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Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images
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Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images
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Rui Wang a , Chao Li a , Jie Wang a , Xiaoer Wei b , Yuehua Li b , Yuemin Zhu c , Su Zhang a,∗
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School of Biomedical Engineering and Med-X Research Institute, Shanghai Jiao Tong University, Shanghai, China Institute of Diagnostic and Interventional Radiology, Sixth Affiliated People’s Hospital, Shanghai Jiao Tong University, Shanghai, China CREATICS; CNRS UMR 5220; Inserm 1044; INSA Lyon, Villeurbanne, France
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\protect\qtoa{Q3} A novel segmentation algorithm is proposed to extract cerebral vessels from brain magnetic resonance angiography (MRA) images. The vessel segmentation algorithm is fast and fully automatic. The performance of the threshold segmentation is acceptable. The segmentation method may be used for three-dimensional visualization and volumetric quantification of cerebral vessels.
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Article history: Received 14 October 2014 Received in revised form 14 November 2014 Accepted 3 December 2014 Available online xxx
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Keywords: Cerebral vessels Magnetic resonance angiography Threshold segmentation Statistical distribution
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1. Introduction
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Background: Cerebrovascular segmentation plays an important role in medical diagnosis. This study was conducted to develop a threshold segmentation algorithm for automatic extraction and volumetric quantification of cerebral vessels on brain magnetic resonance angiography (MRA) images. New methods: The MRA images of 10 individuals were acquired using a 3 Tesla MR scanner (Interaachieva SMI-2.1, Philips Medical Systems). Otsu’s method was used to divide the brain MRA images into two parts, namely, foreground and background regions. To extract the cerebral vessels, we performed the threshold segmentation algorithm on the foreground region by comparing two different statistical distributions. Automatically segmented vessels were compared with manually segmented vessels. Results: Different similarity metrics were used to assess the changes in segmentation performance as a function of a weighted parameter w used in segmentation algorithm. Varying w from 2 to 100 resulted in a false positive rate ranging from 117% to 3.21%, and a false negative rate ranging from 8.23% to 28.97%. The Dice similarity coefficient (DSC), which reflected the segmentation accuracy, initially increased and then decreased as w increased. The suggested range of values for w is [10, 20] given that the maximum DSC (e.g., DSC = 0.84) was obtained within this range. Comparison with existing method(s): The performance of our method was validated by comparing with manual segmentation. Conclusion: The proposed threshold segmentation method can be used to accurately and efficiently extract cerebral vessels from brain MRA images. Threshold segmentation may be used for studies focusing on three-dimensional visualization and volumetric quantification of cerebral vessels. © 2014 Published by Elsevier B.V.
Cerebrovascular segmentation (Kirbas and Quek, 2004; Suri et al., 2002) plays an important role in medical diagnosis. This technique is necessary to perform a three-dimensional (3-D)
∗ Corresponding author. Tel.: +86 21 62933209; fax: +86 21 62932156. E-mail address: [email protected] (S. Zhang).
visualization of cerebral vessels to diagnose, quantify, and grade vascular abnormalities, such as stenosis and aneurysm (Farag et al., 2004). Moreover, an accurate extraction of 3-D structures of cerebral vessels helps in planning and performing neurosurgical procedures (Frangi et al., 2001; Passat et al., 2005). 3-D time-of-flight (TOF) magnetic resonance angiography (MRA) is a noninvasive technique for vessel imaging. After cerebral vessels are segmented from 3-D TOF MRA images, maximum intensity projection (MIP) (Sun and Parker, 1999) method is generally
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Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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utilized to construct a 3-D volumetric visualization of cerebral vessels and assess the size and location of vessels. Cerebral vessels are difficult to accurately segment because of complex geometric structures and limited spatial resolution and image contrast (Bogunovic´ et al., 2011). Various segmentation methods have been developed to extract cerebral vessels from brain MRA images, and these methods can be divided into two main categories (Kirbas and Quek, 2004; Yan and Kassim, 2006): skeleton-based and non-skeleton-based. In skeleton-based methods (Kirbas and Quek, 2004; Sorantin et al., 2002), the centerlines of vessels are extracted and a vessel tree is generated by connecting these centerlines. A centerline structure is simulated explicitly or implicitly by using vessel modeling methods. However, the results of skeleton-based methods provide incomplete volumetric information of the vessels. In non-skeleton-based methods, vessels are directly extracted from 3-D MRA images by using deformable models (Chen and Amini, 2004; Farag et al., 2004; Kozerke et al., 1999; Scherl et al., 2007; Yan and Kassim, 2006) or threshold techniques (Chung and Noble, 1999; Chung et al., 2004; Kim and Park, 2005; Wilson and Noble, 1999). For example, a level set method (Adalsteinsson and Sethian, 1995) is commonly used in deformable model approaches that track the interfaces and shapes of vessels. Level set segmentation is implemented by locally minimizing an energy function with a gradient descent algorithm (Cremers et al., 2007). Different forms of improved level set methods (Adalsteinsson and Sethian, 1995; Chen and Amini, 2004; Farag et al., 2004) have been designed for vessel surface segmentation, but the use of these methods is limited by common factors, such as sensitivity to initial value, speed, and algorithm convergence. Furthermore, threshold segmentation methods (Chung et al., 2004; Kim and Park, 2005) have been extensively investigated. In these methods, a threshold is chosen to distinguish vessels from brain tissues by combining reasonable statistical models and local voxel information. The selection of threshold value directly impacts the segmentation performance. In this paper, a threshold segmentation method was developed to extract cerebral vessels from 3-D TOF MRA images. In general, extreme value theory (De Haan and Ferreira, 2007) can be used to detect outliers of abnormally low or high values, which occur at the tails of specific probability distributions, such as normal distribution. In MRA images, cerebral vessels present signals higher than surrounding brain tissues with intermediate signals. Homogeneous brain tissues excluding the vessels can be represented by normal distribution, and cerebral vessels can be detected using a specific extreme value distribution, namely, the Gumbel distribution (Kotz and Nadarajah, 2000; Roberts, 2000; Wang et al., 2014). To extract the cerebral vessels from brain MRA images, we determine a threshold by comparing the probability density function (PDF) of the two statistical distributions. This study aimed to design a threshold segmentation algorithm that can be used to extract cerebral vessels from 3-D TOF MRA images. Two statistical distributions were applied to determine a threshold that could be used to distinguish vessels from brain tissues. To evaluate the performance of the proposed threshold segmentation, we investigated the MRA images of 10 individuals and compared automatically segmented vessels with manually segmented vessels.
Ten individuals (four males and six females) were enrolled in this study and subjected to cerebrovascular segmentation. These individuals aged between 29 and 85 years (mean age = 59.7 years). 3-D TOF MRA images were acquired using a 3 Tesla MR scanner (Intera-achieva SMI-2.1, Philips Medical Systems). The main imaging parameters were listed as follows: repetition time/echo flip angle = 20◦ ; rows × cols = 960 × 960; time = 30/3.4 ms; pixel spacing = 0.24 × 0.24 mm2 ; FOV = 230 mm; slice thickness = 1.2 mm; spacing between slices = 0.6 mm; and an axial 3-D slab with 180 slices. All of the raw MRA images were loaded by MIPAV software (http://mipav.cit.nih.gov/) and transformed into new bitmap images with intensities between 0 and 255 by using a robust scaling method in MIPAV software. 2.2. Segmentation method
2.3. Normal and Gumbel distributions
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2.1. Subjects and image acquisition This study was approved by our institutional review board, and a written informed consent was obtained from each patient.
