Engineering, Technology & Applied Science Research Vol. 8, No. 3, 2018, 2985-2990 2985  
 

www.etasr.com Gharnali and Alipour: MRI Image Segmentation Using Conditional Spatial FCM Based on …  

 

MRI Image Segmentation Using Conditional Spatial 

FCM Based on Kernel-Induced Distance Measure 
 

Babak Gharnali  

Department of Computer Engineering 

Islamic Azad University, Buinzahra Branch 

Buinzahra, Iran  

babakgharnali.ai@gmail.com 

Siavash Alipour  

Department of Electrical and Electronic Engineering 

Malek-Ashtar University of Technology 

Tehran, Iran 

siavash.alipur@gmail.com 
 

 

Abstract—Fuzzy C-means (FCM) clustering is the widest spread 

clustering approach for medical image segmentation because of 

its robust characteristics for data classification. But, it does not 

fully utilize the spatial information and is therefore very sensitive 

to noise and intensity inhomogeneity in magnetic resonance 

imaging (MRI). In this paper, we propose a conditional spatial 

kernel fuzzy C-means (CSKFCM) clustering algorithm to 

overcome the mentioned problem. The approach consists of two 

successive stages. First stage is achieved through the 

incorporation of local spatial interaction among adjacent pixels in 

the fuzzy membership function imposed by an auxiliary variable 

associated with each pixel. The variable describes the 

involvement level of each pixel for construction of membership 

functions and different clusters. Then, we adapted a kernel-

induced distance to replace the original Euclidean distance in the 

FCM, which is shown to be more robust than FCM. The problem 

of sensitivity to noise and intensity inhomogeneity in MRI data is 

effectively reduced by incorporating a kernel-induced distance 

metric and local spatial information into a weighted membership 

function. The experimental results show that the proposed 

algorithm has advantages in accuracy and robustness against 

noise in comparison with the FCM, SFCM and CSFCM methods 

on MRI brain images. 

Keywords-image segmentation; MRI; fuzzy C-means; noise 

I. INTRODUCTION  

Segmentation is an essential preprocessing step in 
computer-guided medical image analysis and diagnosis [1]. It 
helps doctors extract soft tissue regions from the respective 
organs of the human body for surgical decisions, abnormality 
detection and therapy management. MRI is one of the most 
eminent medical imaging techniques and segmentation is a 
critical stage in the investigation of MRI images. Some factors 
complicate segmentation in medical images such as noise, 
normal anatomic variation, post-surgical anatomic variation, 
vague and incomplete boundaries, variation of contrast, 
inhomogeneities in the boundaries of the object of interest, 
motion blurring artifacts and so on [2]. To address these 
difficulties, clustering methods have been extensively studied 
and widely used in MIS, with promising results [3]. Among the 
different clustering methods devised in the past for medical 
images, the fuzzy c-means (FCM) algorithm has proved its 
efficacy. Unlike hard clustering methods, like k-means 

algorithm, which assign pixels exclusively to one cluster, the 
FCM algorithm allows pixels to have relation with multiple 
clusters with varying degree of memberships. The main 
disadvantage of the FCM is that it is sensitive to noise and 
inhomogeneity which leads to erroneous segmentation results 
and undesired visual quality in case of MRI brain image data. 
To overcome the problems of traditional FCM algorithm, many 
researchers modified the objective function by considering 
different criteria and presented more efficient and robust 
clustering algorithms [4-8].  

Authors in [9] introduced a class of robust non-Euclidean 
distance measure for the objective function to enhance the 
robustness of the original FCM clustering algorithm and to 
reduce noise and outliers. Enhanced FCM is proposed in [10] 
to fasten the segmentation process as well as to reduce the 
noise effect. To deal with the inhomogeneity problem, many 
algorithms have been proposed by adding correction steps 
before image segmenting [11,12] or by modeling the image as 
the product of the original image and a smooth varying 
multiplier field [13,14]. In [15], authors introduced a novel 
energy term based on multilayer structure of local intensity 
information to segment images with intensity inhomogeneity. 
Authors in [16] proposed a region-based method using a local 
similarity factor to enhance the performance in segmenting 
images with intensity inhomogeneity and noise. Authors in [7] 
proposed a conditional spatial fuzzy C-means clustering 
algorithm (CSFCM) to address the FCM problem. The CSFCM 
algorithm incorporates conditioning effects, imposed by some 
auxiliary (conditional) variables, as well as spatial information 
into the final membership function to improve robustness to the 
noise and inhomogeneity, providing thereby superior 
segmentation results. 

