Segmentation of pulmonary nodules using adaptive local region energy with probability density functionbased similarity distance and multifeatures clustering
 Bin Li^{1}Email author,
 QingLin Chen^{1},
 Guangming Peng^{2},
 Yuanxing Guo^{2},
 Kan Chen^{1},
 LianFang Tian^{1},
 Shanxing Ou^{2} and
 Lifei Wang^{3}
Received: 10 January 2016
Accepted: 25 April 2016
Published: 5 May 2016
Abstract
Background
Pulmonary nodules in computerized tomography (CT) images are potential manifestations of lung cancer. Segmentation of potential nodule objects is the first necessary and crucial step in computeraided detection system of pulmonary nodules. The segmentation of various types of nodules, especially for groundglass opacity (GGO) nodules and juxtavascular nodules, present various challenges. The nodule with GGO characteristic possesses typical intensity inhomogeneity and weak edges, which is difficult to define the boundary; the juxtavascular nodule is connected to a vessel, and they have very similar intensities. Traditional segmentation methods may result in the problems of boundary leakage and a small volume oversegmentation. This paper deals with the above mentioned problems.
Methods
A novel segmentation method for pulmonary nodules is proposed, which uses an adaptive local region energy model with probability density function (PDF)based similarity distance and multifeatures dynamic clustering refinement method. Our approach has several novel aspects: (1) in the proposed adaptive local region energy model, the local domain for local energy model is selected adaptively based on knearestneighbour (KNN) estimate method, and measurable distances between probability density functions of multidimension features with high class separability are used to build the cost function. (2) A multifeatures dynamic clustering method is used for the segmentation refinement of juxtavascular nodules, which is based on the nodule segmentation using active contour model (ACM) with adaptive local region energy and vessel segmentation using flow direction feature (FDF)based region growing method. (3) it handles various types of nodules under a united framework.
Results
The proposed method has been validated on a clinical dataset of 113 chest CT scans that contain 157 nodules determined by a ground truth reading process, and evaluating the algorithm on the provided data leads to an average Tanimoto/Jaccard error of 0.17, 0.20 and 0.24 for GGO, juxtavascular and GGO juxtavascular nodules, respectively.
Conclusions
Experimental results show desirable performances of the proposed method. The proposed segmentation method outperforms the traditional methods.
Keywords
Background
Previous work on segmentation of pulmonary nodules
The segmentation under a united framework of kinds of pulmonary nodules, especially for GGO nodules and juxtavascular nodules, is a very difficult task. Active contour models (ACMs) have been one of the most successful methods for image segmentation [6, 7, 8, 9, 10], even in the segmentation of pulmonary nodules [11]. However, GGO nodules possess weak edges, intensity inhomogeneity and irregular shape, so when they is segmented by using traditional edgebased ACMs [12], regionbased ACMs [6, 7], or even some complex integrated ACMs combine edge and region energy [13, 14], they often occur the problem of boundary leakage. Generally, the model using local information commonly can obtain better performance than that of global statistic information in solving the segmentation problems of intensity inhomogeneity and zigzag edge [7, 15, 16, 17]. The idea of defined local neighbor is more reasonable, especially for segmenting the zigzag and inhomogeneous edge. Li et al. [7] presented a regionbased active contour model (ACM) model, in which a data fitting energy is introduced to solve the problem of intensity inhomogeneity. Lankton et al. [16] summarized and proposed different segmentation models based on local information. But typically, the segmentation curve cannot obtain exact edge or deviates from the objects if the local domain is too large or too small [17]. Further, an active contour model based on nonparametric independent and identically distributed statistics of the image may segment an image according to the particular global to local strategy. The local histogram method using Wasserstein distance to measure distribution distance has a good performance in segmenting cluttered scenes [15]. However,the estimation effect in image segmentation is severely influenced by the small cabin volume and the sample distribution, when the pixel density functions are estimated by histogram method. It is difficult to acquire an ideal segmentation effect only by relying on general intensitydatadriven segmentation methods. In order to overcome the limitation, Krinidis et al. [18] used fuzzy energy to solve the problem of “weak” local minima. Also Assen et al. [19] presented a 3D ACM drived by fuzzy inference for cardiac CT and MR images. Zhang et al. [20] added the Bayesian error of edge direction and region statistical information into the ACM model, to improve the convergence speed.