−
(x − ) 2 2
2
(1)
where and stand for the mean and variance of the homogeneous foreground region. However, the intensity distribution of the cerebral vessels did not conform to their corresponding normal distribution. Thus, the extreme value theory was used to solve this problem. Gumbel distribution is a kind of generalized extreme value distribution and can be potentially applied to represent maxima or minima in the data of the generated distributions, such as normal or exponential distributions (Roberts, 2000). Thus, Gumbel distribution is used in some outlier detection methods to find samples with abnormally high or low values, which are far from the expected statistical results of a normal data set. The PDF of the Gumbel distribution is defined as (Roberts, 2000) follows: pGumbel (xi ; , ) =
x−
1 exp −
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Normal distribution is commonly applied to model a homogeneous tissue in brain image segmentation. The contrast between the white matter (WM) and the gray matter (GM) is relatively low in MRA images, thereby producing a homogeneous background region with an intermediate signal. Thus, the intensity distribution of homogeneous brain tissues excluding the cerebral vessels could be effectively represented by normal distribution. For instance, let xi denote the intensity of the ith voxel in a TOF MRA dataset. The PDF of the normal distribution (Bishop, 2006) is expressed as follows:
2. Materials and methods
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The gray histogram plot of a TOF MRA dataset is shown in Fig. 1A. Two distinct peaks are found on the histogram. The leftmost peak represents the background region (namely the whole brain) and the rightmost peak indicates the foreground region, which presents a dark signal on the MRA images. In particular, the intensity distribution of the foreground was investigated in this study using the logarithmic histogram (Fig. 1B). In fact, the rightmost peak indicates homogeneous brain tissues excluding the vessels; by contrast, the long tail (Fig. 1B) on the right side of the peak represents the cerebral vessels. The homogeneous brain tissues excluding the vessels can be efficiently modeled by normal distribution. Nevertheless, the intensity distribution of the cerebral vessels located at the tail in the histogram is not well explained by the normal distribution. Thus, a generalized extreme value distribution, namely, the Gumbel distribution, was used in this study to extract the cerebral vessels from the MRA images.
1 exp pNormal (xi ; , ) = √ 2
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x −
− exp −
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The intensities of the cerebral vessels extremely deviated from the median intensity of the whole brain (including the vessels). Thus, Gumbel distribution was used to detect cerebral vessels
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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Fig. 1. (A) Gray histogram of a TOF MRA dataset. Two peaks are easily found in this plot and represent the background and the foreground, respectively. (B) Logarithmic histogram of the TOF MRA dataset. A long tail on a high-intensity region after the rightmost peak is found in this plot; this long tail indicates cerebral vessels.
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as outliers to the rest of the brain tissues. PDFs were compared between the normal distribution and Gumbel distribution (Fig. 2). 2.4. Threshold segmentation The segmentation framework of our proposed approach included five steps (Fig. 3). Step 1: Foreground and background regions were extracted from the MRA images by using Otsu’s threshold method (Otsu, 1975). The foreground region corresponded to the brain tissues consisting of WM, GM, parts of the eyes, and cerebral vessels; the area of low signal was the background region, including the cerebrospinal fluid, bone, and background air. Step 2: Mean and standard deviation were calculated with respect to the foreground region. To enhance segmentation efficiency, we performed segmentation only in the foreground region, thereby dividing the foreground region into two parts: cerebral vessels and other brain tissues. Step 3: PDFs, namely, pNormal (xi ) and pGumbel (xi ), were calculated for each voxel (xi ) in the foreground region. Mean and standard deviation required in Eqs. (1) and (2) were obtained in step 2. Step 4: A threshold was determined to extract cerebral vessels from brain tissues by comparing pGumbel (xi ) and a weighted
Fig. 2. Comparison of three statistical distributions. The PDFs of these statistical distributions are plotted in the interval of [0, +∞] given that the segmentation only concerns the right tail of the gray histogram. The two intersections (namely, Th1 and Th2) represent two thresholds used to extract the cerebral vessels from the MRA images.
pNormal (xi ). In fact, the cerebral vessels were located on the right side of the other brain tissues in the intensity histogram. In this manner, the unilateral normal distribution was more appropriate to estimate the PDF of the intensity distribution of the brain tissues than other distribution types. Thus, a voxel xi could be a possible cerebral vessel candidate because this variable satisfied the requirements of pGumbel (xi ) ≥ w × pNormal (xi ), where w ≥ 2. w is a weighted coefficient and can be used to control threshold variation. If w = 2, then the PDF of Gumbel distribution was compared with that of the unilateral normal distribution. All of the m voxels that satisfied the requirement (pGumbel (xi) ≥ w × pNormal (xi ) and w ≥ 2) formed a set X = xj ; j = 1, 2, ..., m that included all of the cerebral vessel candidates. The threshold used to distinguish the cerebral vessels from the brain tissues could be determined by finding T = min(X). Any voxel was classified as a cerebral vessel if xi ≥ T. Step 5: False positive (FP) signal was minimized. The possible vessel candidates with sizes as small as one (isolated) or two (connected) voxels were not considered as vessels by an experienced radiologist in manual segmentation. Thus, morphological
Fig. 3. Flow diagram of threshold segmentation.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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Fig. 4. (A) A slice from MRA images of an individual. Cerebral vessels present a high signal on the image. (B) 3-D reconstruction view of the cerebral vessels.
Fig. 5. (A) A sample slice from the MRA images of an individual. ((B)–(G) from left to right) Vessels are automatically extracted using threshold segmentation when w is set as 2, 5, 10, 20, 50, and 100. (H) Segmented vessels derived from manual segmentation. ((I)–(N) from left to right) Reconstructed MIP images by automatic extraction of segmented vessels when w is set as 2, 5, 10, 20, 50, and 100.
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operation, including dilation and erosion, was performed to eliminate these voxels, which were the FP signals in the segmentation results. A 3 × 3 sized convolution kernel was employed to perform the morphological post-processing. The threshold segmentation method was implemented using Matlab R2012b (The MathWorks Inc., Natick, MA, USA).
the maximum intensity on each view throughout a 3-D volume (Fig. 4). MIP is commonly employed in MRA to visualize the topology structure of the vessels and detect vascular abnormalities such as stenosis andaneurysm. In our study, the MIP module in ImageJ (http://rsb.info.nih.gov/ij/) was used to display the 3-D rendering of the segmented vessels.
