation mask. The deformable model [5, 6] decides the boundary of the vessel contour by considering internal and external forces using mathematical formulae such as B-snake. The tracking model [7, 8] repeatably finds the nearby vessel area from the initial seed point with pre-defined rules and constraints. However, such traditional methods require manual input features or parameters, the optimal value of which is different according to the target dataset. They also have difficulty when dealing with exceptional cases, other than machine learning methods [9]. Recently, with the advent of convolutional neural networks (CNN), segmentation models using deep supervised learning are being actively proposed in the medical imaging field. In particular, U-Net [10] has been recognized as the de facto segmentation model for medical imaging as it enables deliberate prediction due to skip connections that bridge the encoder and decoder of the same level. Furthermore, in 3D BVS, there are many kinds of research using U-Net as the baseline. First, there are approaches using the 2D U-Net family which processes a single plane image at a time [11; 12]. Although it is generally applied to 2D BVS regarding optical imaging modalities (e.g., color fundus photography, fluorescein angiography), there is a report that 2D U-Net outperforms the graph cut method--a representative traditional image segmentation method--when segmenting intracranial artery [11]. The limitation of 2D U-Net is that it ignores the z-axis of 3D data. It understands 3D volume as a stack of 2D axial slices and does not consider the relationships with the other slices. Therefore, the information in the z-axis, which can have a positive effect in model training, is not utilized. Next, the 3D U-Net family, which extracts volumetric features instantly using a 3D convolutional operation, is commonly adopted [13; 14; 15; 16]. However, 3D U-Net consumes a considerable amount of memory because it requires sufficient 3D data as input. Although volumetric cropping can be processed to bypass the memory issue, it narrows the sight of the model destroying global anatomical information which can be an important clue when dealing with a medical image. Moreover, 3D U-Net has a difficulty when trained with 3D data such that each volume is comprised of various numbers of axial slices caused by the diversity of the thicknesses and spacings of the images [17; 18]. This characteristic is common in medical image datasets, especially for CT, and to bypass this problem, the additional pre-processing stage which reconstructs the whole dataset with the same voxel size is necessary.