An Improved Fuzzy Connectedness Method for Automatic Three-Dimensional Liver Vessel Segmentation in CT Images

In this paper, an improved fuzzy connectedness (FC) method was proposed for automatic three-dimensional (3D) liver vessel segmentation in computed tomography (CT) images. The vessel-enhanced image (i.e., vesselness image) was incorporated into the fuzzy affinity function of FC, rather than the intensity image used by traditional FC. An improved vesselness filter was proposed by incorporating adaptive sigmoid filtering and a background-suppressing item. The fuzzy scene of FC was automatically initialized by using the Otsu segmentation algorithm and one single seed generated adaptively, while traditional FC required multiple seeds. The improved FC method was evaluated on 40 cases of clinical CT volumetric images from the 3Dircadb (n=20) and Sliver07 (n=20) datasets. Experimental results showed that the proposed liver vessel segmentation strategy could achieve better segmentation performance than traditional FC, region growing, and threshold level set. Average accuracy, sensitivity, specificity, and Dice coefficient of the improved FC method were, respectively, (96.4 ± 1.1)%, (73.7 ± 7.6)%, (97.4 ± 1.3)%, and (67.3 ± 5.7)% for the 3Dircadb dataset and (96.8 ± 0.6)%, (89.1 ± 6.8)%, (97.6 ± 1.1)%, and (71.4 ± 7.6)% for the Sliver07 dataset. It was concluded that the improved FC may be used as a new method for automatic 3D segmentation of liver vessel from CT images.


Introduction
Hepatocellular carcinoma (HCC) is one of the most common malignancies in the world, especially in China with the fifth morbidity and the third mortality [1,2]. Nowadays, main treatments to HCC include surgical resection, liver transplantation, and local thermal ablation [3]. Treatment planning and navigation based on medical imaging are essential for these procedures. Among different medical imaging modalities, computed tomography (CT) is commonly used for the guidance of liver tumor treatment. reedimensional (3D) segmentation of liver vessel is critical in CT-based liver tumor treatment planning and navigation. However, manual segmentation of liver vessel in CT images is time consuming and tedious. us, there is a demand for computerized 3D segmentation of liver vessel in CT images [4,5].
Currently, computerized liver vessel segmentation techniques can be classified into region growing [6][7][8], active contour models or level sets [9], graph cuts [10][11][12], extreme learning [13], deep learning [14], and fuzzy logic [15,16]. However, it is still challenging to extract liver vessel in CT images, especially in those with low contrast [4]. Region growing methods [6][7][8] are simple with low computational cost, but they are sensitive to seed point location and threshold. Active contour models or level sets [9] are among mainstream vessel segmentation algorithms, but they have limitations of complex initialization and typically use speed function which implicitly assumes that images are of good contrast. Graph cuts [10][11][12] are segmentation methods based on graph theory, but they are partly limited by the shrinking bias problem. Machine learning methods [13,14] can take into account the diversity of liver vessel topologies and features, but they generally require plenty of training samples or long training time. Fuzzy connectedness (FC) methods [15,16] are based on fuzzy logic. FC describes spatial connectedness between each voxel, rather than just focusing on intensity. Recently, Guo et al. [15] and Wang et al. [16] have demonstrated the potential of FC in liver vessel segmentation. However, for FC-based liver vessel segmentation in CT images, there are still issues to be addressed, including unsatisfying segmentation accuracy (especially for low-contrast CT images), requirement on multiple seeds, and sensitivity to initialization.
In this paper, an improved FC method was proposed for automatic 3D liver vessel segmentation in CT images. e vessel-enhanced image (i.e., vesselness image) was incorporated into the fuzzy affinity function of FC, rather than the intensity image used by traditional FC. An improved vesselness filter was also proposed based on the Jerman's vesselness filter [17] introduced recently. e fuzzy scene of FC was initialized by using the Otsu segmentation algorithm, and the quantity of seeds required was reduced to one which was generated automatically. e proposed method was evaluated on 40 cases of clinical CT image volumes, including low-contrast images. Experimental results demonstrate that the improved FC method can overcome the drawbacks of traditional FC and yield more satisfying segmentation performance. Figure 1 shows the flow chart of the improved FC method. First, the liver volume of interest (VOI) image was obtained by using the liver mask, which could be obtained by using liver segmentation approaches [18]. e liver VOI image was then contrast enhanced by an adaptive sigmoid filtering which was initialized by K-means clustering and isotropically resampled. Subsequently, the improved vesselness filter was used to enhance the liver vessel and suppress the background, and a 3D vesselness image was obtained. en, a 3D fuzzy scene was constructed with the 3D vesselness image by (1) incorporating the improved vesselness into the fuzzy affinity function of FC, (2) initializing the fuzzy scene by the Otsu algorithm, and (3) generating automatically one single seed. Finally, the 3D liver vessel was segmented on the basis of the 3D fuzzy scene and anisotropically resampled.