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2.6. Statistical analysis
MIP (Sun and Parker, 1999) is a volume rendering technique, which generates a series of 2D images by projecting a voxel with
The performance of our proposed automatic segmentation was evaluated and compared with manual segmentation which was
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Fig. 6. (A) A sample slice from the MRA images of patients diagnosed with aneurysm. (B) 3-D reconstruction view of segmented vessels. Aneurysm is delineated using a red rectangle.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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performed by an experienced radiologist. The number of slices for each individual was 180, which was slightly higher than that obtained by manual segmentation. Thus, 20 slices were chosen from the MRA images of each individual in accordance with the principle of random sampling. The cerebral vessels were manually delineated on 200 images from 10 individuals. The manually segmented vessels were converted to binary images, considered ground truth (GT), and used for the subsequent evaluation process. The performance of our proposed threshold segmentation was assessed using three different similarity metrics: Dice similarity coefficient (DSC) (Dice, 1945), false positive rate (FPR), and false negative rate (FNR) (Gibson et al., 2010; Shiee et al., 2010). These similarity metrics were defined as follows:
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DSC =
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2 × (AS ∩ GT) AS+GT
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Table 1 Similarity measurement comparison between automatic segmentation and manual segmentation for 10 individuals. ID
1 2 3 4 5 6 7 8 9 10 Mean
w=5
w = 10
w = 20
DSC
FPR
FNR
DSC
FPR
FNR
DSC
FPR
FNR
0.73 0.75 0.79 0.81 0.86 0.81 0.79 0.89 0.84 0.83 0.81
0.39 0.38 0.15 0.30 0.15 0.34 0.33 0.15 0.19 0.27 0.26
0.20 0.16 0.25 0.11 0.14 0.10 0.14 0.08 0.14 0.10 0.14
0.79 0.81 0.79 0.86 0.87 0.84 0.84 0.90 0.85 0.86 0.84
0.17 0.17 0.07 0.13 0.07 0.19 0.14 0.08 0.10 0.14 0.13
0.24 0.20 0.30 0.15 0.18 0.13 0.18 0.12 0.19 0.14 0.18
0.80 0.83 0.78 0.87 0.86 0.85 0.84 0.89 0.84 0.86 0.84
0.09 0.09 0.04 0.07 0.04 0.13 0.07 0.06 0.06 0.09 0.07
0.27 0.23 0.34 0.19 0.21 0.17 0.22 0.15 0.23 0.18 0.22
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DSC: Dice similarity coefficient; FPR: false positive rate; FNR: false negative rate. Mean: average similarity metrics; ID: the number provided for each individual Q9 involved in this study. b
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FPR =
AS∩!GT GT
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FNR =
!AS ∩ GT GT
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where AS represents the vessel volume obtained from automatic segmentation and GT corresponds to the vessels detected by manual segmentation. DSC measures the similarity between the results derived from the automatic and manual segmentation. DSC ranges from 0 to 1, where 0 indicates no overlap between the results derived from the two methods and 1 corresponds to the best agreement between the two segmentation methods. FPR and FNR measure the ratios of FP (denoted by AS ∩ ! GT) and FN (denoted by ! AS ∩ GT) in the automatically segmented vessels relative to the volume of cerebral vessels delineated by manual segmentation, namely, the GT. Data were statistically analyzed using SPSS for Windows (version 19.0; SPSS, Chicago, IL, USA).
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3. Results
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The cerebral vessels on the 3-D TOF MRA images were automatically extracted using the proposed threshold segmentation algorithm. A comparison of the cerebral vessels detected using different values of parameter w is illustrated in Fig. 5. The 3-D volumetric visualization of the cerebral vessels was reconstructed on the basis of an MIP technique. The FP signals were relatively more in the segmentation results when the parameter w was small (e.g., w = 2 or 5). An example of automatic segmentation for a patient with aneurysm is illustrated in Fig. 6. On the basis of the volume rendering result (Fig. 6B), the structure and shape of the aneurysm could be observed. Different similarity metrics were computed using the results of automatic and manual segmentation. DSCs, FPRs, and FNRs of segmentation using different w are summarized in Table 1. The curves of the similarity metrics as a function of w are plotted in Fig. 7. The result demonstrated that DSC initially increased and then decreased as w increased. Varying w from 2 to 100 resulted in FPR ranging from 117% to 3.21% and FNR ranging from 8.23% to 28.97%. For medical image segmentation, DSC of ≥0.7 indicates very good agreement between automatic and manual segmentation (GarcíaLorenzo et al., 2013; Shiee et al., 2010). Thus, the performance of our proposed threshold segmentation algorithm was acceptable within a large range of w (e.g., w ∈ [5, 100]). In our experiment, discrete w were chosen to segment the vessels, and the best performance was achieved when w ∈ [10, 20]. For reference, a comparison of the DSCs for different segmentation methods (Bogunovic´ et al., 2011; Firouzian et al., 2011; Forkert et al., 2009) was given in Table 2. The threshold segmentation is comparable to other state-of-art segmentation methods.
Fig. 7. Changes in several similarity metrics as a function of w. DSC of ≥0.7 indicates very good agreement between automatic and manual segmentation.
The average run time required for processing a single slice of 960 × 960 voxels was approximately 0.13 s on a standard PC with the Intel i5-2300 quad-core 2.80 GHz processor and 8 GB of memory. The average processing time for a 3-D TOF MRA dataset including 180 slices was approximately 23 s. The comparison of the run time with respect to different segmentation methods (Bogunovic´ et al., 2011; Forkert et al., 2009) was provided for reference (Table 2).
Table 2 Comparison of the DSCs and the run time with respect to different segmentation methods on different datasets.
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Methods
Theory
DSCs
Run time (per slice)
Our work (w = 10 or 20) Bogunovic´ et al. (2011) Firouzian et al. (2011) Forkert et al. (2009)
Threshold segmentation Deformable model
0.84
0.13 s
0.91
3.98 s
Deformable model
0.821
None
Fuzzybased segmentation
0.695
11.56 s
DSC: Dice similarity coefficient. A larger DSC value indicates a better segmentation performance.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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4. Discussion In this study, a threshold segmentation algorithm was developed to automatically extract cerebral vessels from 3-D TOF MRA images. The performance of our method was validated by comparing with manual segmentation, which was performed by an experienced radiologist. High DSC (>0.7) demonstrated that the proposed segmentation method could be a reliable method which could be used to perform 3-D volumetric visualization and quantification of cerebral vessels. The threshold segmentation of cerebral vessels was implemented by comparing the PDFs of two statistical distributions, namely, weighted normal distribution and Gumbel distribution. Gumbel distribution is a special case of a generalized extreme value distribution, which can be used to explain the distribution of the maxima in the data samples of some generated distributions, such as normal distribution. Homogeneous brain tissues excluding the vessels presented an intermediate signal on the MRA images and were well modeled by normal distribution. Nevertheless, the cerebral vessels showed abnormally high signal, and intensity distribution was different from that of the pre-mentioned homogeneous brain tissues. Thus, these cerebral vessels were considered “abnormal” because of abnormally high intensity, which was far from the expected statistical results of homogeneous brain tissues. Therefore, Gumbel distribution was chosen to detect these abnormally high signals as outlier to the surrounding brain tissues. The threshold segmentation employed a weighted normal distribution to find a threshold T, which distinguished cerebral vessels from brain tissues. The