As mentioned above, juxtavascular nodules account for the largest typology of lung nodules [2]. So besides handling GGO nodules with intensity inhomogeneity and weak edges, it is also important for a segmentation algorithm to be able to treat juxtavascular nodules. In clinic application, even some nodules are not only GGO but also juxtavascular nodules. How to handle various types of pulmonary nodules, including GGO nodules and juxtavascular nodules, under a united framework presents a great challenge [2, 3]. Since vessels can be characterized by the tubular models and a pulmonary nodule is a small round or ovalshaped growth in the lung, so many approaches based on morphological operators [2, 21, 22] have been proposed to segment the juxtavascular nodules. However the sizes and shapes of vessels as well as those of nodules are irregular, it may lead to the problem of a small volume overestimation if only morphological correction is relied upon. Hence a better segmentation refinement method should be taken into consideration furtherly. Besides intensity feature, the analysis of the shape of pulmonary structures has often been adopted to recognize small lung nodules from the background anatomy [2]. However, approaches utilizing simple criteria like shape rule or gray value evidence are typically not suitable to differentiate between different tubular tree structures and nodules. Lung nodules are embodied in a complex and structured background. Their identification and segmentation is usually affected by surrounding anatomical objects [2]. So, in a broad sense, the feature space for the recognition of nodules should be embed more prior information, including the target structures [23, 24].
To our knowledge, there are few literatures aimed at handing GGO and juxtavascular nodules under a united framework and multifeatures classification space. In our previous work, we have built a very preliminary fuzzy integrated ACM incorporated multifeatures analysis to realize segmentation of GGO and juxtavascular nodules [14, 25, 26]. This paper deals with the above mentioned problems further. In our present study, the segmentation problem is converted into the optimization problem of measurable distance between probability density functions of multifeatures. A multifeatures dynamic clustering method is used for the segmentation refinement of juxtavascular nodules.
Our approach
Compared with existing traditional methods, our approach has several novel aspects: (1) in the proposed adaptive local region energy model, the local domain for local energy model is selected adaptively based on knearestneighbour (KNN) estimate method, and measurable distances between probability density functions of multidimension features with high class separability are used to build the cost function. (2) A multifeatures dynamic clustering method is used for the segmentation refinement of juxtavascular nodules, which is based on the nodule segmentation using active contour model with adaptive local region energy and vessel segmentation using flow direction feature (FDF)based region growing method. (3) It handles various types of nodules under a united framework.
The remainder of this paper is organized as follows. In “The proposed integrated ACM with adaptive local region energy and PDFbased similarity distance” section and “Segmentation refinement of juxtavascular nodules based on multifeatures dynamic clustering” section, the proposed segmentation methods of pulmonary nodules are introduced. The experimental results of our method are given in “Experimental results” section, followed by some discussions in “Discussion” section. This paper is summarized in “Conclusions” section.
The proposed integrated ACM with adaptive local region energy and PDFbased similarity distance
 (1)
The KNNbased adaptive local energy function model is proposed. The nodule with GGO characteristic is either partsolid or nonsolid, in which case it possesses typical weak edges and intensity inhomogeneity. The model using local information commonly can obtain better performance than that of global statistic information in solving the segmentation problem [7, 15, 16]. The local domain for local energy model is selected adaptively, which is approached as nonsupervised recognition problem and realized by a KNN estimate method based on medical prior knowledge. It will be explained in detail in “The proposed KNNbased adaptive local energy function” section.
 (2)
The segmentation problem is converted into the optimization problem of measurable distance between PDF of multifeatures. The Bhattacharyya distance function is applied to measure the distance of PDF between the foreground and background, and the PDF in the local region are measured by Wasserstein distance. It will be explained in detail in “The similarity distance based on adaptive local region probability density” section and “The PDFbased Bhattacharyya similarity distance for global energy” section.
 (3)
Multifeatures information with high class separability is reflected and used in the proposed integrated ACM model. It will be explained in detail in “Generation of multidimension feature with high class separability” section.