Dataset.
Both simulated data (n � 60) and clinical CT data (n � 40) were used. e synthetic dataset VascuSynth [19,20] was provided by the Medical Image Analysis Lab, School of Computing Science, Simon Fraser University, Canada. VascuSynth contains 10 groups of data, which are publically available at http://vascusynth.cs.sfu.ca. Each group consists of 12 randomly generated images with different quantity of bifurcations. Six groups of data were randomly selected; among them, the images with bifurcations ≥11 were included in this study. Gaussian white noise was also added to the raw data. e level of the Gaussian white noise was indicated by σ 2 , the variance of the noise. In this study, Gaussian white noise with σ 2 � 30, 45, and 60 were added. e clinical CT image datasets, 3Dircadb and Sliver07, were used. 3Dircadb contains 20 cases of contrastenhanced CT (CE-CT) images. 3Dircadb was provided by the Research Institute against Digestive Cancer, France, and is publically available at http://www.ircad. fr/research/3dircadb. e pixel spacing is 0.56-0.86 mm, and the slice thickness is 1-4 mm. e number of slices ranges from 64 to 502, and the in-plane resolution is 512 × 512 pixels. e gold standard of liver vessel was provided by 3Dircadb, which was manually delineated by radiologists. Sliver07 contains 30 cases of CE-CT images, including 20 training sets and 10 testing sets. e 20 cases of training data are publically available at http://www. sliver07.org and were included in this study. However, Sliver07 did not provide the gold standard of liver vessel. erefore, radiologists were asked to manually delineate the liver vessel to serve as the gold standard for the 20 cases of training data of Sliver07. e number of slices, inplane resolution, and interslice resolution range from 64 to 394, from 0.58 to 0.81 mm, and from 0.7 to 5.0 mm, respectively.

