

ORIGINAL ARTICLE 

Year : 2019  Volume
: 5
 Issue : 1  Page : 3745 

Level set evolution with intensity prior knowledge for multiple sclerosis lesion segmentation
Zhaoxuan Gong^{1}, Wei Guo^{1}, Zhenyu Zhu^{1}, Jia Guo^{2}, Wei Li^{3}, Guodong Zhang^{1}
^{1} Department of Computer, School of Computer, Shenyang Aerospace University, Shenyang, Liaoning Province, China ^{2} Department of Radiology, The General Hospital of Shenyang Military, Shenyang, Liaoning Province, China ^{3} Key Laboratory of Intelligent Computing in Medical Image, Ministry of Education, Shenyang, Liaoning Province, China
Date of Web Publication  29May2019 
Correspondence Address: Guodong Zhang School of Computer, Shenyang Aerospace University, Shenyang 110136, Liaoning Province China
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/digm.digm_5_19
Background and Objectives: Multiple sclerosis (MS) lesion segmentation is important in estimating the progress of the disease and measuring the impact of new clinical treatments. Manual lesion delineation for the segmentation of lesions is timeconsuming and suffers from observer variability. Therefore, a fully automated MS lesion segmentation method is considerable important in clinical practice. Subjects and Methods: In this study, we present a multilabel fusion embedded level set method for white matter lesion segmentation from MS patient images. Specifically, we focus on the validation of the variational level set method. Lesion segmentation is achieved by extending the level set contour which consists of an intensityconstrained term, an image data term, and a regularization term. Results: To compare the performance of our method with other stateoftheart methods, we evaluated the methods with 25 magnetic resonance imaging datasets of MS patients. The dice score reaches an average of 0.55 for the proposed method. The sensitivity value and specificity value reach an average of 0.89 and 0.14, respectively. Conclusions: Experimental results demonstrate that our method is robust to parameter setting and outperforms other methods. The intensityconstrained term plays a key role in improving the segmentation accuracy. The experimental results show that our approach is effective and robust for lesion segmentation, which might simplify the quantification of lesions in basic research and even clinical trials.
Keywords: Intensityconstrained term, level set, magnetic resonance imaging, multiple sclerosis lesion, segmentation
How to cite this article: Gong Z, Guo W, Zhu Z, Guo J, Li W, Zhang G. Level set evolution with intensity prior knowledge for multiple sclerosis lesion segmentation. Digit Med 2019;5:3745 
How to cite this URL: Gong Z, Guo W, Zhu Z, Guo J, Li W, Zhang G. Level set evolution with intensity prior knowledge for multiple sclerosis lesion segmentation. Digit Med [serial online] 2019 [cited 2019 Oct 17];5:3745. Available from: http://www.digitmedicine.com/text.asp?2019/5/1/37/259309 
Introduction   
Multiple sclerosis (MS) is a demyelinating and neurodegenerative disease, which causes morphological and structural changes to the brain. MS could cause various central nervous system dysfunctions such as numbness or weakness of a limb, in coordination, vertigo, or visual dysfunction.^{[1]} Early diagnosis is important due to the availability of therapies that slow the progression of the disease. A radiologist can track the progress of the disease and make further treatment decisions after lesion detection.^{[2]} The positions, size, and changes of threedimensional (3D) visualization will assist the radiologist to diagnose MS disease from magnetic resonance imaging (MRI) data. Hence, it is vital to establish an automatic segmentation method for clinical application.
