Automatic segmentation of corpus collasum using Gaussian mixture modeling and Fuzzy C means methods

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 38–46

journal homepage: www.intl.elsevierhealth.com/journals/cmpb

Automatic segmentation of corpus collasum using Gaussian mixture modeling and Fuzzy C means methods Semra I˙c¸er ∗ Erciyes University, Engineering Faculty, Biomedical Engineering Department, Kayseri, Turkey

a r t i c l e

i n f o

a b s t r a c t

Article history:

This paper presents a comparative study of the success and performance of the Gaussian

Received 2 May 2013

mixture modeling and Fuzzy C means methods to determine the volume and cross-

Received in revised form 5 June 2013

sectionals areas of the corpus callosum (CC) using simulated and real MR brain images. The

Accepted 14 June 2013

Gaussian mixture model (GMM) utilizes weighted sum of Gaussian distributions by apply-

Keywords:

the image classes are represented by certain membership function according to fuzziness

Gaussian mixture modeling

information expressing the distance from the cluster centers. In this study, automatic seg-

ing statistical decision procedures to define image classes. In the Fuzzy C means (FCM),

Fuzzy C means

mentation for midsagittal section of the CC was achieved from simulated and real brain

Image segmentation

images. The volume of CC was obtained using sagittal sections areas. To compare the suc-

Corpus collasum

cess of the methods, segmentation accuracy, Jaccard similarity and time consuming for segmentation were calculated. The results show that the GMM method resulted by a small margin in more accurate segmentation (midsagittal section segmentation accuracy 98.3% and 97.01% for GMM and FCM); however the FCM method resulted in faster segmentation than GMM. With this study, an accurate and automatic segmentation system that allows opportunity for quantitative comparison to doctors in the planning of treatment and the diagnosis of diseases affecting the size of the CC was developed. This study can be adapted to perform segmentation on other regions of the brain, thus, it can be operated as practical use in the clinic. © 2013 Elsevier Ireland Ltd. All rights reserved.

1.

Introduction

Magnetic resonance imaging (MRI) has superior contrast properties according to other medical imaging modalities in soft tissue imaging [1]. Therefore, MRI has been extensively preferred in quantitative image processing studies for brain and other organs. Quantitative volumetric measurement and qualitative representation of brain tissues are quite helpful to

evaluate various pathologies in the brain. For this aim, brain image segmentation plays first and an important role [2]. Each region in the brain has very different and complex functions in connection with each other. The corpus callosum (CC) is located underneath the cerebrum at the center of the brain. CC is the largest white matter region connecting right and left cerebral hemispheres and it is consist of about 200–350 million fibers in humans. CC plays a vital role in the integration by transferring sensorial,

∗ Correspondence address: Erciyes University, Engineering Faculty, Biomedical Engineering Department, Talas, Kayseri, Turkey. Tel.: +90 352 207 66 00x32978; fax: +90 352 437 57 84. E-mail address: [email protected] 0169-2607/$ – see front matter © 2013 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cmpb.2013.06.006

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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 38–46

cognitive, learning, mnemonic and motor information between the two brain hemispheres [3–5]. Many neurological diseases cause changes in the structure and size of the corpus callosum. Alterations in the structure of the corpus callosum (CC) have been observed in schizophrenia [5], autism [6], epilepsy [7], childhood stuttering [8], and in the effects of smoking on corpus callosum volume [9]. Therefore, quantitative calculation by segmentation as precisely as possible of the CC has a great importance in the process of diagnosis and treatment. In recent years, two popular segmentation procedures have been used. These methods are Gaussian mixture modeling (GMM) and Fuzzy-C-means (FCM) known as soft segmentation algorithms. In the soft clustering, one piece of data can be including to two or more clusters in certain degree. The Fuzzy C means algorithm works by estimating the parameters which minimize distance of each voxel in the image to cluster centers according to a certain membership function. Whereas, the method based on the Gaussian mixture modeling (GMM) is a parametric probability density function represented as a weighted sum of Gaussian component densities. GMM parameters are estimated from training data using the iterative expectation-maximization (EM) [10]. These segmentation algorithms have been widely used recently in many studies, especially on biomedical image processing [2]. Ji et al. studied the generalized rough Fuzzy C means algorithm, weighted image patch-based FCM and modified possibilistic Fuzzy C means clustering algorithm for the segmentation of gray and white matter on MR brain images with various levels of noise [2,11,12]. Feng et al. were concentrated for SAR image segmentation using the non-local Fuzzy C-means algorithm with edge preservation [13]. Cai et al. proposed fast and robust Fuzzy C-means clustering algorithms on eight images in Matlab with mixed noise and MR brain images [14]. Forouzanfar et al. studied parameter optimization of the improved Fuzzy C means clustering algorithm for brain MR image segmentation using genetic algorithms (GA) and particle swarm optimization (PSO) in the case of noisy data on a synthetic square image and real T1-weighted MR image [1]. Enciso et al. studied a mixture of Gaussian functions with the parameters calculated using three nature inspired algorithms (particle swarm optimization, artificial bee colony optimization and differential evolution) on blood smear images [15]. Tang et al. studied a neighborhood weighted Gaussian mixture model in synthetic data and slice kidney CT image [10]. Merisaari et al. worked on watershed segmentation with Gaussian mixture model clustering for segmenting the cerebrospinal fluid from brain matter and other head tissues in premature infant brain MR images [16]. Qin et al. proposed a cloud model for four different images have multimodal histogram. They compared the results with related segmentation methods, including Otsu threshold, type-2 fuzzy threshold, Fuzzy C means clustering, and Gaussian mixture models. The index of misclassification error of their results competed well with FCM and GMM [17]. Ertekin et al. compared the Cavalieri method (point-counting) with the semi-automatic FCM algorithm to calculate the volumes of subcortical brain structures [18].