The proposed KNNbased adaptive local energy function
The model using local information commonly can obtain better performance. The proposed local energy function model is inspired initially by literature [7, 15]. But in our proposed local energy function model, the local domain is not fixed, but flexible and adaptive, which is realized by a KNN estimate method here. In order to segment elaborately for the image with zigzag edge and noise interference, we construct knearest neighbors and estimate the corresponding probability density functions with Parzen window method in each pixel/voxel.
 Rule 1::

r and k are selected as large as possible
 Rule 2::

r ≤ (8 mm/2)/(pixel spacing)
 Rule 3::

\( {{k \, \le \,\pi ({8\,mm} /2(pixel \,\,spacing))^2}}/K_{0}, \quad K_{0}=4\)
Reasons are below: (1) The local region Ω_{ τ } is selected by a circle (for 2dimensional space). (2) \( N_{k} \subset \,\Upomega_{\tau } \). (3) Value of k should make boundaries between classes more distinct in the local region. (4) The following experiment of a dataset (the phantom nodules) was performed to determine and test the parameters.
The similarity distance based on adaptive local region probability density
Generation of multidimension feature with high class separability
For one of the major difficults is the task of segmentation of nonsolid and partsolid GGO nodules with faint contrast and fuzzy margins. In particular, nonsolid nodules are extremely subtle with fuzzy boundaries, and partsolid nodules exhibit highly irregular intensity variations (intensity inhomogeneity) and boundary shapes. GGO pulmonary nodules are hard to distinguish if merely the intensity feature is utilized. Multifeatures information with high class separability is reflected and used in the proposed integrated ACM model.
This feature ASM _{ i } is a measure of the smoothness of the image. Indeed, if all pixels are of the same graylevel I = k _{I}, then P(k _{I}, k _{I}) = 1 and P(m, n) = 0, m ≠ k _{I} or n ≠ k _{I}, and ASM = 1. At the other extreme, if we could have all possible pairs of gray levels with equal probability \( \frac{1}{R} \), then \( ASM = \frac{1}{R} \). The less smooth the region is, the more uniformly distributed P(i, j) and the lower the ASM.
Second order histogram (angular second moment, ASM) feature value for different region
1  2  3  4  5  

GGO nodule  Solid nodule  Vessel  Parenchyma  Myocardium  
ASM  0.2212  0.2448  0.4828  0.4817  0.6403 
The segmentation problem is converted into the optimization problem of measurable distance between PDF P(v) of multifeatures O, shown in Eq. (2). In proposed integrated ACM model, P(v) is the probability density of multifeatures vector O _{ i } = (x _{ i }, y _{ i }, z _{ i }, I _{ i }, level of ASM _{ i }) of v. In “The similarity distance based on adaptive local region probability density” section, P(v) is estimated by the Parzen window estimation method. In order to reduce the computation cost and save the memory, ASM _{ i } is sampled as level 0 (from 0.0000 to 0.1500), level 1 (from 0.1501 to 0.2300), level 2 (from 0.2301 to 0.3500), level 3 (from 0.3501 to 0.5000), level 4 (from 0.5001 to 0.8000) and level 5 (from 0.8001 to 1.0000).
The PDFbased Bhattacharyya similarity distance for global energy
The proposed model and its numerical implementation
Implementation of potential pulmonary nodule segmentation based on the proposed integrated ACM model
 (1)The pulmonary parenchyma is segmented by an overall segmentation method combining thresholding and morphology, which is shown in Fig. 8.
 (2)
Multi Feature computation and data structures for data set are constructed.
 (3)
Compute the degree of membership u(v). In the proposed model, the fuzzy energy is used as the model motivation power evolving the active contour. As shown in Eq. (2), u(v): X → [0, 1] defines the membership degree of a voxel v in data set D to the nodule class cluster center. It is different with our previous work [14], the sample in the AFIACM model is X _{ i } = (x _{ i }, y _{ i }, z _{ i }, I _{ i }, ASM _{ i }). Thus, the degree of membership for each sample X _{ i } = (x _{ i }, y _{ i }, z _{ i }, I _{ i }, ASM _{ i }) in our model is calculated by using the fuzzy clustering algorithm based on intensity and angular second moment features.
 (4)
Compute the scale parameters r and k according to “The proposed KNNbased adaptive local energy function” section, and select adaptively local region R _{ L } and B(v).
 (5)
Specify the stop function term using posterior probability.