Improved Vesselness Filter.
e multiscale Hessian matrix-based filter (vesselness filter) is commonly used for vessel enhancement [4,17]. Classical vesselness filters were proposed by Sato et al. [21] and Frangi et al. [22]. Since then, Li et al. [23], Erdt et al. [24], and Xiao et al. [25] proposed  improved methods for enhancing the vasculature. Recently, Jerman et al. [17] proposed a novel vesselness filter and demonstrated that it outperformed traditional vesselness filters. For completeness, the Jerman's filter was introduced briefly as below. Let λ i , i � 1, 2, 3 denotes the Hessian eigenvalues of a 3D image at each coordinate x. Considering the ideal eigenvalues' relationship λ 2 ≈ λ 3 ∧ |λ 2,3 | >> |λ 1 | in vasculature, Jerman et al. [17] constructed a novel Hessian eigenvalues function to improve the enhancement performance by using a two-step piecewise compensation. In CT images, the magnitudes of λ 2 and λ 3 were lower at the vascular boundary or in the low-scale vessel (|λ 3 | ≥ |λ 2 | ≈ |λ 1 | ⟶ Low), which did not match the ideal Hessian eigenvalues relationship in vasculature, resulting in significant attenuation of the vesselness response. erefore, Jerman et al. [17] performed a piecewise compensation on the eigenvalue λ 3 : (1) where σ is the vessel scale and τ is a threshold between 0 and 1. In addition, traditional vesselness filters would suppress blob-like structures and obtain poor response at vascular nodes (|λ 1 | ≈ |λ 2 | ≈ |λ 3 | ⟶ High). us, Jerman et al. [17] compensated the ellipsoid structure conforming to the condition λ 2 ≥ λ ρ /2 > 0 to construct the final vesselness function: Jerman et al. [17] evaluated their method on clinical image datasets of lung, cerebral, and fundus vasculatures. However, for the task of liver vessel enhancement in CT images, the Jerman's filter would enhance the liver contour, liver parenchyma, and noise. erefore, the Jerman's filter was improved by incorporating adaptive sigmoid filter for contrast enhancement and by incorporating a backgroundsuppressing item into the vesselness function of the Jerman's filter (Equation (2)). e adaptive sigmoid filter is defined as where I sigmoid is the filtered image, I VOI is the liver VOI image, and β and α represented the intensity center and the intensity range of the vasculature. In this study, β and α were obtained adaptively by the K-means clustering (K � 5). e internal structure of I VOI was clustered into five regions with corresponding cluster centers. With the value of the intensity centers ranking from low to high, the five regions corresponded to the background, liver tumor, liver parenchyma, low-intensity vessel mixed with liver parenchyma, and highintensity vessel, respectively. With the intensity means of the last two regions (m 1 and m 2 ), parameters β and α are calculated by e background-suppressing item, 1 − e −R 2 s /2c , was incorporated into Equation (2), yielding where R s � ��������� � λ 2 1 + λ 2 2 + λ 2 ρ and c is the background suppression coefficient, which was optimally set at λ ρ /3.
Finally, the vesselness response was combined by calculating the maximum response of υ in each scale σ, σ ∈ [σ min , σ max ]: where I vesselness is the final vessel-enhanced image (vesselness image). e improved vesselness filter algorithm is summarized in Algorithm 1.

Improved Fuzzy
Connectedness. FC involved three kinds of fuzzy relationships: fuzzy adjacency, fuzzy affinity, and fuzzy connectivity. Fuzzy affinity represented the local similarity of the voxel pair (c, d) in the entire image scene C, denoted by μ κ (c, d) ∈ [0, 1]: where μ α (c, d) is the fuzzy adjacency (a monotonic increasing function), and h 1 and h 2 are computed by 2 , where f(·) is the intensity of voxels; m and s are mean and standard deviation of f(·) in the VOI, respectively; and ω 1 and ω 2 are weight parameters, ω 1 + ω 2 � 1.
In this paper, the vesselness image obtained by using the improved vesselness filter was used as the input of the fuzzy affinity function, rather than the intensity image used by traditional FC. e improved fuzzy affinity function, To adaptively set parameters m and s, the Otsu segmentation algorithm was adopted to the vesselness image. Two-threshold Otsu was used to yield a binary liver vessel mask. Parameters m and s are, respectively, set at the mean and standard deviation of the vesselness voxels belonging to the foreground of the vessel mask. e weight parameters ω 1 and ω 2 are adaptively selected by using the method proposed by Pednekar et al. [26]: Journal of Healthcare Engineering e fuzzy scene of liver vessel was initialized with one single seed generated automatically on the vesselness image, binarized by a threshold T, and anisotropically resampled to yield the final liver vessel segmentation. Figure 2 illustrates automatic selection of one single seed. In Figure 2(a), the 3D image I vesselness was divided into several regions R sub of 5 * 5 * 3 voxels. e maximum vesselness voxels at each R sub region were selected as potential seeds (denoted by the blue points in Figure 2(b)). en, the regions of 5 * 5 * 3 voxels around the potential seeds were constructed and denoted as R seed , with each potential seed being the center of each R seed region. e mean of the vesselness of each R seed region was calculated. e potential seed having the largest vesselness mean in its R seed region was automatically selected as the final single seed, which was indicated by the red point in Figure 2(b). e improved FC algorithm is summarized in Algorithm 2.