The aim of this study is to perform automatic segmentation of the CC by using Gaussian mixture modeling and Fuzzy C means algorithms for midsagittal section, and to compare these algorithms. In this study, the volume and other section areas of the CC were calculated using the Gaussian mixture model that estimated the maximum likelihood parameters by the EM algorithm and Fuzzy C means algorithm. For this purpose, the cross-section areas and volume of the CC, success of the segmentation were calculated by performing segmentation of the CC from simulated and real brain images. The quantitative and qualitative comparisons were performed with the results obtained from the two methods. With this study, an accurate and automatic segmentation system that allows opportunity for quantitative comparison to doctors in the planning of treatment and the diagnosis of diseases affecting the size of the CC was developed. This study can be adapted to perform segmentation on other regions of the brain, thus, it can be operated as practical use in the clinic.

2.

Background

2.1.

Segmentation with Gaussian mixture modeling

Mixture models are very preferable in areas where the statistical modeling of data is needed, for instance in signal and image processing, pattern recognition, bioinformatics, and machine learning [19,20]. Gaussian mixture modeling performs segmentation by extracting global statistics from Gaussian distributions of pixel intensity in image data set. The linear mixture of weighted sum of Gaussian distribution determines to how much is involved to which cluster of pixels. GMM is especially well-suited for image segmentation because of implementation facility and efficiency in the representation of data. Gaussian mixture model employs a linear mixture of Gaussian distributions to find the probabilities of any pixel value belonging to different classes/modes or regions in the image [20–23]. The histogram gives a main idea about the probability density function (pdf) of pixel values. Let x ∈ d be a d dimensional measurement vector for a pixel. The GMM algorithm can be given as the following:

f (x) =

K  k=1

wk fk (x; k ,

 k

) with

K 

wk = 1

(1)

k=1

where K is the total number of mixtures, wk s are the weights of each Gaussian component, and k , ˙ k are the mean vector and covariance matrix of the kth Gaussian distribution probability density function fk , respectively. The number of components, K, is usually assumed to be known. The Gaussian approach is flexible in detecting the image dynamics on account of the mixing properties [20]. The expectation maximization generates an efficient algorithm to achieve parameter estimates by maximizing the likelihood function. Given the image vectors f(x1 ). . .f(xN ) at the set of pixels (x1 ,. . .,xN ), we consider that all the vectors are independent of each other. Assume the initial estimate for (0) (0) (0) then the EM the Gaussian mixture model is ˛k , k , k

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algorithm iterates between the following two steps until the parameter estimates converge (t = 0,1,. . .) [20,21]: ◦ E-step: For i = 1,. . .,N (t)

(t−1)

ϕk

(Xi ) =

˛k pk (f (Xi ); k ,

(t)

K

(t) ˛ p (f (Xi ); l , l=1 l l

k

(t)

(2)

l

N (t−1)

=

(t−1) k

(t−1) ϕ (Xi ) i=1 k

N

N =

(t−1)

ϕ i=1 k

N ,

(t−1)

k

(t−1) ϕ (Xi )f (Xi ) i=1 k (t−1) ϕ (Xi ) i=1 k

N

= (t)