Automatization of MS lesion segmentation is highly desirable with regard to time and complexity and visually vague edges of anatomical borders.^{[3]} Their shapes are deformable, and their location and area across patients may differ significantly. There are many proposed approaches, automatic and semiautomatic, for MS lesion segmentation. These approaches include a variety of methods such as voxelbased model,^{[4],[5]} fuzzy clustering,^{[6]} Bayesian model,^{[7]} and active contour model,^{[8],[9]} some of which will be reviewed in the following. Zhao et al.^{[10]} proposed an automated MS lesion segmentation method on multichannel MR images using energy minimization. Lesion segmentation and intensity inhomogeneity correction are obtained simultaneously by multiplicative intrinsic component optimization (MICO). Roy et al.^{[11]} proposed a level set method for MS lesion segmentation, and a threephase level set is used to generated background for each image. Contour detection was performed after skull stripping. Then, the background image can be obtained by the level set image and contour detection image. A binary threshold image has been done by the combination of entropy and standard deviation. The binary image is subtracted by the background image to obtain the final lesion segmentation results. Birenbaum et al.^{[2]} proposed a longitudinal convolutional neural network (CNN) model for MS lesion segmentation, lesion regions are roughly estimated by image intensities and white matter (WM), and then, CNNs are applied to obtain falsepositive reduction and final segmentation result. Valverde et al.^{[12]} proposed a cascaded CNN approach for MS lesion segmentation. Two 3D CNNs are applied in their method. One is used to extract plausible candidate lesion voxels while the other is applied to reduce the falsepositive voxels coming from the first one. The approach by Guizard et al.^{[13]} presented a multicontrast MS lesion segmentation method using nonlocal means model. In their method, the spatial location of the lesion can be captured, and lesions can be segmented accurately regardless of their shape and size. Saurabh et al.^{[14]} proposed a MSmetrix framework for MS lesion segmentation. In MSmetrix, multichannel MR images are applied in a probabilistic model to extract lesions as an outlier to the normal brain. Then, a prior knowledgebased model is used to extract the final lesion. Brosch et al.^{[15]} proposed a deeplearning method for MS lesion segmentation. A neural network is designed which combines two pathways. Image features can be extracted by the convolutional pathway, and the deconvolutional pathway is applied to obtain the final lesion segmentation. Freire and Ferrari.^{[16]} proposed an automatic MS lesion segmentation method using mixture model and probabilistic model. Using their method, brain tissues are classified to small classes until MS lesions are extracted from other tissues. However, the common limitation of those is their sensitivity to lesion quantity. The above methods tend to misclassify some WMs into lesions when there are fewer or no lesions in the image.
In this study, we look for an optimal contour as the desired segmentation of brain lesions through level set evolution. The algorithm is initialized by a multiatlas skull stripping (MASS) method,^{[17]} which helps to eliminate the impact of brain skull, and then, image erosion is used to further removing the residues after skull stripping. Second, fuzzy cmeans (FCM) model is used to roughly estimate the lesion region, and then, the intensity range of the estimated lesion region can be obtained according to the mean and variance information. Finally, an intensityconstrained term is designed and integrated into the level set formulation. The final segmentation can be obtained by the evolution of the level set contour. The workflow of our method is shown in [Figure 1].
Subjects and Methods   
Skull stripping
Occasionally, the skull stripping step either removes more than just the skull, causing part of the brain to be removed as well, or too little, leaving behind portions of the skull. In most cases, both problems need to be corrected before continuing to the next step. We adopt a MASS method, which designed by SBIA laboratory from the University of Pennsylvania. Results of skull stripping are shown as in [Figure 2].  Figure 2: Implementation of skull stripping. Left column: Original image; Right column: results of skull stripping
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Fuzzy cmeans model
FCM^{[18]} is one of the most popular algorithms in fuzzy clustering and has been widely applied to medical problems. Standard FCM clustering attempts to minimize the cost function:
Where P_{i} is the specific image pixel, μ_{j} is the center of cluster j and can be initialized by random select c pixels on the image, and w and m are the weighting exponent and the exponent parameter, respectively, and fixed in this study. ∥.∥denotes the norm. The membership functions are subject to the following constraints:
, the membership functions u_{ij} and the centroids μ_{j} are updated iteratively.
FCM algorithm is optimized when pixels close to their centroid are assigned high membership P values while those that are far away are assigned low values.^{[19]} Hence, lesion class can be extracted from the FCM model.
μ_{lesion} and σ_{lesion} can be computed as:
Where is the mean intensity value of the lesion class and σ_{lesion} is its variance, and N_{lesion} is the total pixel number in the lesion class. Then, the intensity range of lesions can be defined by:
Where k_{1} and k_{2} are constants and fixed in this study.