In this paper, we propose a conditional spatial kernel fuzzy 
C-means (CSKFCM) clustering algorithm that can effectively 
segment MRI brain images with the presence of noise and 
intensity inhomogeneity. The proposed algorithm incorporates 
a kernel-induced distance to replace the original Euclidean 
distance in CSFCM algorithm which leads to better results. It is 
shown that the proposed algorithm has better segmentation 
results on simulated or real MR images corrupted by noise and 
other artifacts than the standard algorithms such as CSFCM. 
The rest of the paper is organized as follows: in section II, we 



Engineering, Technology & Applied Science Research Vol. 8, No. 3, 2018, 2985-2990 2986  
 

www.etasr.com Gharnali and Alipour: MRI Image Segmentation Using Conditional Spatial FCM Based on …  

 

briefly introduce the CSKFCM method to prepare the 
description of our proposed segmentation framework which is 
explained in Section III in detail. The experimental results and 
conclusions are presented in Sections IV and V respectively. 

II. BACKGROUND 

FCM clustering [17-19] is an unsupervised technique that 
has been successfully applied to feature analysis, clustering, 
and classifier designs in fields such as astronomy, geology, 
medical imaging, target recognition, and image segmentation. 
The FCM algorithm, where the correlation between the 
neighboring pixels is not considered, fails to generate accurate 
clusters. Authors in [7] proposed a conditional spatial fuzzy c–
means algorithm (CSFCM) to address this issue. This 
mechanism ensures that if the neighboring pixels share similar 
characteristics, the center pixel should have higher probability 
of being grouped to the same cluster as the neighboring pixels. 
Thus, the algorithm takes the level of involvement of a pixel 
into a cluster by considering its neighborhood. A local 
membership function is defined as follows: 

𝑈𝑖𝑘 =  
𝑓𝑖𝑘

||(𝑥𝑖)−(𝑣𝑖)||
2

𝑚−1/ ∑ ||(𝑥𝑘)−(𝑣𝑐)||
2

𝑚−1𝐶
𝑐=1

       () 

𝑓𝑖𝑘 =  
∑ µ𝑖𝑘𝑗∈𝑁(𝑥𝑘)

𝑀
        () 

Where fik is the conditioning variable which defines the level 

of involvement of pixel 𝑋𝑖  into the ith cluster by considering its 
neighborhood in a spatial domain. N(xk) is the square box 

having the pixel Xi as its center and M is the number of pixels 

in the box. The membership value function of the CSFCM is 

the combination of the global membership values μik and the 

local membership values Uik  as following: 

𝑍𝑖𝑘 =
(µ𝑖𝑘)

𝑝𝑈𝑖𝑘
𝑞

∑ (µ𝑐𝑘)
𝑝(𝑈𝑐𝑘)

𝑞𝐶
𝑐=1

                () 

𝑊𝑖 =
∑ 𝑧𝑖𝑘

𝑚𝑁
𝑘=1 𝑥𝑘

∑ 𝑧𝑖𝑘
𝑚𝑁

𝑘=1
                   () 

where p and q are the parameters to control the relative 
importance of both global and local membership functions. 
Figure 1 displays the full explanation of the CSFCM method. 

III. PROPOSED ALGORITHM 

The CSFCM algorithm employs squared-norm in similarity 
measurement which is effective in grouping “spherical” 
clusters. In fact, due to the use of nonrobust Euclidean distance, 
it leads to nonrobust results. In this paper, based on the 
recognized power of the “kernel method” [20, 21] in recent 
machine learning community, we present a kernelized CSFCM 
algorithm to address this issue. Unlike the CSFCM algorithm 
which adopts the squared-norm distance metric in the objective 
function, the proposed algorithm uses a kernel-induced metric 
and is shown to be more robust to noise and outlier than 
classical algorithms. Here, we adapted a kernel-induced 
distance to replace the original Euclidean distance in the 
CSFCM. By replacing the inner product with an appropriate 

“kernel” function, one can implicitly perform a nonlinear 
mapping to a higher-dimensional feature space without 
increasing the number of parameters. The philosophy of the 
“kernel method” is that every (linear) algorithm that only uses 
scalar products can be extended to the corresponding 
(nonlinear) version of this algorithm which is implicitly 
executed in a higher feature space through kernels [22]. 

 
input: set values for the number of cluster C, the degree of fuzziness 

m=2, q=2, q=2 and the error ∈. 

1. Initialize randomly the centers of clusters 𝑉
𝑖
(0)

. 

2. Initialize randomly the centers of clusters 𝑊
𝑖
(0)

. 

3. j=1. 