threshold T increased as the weight coefficient w increased. In fact, the manually chosen w was designed to control the number of FP and FN signals in the segmentation results. For example, the threshold derived from unilateral normal distribution (w = 2) was greater than that derived from normal distribution (w = 1). More voxels were rejected from vessel candidates by increasing w (or T), thereby producing less FP signals and more FN signals. The suggested range of w was [10, 20]; thus, the maximum DSC (e.g., DSC = 0.84) could be obtained. In fact, the numerical value of w was used to obtain the degree of intensity distribution in which vessels failed to conform to normal distribution. The proposed threshold segmentation method achieved the best performance when w ∈ [10, 20]. Thus, the intensity distribution of the cerebral vessels was not fully explained by the normal distribution (w = 1). The primary source of some FP errors with threshold segmentation was directly linked to possible vessel candidates with sizes as small as one or two voxels. Some bright signals near the skull and scalp may be falsely classified as cerebral vessels when w was small. Thus, two strategies could be used to reduce the influence of these FP errors. First, w could be increased to effectively reduce the FP signal near the skull and scalp. Second, morphological operation, including dilation and erosion, could be employed to eliminate FP vessel candidates with sizes as small as one or two voxels. With the proposed threshold segmentation method, T could be determined by comparing the PDFs of the two statistical distributions. Thus, the mechanism by which threshold was determined was not subjective and unlikely suffered from errors caused by image heterogeneities. Moreover, the cerebrovascular segmentation method is independent of the acquisition protocol. Thus, the results of the cerebrovascular segmentation can be generalized to other scanners. The proposed segmentation method was relatively advantageous compared with other segmentation methods, such as region growing approach (Passat et al., 2005) and level set methods (Adalsteinsson and Sethian, 1995; Chen and Amini, 2004; Farag et al., 2004). Segmentation was performed using region growing techniques (Passat et al., 2005) by incrementally recruiting the neighboring voxels in one region based on various
growing/merging criteria. Nevertheless, the main weakness of the region growing approach is that segmentation results are sensitive to user-supplied seeds (namely, starting points). Level set methods are commonly used to segment cerebral vessels from MRA images. However, the deformable model employed in the level set methods exhibits limitations, such as initialization, run time, high computation complexity, and poor convergence (Gao et al., 2011). These factors constrained the use of level set methods. MIP, which is considered as one of the simplest 3-D rendering techniques, was employed to visualize the morphological structure of cerebral vessels. The whole brain vessels were reconstructed, and abnormalities, such as aneurysm, were found in MIP results. The visualization of local vessels (e.g., carotid artery) provided valuable information for clinical research. In fact, the carotid artery could be further extracted in our segmented vessels if the diameter of the carotid artery is known. In the field of cerebrovascular segmentation for certain applications, segmentation performance was difficult to quantitatively compare with that of other methods. This difficulty could be attributed to differences in data set usage, scanner specifications, and MRI protocols. The lack of GT is another limitation when cerebrovascular segmentation is validates. Thus, manual segmentation of cerebral vessels was considered as GT or gold standard during validation. Considering that the number of slices for all of the patients was slightly high, we chose 200 slices from the MRA images of 10 patients in accordance with the principle of random sampling. Validation results showed that automatic segmentation was similar to manual segmentation. Thus, threshold segmentation method could be an acceptable alternative for vessel segmentation and volumetric quantification. In conclusion, we developed a threshold segmentation algorithm to automatically extract cerebral vessels from brain MRA images. The performance of the threshold segmentation on 3-D TOF MRA images from 10 individuals was acceptable. For practical applications, cerebrovascular segmentation method could be used to quantify the volume of the whole (or local) brain vessels and vascular abnormalities, such as stenosis and aneurysm. Acknowledgments This research is supported by National Basic Research Program of China (973 Program, No. 2010CB732506), National Natural Q6 Science Foundation of China (no. 81301213), National Natural Science Foundation of China (no. 81000609), National Natural Science Foundation of China (no. 60972110), and Major Program of Social Science Foundation of China (no. 11&ZD174). We thank the radiologists of Shanghai Sixth People’s Hospital for providing their clinical images and ground truth data. References Adalsteinsson D, Sethian JA. A fast level set method for propagating interfaces. J Comput Phys 1995;118(2):269–77. Bishop CM. Pattern recognition and machine learning. New York, NY: Springer; 2006. Bogunovic´ H, Pozo JM, Villa-Uriol MC, Majoie CB, van den Berg R, van Andel HAG, et al. Automated segmentation of cerebral vasculature with aneurysms in 3DRA and TOF-MRA using geodesic active regions: an evaluation study. Med Phys 2011;38(1):210–22. Chen J, Amini AA. Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models. IEEE Trans Med Imaging 2004;23(10):1251–62. Chung AC, Noble JA. Statistical 3D vessel segmentation using a Rician distribution. In: Medical image computing and computer-assisted intervention MICCAI’99. New York, NY: Springer; 1999. p. 82–9. Chung AC, Noble JA, Summers P. Vascular segmentation of phase contrast magnetic resonance angiograms based on statistical mixture modeling and local phase coherence. IEEE Trans Med Imaging 2004;23(12):1490–507. Cremers D, Rousson M, Deriche R. A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. Int J Comput Vision 2007;72(2):195–215.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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De Haan L, Ferreira A. Extreme value theory: an introduction. New York, NY: Springer; 2007. Dice LR. Measures of the amount of ecologic association between species. Ecology 1945;26(3):297–302. Farag AA, Hassan H, Falk R, Hushek SG. 3D volume segmentation of MRA data sets using level sets: image processing and display. Acad Radiol 2004;11(4):419–35. Firouzian A, Manniesing R, Flach ZH, Risselada R, van Kooten F, Sturkenboom MCJM, et al. Intracranial aneurysm segmentation in 3D CT angiography: method and quantitative validation with and without prior noise filtering. Eur J Radiol 2011;79:299–304. Forkert ND, Saring D, Wenzel K, Illies T, Fiehler J, Handels H. Fuzzy-based extraction of vascular structures from time-of-flight MR images. Stud Health Technol Inform 2009;150:816–20. Frangi AF, Niessen WJ, Nederkoorn PJ, Bakker J, Mali WPTM, Viergever MA. Quantitative analysis of vascular morphology from 3D MR angiograms: in vitro and in vivo results. Magn Reson Med 2001;45(2):311–22. Gao X, Uchiyama Y, Zhou X, Hara T, Asano T, Fujita H. A fast and fully automatic method for cerebrovascular segmentation on time-of-flight (TOF) MRA image. J Digit Imaging 2011;24(4):609–25. García-Lorenzo D, Francis S, Narayanan S, Arnold DL, Collins DL. Review of automatic segmentation methods of multiple sclerosis white matter lesions on conventional magnetic resonance imaging. Med Image Anal 2013;17(1):1–18. Gibson E, Gao F, Black SE, Lobaugh NJ. Automatic segmentation of white matter hyperintensities in the elderly using FLAIR images at 3T. Magn Reson Imaging 2010;31(6):1311–22. Kim DY, Park JW. Connectivity-based local adaptive thresholding for carotid artery segmentation using MRA images. Image Vision Comput 2005;23(14): 1277–87. Kirbas C, Quek F. A review of vessel extraction techniques and algorithms. ACM Comput Surv 2004;36(2):81–121. Kotz S, Nadarajah S. Extreme value distributions. World Scientific; 2000.