Evaluation.
To analyze quantitatively the performance of the proposed vessel segmentation method, evaluation metrics including accuracy, sensitivity, specificity, and Dice coefficient were used: where TP and TN are the numbers of voxels correctly segmented as vessel and background (i.e., nonvessel), respectively; FP and FN are the numbers of voxels incorrectly segmented as vessel and background, respectively. Figure 3 shows the vessel segmented from the simulated data by using the improved FC method. Figure 3(a) represents the ground truth; Figure 3(b) shows the segmented vessel on the synthetic data; and Figures 3(c)-3(e) show the segmented vessel on the synthetic data added with Gaussian white noise σ 2 � 30, 45, and 60, respectively. e segmentation performance of the improved FC method on the synthetic dataset (n � 60) is shown in Table 1, in terms of accuracy, sensitivity, specificity, and Dice coefficient. Although the sensitivity and Dice coefficient were decreased to some extent with increasing the level of Gaussian white noise, the segmentation performance was generally kept stable. It is thus indicated that the improved FC method is insensitive to Gaussian white noise. Figure 4 shows the vessel-enhanced image by using the improved vesselness filter. (1) Set the vessel scales σ min ⟵ 1, σ max ⟵ 4; threshold τ ⟵ 0.6.

Results
(2) Perform adaptive sigmoid filtering to I VOI by using Equations (3) and (4) to obtain the filtered image I sigmoid .
(4) For σ ⟵ σ min do (5) Compute the Hessian matrix elements at each coordinate H ij (x, σ); Compensate λ 3 by using Equation (1); (9) Perform vesselness filtering by using Equation (5); (10) σ ⟵ σ next until σ � σ max . (11) End for (12) Compute the vesselness image by using Equation (6).  Journal of Healthcare Engineering Figure 6 shows the liver vessel segmented by using the improved FC, depicted by yellow contour or surface. e gold standard of liver vessel is indicated by red contour or surface. e axial slices, sagittal slices, coronal slices, and 3D view are shown in Figures 6(a)-6(c), 6(d)-6(f), 6(g)-6(i), and 6(j)-6(k), respectively. It can be seen that the proposed method yielded satisfying segmentation performance. Figure 7 shows typical CT images from the 3Dircadb (Figures 7(a) Figures 8 and 9 show the comparison of the improved FC method with traditional segmentation algorithms, including traditional FC [27], region growing [27], and threshold level set [27].  Input: the vesselness image I vesselness Output: the liver vessel segmentation (1) Initialize the parameters, and set threshold T ⟵ 0.05 (2) Perform two-threshold Otsu to I vesselness to obtain the parameters m and s (3) Calculate the fuzzy affinity by using Equation (9) (4) Calculate adaptively the weights ω 1 and ω 2 by using Equation (10) (5) Compute potential seeds in R sub regions, and select automatically the single seed with the largest vesselness mean in its R seed region (6) Binarize the fuzzy scene and perform anisotropic resampling to obtain the final liver vessel segmentation ALGORITHM 2: Improved fuzzy connectedness.     When multiple potential seeds were used for traditional FC, the segmentation performance show the vessel segmented by using traditional FC with one single seed indicated by the red point in Figure 2 (Figures 8(m) and 8(p)) and the periphery vessel was not segmented (Figures 8(g) and 9(m), 9(p)), as indicated by green arrows. By contrast, the proposed method was capable to segment completely the liver vessel, even for the lowcontrast images.
To compare further the improved vesselness filter with the Jerman's vesselness filter, the liver vessel segmented by using the improved FC method on the basis of the Jerman's vesselness filtering, rather than the improved vesselness filtering, is shown in Figure 10. Figures 10(a) and 10 (a) show that the Jerman's vesselness filter falsely enhanced the liver contour. Figure 10(c) shows that the Jerman's vesselness filter could not effectively suppress the background (nonvessel) tissues. Quantitative comparison of the improved FC (with one single seed) with traditional FC, region growing, and threshold level set (with multiple  Table 2 and shown in Figure 11, in terms of accuracy, sensitivity, specificity, and Dice coefficient. It can be observed that the improved FC outperformed traditional FC, region growing, and threshold level set. e average accuracy, sensitivity, specificity, and Dice coefficient of the improved FC method were, respectively, (96.4 ± 1.1)%, (73.7 ± 7.6)%, (97.4 ± 1.3)%, and (67.3 ± 5.7)% for the 3Dircadb dataset and (96.8 ± 0.6)%, (89.1 ± 6.8)%, (97.6 ± 1.1)%, and (71.4 ± 7.6)% for the Sliver07 dataset.