4. Repeat 
   a. j= j+1 

   b. Calculate membership values𝑈(𝑗) using the cluster centers𝑣
𝑖
(𝑗−1)

as 

follows : 

µ𝑖𝑘 =  
1

||(𝑥𝑖 ) − (𝑣𝑖 )||
2

𝑚−1/ ∑ ||(𝑥𝑖 ) − (𝑣𝑐 )||
2

𝑚−1𝐶
𝑐=1

 

 

   c. Calculate conditional spatial membership values 𝑢
𝑖𝑘
(𝑗)

 using the 

cluster centers𝑣
𝑖
(𝑗=1)

 as follows : 

𝑈𝑖𝑘 =  
𝑓𝑖𝑘

||(𝑥𝑖 ) − (𝑣𝑖 )||
2

𝑚−1/ ∑ ||(𝑥𝑘 ) − (𝑣𝑐 )||
2

𝑚−1𝐶
𝑐=1

 

where 𝑓𝑖𝑘 =  
∑ µ𝑖𝑘𝑗∈𝑁(𝑥𝑘)

𝑀
 

d. Calculate weighted  membership values𝑧
𝑖𝑘
(𝑗)

as follows : 

 

𝑍𝑖𝑘 =
(µ𝑖𝑘 )

𝑝𝑈𝑖𝑘
𝑞

∑ (µ𝑐𝑘 )
𝑝(𝑈𝑐𝑘)

𝑞𝐶
𝑐=1

 

 

e. Update joint cluster value 𝑊
𝑖
(𝑗)

 as:𝑊𝑖 =
∑ 𝑧𝑖𝑘

𝑚𝑁
𝑘=1 𝑥𝑘

∑ 𝑧𝑖𝑘
𝑚𝑁

𝑘=1

 

f. Update centers𝑉𝑖
(𝑗)

as: 𝑉𝑖 =
∑ µ𝑖𝑘

𝑚𝑁
𝑘=1 𝑥𝑘

∑ µ𝑖𝑘
𝑚𝑁

𝑘=1

 

5. until‖𝑊𝑖
(𝑗)

− 𝑊
𝑖
(𝑗−1)

‖ <∈ 

6. Return the cluster center Wi and membership value 

𝑍𝑖𝑗 : 1,2, … , 𝐶; 𝑘: 1,2, … , 𝑁 

Fig. 1.  The CSFCM Algorithm 

A kernel in the feature space can be represented as a 
function K below: 

𝐾(𝑥, 𝑦) = 〈𝛷(𝑥), 𝛷(𝑦)〉      () 

where Φ stands as implicit nonlinear map, and  <Φ(x), Φ(y)> 
denotes the inner product operation.  

In the CSFCM objective function, we express the distance 
function using inner product space. By constraining ourselves 
to the Euclidean distance in ||Φ(xk)-Φ(vi)|| the squared distance 
is computed in the kernel space using a kernel function. Here 
we use only the Gaussian RBF kernel for simplicity. So, if we 
employ the nonlinear map with the Gaussian kernel substitution 
in the CSFCM objective function, the global and local 
membership function of CSFCM can be rewritten as follows: 

µ𝑖𝑘 =  
1

(1−K(𝑥𝑘,𝑣𝑖 ))
2

𝑚−1/ ∑ (1−K(𝑥𝑘,𝑣𝑐 ))
2

𝑚−1𝐶
𝑐=1

        () 



Engineering, Technology & Applied Science Research Vol. 8, No. 3, 2018, 2985-2990 2987  
 

www.etasr.com Gharnali and Alipour: MRI Image Segmentation Using Conditional Spatial FCM Based on …  

 

𝑈𝑖𝑘 =  
𝑓𝑖𝑘

(1−K(𝑥𝑘,𝑣𝑖 ))
2

𝑚−1/ ∑ (1−K(𝑥𝑘,𝑣𝑖 ))
2

𝑚−1𝐶
𝑐=1

        () 

Where K(x, y)=Φ(x)TΦ(y) is an inner product Gaussian RBF 
kernel function, and K(x, y)=exp[-(||x-y||2)/2σ2]. Moreover, 
cluster centers can be rewritten as follow: 

𝑣𝑖 =
∑ 𝑢𝑖𝑘

𝑚𝐾(𝑥𝑘,𝑣𝑖)𝑥𝑘
𝑛
𝑘=1

∑ 𝑢𝑖𝑘
𝑚𝐾(𝑥𝑘,𝑣𝑖)

𝑛
𝑘=1

         () 

According to (6)-(8), the data point  is endowed with an 

additional weight 𝐾(𝑥𝑘 , vi), which measures the similarity 
between 𝑥𝑘  and vi based on their effects with respect to the 
pixels’ distance. It means that the kernel function gives more 
weight to nearer pixels and vice versa. The proposed CSKFCM 
algorithm is be summarized in the Figure 2. 

 
input: set values for the number of cluster C, the degree of fuzziness 

m=2, q=2, q=2 and the error ∈. 