 (6)Implement the numerical algorithm of the proposed model according to Eq. (14). Here P(v), P _{1}(τ) and P _{2}(τ) in the local region Ω_{ τ } are computed according to “The similarity distance based on adaptive local region probability density” section and “Generation of multidimension feature with high class separability” section. In each iteration, only P(v) in the local region Ω_{ τ } near to the curve/surface \( \phi\) need to be computed, so pixels/voxels need to be computed are a very small proportion of the total data set. An example is illustrated in Fig. 9. Only P(v) in the local region Ω_{ τ } near to the green curve \( \phi\) need to be computed. The numbers are 1591, which is 0.6 % of the whole data set (512 × 512).
Segmentation refinement of juxtavascular nodules based on multifeatures dynamic clustering
In order to overcome the problem of a small volume oversegmentation in the adhesion region between the juxtavascular nodule and its attached vessel, and obtain a better segmentation result, a multifeatures dynamic clustering method is used for the segmentation refinement of juxtavascular nodules, which is based on the nodule segmentation using the proposed integrated ACM model and vessel segmentation using FDFbased region growing method. Various types of pulmonary nodules, including GGO nodules (part solid and nonsolid) and juxtavascular nodules, are segmented under a united segmentation framework. The refinement procession is just used for the pixels/voxels in some boundary regions between the juxtavascular nodules and blood vessels, without modifying the nodule boundary elsewhere.
The refinement region selection using the proposed nodule and vessel segmentation method
3D potential vessel segmentation by FDFbased region growing method
In this paper, the 3D vessel segmentation is used as the rough segmentation process of segmentation refinement of juxtavascular nodules. 3D vessel segmentation can be accomplished by some traditional methods, such as region growing [23] and vessel enhancement filter [29, 30]. However shapes and appearances of vessels are irregular, a satisfactory result often cannot be achieved if only these traditional methods are relied upon. According to the medical prior knowledge, vessels are characterized by a tubular model, the 3D gradient vectors in a vessel can be used to extract a vector in the direction of the vessel by identifying a vector that is approximately orthogonal to the gradients in a local neighborhood [21, 22, 31]. Moreover, an ideal vascular structure not only keeps a certain elongation, but also has no holes. Simply connected domain is a particular connected domain, in which every loop can be continuously pulled to a point without leaving the space [24]. So we can use these shapes and appearances as the constraints of the segmentation method, which are as follows. (1) Since vascular structures should have no holes, the segmented objects must be removed if they are not simply connected. (2) the flow direction can be used as the growing direction constraint condition, which is one of the constraint conditions of region growing method for segmentation of blood vessels and attached nodules.
Refinement region selection
 (1)
The rough 3D potential vessel segmentation result S _{ c1} is gotten by using the flow direction feature based region growing method which is described in “3D potential vessel segmentation by FDFbased region growing method” section.
 (2)
The segmentation result S _{ c2} is gotten by using the segmentation method based on the proposed integrated ACM model described in “The proposed integrated ACM with adaptive local region energy and PDFbased similarity distance” section.
 (3)
The potential object S _{ r } for segmentation refinement is \({S_r} = {S_{{c_1}}} \cap {S_{{c_2}}}\).
Generation and construction of multifeatures vector in clustering space
Implementation of segmentation refinement based on multifeatures dynamic clustering
 (1)
The segmentation refinement region S _{ r } is selected according to “The refinement region selection using the proposed nodule and vessel segmentation method” section.
 (2)
The feature vector X _{ i } = (x _{ i }, y _{ i }, z _{ i }, I _{ i }, SI _{ i }) is constructed and computed for the points in the region S _{ r }, according to “Generation and construction of multifeatures vector in clustering space” section.
 (3)
The refinement region S _{ r } is segmented by dynamic clustering method (KMeans clustering method [32]), then the juxtavascular nodules is segmented exactly.