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Kozerke S, Botnar R, Oyre S, Scheidegger MB, Pedersen EM, Boesiger P. Automatic vessel segmentation using active contours in cine phase contrast flow measurements. J Magn Reson Imaging 1999;10(1):41–51. Otsu N. A threshold selection method from gray-level histograms. Automatica 1975;11:23–7. Passat N, Ronse C, Baruthio J, Armspach JP, Maillot C, Jahn C. Region-growing segmentation of brain vessels: an atlas-based automatic approach. J Magn Reson Imaging 2005;21(6):715–25. Roberts SJ. Extreme value statistics for novelty detection in biomedical data Q8 processing. Sci Meas Technol, IEE Proc: IET 2000:363–7. Scherl H, Hornegger J, Prümmer M, Lell M. Semi-automatic level-set based segmentation and stenosis quantification of the internal carotid artery in 3D CTA data sets. Med Image Anal 2007;11(1):21–34. Shiee N, Bazin P-L, Ozturk A, Reich DS, Calabresi PA, Pham DL. A topology-preserving approach to the segmentation of brain images with multiple sclerosis lesions. NeuroImage 2010;49(2):1524–35. Sorantin E, Halmai C, Erdohelyi B, Palágyi K, Nyúl LG, Ollé K, et al. Spiral-CT-based assessment of tracheal stenoses using 3-D-skeletonization. IEEE Trans Med Imaging 2002;21(3):263–73. Sun Y, Parker DL. Performance analysis of maximum intensity projection algorithm for display of MRA images. IEEE Trans Med Imaging 1999;18(12):1154–69. Suri JS, Liu K, Reden L, Laxminarayan S. A review on MR vascular image processing: skeleton versus nonskeleton approaches: part II. IEEE Trans Inf Technol Biomed 2002;6(4):338–50. Wang R, Li C, Wang J, Wei X, Li Y, Hui C, et al. Automatic segmentation of white matter lesions on magnetic resonance images of the brain by using an outlier detection strategy. Magn Reson Imaging 2014;32(10):1321–9. Wilson DL, Noble JA. An adaptive segmentation algorithm for time-of-flight MRA data. IEEE Trans Med Imaging 1999;18(10):938–45. Yan P, Kassim AA. Segmentation of volumetric MRA images by using capillary active contour. Med Image Anal 2006;10(3):317–29.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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Contents lists available at ScienceDirect
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Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images
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Rui Wang a , Chao Li a , Jie Wang a , Xiaoer Wei b , Yuehua Li b , Yuemin Zhu c , Su Zhang a,∗
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School of Biomedical Engineering and Med-X Research Institute, Shanghai Jiao Tong University, Shanghai, China Institute of Diagnostic and Interventional Radiology, Sixth Affiliated People’s Hospital, Shanghai Jiao Tong University, Shanghai, China CREATICS; CNRS UMR 5220; Inserm 1044; INSA Lyon, Villeurbanne, France
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\protect\qtoa{Q3} A novel segmentation algorithm is proposed to extract cerebral vessels from brain magnetic resonance angiography (MRA) images. The vessel segmentation algorithm is fast and fully automatic. The performance of the threshold segmentation is acceptable. The segmentation method may be used for three-dimensional visualization and volumetric quantification of cerebral vessels.
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Article history: Received 14 October 2014 Received in revised form 14 November 2014 Accepted 3 December 2014 Available online xxx
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Keywords: Cerebral vessels Magnetic resonance angiography Threshold segmentation Statistical distribution
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1. Introduction
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Background: Cerebrovascular segmentation plays an important role in medical diagnosis. This study was conducted to develop a threshold segmentation algorithm for automatic extraction and volumetric quantification of cerebral vessels on brain magnetic resonance angiography (MRA) images. New methods: The MRA images of 10 individuals were acquired using a 3 Tesla MR scanner (Interaachieva SMI-2.1, Philips Medical Systems). Otsu’s method was used to divide the brain MRA images into two parts, namely, foreground and background regions. To extract the cerebral vessels, we performed the threshold segmentation algorithm on the foreground region by comparing two different statistical distributions. Automatically segmented vessels were compared with manually segmented vessels. Results: Different similarity metrics were used to assess the changes in segmentation performance as a function of a weighted parameter w used in segmentation algorithm. Varying w from 2 to 100 resulted in a false positive rate ranging from 117% to 3.21%, and a false negative rate ranging from 8.23% to 28.97%. The Dice similarity coefficient (DSC), which reflected the segmentation accuracy, initially increased and then decreased as w increased. The suggested range of values for w is [10, 20] given that the maximum DSC (e.g., DSC = 0.84) was obtained within this range. Comparison with existing method(s): The performance of our method was validated by comparing with manual segmentation. Conclusion: The proposed threshold segmentation method can be used to accurately and efficiently extract cerebral vessels from brain MRA images. Threshold segmentation may be used for studies focusing on three-dimensional visualization and volumetric quantification of cerebral vessels. © 2014 Published by Elsevier B.V.
Cerebrovascular segmentation (Kirbas and Quek, 2004; Suri et al., 2002) plays an important role in medical diagnosis. This technique is necessary to perform a three-dimensional (3-D)
∗ Corresponding author. Tel.: +86 21 62933209; fax: +86 21 62932156. E-mail address: [email protected] (S. Zhang).
visualization of cerebral vessels to diagnose, quantify, and grade vascular abnormalities, such as stenosis and aneurysm (Farag et al., 2004). Moreover, an accurate extraction of 3-D structures of cerebral vessels helps in planning and performing neurosurgical procedures (Frangi et al., 2001; Passat et al., 2005). 3-D time-of-flight (TOF) magnetic resonance angiography (MRA) is a noninvasive technique for vessel imaging. After cerebral vessels are segmented from 3-D TOF MRA images, maximum intensity projection (MIP) (Sun and Parker, 1999) method is generally
http://dx.doi.org/10.1016/j.jneumeth.2014.12.003 0165-0270/© 2014 Published by Elsevier B.V.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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utilized to construct a 3-D volumetric visualization of cerebral vessels and assess the size and location of vessels. Cerebral vessels are difficult to accurately segment because of complex geometric structures and limited spatial resolution and image contrast (Bogunovic´ et al., 2011). Various segmentation methods have been developed to extract cerebral vessels from brain MRA images, and these methods can be divided into two main categories (Kirbas and Quek, 2004; Yan and Kassim, 2006): skeleton-based and non-skeleton-based. In skeleton-based methods (Kirbas and Quek, 2004; Sorantin et al., 2002), the centerlines of vessels are extracted and a vessel tree is generated by connecting these centerlines. A centerline structure is simulated explicitly or implicitly by using vessel modeling methods. However, the results of skeleton-based methods provide incomplete volumetric information of the vessels. In non-skeleton-based methods, vessels are directly extracted from 3-D MRA images by using deformable models (Chen and Amini, 2004; Farag et al., 2004; Kozerke et al., 1999; Scherl et al., 2007; Yan and Kassim, 2006) or threshold techniques (Chung and Noble, 1999; Chung et al., 2004; Kim and Park, 2005; Wilson and Noble, 1999). For example, a level set method (Adalsteinsson and Sethian, 1995) is commonly used in deformable model approaches that track the interfaces and shapes of vessels. Level set segmentation is implemented by locally minimizing an energy function with a gradient descent algorithm (Cremers et al., 2007). Different forms of improved level set methods (Adalsteinsson and Sethian, 1995; Chen and Amini, 2004; Farag et al., 2004) have been designed for vessel surface segmentation, but the use of these methods is limited by common factors, such as sensitivity to initial value, speed, and algorithm convergence. Furthermore, threshold segmentation methods (Chung et al., 2004; Kim and Park, 2005) have been extensively investigated. In these methods, a threshold is chosen to distinguish vessels from brain tissues by combining reasonable statistical models and local voxel information. The selection of threshold value directly impacts the segmentation performance. In this paper, a threshold segmentation method was developed to extract cerebral vessels from 3-D TOF MRA images. In general, extreme value theory (De Haan and Ferreira, 2007) can be used to detect outliers of abnormally low or high values, which occur at the tails of specific probability distributions, such as normal distribution. In MRA images, cerebral vessels present signals higher than surrounding brain tissues with intermediate signals. Homogeneous brain tissues excluding the vessels can be represented by normal distribution, and cerebral vessels can be detected using a specific extreme value distribution, namely, the Gumbel distribution (Kotz and Nadarajah, 2000; Roberts, 2000; Wang et al., 2014). To extract the cerebral vessels from brain MRA images, we determine a threshold by comparing the probability density function (PDF) of the two statistical distributions. This study aimed to design a threshold segmentation algorithm that can be used to extract cerebral vessels from 3-D TOF MRA images. Two statistical distributions were applied to determine a threshold that could be used to distinguish vessels from brain tissues. To evaluate the performance of the proposed threshold segmentation, we investigated the MRA images of 10 individuals and compared automatically segmented vessels with manually segmented vessels.
