Fuzzy Based Segmentation of Multiple Sclerosis Lesions in Magnetic Resonance Brain Images
Ahmad Bijar
1, Rasoul Khayati
1, and Antonio Pe˜ nalver Benavent
21
Department of Biomedical Engineering, Shahed University, Tehran, Iran
2
Departamento de Estad´ıstica, Matem´aticas e Inform´atica, Universidad Miguel Hern´andez, Elche, Spain [email protected], [email protected], [email protected]
Abstract—Segmentation is an important step for the diagnosis of multiple sclerosis. This paper presents a new approach for fully automatic segmentation of MS lesions in fluid attenuated inversion recovery (FLAIR) Magnetic Resonance (MR) images.
At first, Brain image is considered to be three parts, namely the dark, the gray, and the white part. Then, the fuzzy regions of their member functions are determined by maximizing fuzzy entropy through the Genetic algorithm. Finally, MS lesions and CSF areas are determined by applying a localized weighted filter to the Bright and Dark membership images. To evaluate the result of the proposed method, similarity criteria of different slices related to 20 MS patients are calculated and compared with other methods which include manual segmentation. Also, volume of segmented lesions are computed and compared with Gold standard using correlation coefficient. The proposed method has better performance in comparison with previous works which are reported here.
Index Terms—Multiple Sclerosis, Segmentation, Fuzzy mem- bership function, Genetic algorithm.
I. INTRODUCTION
Magnetic Resonance Imaging (MRI) is a noninvasive method for imaging internal tissues and organs. MRI is in- creasingly being used to assess the progression of the disease and to evaluate the effect of drug therapy, supplementing traditional neurological disability scales such as the extended disability status scale (EDSS) [1]. MRI is the primary com- plementary examination for the monitoring and diagnosis of multiple sclerosis (MS) [2]. Segmentation of multiple sclerosis (MS) lesions from MR brain images is important in the diagnosis of the disease [3]. However, manual detection and analysis of these lesions from MR brain images are usually time consuming, expensive and can produce unacceptably high intra-observer and inter-observer variability [4], [5]. So, automatic and semi automatic methods for segmentation of MS lesions are recommended and have been investigated extensively.
In this paper, we have presented a method, based on the fuzzy membership functions, for fully automatic segmentation of MS lesions in FLAIR-MR images. The brain image is partitioned into three parts, including dark (CSF), gray (normal tissues) and white part (MS lesions), whose member functions of the fuzzy region are Z−function, P−function and S−function, respectively. Then, the fuzzy regions of their member functions are determined by maximizing fuzzy entropy through the Genetic algorithm. The image can keep as much information
as possible when the image is transformed from the inten- sity domain to the fuzzy domain [11]. In the next stage, using obtained images from the fuzzy membership functions, brain tissues are classified. In the next sections, details of the research procedure including MR imaging type, manual segmentation of MS lesions, brain segmentation, utilization of the maximum fuzzy entropy and genetic algorithm to segment brain tissues, are explained. Then, the proposed approach is introduced and its efficiency is compared with some of the previous approaches.
II. METHODS
A. Patients and MR imaging
The proposed procedure in this research was implemented on MR images that were captured and used in [6]. This dataset contains 16 female and 4 male with average age of29+−8years old, and is selected according to the revised Mc Donald criteria 2005 [7]. All images were acquired according to full field MRI criteria of MS [7] in T2-weighted (T2-w), T1-weighted (T1- w), Gadolinium enhanced T1-weighted, and FLAIR in axial, sagittal and coronal surfaces. We selected the FLAIR images, especially axial ones, with lesions in deep, priventricular, subcortical, and cortical white matters (supratentorial lesions).
More lesion load and higher accuracy of FLAIR in revealing of these MS lesions were the reason for this selection [8]. Each image volume (patient data) consisted of averagely 40 slices with a256×256scan matrix. The pixel size was 1mm2, and the slice thickness was3mm without any gap.