Experimental results
The list of 60 CT scans from LIDCIDRI databases
CT scans  Nodule  Type  CT scans  Nodule  Type  

1  LIDCIDRI0003  Nodule 1  GGO  27  LIDCIDRI0160  Nodule 1  JV 
Nodule 2  GGOJV  Nodule 2  Others  
Nodule 3  Others  Nodule 3  Others 10  
Nodule 4  GGO  Nodule 4  JV  
2  LIDCIDRI0007  Nodule 1  Others  28  LIDCIDRI0162  Nodule 1  Others 
3  LIDCIDRI0008  Nodule 1  GGOJV  Nodule 2  JV  
Nodule 2  GGO  Nodule 3  JV  
Nodule 3  Others  Nodule 4  Others 6  
4  LIDCIDRI0011  None  Nodule 5  Others 7  
5  LIDCIDRI0015  Nodule 1  Others  29  LIDCIDRI0167  Nodule 1  Others 
6  LIDCIDRI0017  Nodule 1  JV  30  LIDCIDRI0168  Nodule 1  JV 
7  LIDCIDRI0018  None  Nodule 2  Others 12  
8  LIDCIDRI0019  None  31  LIDCIDRI0173  Nodule 1  Others  
9  LIDCIDRI0021  Nodule 1  GGO  32  LIDCIDRI0175  Nodule 1  JV 
Nodule 2  JV  33  LIDCIDRI0177  Nodule 1  JV  
10  LIDCIDRI0025  None  34  LIDCIDRI0252  Nodule 1  JV  
11  LIDCIDRI0032  Nodule 1  Others 2  Nodule 2  GGOJVvascul  
12  LIDCIDRI0037  Nodule 1  GGO  35  LIDCIDRI0273  nodule 1  JV 
Nodule 2  GGO  36  LIDCIDRI0350  Nodule 1  Others 14  
Nodule 3  Others  37  LIDCIDRI0477  Nodule 1  JV  
13  LIDCIDRI0044  Nodule 1  GGO  Nodule 2  JV  
Nodule 2  JV  38  LIDCIDRI0580  Nodule 1  JV  
Nodule 3  JV  39  LIDCIDRI0626  Nodule 1  GGO  
Nodule 4  GGO  40  LIDCIDRI0645  Nodule 1  Others  
Nodule 5  Others  41  LIDCIDRI0652  Nodule 1  Others  
Nodule 6  GGO  42  LIDCIDRI0681  Nodule 1  GGO  
14  LIDCIDRI0046  None  43  LIDCIDRI0684  Nodule 1  Others  
15  LIDCIDRI0047  Nodule 1  GGO  44  LIDCIDRI0703  Nodule 1  Others 
Nodule 2  JV  45  LIDCIDRI0723  Nodule 1  Others  
16  LIDCIDRI0050  Nodule 1  GGO  46  LIDCIDRI0796  Nodule 1  GGO 
17  LIDCIDRI0051  None  47  LIDCIDRI0803  Nodule 1  GGO  
18  LIDCIDRI0052  Nodule 1  GGO  48  LIDCIDRI0818  Nodule 1  Others 
Nodule 2  Others  49  LIDCIDRI0828  Nodule 1  GGO  
19  LIDCIDRI0082  Nodule 1  Others 5  50  LIDCIDRI0840  nodule 1  Others 
20  LIDCIDRI0114  Nodule 1  JV  51  LIDCIDRI0865  Nodule 1  GGO 
21  LIDCIDRI0131  Nodule 1  GGOJV  52  LIDCIDRI0882  Nodule 1  Others 
Nodule 2  JV  53  LIDCIDRI0914  Nodule 1  Others  
22  LIDCIDRI0133  Nodule 1  Others  54  LIDCIDRI0928  Nodule 1  GGO 
23  LIDCIDRI0141  Nodule 1  Others 7  Nodule 2  JV  
Nodule 2  GGO  55  LIDCIDRI0938  Nodule 1  GGO  
Nodule 3  Others  56  LIDCIDRI0986  Nodule 1  JV  
Nodule 4  JV  57  LIDCIDRI0915  Nodule 1  JV  
Nodule 5  GGO  58  LIDCIDRI0941  Nodule 1  JV  
Nodule 6  JV  Nodule 2  JV  
24  LIDCIDRI0146  Nodule 1  JV  Nodule 3  JV  
25  LIDCIDRI0152  Nodule 1  JV  59  LIDCIDRI0953  Nodule 1  JV 
26  LIDCIDRI0159  Nodule 1  JV  Nodule 2  JV  
60  LIDCIDRI1012  Nodule 1  GGO 
The number of GGO, juxtavascular, GGO juxtavascular and other nodules
Nodule type  GGO pulmonary nodule  Juxtavascular pulmonary nodule  GGO Juxtavascular pulmonary nodule  Others  Total 

Number  42  73  7  35  157 
The different nodule sizes on testing data
Nodule type  ≤ 5 mm  5–10 mm  10–20 mm  Total 

GGO pulmonary nodule  7  18  17  42 
Juxtavascular pulmonary nodule  5  49  19  73 
GGO Juxtavascular pulmonary nodule  1  3  3  7 
Others  7  15  13  35 
Qualitative validation
Validation of the proposed integrated ACM model
Validation of 3D potential vessel segmentation by FDFbased region growing method
Validation of multifeatures dynamic clustering method
Validation of the proposed segmentation method of nodules
In order to validate the effect of the proposed segmentation method, the clinical data with GGO nodules and juxtavascular nodules should be segmented and explored.