An intensityconstrained Chan–Vese model
Chan–Vese (CV) model^{[20]} is a classical active contour model based on a special case of Mumford–Shah functional. The basic idea is to look for a partition of a given image I(x) into two regions. For a given image I(x) on the image domain Ω, the energy functional is defined by:
Where_{λ}_{1},_{λ}_{2 } and μ are positive parameters and fixed in this study. The constants c_{1} and c_{2} denote the average intensities inside and outside the curve C, respectively. The length term is used to regularize the contour. To solve this minimization problem, we can replace the unknown contour variable C by the unknown variable ϕ(x). Assuming
, then the energy functional (1) can be converted to
Where H(.) and δ(.) are the Heaviside function and Dirac function, respectively. The regularized versions are defined as:
Keeping ϕ(x) fixed and minimizing the energy with respect to the constants C_{1} and C_{2}, we have
Keeping C_{1} and C_{2} fixed, we minimize with respect to ϕ(X) and have the gradient descent flow
CV model has been widely used in many applications. However, when background intensities are of similar value to that of the object to be segmented and their regions are separated with vague boundaries, the contour can leak and start expanding on the background (lesions and WM).^{[21]} CV model cannot effectively separate the lesions from the rest of the brain structures, mainly because it adopts global information strategy. To increase the effectiveness of CV model, the local image information needs to be included. Let I*: be an input image, where is the lesion region obtained from FCM, and then, the fitting energy can be revised as:
To increase the ability of the level set approach to detect MS lesions, we design an intensityconstrained term that is used in our level set framework. The energy of intensityconstrained term can be defined as:
Where I_{down } and I_{up} are obtained from (5), σ is the variance of lesion class in (4), ξ is a constant and fixed in this study.
The final level set energy functional can be written as:
We minimize the energy functional (14) to obtain the following gradient descent flow by the steepest gradient descent method:
Results   
Our method has been tested on 25 fluid attenuated inversion recovery (flair) images which acquired from MICCAI 2008 MS segmentation challenge^{[22]} provided with manual expert annotations. The manual expert annotations can be viewed as ground truth, which are the criteria for evaluating our method. The dataset contains highly heterogeneous cases and can thus be considered as a realistic test case. The following parameters are fixed in this study: k_{1}= 1.5, k_{2}= 4, μ = 0.001*255*255, λ_{1}= λ_{2}= 1, ξ = 70, w = 2, m = 2. k_{1} has been optimized as shown in [Figure 3], and the other parameters are chosen based on numerous experiments. The method is implemented on Intel i7 7700HQ@ 2.8 GHz processor and 16 GB RAM with Windows 10 home basic 64 bits operating system.  Figure 3: Demonstration of the impact of parameter. (a) The original image and (b) the amount curve of lesions
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The progression of the MS lesions shows considerable variability in shape, location, and area between patients and even for the same patient.
Effectiveness of the proposed method
The segmentation results for patients with different lesions are shown in [Figure 4]. The original images, the segmentation results of the proposed method, and the manual segmentations are shown in columns 1, 2, and 3, respectively. From the picture, we can see that the proposed method generates a very similar result as reference image shown in the above figure for all images.  Figure 4: Comparison of segmentation results of proposed method with four twodimensional images. The first column. Original image; The middle column; The third column: results of proposed method
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We compare our method with four stateoftheart methods: FCM model,^{[23]} expectation–maximization (EM) model,^{[24]} Zhao's model.,^{[25]} and MICO model.^{[26]}
From [Figure 5], we can see that FCM and EM produced too much WM, whereas some pixels in cerebrospinal fluid (CSF) and WM are misclassified to lesions. Zhao's model and MICO produced too much CSF in segmentation results, which reduced the dice scores. Segmentation results of the proposed method give the best match with the manual segmentation.  Figure 5: Comparison of segmentation results of proposed method with four stateoftheart methods. (a) Original image. (b) Result of expectation–maximization. (c) Result of Fuzzy cmeans. (d) Result of multiplicative intrinsic component optimization. (e) Result of Zhao's model. (f) Result of proposed method. (g) Manual segmentations by expert
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Qualitative evaluation of segmentation accuracy
To illustrate the effectiveness of our method, several metrics were used to evaluate the algorithm performance. The overall segmentation accuracy in terms of the dice similarity coefficient (DSC) is used to estimate the difference between manual lesion annotations and output segmentation masks:
Where (·) indicates the number of pixels in the enclosed region, S is the region segmented by an algorithm, and G is the corresponding region obtained from the ground truth. A value of 100% indicates a perfect overlap of the produced segmentation and the ground truth.