(3)

(t)

(Xi )(f (Xi ) − k ) (f (Xi ) − k )

N

(t−1) ϕ (Xi ) i=1 k

After reaching the estimated parameters for examined the image data, the image segmentation is realized by classifying pixels into the class (or segment) according to the largest conditional probability of each pixel Xi label(f (Xi )) = arg

max ϕk (Xi ) = arg

1≤k≤K

max ˛k pk (f (Xi ); k ,

1≤k≤K

 k

The GMM can be evaluated as a global method in the sense that all data contribute evenly to the final parameter estimate. The EM algorithm is computationally fast, therefore, it is proper for image or data analysis [20].

Segmentation with Fuzzy C means clustering

The FCM method proposes a fuzzy membership that assigns a degree of membership for each class. The significance of degree of membership in fuzzy clustering is similar to the pixel probability in a mixture modeling assumption. By obtaining data points that have close membership values to existing classes, the forming of new clusters is possible; this is the major advantage of FCM clustering [22]. FCM clustering minimizes the objective function JFCM which is improved by Bezdek [23,24] as follows:

JFCM (u, ) =

C N  

2 um ij d (xj , i )

(5)

j=1 i=1

where N is the number of samples and C is the number of clusters; 2 ≤ C < N, i is the d-dimension center of the cluster; m is a weighting exponent and any real number greater than 1; 1 < m < ∞, xj is the d-dimensional data set. d2 (xj , i ) represents the Euclidean distance or its generalizations. The membership matrix u satisfies the condition C 

uij = 1,

∀j = 1, . . . , N

N

um ij =

C 

(i = 1, . . . , C) and

u j=1 ij

1

2/(m−1)

(7)

||xj − i ||/||xj − k ||

The FCM algorithm is very similar and works as follows [24]: 1. Choose the number of clusters or region. In this study, the number of clusters was taken as 3. 2. Assign pixels their initial, membership values according to Eq. (6). 3. Compute the centroid for each cluster, and the membership values using the formula in Eq. (7). 4. Iterate until maxij {||uk+1 − ukij ||} < ε where k is the iteration ij number and ε is the error threshold; otherwise return to step 2. 5. Assign each pixel the cluster number for which its membership is maximum.

2.3. Magnetic resonance imaging and quantitative calculations

)

(4)

2.2.

u x j=1 ij j

i =

k=1

)

◦ M-step

˛k

N

Magnetic resonance real brain images were acquired with 1.5 T Magnetom Aera Siemens MR system from Faculty of Medicine in Erciyes University. T1-weighted sagittal plane thin section brain images were obtained with T1-mprage gradient echo sequence (TR/TE/TI = 1900/2.67/1100 ms), slice thickness = 1.0 mm, number of slices = 160, distance between images (slice gap) = 1.0 mm; matrix size = 512 × 512; and field of view = 25 cm × 25 cm). MR images from 28 subjects (12 males, 16 females) were obtained in the Department of Radiology at the Faculty of Medicine in Erciyes University. All participants were healthy volunteers with no history of neurological, cognitive and other mental degenerations. The mean age of all subjects was 36.3 ± 16.05 and the age range was 17–63 years. For the purposes in this study, the wide age range of the subjects was not critical because disease diagnosis was not made in this study. This study was approved by the Ethics Committee of Erciyes University (decision no. 2013/112). The study was conducted on approximately 15 crosssections that can be seen of the CC for each subject. The areas of CC cross-sections were obtained using GMM and FCM methods and then the volume of the CC were calculated by the following formula: VCC =





k i=1

Ai

× (St + Sg ) ×

 dimension size matrix size

(8)

In Eq. (8), k is the number of slices, Ai is the area in examined slice, St is the slice thickness, and Sg is the slice gap. In this study, St = Sg = 1 mm, k = average of 15, dimension size = 25 × 25 = 625, and matrix size = 512 × 512 = 262,144.

(6)

i=1

The FCM algorithm is iteration through the necessary conditions for minimizing JFCM by the following update equations:

2.4.

Statistical analyses and evaluation

T-test was applied to all the data in Matlab 7.12 software and p < 0.05 was accepted as significant results. Jaccard similarity

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Fig. 1 – True positives, true negatives, false positives and false negatives.