1. Initialize randomly the centers of clusters V
i
(0)

. 

2. Initialize randomly the centers of clusters W
i
(0)

. 
3. j=1. 
4. Repeat 

   a. j= j+1 

   b. Calculate membership valuesU(j) using the cluster centers𝑣
𝑖
(𝑗−1)

 as 

follows : 

µ𝑖𝑘 =  
1

(1 − K(𝑥𝑘 , 𝑣𝑖  ))
2

𝑚−1/ ∑ (1 − K(𝑥𝑘 , 𝑣𝑐  ))
2

𝑚−1𝐶
𝑐=1

 

 
   c. Calculate kernel conditional spatial membership  

values 𝑢
𝑖𝑘
(𝑗)

using the cluster centers 𝑣
𝑖
(𝑗=1)

 as follows : 

𝑈𝑖𝑘 =  
𝑓𝑖𝑘

(1 − K(𝑥𝑘 , 𝑣𝑖  ))
2

𝑚−1/ ∑ (1 − K(𝑥𝑘 , 𝑣𝑖  ))
2

𝑚−1𝐶
𝑐=1

 

 

Where𝑓𝑖𝑘 =  
∑ µ𝑖𝑘𝑗∈𝑁(𝑥𝑘)

𝑀
 

d. Calculate weighted  membership values 𝑧
𝑖𝑘
(𝑗)

 as follows : 

 

𝑍𝑖𝑘 =
(µ𝑖𝑘 )

𝑝𝑈𝑖𝑘
𝑞

∑ (µ𝑐𝑘 )
𝑝(𝑈𝑐𝑘)

𝑞𝐶
𝑐=1

 

 

e. Update joint cluster value𝑊
𝑖
(𝑗)

 as:   𝑊𝑖 =
∑ 𝑧𝑖𝑘

𝑚𝑁
𝑘=1 𝑥𝑘

∑ 𝑧𝑖𝑘
𝑚𝑁

𝑘=1

 

f. Update centers 𝑉𝑖
(𝑗)

 as:𝑣𝑖 =
∑ µ𝑖𝑘

𝑚𝐾(𝑥𝑘,𝑣𝑖 )𝑥𝑘
𝑁
𝑘=1

∑ µ𝑖𝑘
𝑚𝐾(𝑥𝑘,𝑣𝑖 )

𝑁
𝑘=1

 

 

5. Until‖𝑊𝑖
(𝑗)

− 𝑊
𝑖
(𝑗−1)

‖ <∈ 

 

6. Return the cluster center 𝑊𝑖 and membership value 
𝑍𝑖𝑘 : 1,2, … , 𝐶; 𝑘: 1,2, … , 𝑁 

Fig. 2.  The Proposed CSKFCM Algorithm 

IV. EXPERIMENTAL RESULTS 

This paper performs two groups of experiments to evaluate 
the proposed algorithm qualitatively and quantitatively. The 
qualitative evaluation compares the output of the proposed 
algorithm with the following algorithms: FCM [23], SFCM 
[24], and CSFCM [7].The quantitative evaluation shows the 
final output with the reference segmented image and compares 
the segmentation results of the proposed method with three 

fuzzy-based mentioned algorithms along the same line based 
on ground-truth images. The quantitative evaluation is 
computed based on Dice criteria [25,26]. The Dice factor 
which is common in image segmentation has been measured 
for segmentation algorithms as a quantitative evaluation. The 
experiments and performance evaluation were carried out on 
three different datasets. One is a simple synthetic image, 
another is the classical simulated brain database borrowed from 
McConnell Brain Imaging Centre of the Montreal Neurological 
Institute, McGill University [27], and the last one is an MR 
Image borrowed from [2]. The original images are stored in 
gray scale space. These images are commonly used in papers 
[28, 29–34] for image segmentation purposes and the 
algorithms compared have employed these images in their 
experiments. Next, the setting of parameters, the comparison of 
algorithms and the evaluation of each performance are 
explained in detail. 