Significance of is Study. 3D liver vessel segmentation
is critical in computer-assisted liver tumor treatment planning and navigation. FC is an emerging method for image segmentation. However, traditional FC obtained unsatisfying performance for liver vessel segmentation in CT images, and it required multiple seeds and was sensitive to initialization. To address these issues, an improved FC method was proposed in this paper. Our method was fully automatic. e main contributions of this study were as follows.
e Jerman's vesselness filter was improved by incorporating adaptive sigmoid filtering and a background-suppressing item. e improved vesselness filter effectively enhanced the vessel and suppressed the background. e improved vesselness response was incorporated into the fuzzy affinity function, increasing the segmentation performance of FC. e fuzzy scene was initialized by two-threshold Otsu with one single seed, reducing the number of seeds and the sensitivity to initialization in traditional FC.

Implementation Details of the Algorithms.
e algorithms described in this paper were implemented by using C++ and the Insight Segmentation and Registration Toolkit (ITK) (http://itk.org) [27]. e following ITK classes were mainly used: (1) e improved vesselness filter was implemented on the basis of the class itk::HessianToObjectness MeasureImageFilter. (2) e improved FC method was implemented on the basis of the class itk::SimpleFuzzyConnectedness ScalarImageFilter. is class was also used for the traditional FC segmentation.  e improved FC segmentation also took nearly 30 s. Each of the isotropic resampling and anisotropic resampling took around 60 s.

Sensitivity of the Proposed Algorithm to Key Algorithmic
Parameters. Sensitivity analysis of key algorithmic parameters in Algorithms 1 and 2 was performed. e vessel scales σ min and σ max were set on the basis of the findings of Luu et al. [4]. Here, two key algorithmic parameters were analyzed: the threshold τ in the improved vesselness filter and the threshold T in the improved FC. e threshold τ in vesselness filter determined the degree of piecewise compensation on the eigenvalue λ 3 . In theory, the smaller the threshold τ is, the more enhancement on the vessel boundary would be obtained; however, a too small τ is prone to cause undersegmentation. e threshold T in FC determined the degree of undersegmentation or oversegmentation. A too small T caused undersegmentation, while a too large T resulted in oversegmentation. e value of T from 0.01 to 0.09 was tested, as the segmented vasculature would be incomplete when T > 0.1. For the compromise between undersegmentation and oversegmentation, the value of T was firstly fixed to 0.05 to analyze the sensitivity of the proposed algorithm to the threshold τ. Figure 12 shows the average accuracy, sensitivity, specificity, and Dice coefficient of the proposed method on 10 cases randomly selected from the 3Dircadb dataset. e threshold τ ranged from 0.1 to 0.9 (T � 0.05). e accuracy and Dice coefficient reached peak when τ was optimally set at 0.6. en, the value of τ was fixed to 0.6 to analyze the sensitivity of the proposed algorithm to the threshold T. Figure 13 shows the segmentation performance of the proposed method on the 10 randomly selected cases, with T ranging from 0.01 to 0.09 (τ � 0.6). Based on the maximum value of the accuracy and Dice coefficient, the parameter T was optimally set at 0.05. Table 3 shows a comparison of the improved FC method with related work in terms of segmentation method, dataset, number of cases, automation, precision, and run time. For the run time of the proposed method, it should be noted that each of the improved vesselness filtering and the improved FC segmentation only took around 30 s. Firstly, the proposed method was compared with related work that used the 20 cases of the Sliver07 training dataset. Oliveira et al. [7] used region growing for liver vessel segmentation, but they only performed visual assessment for the segmentation. Ahmadi et al. [28] segmented liver vessel by using fuzzy C-means clustering and initialized the parameters by the genetic algorithm. ough the run time was shorter, the training process was more complex, and the accuracy and specificity of Ahmadi et al. [28] were lower than those of the proposed method. en, the proposed method was compared with related work that used the 3Dircadb dataset. Huang et al. [14] segmented liver vessel on the 20 cases of 3Dircadb by using the 3D U-Net network. eir method reduced the need for the quantity of training data, but it required long training time (48 h). e accuracy, sensitivity, specificity, and Dice coefficient of Huang et al. [14] were slightly higher than those of the proposed method. Sangsefidi et al. [11] employed graph cuts for segmenting liver vessel, but they evaluated their method on only few cases of 3Dircadb.