(JS) was used to compute the quantitative evaluation success of the segmentations [2]. It is defined as the ratio between the intersection and union of two sets S1 and S2, representing the obtained and reference segmentations, respectively. If the JS values are closer to 1, it shows the better the segmentation. The equation is shown as follows: |S1 ∩ S2| : logical and process, |S1 ∪ S2| : logical or process JS(S1, S2) =

|S1 ∩ S2| |S1 ∪ S2|

(9)

Also, segmentation accuracy was calculated for the GMM and FCM methods, separately. Segmentation accuracy defined as follows: Segmentation accuracy = Sensitivity =

TP , TP + FN

TP + TN TP + FP + TN + FN

Specificity =

TN TN + FP

(10)

(11)

TP: true positives, TN: true negatives, FP: false positives, FN: false negatives are given in Fig. 1.

2.5.

Comparisons of segmentation time

In this study, the time consuming was calculated to analyze the computational complexity for the GMM and FCM methods. Time consuming on midsagittal section was calculated in terms of segmentation time (s). Generally, the segmentation process will dramatically increase the algorithm’s computational complexity [11]. To compare the computational complexity of the GMM and FCM algorithms, each segmentation was performed two times, and the computational complexity of every one algorithm was measured in terms of the average running time (Core 2 Duo CPU: 2.4 GHz, RAM: 1.92 GB, Operating system: Windows XP, Software: Matlab 7.12).

3.

Results

3.1. Segmentation results with synthetic brain MR images The simulated brain MR sample image was used from the BrainWeb [25] data base to compare the Gaussian mixture modeling and Fuzzy C means method. Brain Web provides T1, T2, and proton density (PD) weighted images and a variety of slice thicknesses, noise levels, and levels of intensity

Fig. 2 – The results for sample simulated image data: (a) midsagittal section, (b) ground truth WM regions of midsagittal section, (c) CC segmentation of using GMM, (d) CC segmentation of using FCM, (e) CC manual segmentation from (b).

non-uniformity. In this study, a normal brain MR image (T1 modality, 1 mm slice thickness) was selected with 0% noise and intensity non-uniformity. The simulated image size was (181 × 217 × 181) voxels of (1 × 1 × 1) mm and the matrix size was 258 × 258. In the selected sample image, CC can be seen between slice 58 and slice 70; so, a total of 13 slices were studied. CC midsagittal section area calculated from WM midsagittal ground truth image (679 pixel = 4 cm2 ). The CC volume calculated from WM Ground truth images (3.68 cm3 ). Fig. 2 shows the segmentation of CC for sample simulated image data. Tables 1 and 2 give calculated qualitative results for BrainWeb data and real brain images.

3.2.

Segmentation results with real brain MR images

In this section, the effectiveness and accuracy of the GMM and FCM algorithms were compared on real images. The quantile–quantile (qq) plot is a powerful tool for assessing the goodness of fit of a mixture model [24,26]. To verify that the normal mixture model fits the underlying distribution of the data well, random data were generated from estimated mixture model with three components and their quantiles compared against the quantiles of the actual pixel data, and the qq plot was constructed as shown in Fig. 3. Indeed, the qq plot shows that the normal mixture model with K = 3 fits the distribution of the actual data well. The stages of CC segmentation with GMM and the FCM algorithm for volumes and section areas calculation are given in Fig. 4. Firstly, the CC region was determined automatically by reducing a certain amount from the sides of the examined cross-sectional image (Fig. 4(a)) because the run-time of the algorithm depends on the size of the input image. To reveal better differences in the gray scale image histogram equalization was done (Fig. 4(b)). Then the images were made separately by the GMM and FCM segmentation methods and were divided into three regions. In the results of the GMM and FCM methods, morphological open process was performed using square structure with 9 neighbors to separate junction points of other small white

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Table 1 – The results of midsagittal section area for Brain Web data and real brain images. Midsagittal section area of CC (cm2 )

4.6 5.98 ± 1.13

FCM 4.8 6.46 ± 1.32

GMM 96.74 98.30 ± 0.72

GMM 95.55 97.01 ± 0.84

Jaccard similarity (100×) GMM 92.01 96.66 ± 0.83

FCM 89.88 94.2 ± 0.92

Time-consuming (s) GMM 5.62 5.814 ± 0.58

FCM 3.84 4.012 ± 0.25

Sensitivity and specificity: 95.56 and 97.71 for GMM, 93.94 and 89.73 for FCM in the Brain Web data; 96.68 and 97.04 for GMM, 98.6 and 93.47 for FCM in the real brain images, respectively.

