## 2 Related Work  
There are a number of existing models and algorithms in the area of lung parenchyma segmentation and related to the work of this paper. The existing work can be mainly classified according to the methods used, which are the threshold [4; 5; 6; 7; 8], clustering [9], region-growing [10], graph theory-based [11], and active contour model [12; 13] methods. [PERSON] and [PERSON] [14] proposed a method of partial lung cutting based on the combination of the threshold method and the opening operation in morphology in order to extract pulmonary nodules. However, when there are pulmonary nodules presenting lung adhesion, these nodular areas are excluded by the method of threshold segmentation and the region growing. The reason for this is the similar gray level of the pulmonary nodules and the surrounding lung parenchyma. In addition, the lung boundary appears concave, making difficult the extraction and identification of the tumor, blood vessels, and trachea. Therefore, it is necessary to analyze and repair the concave and depressed lung parenchyma boundary. [PERSON] et al. [15] demonstrated that the rolling sphere CT image processing method of pulmonary nodules can effectively reduce false positives when analyzing juxtapleural stretch-type pulmonary nodules. [PERSON] and [PERSON] [16] combined the methods of threshold and regional growth to segment the lung parenchyma. They used the ball method to repair the extracted lung boundary. [PERSON] et al. [17] used morphological methods to detect and segment the pulmonary nodules. Their computer-aided diagnostic system was sensitive in 82.66% of cases. In [PERSON] et al. [18] method of image segmentation for lung CT images with juxtapleural nodules, the iterative adaptive averaging algorithm and adaptive curvature threshold method was used to reinsert the missing juxtapleural nodules. [PERSON] et al. [19] proposed a lung parenchyma segmentation algorithm, which was based on gray integral projection and fuzzy C means clustering combined with the rolling sphere method to repair the boundary area. However, the selection of the sphere radius was a critical problem. If the radius was too large, the lung parenchyma would be over-segmented. If the radius was too small, it would be under-segmented, and the repaired lung boundary would be incomplete. [PERSON] et al. [20] proposed a method to repair lung parenchyma boundary by combining an improved chain code algorithm and the Bresenham algorithm. [PERSON] et al. [21] presented a lung parenchyma segmentation algorithm combining the regional growth and the morphology methods. They also proposed a two-dimensional convex hull algorithm to repair the profile of the lung parenchyma. Compared to the previous work, this algorithm had a higher accuracy, and the depression of the juxtapleural nodules could be accurately repaired. However, similar to the previous convex hull algorithm, the proposed one was still unable to repair vascular depression. On the basis of the above review, the rolling-ball method and morphology-based method are the most commonly used methods of boundary restoration, characterized by simple and fast implementation. However, because of the randomness of the shape and size of pulmonary nodules, it is difficult to find morphological templates of appropriate size. Small-size templates cannot include all lung nodules, whereas oversizing can include a too large non-lung area and other border areas. The curvature-based method [22; 23; 24] is also a commonly used method, which considers the sudden change of the boundary curvature corresponding to the defective boundary region. However, this assumption is not suitable in case of sudden changes in noise and local curvature. The boundary repair of by this method is not satisfactory when these sudden changes are present in the pulmonary boundary. An observation regarding the existing lung parenchymal segmentation algorithms is that the majority of the images are segmented as single-slice CT images, ignoring the correlation between adjacent images in a sequence.