A. Setting Experimental Parameters 

The max iteration, 𝑡𝑚𝑎𝑥 , was considered 200. The 
parameters in the FCM based methods were set as follows: (i) 
The weighting exponent was set to be m=2 since it had been 
shown to be the most effective one [35]. (ii) The termination 
criteria was set to be ε=0.01 since most reports showed good 
success with ε ∈[0.01, 0.0001] [ 36 ]. (iii) The Gaussian RBF 
kernel width as proposed method parameter was set to be 
σ=150 since it showed better results than other σ values [36]. 
Moreover, the parameters in the CSFCM [7] method were set 
as follows: (i) The parameters of weighted membership 
function were set to be p=2 and q=2 since it had been shown 
that the algorithm provides superior results using these values 
[CSFCM]. (ii) The size of the neighborhood was set to N(xk)=9 
(3 × 3 window centered around each pixel). 

B. Qualitative Evaluation 

The synthetic image is shown in Figure 3(a). It contains a 
two-class pattern corrupted by Gaussian noise with mean=0, 
variance=0.02. Figures 3(b)-(e) show the segmentation results 
of FCM, SFCM, CSFCM and the proposed CSKFCM 
respectively. As shown in Figure 3(b), without spatial 
constraints, the FCM cannot separate the two classes. 
Although, the SFCM and CSFCM employ the correlation 
between the neighboring pixels, they fail to generate accurate 
clusters as shown in Figures 3(c) and (d). By comparing Figure 
3(d) with the others, we can see that the proposed CSKFCM 
method provides a better segmentation result than its 
counterparts. Note that because of the injection of the kernel, 
CSKFCM needs more execution time than CSFCM, and 
correspondingly, CSKFCM is slower than CSFCM. Typically, 
the algorithms without kernel are several times faster than those 
with injection of kernels. 

The next experiment is designed to evaluate the 
performance of the proposed method on a T1-weighted 
simulated brain image with the presence of noise and intensity 
inhomogeneity. The target is to segment different tissue 
regions: cerebrospinal fluid (CSF), grey matter (GM) and white 
matter (WM). Figure 4 shows the segmentation results of a T1-
weighted MR image (slice 100, Figure 4(a) with 7% noise and 
20% inhomogeneity. Figure 4(b)–(d) shows the segmented 
regions of the CSF, GM and WM, respectively by the FCM 



Engineering, Technology & Applied Science Research Vol. 8, No. 3, 2018, 2985-2990 2988  
 

www.etasr.com Gharnali and Alipour: MRI Image Segmentation Using Conditional Spatial FCM Based on …  

 

algorithm. Figures 4(e)–(g) show the segmented regions of the 
CSF, GM and WM, respectively by the SFCM algorithm. 
Figures 4(h)–(j) show the segmented regions of the CSF, GM 
and WM, respectively by the CSFCM algorithm. Figures 4(k)–
(m) show the segmented regions of the CSF, GM and WM, 
respectively by the proposed CSKFCM algorithm. 

 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

 
(e) 

Fig. 3.  Comparison of segmentation results on a synthetic image 
corrupted by Gaussian noise with variance=0.02. (a) The original image, (b) 

using FCM, (c) using SFCM, (d) using CSFCM, and (e) using CSKFCM 

The last row of Figure 4 shows the result of the proposed 
algorithm. It can be seen that this algorithm performs well for 
the MRI brain image with the presence of noise and intensity 
inhomogeneity. However, the rest fails in most situations and 
also several artifacts are present in the segmented regions of the 
CSF, GM and WM. The reason is that the CSKFCM attempts 
to unify the intensity and spatial information as a whole and it 
employs a kernel-induced new metric to replace the Euclidean 
norm in the original space. Consequently, it shows less 
susceptibility to noise. 

In the last experiment of this section, we tested the 
performance of the proposed CSKFCM algorithm on another 
MRI image data from [2] corrupted by Gaussian noise with 
mean=0, variance=0.003 as shown in Figure 5(a). The second 
to fifth rows of Figure 5 show segmentation results by FCM, 
SFCM, CSFCM, and CSKFCM respectively. By comparing 
them, we can see that the proposed method provides a better 
segmentation result than its counterparts. 

C. Qualitative Evaluation 

To evaluate the results of Brain MRI mage segmentation, it 
is necessary to make a quantitative evaluation of different 
algorithms. The comparisons are illustrated using the Dice 
Similarity coefficient (DSC) [11, 23] as a similarity criterion, 
which is defined by: 

DSC(Ωs, Ωr) =
2Area(Ωs∩ Ωr)

(Area(Ωs)+Area(Ωr))
        () 

 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

 
(e) 

 
(f) 

 
(g) 

 
(h) 

 
(i) 

 
(j) 

 
(k) 

 
(l) 

 
(m) 

Fig. 4.  Segmentation results of the CSF, GM and WM (from left to 
right) by the different algorithms on a T1-weighted MRI brain image with 
7% noise and 20% inhomogeneity (a). (b)–(d): FCM algorithm; (e)–(g): 

SFCM algorithm; (h)–(j): CSFCM algorithm and (k)–(m): the proposed 

CSKFCM algorithm. 