From Figs. 13, 14, 15 and 16, the described segmentation method outperforms the traditional methods.
Quantitative validation
Beyond the visual inspection, a quantitative analysis is necessary to ascertain the accuracy of the proposed segmentation method. Here, the well known Tanimoto/Jaccard error A(C _{ m }, C _{ o }) as Eq. (5) is used as the validation merics, which refers to distances between segmentation results or to volume overlaps between the gold standard and the proposed segmentation method. The gold standard typically is a highquality reference segmentation carried out by experts.
Segmentation measure results (error rate)
CT image  The edgebased active contour model  The region based active contour model  The traditional integrated active contour model  The proposed active contour model 

GGO pulmonary nodule  Mean 0.31 Std. 0.11  Mean 0.36 Std. 0.13  Mean 0.36 Std. 0.09  Mean 0.17 Std. 0.07 
Juxtavascular pulmonary nodule  Mean 0.32 Std. 0.13  Mean 0.39 Std. 0.12  Mean 0.29 Std. 0.12  Mean 0.20 Std. 0.09 
GGO Juxtavascular nodule  Mean 0.43 Std. 0.12  Mean 0.47 Std. 0.09  Mean 0.41 Std. 0.13  Mean 0.24 Std. 0.08 
In our experiment, there are 3 nodules missed in the experimental test set of 157 nodules in total. Two of them are small GGO nodules close to 3 mm, and one of missing nodules is a small juxtapleural nodule with very low contrast and close to 3 mm.
The proposed segmentation algorithm was implemented and tested on the computer with 3.46 × 2 GHz CPU, 192 GB Memory and Graphic Card (GPU memory 12 GB GDDRS, 317 GB/s). On average, it takes about 3.14 min/scan (about 1.37 s/each image), which does not include the cost for data preprocessing.
Discussion
Experimental results of segmentation for pulmonary nodules show desirable performances of the proposed segmentation method using the test dataset. The segmentation performance for GGO, juxtavascular and GGO juxtavascular nodules was an average Tanimoto/Jaccard error of 0.17, 0.20 and 0.24, respectively.
We attempt a comparison with the results reported by other research groups. Kubota et al. [1] proposed a segmentation method based on morphological approaches and convexity models for segmenting the pulmonary nodules of various densities. Results on 21 LIDC cases were reported with segmentation overlap measures of mean 0.69 and standard deviation 0.18. Diciotti et al. [2]. presented a refinement method for the segmentation of juxtavascular nodules, which was based on a local shape analysis of the initial segmentation making use of geodesic distance map representations. They observed a percentage of successful segmentations of 84.8 % in fully automated mode and of 91.0 % by using an additional interactive mode for improving the segmentation quality of juxtavascular nodules. However, GGO juxtavascular nodules were not reported in their work. Kostis et al. [21] collected 21 juxtavascular nodules, and observed an 80 % successful rate. Okadaetal et al. [35] reported an 81.2 % estimation rate on a dataset of 1310 various types of nodules (3–30 mm in diameter). Unfortunately, though most of algorithms have been developed for lung nodules, most authors did not report quantitative results for various types of nodules. Ye et al. [5] proposed a shapebased SVM method for detecting nodules. The 3D local geometric and statistical intensity features were used to detect potential solid and GGO nodule. But the segmentation results were not been reported. Murphy [32] used the local image features of shape index and curvedness to detect candidate structures in the lung volume, but the segmentation results were not been reported yet.