Comparison with Related Work.
Finally, the proposed method was compared with related work that used clinical data other than Sliver07 and 3Dircadb.
ese studies mostly used CT angiography (CTA) images, which were specific CT for vasculature with clear vascular boundary. However, in the context of computer-assisted liver tumor treatment planning and  navigation, CE-CT images may be used more commonly, as liver tumors could be observed in CE-CT images. ough region growing methods had relatively higher operation efficiency, they are depended on the number and distribution of seeds, resulting in unsatisfied segmentation performance even in high-contrast CTA images [4]. Graph cuts and level set methods would take long time to segment liver vessel [9][10][11][12]. Esneault et al. [10] just showed the segmentation on one case of data, and they reported that the segmented vascular branches needed to be registered, which would take more time. Zeng et al. [12] reported that their method only achieved good performance on highcontrast CTA images, so their method might be restricted in practical applications when only low-contrast CT images are available. e similar issue existed in Shang et al. [9] and Zeng et al. [13]. Shang et al. [9] evaluated the sensitivity by the number of vascular nodes (denoted as SEN * in Table 3), but this evaluation metric may not be rigorous. In comparison with Guo et al. [15] and Wang et al. [16] which increased the time efficiency of traditional FC, this study focused on improving the segmentation performance and reducing the number of seeds and the sensitivity to initialization. In addition, our method did not require manual interaction to select the seed.

Limitations and Future
Work. One limitation of this study is the small number of clinical data with the gold standard (40 cases). More clinical data may be used in future (if possible) to further verify the performance of the proposed method. In addition, the algorithmic steps of isotropic resampling and anisotropic resampling are time consuming, each taking around 60 s. is limitation may be overcome in future work.

Conclusions
An improved FC method was presented for automatic liver vessel segmentation in CT volumetric images. e Jerman's vesselness filter was improved by incorporating adaptive sigmoid filtering and a background-suppressing item. e improved vesselness filter effectively enhanced the liver vessel while suppressing the background. e improved vesselness response was incorporated into the fuzzy affinity function of FC. e fuzzy scene was initialized by twothreshold Otsu with one single seed generated automatically, reducing the number of seeds and the sensitivity to initialization in traditional FC. e improved FC method was evaluated on 40 cases of clinical CT volumetric images. Experimental results showed that the proposed liver vessel segmentation strategy could achieve better segmentation performance than traditional FC, region growing, and threshold level set. It is concluded that the proposed algorithm may be used as a new method for automatic 3D liver vessel segmentation in CT images.

Conflicts of Interest
e authors declare that they have no conflicts of interest.