B. Manual segmentation of MS lesions and brain segmenta- tion
The segmentation of MS lesions was performed manually by neurologist and radiologist in Flair images with visual inspection of corresponding T1-w and T2-w images. These manually segmented images were used as Gold standard [9]
to evaluate the performance of the proposed method. To evaluate the proposed method, different type of images which have different lesion volumes were applied. Also, the brain segmentation was performed using a fully automatic object- oriented approach [10].
C. Maximum fuzzy entropy based on probability partition The Brain image is partitioned into three parts, namely the dark, the gray, and the white part, whose mem- ber functions of the fuzzy region are, respectively,
978-1-4673-2051-1/12/$31.00 IEEE 2012
Z−, Π−, and S−functions [11]. Z(a, b, c, k)−function, Π(a, b, c, k)−function and S(a, b, c, k)−function are used to approximate the memberships of µd, µm and µb the image with 256 gray levels. The three membership functions are shown in the following:
µd(k) =
1 k≤a1
1−(c (k−a1)2
1−a1)∗(b1−a1) a1< k≤b1 (k−c1)2
(c1−a1)∗(c1−b1) b1< k≤c1
0 k > c1
(1)
µm(k) =
0 k≤a1
(k−a1)2
(c1−a1)∗(b1−a1) a1< k≤b1
1−(c (k−c1)2
1−a1)∗(c1−b1) b1< k≤c1
1 c1< k≤a2
1−(c (k−a2)2
2−a2)∗(b2−a2) a2< k≤b2 (k−c2)2
(c2−a2)∗(c2−b2) b2< k≤c2
0 k > c2
(2)
µb(k) =
0 k≤a2
(k−a2)2
(c2−a2)∗(b2−a2) a2< k≤b2
1−(c (k−c2)2
2−a2)∗(c2−b2) b2< k≤c2
1 k > c2
(3)
Wherekis the gray level of the pixel and the six parameters a1, b1, c1, a2, b2, c2 satisfy the following condition:
0≤a1≤b1≤c1≤a2≤b2≤c2<255
Assume that image is separated into dark (Ed), medium (Em) and bright (Eb) regions using thresholds t1 andt2, then their probability are pd = p(Ed), pm = p(Em), and pb =p(Eb).
The fuzzy regions can be determined by maximizing fuzzy entropy. The fuzzy entropy function of each class is given below:
Hd = −
255
X
k=0
pk∗µd(k) pd
∗ln(pk∗µd(k) pd
)
Hm = −
255
X
k=0
pk∗µm(k) pm
∗ln(pk∗µm(k) pm
) (4)
Hb = −
255
X
k=0
pk∗µb(k) pb
∗ln(pk∗µb(k) pb
)
Where pk = Mnk
∗N and nk is the number of pixel with gray level k. Then the total fuzzy entropy function is given by H(a1, b1, c1, a2, b2, c2) = Hd +Hm+Hb. We can find a combination of a1, b1, c1, a2, b2, c2 such that the total fuzzy entropyH(a1, b1, c1, a2, b2, c2)achieves the maximum value.
The procedure for finding the optimal combination of all the fuzzy parameter is implemented by Genetic algorithms.
Membership Functions
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 50 100 150 200 250 300
(a) (b) (c)
(d) (e) (f)
Fig. 1. Brain tissues segmentation examples, using the three-level threshold- ing: (a) Shows the original brain image. (b) The obtained member functions plots. (c) Shows the segmentation result using the three-level threshold (maximum fuzzy entropy approach). (d) Dark membership image. (e) Medium membership image. (f) Bright membership image.