Ten individuals (four males and six females) were enrolled in this study and subjected to cerebrovascular segmentation. These individuals aged between 29 and 85 years (mean age = 59.7 years). 3-D TOF MRA images were acquired using a 3 Tesla MR scanner (Intera-achieva SMI-2.1, Philips Medical Systems). The main imaging parameters were listed as follows: repetition time/echo flip angle = 20◦ ; rows × cols = 960 × 960; time = 30/3.4 ms; pixel spacing = 0.24 × 0.24 mm2 ; FOV = 230 mm; slice thickness = 1.2 mm; spacing between slices = 0.6 mm; and an axial 3-D slab with 180 slices. All of the raw MRA images were loaded by MIPAV software (http://mipav.cit.nih.gov/) and transformed into new bitmap images with intensities between 0 and 255 by using a robust scaling method in MIPAV software. 2.2. Segmentation method
2.3. Normal and Gumbel distributions
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2.1. Subjects and image acquisition This study was approved by our institutional review board, and a written informed consent was obtained from each patient.
−
(x − ) 2 2
2
(1)
where and stand for the mean and variance of the homogeneous foreground region. However, the intensity distribution of the cerebral vessels did not conform to their corresponding normal distribution. Thus, the extreme value theory was used to solve this problem. Gumbel distribution is a kind of generalized extreme value distribution and can be potentially applied to represent maxima or minima in the data of the generated distributions, such as normal or exponential distributions (Roberts, 2000). Thus, Gumbel distribution is used in some outlier detection methods to find samples with abnormally high or low values, which are far from the expected statistical results of a normal data set. The PDF of the Gumbel distribution is defined as (Roberts, 2000) follows: pGumbel (xi ; , ) =
x−
1 exp −
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Normal distribution is commonly applied to model a homogeneous tissue in brain image segmentation. The contrast between the white matter (WM) and the gray matter (GM) is relatively low in MRA images, thereby producing a homogeneous background region with an intermediate signal. Thus, the intensity distribution of homogeneous brain tissues excluding the cerebral vessels could be effectively represented by normal distribution. For instance, let xi denote the intensity of the ith voxel in a TOF MRA dataset. The PDF of the normal distribution (Bishop, 2006) is expressed as follows:
2. Materials and methods
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The gray histogram plot of a TOF MRA dataset is shown in Fig. 1A. Two distinct peaks are found on the histogram. The leftmost peak represents the background region (namely the whole brain) and the rightmost peak indicates the foreground region, which presents a dark signal on the MRA images. In particular, the intensity distribution of the foreground was investigated in this study using the logarithmic histogram (Fig. 1B). In fact, the rightmost peak indicates homogeneous brain tissues excluding the vessels; by contrast, the long tail (Fig. 1B) on the right side of the peak represents the cerebral vessels. The homogeneous brain tissues excluding the vessels can be efficiently modeled by normal distribution. Nevertheless, the intensity distribution of the cerebral vessels located at the tail in the histogram is not well explained by the normal distribution. Thus, a generalized extreme value distribution, namely, the Gumbel distribution, was used in this study to extract the cerebral vessels from the MRA images.
1 exp pNormal (xi ; , ) = √ 2
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x −
− exp −
(2)
The intensities of the cerebral vessels extremely deviated from the median intensity of the whole brain (including the vessels). Thus, Gumbel distribution was used to detect cerebral vessels
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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Fig. 1. (A) Gray histogram of a TOF MRA dataset. Two peaks are easily found in this plot and represent the background and the foreground, respectively. (B) Logarithmic histogram of the TOF MRA dataset. A long tail on a high-intensity region after the rightmost peak is found in this plot; this long tail indicates cerebral vessels.
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as outliers to the rest of the brain tissues. PDFs were compared between the normal distribution and Gumbel distribution (Fig. 2). 2.4. Threshold segmentation The segmentation framework of our proposed approach included five steps (Fig. 3). Step 1: Foreground and background regions were extracted from the MRA images by using Otsu’s threshold method (Otsu, 1975). The foreground region corresponded to the brain tissues consisting of WM, GM, parts of the eyes, and cerebral vessels; the area of low signal was the background region, including the cerebrospinal fluid, bone, and background air. Step 2: Mean and standard deviation were calculated with respect to the foreground region. To enhance segmentation efficiency, we performed segmentation only in the foreground region, thereby dividing the foreground region into two parts: cerebral vessels and other brain tissues. Step 3: PDFs, namely, pNormal (xi ) and pGumbel (xi ), were calculated for each voxel (xi ) in the foreground region. Mean and standard deviation required in Eqs. (1) and (2) were obtained in step 2. Step 4: A threshold was determined to extract cerebral vessels from brain tissues by comparing pGumbel (xi ) and a weighted
Fig. 2. Comparison of three statistical distributions. The PDFs of these statistical distributions are plotted in the interval of [0, +∞] given that the segmentation only concerns the right tail of the gray histogram. The two intersections (namely, Th1 and Th2) represent two thresholds used to extract the cerebral vessels from the MRA images.
pNormal (xi ). In fact, the cerebral vessels were located on the right side of the other brain tissues in the intensity histogram. In this manner, the unilateral normal distribution was more appropriate to estimate the PDF of the intensity distribution of the brain tissues than other distribution types. Thus, a voxel xi could be a possible cerebral vessel candidate because this variable satisfied the requirements of pGumbel (xi ) ≥ w × pNormal (xi ), where w ≥ 2. w is a weighted coefficient and can be used to control threshold variation. If w = 2, then the PDF of Gumbel distribution was compared with that of the unilateral normal distribution. All of the m voxels that satisfied the requirement (pGumbel (xi) ≥ w × pNormal (xi ) and w ≥ 2) formed a set X = xj ; j = 1, 2, ..., m that included all of the cerebral vessel candidates. The threshold used to distinguish the cerebral vessels from the brain tissues could be determined by finding T = min(X). Any voxel was classified as a cerebral vessel if xi ≥ T. Step 5: False positive (FP) signal was minimized. The possible vessel candidates with sizes as small as one (isolated) or two (connected) voxels were not considered as vessels by an experienced radiologist in manual segmentation. Thus, morphological
Fig. 3. Flow diagram of threshold segmentation.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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Fig. 4. (A) A slice from MRA images of an individual. Cerebral vessels present a high signal on the image. (B) 3-D reconstruction view of the cerebral vessels.
