# Semi-Automatic Segmentation of Vertebral Bodies in MR Images of Human Lumbar Spines
## 1 Introduction  
Low back pain is a common disease in modern society [1; 2]. As a multifactorial disease, numerous lumbar components including intervertebral discs, parasipinal muscle, or alterations of the vertebral body may contribute to low back pain. Magnetic resonance (MR) imaging is a noninvasive imaging modality that is widely used for both morphological and quantitative evaluation of the human lumbar spine. Evaluation of the vertebral bodies in MR images (Figure 1a) plays a key role in the diagnosis and establishing treatment strategies. Vertebral body segmentation on MR images provides clinically useful information including quantitative biomarkers, volume, and shape. Previous methods for vertebral body segmentation are inherently challenging, owing to the similar signal intensity of the vertebral body and anatomically contiguous tissues and the inconsistent boundaries [3; 4]. The segmentation of grayscale medical images has been extensively researched [5]. Some of the classical methods are described here. Histogram-based segmentation is one of the most commonlyused methods [6; 7]; it uses only pixel intensity to segment the image by applying a threshold. However, this method faces many limitations, because it does not include shape or position information. Another conventional method is the region-growing method that begins by placing a seed [8; 9; 10; 11]. This seed point grows on the basis of the similarity of its neighboring pixels and extends out to fill a region of interest (ROI). This method is also based on pixel intensity, which is disadvantageous in the case of noisy images. Another approach employs an edge detection algorithm. For example, the Canny edge-detection algorithm obtains vertical and horizontal gradients using various kernels after limitation of noise via medial or Gaussian filters [12]. Subsequently, non-maximum suppression is used to make the edge thinner and more precise, whereas thresholding and edge tracking further improves the edge. Clustering is another commonly used method. The K-means clustering algorithm determines the number of clusters, k, with the initial center position of the clusters and repeats the process until the center position of the clusters and their corresponding data converge [13; 14; 15]. The fuzzy C-means algorithm is another clustering method that sets the number of clusters and the objective function with initial values and repeats the calculation until the objective function is minimized [16; 17; 18; 19]. The actively investigated segmentation method in recent medical imaging is the graph-cut algorithm. This algorithm transforms an image into a graph G = (V, E), where V (node) is the actual spatial element to be segmented and E (edge) is the similarity of each pixel [20; 21; 22; 23; 24]. Depending on how V and E are specified, various graphs can be created. The generated graph is transformed into a similarity matrix to perform division. Various algorithms, such as the min-cut max-flow algorithm, are used for the division [25; 26]. Use of the graph-cut algorithm for medical image segmentation has shown good results. [PERSON] and [PERSON] reported a 91% Dice similarity coefficient (DSC) [27], whereas [PERSON] and [PERSON] reported an 81% DSC using the graph-cut method for vertebral body segmentation [3]. However, in both these studies, each vertebral body was individually segmented, and the method required repeated user inputs to assign a seed point at the center of each vertebral body. Furthermore, because the performance of the algorithm depends on the number of nodes and the connection method, the method requires the user to calibrate multiple parameters for each segmentation. The most recent approaches are the deep-learning-based methods, which exhibit superior performance over existing mathematical algorithms. [PERSON] reported successful segmentation of medical images using a U-net image segmentation network [28]. [PERSON] also showed the possibility of a deep learning segmentation for vertebral bodies in MR lumbar spine images [29].