In (9), Ωs is the final segmented region and Ωr is the 
corresponding reference region. This coefficient varies from 0 
to 1 and measures the degree of agreement between the two 
regions. It is 1 if the two regions are identical and 0 when they 
are completely different. Table I gives the segmentation 
accuracy of four methods in Figure 3(a) based on ground-truth 
image in Figure 6(a), where the segmentation accuracy is 
computed using the Dice similarity coefficient. Table II shows 
the results of applying the Dice similarity coefficient for three 
segmented parts of the simulated MRI brain image in Figures 
2(a): CSF, GM and WM using the FCM, SFCM, CSFCM and 
the proposed method. The second row of Figure 6 shows the 
reference or the region of interest (ROI) of the CSF, GM and 
WM regions of the brain image in Figure 4(a). Table III shows 
the results of applying the Dice similarity coefficient for the 
WM segmented parts of the MRI brain image in Figure 3(a) 



Engineering, Technology & Applied Science Research Vol. 8, No. 3, 2018, 2985-2990 2989  
 

www.etasr.com Gharnali and Alipour: MRI Image Segmentation Using Conditional Spatial FCM Based on …  

 

using the FCM, SFCM, CSFCM and the proposed method. 
Figure 4(e) shows the reference of the WM region of the brain 
image in Figure 5(a). From Tables I-III, it can be seen that the 
best results in term of the Dice coefficient (highest value) are 
achieved by our proposed method. In addition, by comparing 
the CSFCM and the proposed CSKFCM results from the 
Tables, we can see the advantages in using the kernel-induced 
metric to replace the original Euclidean norm metric in 
CSFCM objective function. 

 

 
 (a) 

 
(b) 

 
(c) 

 
(d) 

 
(e) 

 
(f) 

 
(g) 

 
(h) 

 
(i) 

 
(j) 

 
(k) 

 
(l) 

 
(m) 

Fig. 5.  Segmentation results of the CSF, GM and WM (from left to right) 
by the different algorithms on an MRI brain image contaminated with Gaussian 

noise (mean=0 and variance=0.003)(a). (b)–(d): FCM algorithm. (e)–(g): 
SFCM algorithm. (h)–(j): CSFCM algorithm. (k)–(m): Proposed CSKFCM 

algorithm. 

 

 
(a) 

 
(b) 

 
(c) 

 
(d) 

 
(e) 

Fig. 6.  Ground-truth segmentation of images. a ROI of the synthetic 
image in Figure 4(a). (b)-(d): CSF, GM and WM ROI of the simulated brain 

image in Figure 4(a). (e): WM ROI of the brain image in Figure 5(a) 

TABLE I.  COMPUTATION DICE SIMILARITY COEFFICIENTS (FIGURE 3(A)) 

 FCM SFCM CSFCM Proposed method 

Figure. 1a 0.9560 0.9856 0.9904 0.9982 

TABLE II.  COMPUTATION DICE SIMILARITY COEFFICIENTS (FIGURE 4(A)) 

 FCM SFCM CSFCM Proposed method 

CSF 0.9560 0.9856 0.9904 0.9982 

GM 0.8423 0.8623 0.8930 0.9086 

WM 0.8621 0.8876 0.9030 0.9191 

TABLE III.  COMPUTATION DICE SIMILARITY COEFFICIENTS (FIGURE 5(A)) 

 FCM SFCM CSFCM Proposed method 

WM 0.8015 0.8230 0.8446 0.8594 

V. CONCLUSION 

In this paper, a new approach for segmentation of corrupted 
by noise MRI images has been presented. The proposed 
algorithm is based on incorporating the kernel method and the 
spatial information into the final membership function of the 
FCM to effectively segment MR images corrupted by noise and 
inhomogeneity. We assessed the effectiveness of the proposed 
algorithm, qualitatively and quantitatively, on synthetic and 
MR images available in segmentation data-bases that are 
commonly used in papers. In the qualitative evaluation, the 
output of the proposed algorithm was compared with the FCM, 
SFCM and CSFCM methods in noisy cases. The quantitative 
evaluation was calculated based on the Dice factor. 
Experimental results demonstrate that the proposed algorithm 
produces better results by successfully detecting the object 



Engineering, Technology & Applied Science Research Vol. 8, No. 3, 2018, 2985-2990 2990  
 

www.etasr.com Gharnali and Alipour: MRI Image Segmentation Using Conditional Spatial FCM Based on …  

 

boundaries and also is more robust to Gaussian noise than other 
fuzzy clustering algorithms in segmenting MRI images. 