Comparing with different segmentation methods covered in literature [3] and other reported literatures above, it seems that the proposed method’s relatively precise segmentation performances. The reasons why the proposed method has a better performance for segmenting all types of GGO and juxtavascular nodules are as follows. In the proposed integrated ACM model, the local domain for local energy model is selected adaptively, and measurable distances between probability density functions of multidimension features with high class separability are used. The model using local information commonly can obtain better performance than that of global statistic information in solving the segmentation problems of intensity inhomogeneity, such as part solid and nonsolid GGO nodules. Multidimension features are also important and helpful for the segmentation of GGO nodules. In many research papers, juxtavascular nodules observed in CT images are outlined applying a global refinement procedure (i.e., throughout the initial segmentation boundary) after an initial rough segmentation. Differently, as is mentioned before, our solution for efficiently segmenting the potential nodule objects involves two steps: (1) a segmentation method is proposed for a whole segmentation, which is based on the proposed integrated ACM model. The method uses an adaptive local region energy model with PDFbased similarity distance, which is especially used for lowcontrast nodules such as part solid and nonsolid GGO nodules, to overcome the problems of boundary leakage, intensity inhomogeneity; (2) a segmentation refinement method based on multifeatures dynamic clustering method, which is referred to as a fine segmentation, is used to segment potential juxtavascular nodules. So the correction method has the advantage that it locally refines the nodule segmentation along recognized vessel attachments only, without modifying the nodule boundary elsewhere.
However, some nodules are missed by the proposed segmentation method. Typically, these nodules are too small (almost 3 mm), or small juxtapleural nodules with very low contrast, which makes it difficult to segment. The small GGO juxtapleural nodule with pleural tail is very near to the edge of lung wall.
To further improve the segmentation performance, some improvements need to be further investigated as follows: in order to recognize small and juxtapleural pulmonary nodules in noisy image more effectively, an adaptive smoothing method needs to be further investigated, and the juxtapleural nodules should be further researched; This requires further investigated in more detail.
Conclusions
When the traditional segmentation method is used to segment the GGO and juxtavascular nodules with weak edges and intensity inhomogeneity characteristic, the problems of boundary leakage and small volume oversegmentation often appear. To solve these problems, a novel segmentation method is proposed for pulmonary nodules in CT images, which is based on the proposed integrated ACM model and multifeatures dynamic clustering method, especially for GGO nodules (part solid and nonsolid) and juxtavascular nodules. This study demonstrates the superiority of the proposed method. The described segmentation method outperforms the traditional methods, and evaluating the algorithm on the provided test data leads to an average Tanimoto/Jaccard error of 0.17, 0.20 and 0.24 for GGO, juxtavascular and GGO juxtavascular nodules, respectively.
Declarations
Authors’ contributions
BL designed the study and carried out the whole proposed segmentation method. QC studies the local region energy model. GP, YG, SO and LW participated in data collection and constituted the members of a qualified panel. KC and LF participated in the statistical analysis. All authors read and approved the final manuscript.
Acknowledgements
The authors would like to thank Dr. W.B. Zhu, Dr. P. Chen, Dr. R. Bai, Dr. L. Zhang, Dr. F. Long, Radiologist G.Q. Qiao, and Engineer L. Tang for their helpful comments and advice which contributed much to this paper. This work is supported by National Natural Science Foundation of China (61305038, 61273249), the Public Science and Technology Research Funds Projects of Ocean (201505002), the Fundamental Research Funds for the Central Universities, SCUT (No. 2015ZZ028), Key Laboratory of Autonomous Systems and Network Control of Ministry of Education (SCUT of China), the National Engineering Research Center for Tissue Restoration and Reconstruction and the Guangdong Key Laboratory for Biomedical Engineering (SCUT of China).
Sources of support
This work is supported by National Natural Science Foundation of China (61305038, 61273249), the Public Science and Technology Research Funds Projects of Ocean (201505002), the Fundamental Research Funds for the Central Universities, SCUT (No.2015ZZ028), Key Laboratory of Autonomous Systems and Network Control of Ministry of Education (SCUT of China), the National Engineering Research Center for Tissue Restoration and Reconstruction and the Guangdong Key Laboratory for Biomedical Engineering (SCUT of China).
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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