D. Brain tissues segmentation
Fig. 1(a) shows a typical FLAIR image, as a sample slice of a patient with large lesion. The obtained membership functions and the three-level threshold images are shown in Fig. 1(b) and (c), respectively. As it is seen in Fig. 1(c), brain tissues are not segmented well using the three-level threshold. To give more understanding, the membership functions values (dark, medium, bright) are computed for each pixel using Eqs. 1 to 3 and shown in Fig. 1(d) to (f). In dark membership image, CSF areas have high intensity values in comparison with the rest of the brain areas. Also, in bright membership image, MS lesions have high intensity values in comparison with CSF and normal areas. We have used these two membership images to segment CSF and MS lesions. Figure 2(a) shows a section of brain image which is zoomed in, its bright membership image has been shown in Fig. 2(b), (to give more understanding, the obtained image has been inverted). As it is seen, there are a lot of pixels which do not belong to MS lesion class, but their bright membership values are similar to the MS lesions.
Moreover, in manual segmentation, the possible lesions with sizes as small as one or two pixels are not usually considered as MS lesions by experts. These objects are recognized as noise and must be removed [6]. So, simple thresholding of the fuzzy membership images end up with noise pixels in all classes. To tackle these problems, a localized weighted filter (in ak×kneighborhood) is applied to the bright membership image as follow:
Bf(x, y) = U(B(x, y)−BM)× (5) (α.(
x+k
X
i=x−k y+k
X
j=y−k
B(i, j))−β.B(x, y))
Where B(x, y) is the value of bright membership image at pixel (x, y), Bf(x, y) is its value in the filtered image, U is the unit step function, α and β determine the affect
(c) (d)
(a) (b)
Fig. 2. Applying the localized weighted filter to a typical brain image:
(a) Shows a section of original brain image. (b) Shows bright membership image (to give more understanding, the obtained image has been inverted).
(c) Results of applying the localized weighted filter to the bright membership image. (d) The twice-applied filtering result.
of pixel’s neighborhood and the pixel itself, respectively, k controls the neighborhood size. BM is a threshold which determines candidate MS lesions. As mentioned before, brain tissues are not segmented well using the three-level threshold, and as it is seen in Fig. 1e and f, most of lesion pixels have been considered as other tissues, this means that they have low value of bright membership function. So, setting theBM is very important for all types of brain images with different lesions load. If we lose a candidate MS lesion, which is MS lesion, this means that it has been eliminated from the final segmentation result. So, to avoid any unwanted elimination of MS lesions, BM is set to 0.05, manually. The parameters of the filter, i.e.,α,β andkhave been experimentally set to 0.9, 0.6 and 3 for the best result. Moreover, experimental results show that if the introduced filter in Eq. 5 runs twice over the bright membership image, it gives better results. The obtained results for two brain images have been shown in Fig. 2(c) and (d). In the next stage, all pixels whose intensity value is above a threshold are considered as a primary mask of MS lesion areas: L1(x, y) = {1, Bf(x, y) > thr1}. Where thr1 = BM.(µ1 − σ1), in which µ1, σ1 are mean and standard deviation of the non zero pixels of the Bf(x, y), respectively. L1 is considered as a mask which determines areas of MS lesions. To have an accurate segmentation, the bright membership image is also thresholded: L2(x, y) = {1, B(x, y)> BM}. As mentioned before,BM was used as a threshold to determine candidate MS lesions whose bright membership value is greater than BM. So, in comparison with L1, L2 is a mask which contains all candidate MS lesions.
Finally, to segment MS lesions, each individual area in L2
which has overlap with L1 is selected as MS lesions.
To segment CSF areas using dark membership image, same method has also been used. At first, dark membership image is filtered using
Df(x, y) = U(D(x, y)−DM)× (6) (α.(
x+k
X
i=x−k y+k
X
j=y−k
D(i, j))−β.D(x, y))
(b) (a)
Fig. 3. Brain tissues segmentation examples. Each column shows the result of proposed method for a brain image with different lesion loads. (a) Shows the original brain images. (b) Shows the result of automatic segmentation.
Where D(x, y) is the value of dark membership image at pixel (x, y), Df(x, y) is its value in the filtered image, U is the unit step function, α and β determine the affect of pixel’s neighborhood and the pixel itself, respectively, and k controls the neighborhood size. DM is considered as a threshold which determines candidate CSF pixels, and is equal to DM =µ2+σ2, in which µ2, σ2 are mean and standard deviation of non zero pixels of the D(x, y), respectively.