Sensitivity measures the fraction of the segmented lesions that are in the ground truth and is defined as:
Where TN is true negative, which is the number of voxels marked as nonMS in both sets, and FP is the false positive, which is the number of voxels only appeared in automatic segmentation, κ.
A sensitivity with a value of 100% indicates that all lesions are correctly identified.
Specificity measures the fraction of the segmented lesions that are not in the ground truth and is defined as:
A specificity with a value of 0% indicates that no lesions were incorrectly identified.
Volume difference (VD) measures the differences between the segmented lesions (S) and ground truth (G) by calculating their volume (Vol). It is defined as:
The value of VD is between 0 and 1, and a VD with a value of 0% indicates a better automatic segmentation result.
We tested dice coefficient for the 25 sets of MR images. It can be obviously seen from [Figure 6] that the proposed method produced significantly higher dice scores than other methods. The dice scores reach an average of 0.56 for the proposed method, followed by 0.5 for MICO, 0.52 for Zhao's model, 0.35 for EM, and 0.34 for FCM. All in all, our method outperformed other methods for most of the cases.  Figure 6: Comparison of the proposed method with Fuzzy cmeans, expectation–maximization, Zhao's model, and multiplicative intrinsic component optimization in terms of dice coefficient
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Segmentation accuracy of FCM, EM, Zhao's model, and MICO and the proposed method in term of specificity and sensitivity are shown in [Figure 7]. All the other methods considered parts of WM and CSF as lesions. Especially for an image with little or no lesions, all the other methods produced a large amount of noise, which drastically increased the number of misclassified voxels. Compared to other four methods, the proposed approach yielded the highest sensitivity value with respect to manual delineation. Furthermore, our method also has a very low specificity value, which means that the lesion segmentation results from our method are very similar to the manual delineation.  Figure 7: Comparison of the proposed method with Fuzzy cmeans, expectation–maximization, Zhao's model, and multiplicative intrinsic component optimization in terms of specificity and sensitivity
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We randomly select ten cases to test the VD scores of our method, as shown in [Table 1]. It can be seen from the table that our method has a very low VD value for most of the cases. It is obvious that case 05 and case 07 received unsatisfactory results, mainly because very few lesion pixels exist in the two cases, and thus, there is a significant decrease in the quantity of the VD scores.  Table 1: The detailed index of our method and manual segmentation in terms of volume difference
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Discussion   
In this study, we compared the proposed method against four stateoftheart methods. In FCM model and EM model, lesions are classified to a cluster. However, both produced too much noise and misclassified a large amount of WM to lesions. Zhao's model and MICO obtain high sensitivity scores; however, both received low scores when no lesion pixels exist in the image. The experiment results demonstrated that the proposed automatic lesion segmentation method outperformed other methods.
Two characteristics of the proposed method are included as follows: (1) we integrate the lesion intensity information into the level set model by incorporating the intensityconstrained term. The level set model can obtain accurately segmentation results regardless of lesion's shape and size. (2) The proposed framework can obtain better results when there are no lesions in the image, while other methods produce noisy and misclassify some WM regions into lesions.
Proper setting of parameter k_{1} is important to our method. To demonstrate the impact of k_{1} on our model, we segment a twodimensional (2D) image with k_{1} taking values in (0, 2.5) and give results in [Figure 3]. There are 121 lesion pixels in [Figure 3]a. It can be seen from this figure that our method achieved the best performance when k_{1 }=1.5 [Figure 3]b.
We recommend further studies with more data for checking possible improvements of algorithms. For worldwide, objectifiable comparison of algorithms would be advisable or even necessary:
Conclusions   
In this study, we proposed an intensity prior knowledgebased level set model for MS lesion segmentation. Skull stripping is first applied to remove the brain skull, and FCM model is then used to construct the intensity information model, which is used to construct the intensityconstrained term. The proposed level set framework consists of an intensityconstrained term, a regularization term, and an image data term. The final segmentation is achieved by evolving the level set contour. In our experiments, the proposed method shows more accuracy than the other compared stateoftheart methods. We expect that the proposed method will find its utility in more applications in the area of MRI segmentation, as well as other areas where level set method has been and could be applied.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China (No. 61373088 and 61402298), Liaoning Provincial Natural Science Foundation (No. 20170540702), and the Scientific Research Funds of Shenyang Aerospace University under Grant No. 18YB01.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]
[Table 1]