Table 2 – The results of CC volume for Brain Web data and real brain images. Volume of CC (cm3 ) GMM

FCM

Segmentation accuracy (%) GMM

FCM

Jaccard similarity (100×) GMM

FCM

Sample image in Brain Web

3.83

4.12

95.16

93.67

90.76

88.09

Real brain images (n = 28)

8.97 ± 1.15

9.68 ± 1.38

96.99 ± 1.19

95.05 ± 1.21

94.21 ± 1.37

90.63 ± 1.38

Sensitivity Specificity GMM

FCM

97.6 98.5 95.97 97.75

92.74 89.32 97.42 92.83

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GMM Sample image in Brain Web Real brain images (n = 28)

Segmentation accuracy (%)

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QQ Plot of Random Data from Mixture Model…versus Actual Pixel Values

Quantiles of Random Data from Mixture Model

250

200

150

100

50

0

Fig. 5 – CC three dimensional image (a) with GMM and (b) with FCM algorithm.

0

50

100 150 200 Quantiles of Actual Pixel Values

250

Fig. 3 – Quantile–quantile (qq) plot for mixture model.

matter regions of the brain with the CC region (Fig. 4(c) and (d)). Then, the obtained image was labeled by giving a different label to each region. The image was scanned for the same label information by centering horizontally and vertically. The midsagittal CC area was automatically determined by selecting the CC label information (Fig. 4(e) and (f)).

As can be seen in Fig. 4(e) and (f) satisfactory results were obtained for the GMM and FCM methods. The CC crosssectional area for each section was studied twice with GMM and FCM and the calculated areas for each cross-section were averaged. The same process was repeated for approximately 15 sections can be seen of the CC for every person and CC volume was calculated using Eq. (8). Also, the three dimensional image of CC by placing consecutive calculated sections was obtained, and was shown as an example in Fig. 5. Jaccard similarity, segmentation accuracy and time-consuming were calculated with the obtained results. Average results are presented in Tables 1 and 2 for real brain images. As can be seen in Tables 1 and 2 GMM method has higher segmentation accuracy although it requires longer computation time than the FCM. GMM method was more successful in classifying gray tone gradations. The area and volume results obtained by FCM were greater than the GMM and the manual segmentation results which were used for comparison. This situation shows that FCM method tends to over-segmentation. The FCM works fairly quickly, however the accuracy of the calculated segmentation was slightly better with the GMM.

4.

Fig. 4 – CC segmentation with GMM (left) and the FCM (right) algorithm.

Discussion and conclusion

The segmentation process in brain images is aimed at classifying the tissues component of the brain, and quantifying the volume and other morphological, architectural features, and at separating different brain tissues to aid in various neurological and neurosurgical applications (neuropathological changes) [16–18]. The segmentation of brain images into the three main regions (GM, WM, CSF) is a fundamental step in the analysis of MR brain images. Many studies that used different segmentation methods to distinguish these basic brain tissues are available in the literature [27–29]. The corpus callosum is the largest myelinated interhemispheric structure and links the corresponding cortical areas of the two hemispheres. Therefore, changes in the corpus callosum could affect the integrity of the functions between two hemispheres [30]. In addition to all of these vital importances, CC is an area suitable for automatic segmentation. Many brain diseases change the size of the corpus callosum. Doctors in

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Publications in recent years

Segmentation algorithm

Used images

Accuracy of results (%)

Time-consuming

Ji et al. (2011–2012) [2,11,12,32]

[2011] weighted image patch based FCM-WIPFCM [2011] modified possibilistic Fuzzy C-means clustering algorithm-MPFCM [2012] generalized rough Fuzzy C-means algorithm-GRFCM [2012] fuzzy local GMM algorithm-FLGMM

MR brain images with different level noise (segmentation of GM, WM, CSF)

As Jaccard similarity WIPFCM 93.94 and 84.93 for WM and GM MPFCM 93.60 and 89.12 and for WM and GM GRFCM 95.73 and 86.05 for WM and GM as dice values FLGMM 93.39 and 81.38 for WM and GM

Not calculated for brain images No more than 2 min 18.00 ± 0.30 s for BrainWeb 2D dataset 21.18 ± 2.36 s for 2D BrainWeb dataset

Forouzanfar et al. [1]

Improved FCM optimizing parameter with ANN, GA, PSO, BS

MR brain images with different level noise (segmentation of GM, WM, CSF)

As Jaccard similarity 93.7 for FCM, 96.5 for BS-IFCM (breeding swarm improved FCM) for WM