The parameters of the filter, i.e., α, β and k have been experimentally set to 0.9, 0.6 and 3 for the best result. Then, Non zero pixels of the Df are selected and considered as a primary mask of CSF areas (C1). To segment CSF areas accurately, the dark membership image is also thresholded:
C2(x, y) ={1, D(x, y)>0.5DM}. Finally, to segment CSF areas, each individual area inC2 which has overlap with C1
has been selected as CSF areas.
III. RESULTS
The proposed algorithm was implemented on different FLAIR images. In Fig. 3, results of applying the proposed algorithm to the images of patients with different lesion load have been shown. As it is seen, there is a good correlation between the input image (Fig. 3(a)) and the resulted image (Fig. 3(b)) indicating the acceptable performance of the sug- gested algorithm in detecting the lesion borders as well as CSF regions. The evaluation of the results performed qualitatively and quantitatively as follows. The quality performance of the results was confirmed by the neurologist and the radiologist separately. Then, in quantitative evaluation step, the similarity criteria (SI) [12], overlap fraction (OF), and extra fraction (EF) [13] were calculated for all selected slices. Mean values of the similarity criteria are given in Table I for each patient group. As can be seen in this table, SI, OF and EF are improved with an increase in lesion load. It is noticeable that lesion volumes segmented automatically are relatively smaller than those found by the experts. The results of volumetric
TABLE I
SIMILARITY CRITERIA AND VOLUMETRIC COMPARISON OF LESIONS FOR EACH PATIENT GROUP
Patient category N
Similarity criteria Correlation analysis
SI OF EF MGS±SDGS(cc) M±SD(cc) Correlation Coefficient
Small lesion load 7 0.7731 0.7728 0.2451 1.87±1.11 1.79±1.13 0.95
Moderate lesion load 10 0.8194 0.8059 0.2058 11.58±3.08 11.29±3.17 0.96
Large lesion load 3 0.8669 0.8425 0.1759 22.23±3.52 21.97±4.06 0.98
N: number of patients in each group, M : mean, SD : standard deviation
TABLE II
SIVALUES FOR THE PROPOSED METHOD AND THE OTHER METHODS
Article Algorithms Patient category
Small lesion load Moderate lesion load Large lesion load All patients
Anbeeket al. [9] k-nearest neighbour rule 0.50 0.75 0.85 0.8
Admiraal-Behloulet al. [14] Fuzzy C-means algorithm 0.70 0.75 0.82 0.75
khayatiet al. [6] Bayes+AMM+MRF 0.7253 0.7520 0.8096 0.7504
Proposed method MFE+GA 0.7731 0.8194 0.8669 0.8103
AMM: Adaptive Mixture Method, MRF: Markov Random Field model, MFE: Maximum Fuzzy Entropy, GA: Genetic algorithm
comparison of lesions between the proposed method and the Gold standard are presented in Table I, too. As it is seen in this table, according to the value of CC, accuracy of the proposed method is increased for patients with large lesion load.
IV. DISCUSSION
In this paper a new approach, for fully automatic segmenta- tion of brain tissues in MR FLAIR images of MS patients, is proposed. At first, brain image is partitioned into three parts, including dark (CSF), gray (normal tissues) and white part (MS lesions), whose member functions of the fuzzy region are Z−function, P−function and S−function, respectively. The fuzzy regions are determined using maximizing fuzzy entropy.
Then, each individual fuzzy region is used to determine brain tissues using a localized weighted filter. The proposed approach is evaluated via similarity criteria (i.e., SI, OF, and EF) in a data set of MR FLAIR images of 20 MS patients and its efficiency is compared with some of the previous approaches in Table II. It is reminded that these researchers have used real data set and manual segmentation for evaluation of their methods. The results show a better performance for the proposed approach, compared to those of previous works.
Future work will include improving accuracy and correlation value using different kinds of fuzzy membership functions.
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