Fig. 5. (A) A sample slice from the MRA images of an individual. ((B)–(G) from left to right) Vessels are automatically extracted using threshold segmentation when w is set as 2, 5, 10, 20, 50, and 100. (H) Segmented vessels derived from manual segmentation. ((I)–(N) from left to right) Reconstructed MIP images by automatic extraction of segmented vessels when w is set as 2, 5, 10, 20, 50, and 100.
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operation, including dilation and erosion, was performed to eliminate these voxels, which were the FP signals in the segmentation results. A 3 × 3 sized convolution kernel was employed to perform the morphological post-processing. The threshold segmentation method was implemented using Matlab R2012b (The MathWorks Inc., Natick, MA, USA).
the maximum intensity on each view throughout a 3-D volume (Fig. 4). MIP is commonly employed in MRA to visualize the topology structure of the vessels and detect vascular abnormalities such as stenosis andaneurysm. In our study, the MIP module in ImageJ (http://rsb.info.nih.gov/ij/) was used to display the 3-D rendering of the segmented vessels.
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2.6. Statistical analysis
MIP (Sun and Parker, 1999) is a volume rendering technique, which generates a series of 2D images by projecting a voxel with
The performance of our proposed automatic segmentation was evaluated and compared with manual segmentation which was
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Fig. 6. (A) A sample slice from the MRA images of patients diagnosed with aneurysm. (B) 3-D reconstruction view of segmented vessels. Aneurysm is delineated using a red rectangle.
Please cite this article in press as: Wang R, et al. Threshold segmentation algorithm for automatic extraction of cerebral vessels from brain magnetic resonance angiography images. J Neurosci Methods (2014), http://dx.doi.org/10.1016/j.jneumeth.2014.12.003
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performed by an experienced radiologist. The number of slices for each individual was 180, which was slightly higher than that obtained by manual segmentation. Thus, 20 slices were chosen from the MRA images of each individual in accordance with the principle of random sampling. The cerebral vessels were manually delineated on 200 images from 10 individuals. The manually segmented vessels were converted to binary images, considered ground truth (GT), and used for the subsequent evaluation process. The performance of our proposed threshold segmentation was assessed using three different similarity metrics: Dice similarity coefficient (DSC) (Dice, 1945), false positive rate (FPR), and false negative rate (FNR) (Gibson et al., 2010; Shiee et al., 2010). These similarity metrics were defined as follows:
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2 × (AS ∩ GT) AS+GT
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Table 1 Similarity measurement comparison between automatic segmentation and manual segmentation for 10 individuals. ID
1 2 3 4 5 6 7 8 9 10 Mean
w=5
w = 10
w = 20
DSC
FPR
FNR
DSC
FPR
FNR
DSC
FPR
FNR
0.73 0.75 0.79 0.81 0.86 0.81 0.79 0.89 0.84 0.83 0.81
0.39 0.38 0.15 0.30 0.15 0.34 0.33 0.15 0.19 0.27 0.26
0.20 0.16 0.25 0.11 0.14 0.10 0.14 0.08 0.14 0.10 0.14
0.79 0.81 0.79 0.86 0.87 0.84 0.84 0.90 0.85 0.86 0.84
0.17 0.17 0.07 0.13 0.07 0.19 0.14 0.08 0.10 0.14 0.13
0.24 0.20 0.30 0.15 0.18 0.13 0.18 0.12 0.19 0.14 0.18
0.80 0.83 0.78 0.87 0.86 0.85 0.84 0.89 0.84 0.86 0.84
0.09 0.09 0.04 0.07 0.04 0.13 0.07 0.06 0.06 0.09 0.07
0.27 0.23 0.34 0.19 0.21 0.17 0.22 0.15 0.23 0.18 0.22
a
DSC: Dice similarity coefficient; FPR: false positive rate; FNR: false negative rate. Mean: average similarity metrics; ID: the number provided for each individual Q9 involved in this study. b
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FPR =
AS∩!GT GT
(4)
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FNR =
!AS ∩ GT GT
(5)
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where AS represents the vessel volume obtained from automatic segmentation and GT corresponds to the vessels detected by manual segmentation. DSC measures the similarity between the results derived from the automatic and manual segmentation. DSC ranges from 0 to 1, where 0 indicates no overlap between the results derived from the two methods and 1 corresponds to the best agreement between the two segmentation methods. FPR and FNR measure the ratios of FP (denoted by AS ∩ ! GT) and FN (denoted by ! AS ∩ GT) in the automatically segmented vessels relative to the volume of cerebral vessels delineated by manual segmentation, namely, the GT. Data were statistically analyzed using SPSS for Windows (version 19.0; SPSS, Chicago, IL, USA).
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The cerebral vessels on the 3-D TOF MRA images were automatically extracted using the proposed threshold segmentation algorithm. A comparison of the cerebral vessels detected using different values of parameter w is illustrated in Fig. 5. The 3-D volumetric visualization of the cerebral vessels was reconstructed on the basis of an MIP technique. The FP signals were relatively more in the segmentation results when the parameter w was small (e.g., w = 2 or 5). An example of automatic segmentation for a patient with aneurysm is illustrated in Fig. 6. On the basis of the volume rendering result (Fig. 6B), the structure and shape of the aneurysm could be observed. Different similarity metrics were computed using the results of automatic and manual segmentation. DSCs, FPRs, and FNRs of segmentation using different w are summarized in Table 1. The curves of the similarity metrics as a function of w are plotted in Fig. 7. The result demonstrated that DSC initially increased and then decreased as w increased. Varying w from 2 to 100 resulted in FPR ranging from 117% to 3.21% and FNR ranging from 8.23% to 28.97%. For medical image segmentation, DSC of ≥0.7 indicates very good agreement between automatic and manual segmentation (GarcíaLorenzo et al., 2013; Shiee et al., 2010). Thus, the performance of our proposed threshold segmentation algorithm was acceptable within a large range of w (e.g., w ∈ [5, 100]). In our experiment, discrete w were chosen to segment the vessels, and the best performance was achieved when w ∈ [10, 20]. For reference, a comparison of the DSCs for different segmentation methods (Bogunovic´ et al., 2011; Firouzian et al., 2011; Forkert et al., 2009) was given in Table 2. The threshold segmentation is comparable to other state-of-art segmentation methods.
Fig. 7. Changes in several similarity metrics as a function of w. DSC of ≥0.7 indicates very good agreement between automatic and manual segmentation.
The average run time required for processing a single slice of 960 × 960 voxels was approximately 0.13 s on a standard PC with the Intel i5-2300 quad-core 2.80 GHz processor and 8 GB of memory. The average processing time for a 3-D TOF MRA dataset including 180 slices was approximately 23 s. The comparison of the run time with respect to different segmentation methods (Bogunovic´ et al., 2011; Forkert et al., 2009) was provided for reference (Table 2).
