## 1 Introduction  
An accurate segmentation of individual vertebra in computed tomography (CT) images is an essential step for the clinical diagnosis and treatment of pathologic conditions. It is used in various applications of image-based vertebrae assessment, biomechanical modeling, and surgery planning [1]. It plays a vital role in computer-aided diagnoses (CAD) as it used for different clinical tasks to diagnose various diseases like scoliosis, kyphosis, spondylolisthesis, degenerative disc disease, etc. However, the exact vertebral boundaries cannot be determined due to the articulation of the vertebrae with each other that may induce vertebral overlaps in the segmentation of adjacent vertebrae. Despite an increasing attention in vertebra segmentation recently, robust and accurate spine segmentation methodologies are still deficient. Previous works on vertebra segmentation have used a multistep approach incorporating localization of spine and vertebra detection, followed by segmentation [2; 3]. Multiple techniques have been applied to vertebra segmentation, such as active shape model and snake-based methods [4; 5], level sets, or graph-based techniques using normalized cuts [6; 7]. Most of these models depend on prior knowledge in the form of a statistical shape model or spine atlases. The performance of such methods is high on healthy spines with a good score of DICE coefficient. However, some of these methods fail in accurate segmentation with patients of osteoporortic fractures because such patients often suffer vertebral fractures in different stages and spinal deformities, such as scoliosis. In such kind of fractures, model-dependent segmentation may fail due to that the variability of a unique shape is different from the mean shape model. Machine learning methods can fulfill these requirements in the condition that sufficient datasets are available for their training. Without sufficient data [8], the machine learning methods can find many different hypotheses, that all give the same accuracy on training data and the problem appears when data available is too small. Many methods work by performing in local search form that gets stuck in local optima. For instance, neural network algorithms minimize an error function over training data by employ gradient descent, and decision tree algorithms employ a greedy splitting rule for growing of decision tree. In addition, in cases where there is enough training data, it may still computationally very difficult for the learning algorithm to find the best hypothesis. A previous work [9; 10] proposed to solve the verteb detection issue on arbitrary FOVs using random forests and multilayer perceptron. In the current scanning techniques, CT is an accurate modality to access the vertebral morphology. Several verteb segmentation techniques from CT images have been proposed in the recent years. In an earlier study, verteb segmentation is achieved by unsupervised approaches, such as region growing, adaptive threshold, boundary adjustment [11], graph cut [12], and watershed [13]. [PERSON] et al. [14] presented the Willmore flow technique in a level set method to conduct a surface model evaluation. The edge- and region-based level set function combination approach [6] for verteb segmentation is proposed in CT images. The hybrid morphological filter and Gaussian mixture for automatic initialization of level set is presented in [15] to handle topological variations. In region-based approach, vertebral body segmentation is conducted to detect the key features from statistical and heuristic methods in [16]. Another technique based on a watershed algorithm for automatic spinal column segmentation has been proposed previously [17]. The verteb segmentation and labeling methodology presented from the watershed and mathematical morphology was proposed by [PERSON] et al. [18]. [PERSON] et al. [2] presented a method based on statistical shape model (SSM) by integrating detection, identification, and segmentation of the spine.