REFERENCES 

[1] J. S. Duncan, N. Ayache, “Medical image analysis: Progress over two 
decades and the challenges ahead”, IEEE Transactions on Pattern 
Analysis and Machine Intelligence, Vol. 22, No. 1, pp. 85-106, 2000 

[2] T. Dietenbeck, M. Alessandrini, D. Friboulet, O. Bernard, “CREASEG: 
a free software for the evaluation of image segmentation algorithms 
based on level-set”, 2010 17th IEEE International Conference on Image 
Processing (ICIP), Hong Kong, China, Vol. 1, No. 1, pp. 665-668, 
September 26-29, 2010 

[3] C. Xu, D. Pham, J. Prince, Image segmentation using deformable 
models. Handbook of medical imaging, Elsevier, 2000 

[4] A. W. C. Liew, S. H. Leung, W. H. Lau, “Fuzzy image clustering 
incorporating spatial continuity”, IEE Proceedings-Vision, Image and 
Signal Processing, Vol. 147, No. 2, pp. 185-192, 2000 

[5] D. L. Pham, “Spatial models for fuzzy clustering. Computer vision and 
image understanding”, Computer Vision and Image Understanding, Vol. 
84, No. 2, pp. 285-297, 2001 

[6] A. W. Liew, H. Yan, “An adaptive spatial fuzzy clustering algorithm for 
3-D MR image segmentation”, IEEE Transactions on Medical Imaging, 
Vol. 22, No. 9, pp. 1063-1075, 2003 

[7] S. K. Adhikari, J. K. Sing, D. K. Basu, M. Nasipuri, “Conditional spatial 
fuzzy C-means clustering algorithm for segmentation of MRI images”, 
Applied Soft Computing, Vol. 34, pp.758-769, 2015 

[8] J. K. Sing, S. K. Adhikari, D. K. Basu, “A modified fuzzy C-means 
algorithm using scale control spatial information for MRI image 
segmentation in the presence of noise”, Journal of Chemometrics, Vol. 
29, No. 9, pp. 492-505, 2015 

[9] S. R. Kannan, R. Devi, S. Ramathilagam, K. Takezawa, “Effective FCM 
noise clustering algorithms in medical images”, Computers in biology 
and medicine, Vol. 43, No. 2, pp. 73-83, 2013 

[10] L. Szilagyi, Z. Benyo, S. M. Szilágyi, H. Adam, “MR brain image 
segmentation using an enhanced fuzzy c-means algorithm”, Proceedings 
of the 25th Annual International Conference of the IEEE Engineering in 
Medicine and Biology Society, pp. 724-726, Cancun, Mexico, 
September 17-21, 2003 

[11] B. M. Dawant, A. P. Zijdenbos, R. A. Margolin “Correction of intensity 
variations in MR images for computer-aided tissue classification”, IEEE 
Transactions on Medical Imaging, Vol. 12, No, 4, pp. 770-781, 1993 

[12] B. Johnston, M. S. Atkins, B. Mackiewich, M. Anderson, “Segmentation 
of multiple sclerosis lesions in intensity corrected multispectral MRI”, 
IEEE Transactions on Medical Imaging, Vol. 15, No. 2, pp. 154-169, 
1996 

[13] W. M. Wells, W. L. Grimson, R. Kikinis, F. A. Jolesz, “Adaptive 
segmentation of MRI data”, IEEE Transactions on Medical Imaging, 
Vol. 15, No. 4, pp. 429-442, 1996 

[14] D. L. Pham, J. Prince, “An adaptive fuzzy C-means algorithm for image 
segmentation in the presence of intensity inhomogeneities”, Pattern 
Recognition Letters, Vol. 20, No. 1, pp. 57-68, 1999 

[15] H. Min, X.-F. Wang, D.-S. Huang, W. Jia, “A novel dual minimization 
based level set method for image segmentation”, Neurocomputing, Vol. 
214, pp. 910-926, 2016 

[16] S. Niu, Q. Chen, L. de Sisternes, Z. Ji, Z. Zhou, D. Rubin, “Robust noise 
region-based active contour model via local similarity factor for image 
segmentation”, Pattern Recognition, Vol. 61, pp. 104-119, 2017 

[17]  J. Bezdek, L. Hall, L. Clarke, “Review of MR image segmentation 
techniques using pattern recognition”, Medical physics, Vol. 20, No. 4, 
pp. 1033-1048, 1993 