Time consuming not calculated

Tian et al. [33]

Hybrid genetic and variational EM – (GA-VEM)

MR brain images (segmentation of GM, WM, CSF)

Jaccard similarity 77.02 and 85.70 low and high resolution T1-weighted brain MR images

Time consuming not calculated

Foruzan et al. [34]

Multilayer Hidden Markov model

MR brain images (segmentation of GM, WM)

Dice index 88.83 and 83.17 for WM and GM

8.7 min using the IBSR 18 dataset

Roy et al. [35]

Rician classifier using EM (RICE) GMM, SPM, Freesurfer and others

MR brain images (segmentation of GM, WM, CSF)

Dice coefficient 85.35 and 82.05 for RICE and GMM for WM, and weighted average results were RICE > SPM > Freesurfer for WM, GM and CSF on 14 BLSA data.

Time consuming not calculated

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Table 3 – Some publication in recent years on brain WM, GM and CSF segmentation (after 2010).

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clinics visually assess the size of the CC usually looking at the midsagittal section from MR images. For this reason, to obtain numerical results about CC size and volume with the aid of segmentation of the CC from brain MR images is very important. This paper proposes two efficient segmentation algorithms to calculate automatic midsagittal area of the CC from simulated and real brain images. In the first phase, a typical GMM with the EM method can classify pixels into different classes depending on the similarity in their probability density functions. In the second, for comparison, the FCM method was used for the same purpose. Then the other sections and volume of CC were calculated using the two methods. Recently, GMM and FCM algorithm have frequently been used for brain image segmentation. Lorenzo et al. presented a systematic review of the literature to evaluate the state of the approaches in automated multiple sclerosis lesion segmentation. In this way, they compared different methods used for brain segmentation. They showed that GMM and FCM are frequently preferred by researchers as unsupervised methods for brain segmentation [31]. Studies made using these and other techniques were developed to achieve optimum separation of the three basic brain tissues: WM, GM and CSF. Most of these studies focus on implementing methods and their modifications by adding different levels of noise to brain images and other images. Table 3 presents the results and works related to the segmentation of brain WM, GM and CSF regions using GMM and FCM methods in recent years (after 2010). As seen in Table 3, the GMM and FCM algorithms and their modifications were preferred as the popular for WM, GM and CSF segmentations [32–35]. At the same time, to perform a lot of modifications on the algorithm can complicate and prolong the process duration in practice. In addition to the difficulty of making a successful segmentation of noisy MR images, to obtain images with minimal noise may no longer be possible with the latest technological MR devices. It was possible to expand Table 3, however, a study on the automatic segmentation and numerical calculation of the CC with the help of the GMM and FCM algorithms was not observed in the literature review. When the studies in Table 3 are examined, it is believed that results of this study will contribute to the literature. Most of the researchers in the literature separate the GM, WM and CSF regions for the 3D brain image segmentation process using automatic or semi-automatical professional programs [6]. These programs (SPM, Freesurfer, FSL, etc.) are Mac or Windows-based programs that work with images in DICOM, Analyze and other formats. SPM utilizes a Gaussian intensity model and it tries to recover the non-Gaussianity of the intensity PDF by modeling it with multiple Gaussians. FAST operates with a Gaussian model on the log transformed intensities. Freesurfer and FANTASM use different variations of FCM [35]. However, studies conducted with these programs are not practical for clinical use in terms of the operation installation of programs, performing format conversions, realizing of analysis procedures and presenting the results in numerical terms.

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In this study, the midsagittal section area of the CC was calculated automatically using the GMM and FCM methods. In the scope of this work, thin-section sagittal brain images obtained from normal individuals were used in order to focus on accurate segmentation and the implementation of the algorithms. The area and volume results obtained by the both algorithms have high accuracy in comparison with manual segmentation. Because the algorithms work very quickly they may be preferred for practical use in the clinic. Thus, an accurate and automatic segmentation system that allows opportunity for quantitative comparison to doctors in the planning of treatment and the diagnosis of diseases affecting the size of the CC was developed. The performed methodology can be improved for the segmentation of other regions in the brain. In future the developed system could be used in clinical practice by combining with a GUI operation.

Conflict of interest statement The author declares that there is no conflict of interest with any financial organization regarding the material discussed in the manuscript.

Acknowledgment The author would like to thank Prof. Dr. Abdulhakim Cos¸kun head of Medical Faculty Radiology Department in Erciyes University for his help in recording of real brain images.

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