Table 2 Comparison of the DSCs and the run time with respect to different segmentation methods on different datasets.
a b
Methods
Theory
DSCs
Run time (per slice)
Our work (w = 10 or 20) Bogunovic´ et al. (2011) Firouzian et al. (2011) Forkert et al. (2009)
Threshold segmentation Deformable model
0.84
0.13 s
0.91
3.98 s
Deformable model
0.821
None
Fuzzybased segmentation
0.695
11.56 s
DSC: Dice similarity coefficient. A larger DSC value indicates a better segmentation performance.
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4. Discussion In this study, a threshold segmentation algorithm was developed to automatically extract cerebral vessels from 3-D TOF MRA images. The performance of our method was validated by comparing with manual segmentation, which was performed by an experienced radiologist. High DSC (>0.7) demonstrated that the proposed segmentation method could be a reliable method which could be used to perform 3-D volumetric visualization and quantification of cerebral vessels. The threshold segmentation of cerebral vessels was implemented by comparing the PDFs of two statistical distributions, namely, weighted normal distribution and Gumbel distribution. Gumbel distribution is a special case of a generalized extreme value distribution, which can be used to explain the distribution of the maxima in the data samples of some generated distributions, such as normal distribution. Homogeneous brain tissues excluding the vessels presented an intermediate signal on the MRA images and were well modeled by normal distribution. Nevertheless, the cerebral vessels showed abnormally high signal, and intensity distribution was different from that of the pre-mentioned homogeneous brain tissues. Thus, these cerebral vessels were considered “abnormal” because of abnormally high intensity, which was far from the expected statistical results of homogeneous brain tissues. Therefore, Gumbel distribution was chosen to detect these abnormally high signals as outlier to the surrounding brain tissues. The threshold segmentation employed a weighted normal distribution to find a threshold T, which distinguished cerebral vessels from brain tissues. The threshold T increased as the weight coefficient w increased. In fact, the manually chosen w was designed to control the number of FP and FN signals in the segmentation results. For example, the threshold derived from unilateral normal distribution (w = 2) was greater than that derived from normal distribution (w = 1). More voxels were rejected from vessel candidates by increasing w (or T), thereby producing less FP signals and more FN signals. The suggested range of w was [10, 20]; thus, the maximum DSC (e.g., DSC = 0.84) could be obtained. In fact, the numerical value of w was used to obtain the degree of intensity distribution in which vessels failed to conform to normal distribution. The proposed threshold segmentation method achieved the best performance when w ∈ [10, 20]. Thus, the intensity distribution of the cerebral vessels was not fully explained by the normal distribution (w = 1). The primary source of some FP errors with threshold segmentation was directly linked to possible vessel candidates with sizes as small as one or two voxels. Some bright signals near the skull and scalp may be falsely classified as cerebral vessels when w was small. Thus, two strategies could be used to reduce the influence of these FP errors. First, w could be increased to effectively reduce the FP signal near the skull and scalp. Second, morphological operation, including dilation and erosion, could be employed to eliminate FP vessel candidates with sizes as small as one or two voxels. With the proposed threshold segmentation method, T could be determined by comparing the PDFs of the two statistical distributions. Thus, the mechanism by which threshold was determined was not subjective and unlikely suffered from errors caused by image heterogeneities. Moreover, the cerebrovascular segmentation method is independent of the acquisition protocol. Thus, the results of the cerebrovascular segmentation can be generalized to other scanners. The proposed segmentation method was relatively advantageous compared with other segmentation methods, such as region growing approach (Passat et al., 2005) and level set methods (Adalsteinsson and Sethian, 1995; Chen and Amini, 2004; Farag et al., 2004). Segmentation was performed using region growing techniques (Passat et al., 2005) by incrementally recruiting the neighboring voxels in one region based on various
growing/merging criteria. Nevertheless, the main weakness of the region growing approach is that segmentation results are sensitive to user-supplied seeds (namely, starting points). Level set methods are commonly used to segment cerebral vessels from MRA images. However, the deformable model employed in the level set methods exhibits limitations, such as initialization, run time, high computation complexity, and poor convergence (Gao et al., 2011). These factors constrained the use of level set methods. MIP, which is considered as one of the simplest 3-D rendering techniques, was employed to visualize the morphological structure of cerebral vessels. The whole brain vessels were reconstructed, and abnormalities, such as aneurysm, were found in MIP results. The visualization of local vessels (e.g., carotid artery) provided valuable information for clinical research. In fact, the carotid artery could be further extracted in our segmented vessels if the diameter of the carotid artery is known. In the field of cerebrovascular segmentation for certain applications, segmentation performance was difficult to quantitatively compare with that of other methods. This difficulty could be attributed to differences in data set usage, scanner specifications, and MRI protocols. The lack of GT is another limitation when cerebrovascular segmentation is validates. Thus, manual segmentation of cerebral vessels was considered as GT or gold standard during validation. Considering that the number of slices for all of the patients was slightly high, we chose 200 slices from the MRA images of 10 patients in accordance with the principle of random sampling. Validation results showed that automatic segmentation was similar to manual segmentation. Thus, threshold segmentation method could be an acceptable alternative for vessel segmentation and volumetric quantification. In conclusion, we developed a threshold segmentation algorithm to automatically extract cerebral vessels from brain MRA images. The performance of the threshold segmentation on 3-D TOF MRA images from 10 individuals was acceptable. For practical applications, cerebrovascular segmentation method could be used to quantify the volume of the whole (or local) brain vessels and vascular abnormalities, such as stenosis and aneurysm. Acknowledgments This research is supported by National Basic Research Program of China (973 Program, No. 2010CB732506), National Natural Q6 Science Foundation of China (no. 81301213), National Natural Science Foundation of China (no. 81000609), National Natural Science Foundation of China (no. 60972110), and Major Program of Social Science Foundation of China (no. 11&ZD174). We thank the radiologists of Shanghai Sixth People’s Hospital for providing their clinical images and ground truth data. References Adalsteinsson D, Sethian JA. A fast level set method for propagating interfaces. J Comput Phys 1995;118(2):269–77. Bishop CM. Pattern recognition and machine learning. New York, NY: Springer; 2006. Bogunovic´ H, Pozo JM, Villa-Uriol MC, Majoie CB, van den Berg R, van Andel HAG, et al. Automated segmentation of cerebral vasculature with aneurysms in 3DRA and TOF-MRA using geodesic active regions: an evaluation study. Med Phys 2011;38(1):210–22. Chen J, Amini AA. Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models. IEEE Trans Med Imaging 2004;23(10):1251–62. Chung AC, Noble JA. Statistical 3D vessel segmentation using a Rician distribution. In: Medical image computing and computer-assisted intervention MICCAI’99. New York, NY: Springer; 1999. p. 82–9. Chung AC, Noble JA, Summers P. Vascular segmentation of phase contrast magnetic resonance angiograms based on statistical mixture modeling and local phase coherence. IEEE Trans Med Imaging 2004;23(12):1490–507. Cremers D, Rousson M, Deriche R. A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. Int J Comput Vision 2007;72(2):195–215.
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