[18] N. Iyer, A. Kandel, M. Schneider, “Feature-based fuzzy classification for 
interpretation of mammograms”, Fuzzy Sets and Systems, Vol. 114, No. 
2, pp. 271-280, 2000 

[19] M. S. Yang, Y. J. Hu, K. C. Lin, C. C. Lin, “Segmentation techniques 
for tissue differentiation in MRI of ophthalmology using fuzzy clustering 

algorithms”, Magnetic Resonance Imaging, Vol. 20, No. 2, pp. 173-179, 
2002 

[20] K.-R. Muller, S. Mika, G. Ratsch, K. Tsuda, B. Scholkopf, “An 
introduction to kernel-based learning algorithms”, IEEE Transactions on 
Neural Networks, Vol. 12, No. 2, pp. 181-201, 2001 

[21] N. Cristianini, J. Shawe-Taylor, An introduction to support vector 
machines and other kernel-based learning methods, Cambridge 
University Press, 2000 

[22] D.-Q. Zhang, S.-C. Chen , “Kernel-based fuzzy and possibilistic c-means 
clustering”, Proceedings of the International Conference Artificial 
Neural Network, Vol. 122, pp. 122-125, 2003 

[23] J. Bezdek, Pattern Recognition with Fuzzy Objective Function 
Algorithms, Kluwer Academic Publishers, 1983 

[24] K. S. Chuang, H. L. Tzeng, S. Chen, J. Wu, T. J. Chen, “Fuzzy c-means 
clustering with spatial information for image segmentation. 
computerized medical imaging and graphics”, Vol. 30, No. 1, pp. 9-15, 
2006 

[25] Y. Shi, W. C. Karl, “A real-time algorithm for the approximation of 
level-set-based curve evolution”, IEEE Transactions on Image 
Processing, Vol. 17, No. 5, pp. 645-656, 2008 

[26] L. R. Dice, “Measures of the amount of ecologic association between 
species”, Ecology, Vol. 26, No. 3, pp. 297-302, 1945 

[27] C. A. Cocosco, V. Kollokian, R. K.-S. Kwan, G. Bruce Pike, A. C. 
Evans, “Brainweb: Online interface to a 3D MRI simulated brain 
database”, Neuro Image, 1997 

[28] T. F. Chan, L. A. Vese, “Active contours without edges”. IEEE 
Transactions on Image Processing, Vol. 10, No. 2, pp. 266-277, 2001 

[29] O. Bernard, D. Friboulet, P. Thévenaz, M. Unser, “Variational B-spline 
level-set: a linear filtering approach for fast deformable model 
evolution”, IEEE Transactions on Image Processing, Vol. 18, No. 6, 
1179-1191, 2009 

[30] E .Nadernejad, S. Sharifzadeh, “A new method for image segmentation 
based on Fuzzy C-means algorithm on pixonal images formed by 
bilateral filtering”, Signal, Image and Video Processing, Vol. 7, No. 5, 
pp. 855-863, 2013 

[31] S. Hu, E. A. Hoffman, J. M. Reinhardt, “Automatic lung segmentation 
for accurate quantitation of volumetric X-ray CT images”, IEEE 
Transactions on Medical Imaging, Vol. 20, No. 6, pp. 490-498, 2001 

[32] R. Chan, H. Yang, T. Zeng, “A two-stage image segmentation method 
for blurry images with Poisson or multiplicative gamma noise”, SIAM 
Journal on Imaging Sciences, Vol. 7, No. 1, pp. 98-127, 2014 

[33] M. Droske, B. Meyer, M. Rumpf, C. Schaller, “An adaptive level set 
method for medical image segmentation”, Lecture Notes in Computer 
Science, Vol. 2082, pp. 416-422, Springer, Berlin, Heidelberg, 2001 

[34] C. Li, C.-Y. Kao, J. C. Gore, Z. Ding, “Minimization of region-scalable 
fitting energy for image segmentation”, IEEE Transactions on Image 
Processing, Vol. 17, No. 10, pp. 1940-1949, 2008 

[35] J. C. Bezdek, J. Keller, R. Krisnapuram, N. Pal, Fuzzy models and 
algorithms for pattern recognition and image processing, Springer 
Science & Business Media, Vol. 4, 1999 

[36] D. -Q. Zhang, S.-C. Chen , “A novel kernelized fuzzy c-means algorithm 
with application in medical image segmentation”, Artificial Intelligence 
in Medicine, Vol. 32, No. 1, pp. 37-50, 2004