Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

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Journal of King Saud University –

Computer and Information Sciences
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MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy

C-Means and Shape Based Properties
Abhishek Bal a,⇑, Minakshi Banerjee a, Amlan Chakrabarti b, Punit Sharma c
a
RCC Institute of Information Technology, Kolkata, India
b
A.K. Choudhury School of Information Technology, University of Calcutta, Kolkata, India
c
Apollo Gleneagles Hospital, Kolkata, India

a r t i c l e i n f o a b s t r a c t

Article history: Automated brain tumor segmentation of MR image is a very challenging task in a medical point of view.
Received 6 June 2018 As the nature of the tumor, it can appear anywhere in the brain region with any size, shape, and contrast,
Revised 17 October 2018 that makes the segmentation process more difficult. In order to handle such issues, present work pro-
Accepted 1 November 2018
poses an automated brain tumor segmentation method using rough-fuzzy C-means (RFCM) and shape
Available online xxxx
based topological properties. In rough-fuzzy C-means, overlapping partition is efficiently handled by
fuzzy membership and uncertainty in the datasets is resolved by lower and upper bound of the rough
Keywords:
set. Fuzzy boundary and crisp lower approximation in RFCM play an effective contribution in brain tumor
Segmentation
Brain tumor
segmentation on MR images. Initial centroids selection is a major issue in C-means algorithms. Present
MRI work has introduced a method for initial centroids selection by which the execution time of RFCM is
Threshold reduced as compared to random initial centroids. A patch based K-means method is also implemented
Rough sets for skull stripping as a preprocessing step. The proposed method was tested on MRI standard benchmark
Fuzzy sets datasets. Experimental results show that the proposed method has achieved better performance based on
RFCM statistical volume metrics than previous state-of-the-art algorithms with respect to ground truth
(manual segmentation). It is also experimentally noticed that RFCM method achieves most promising
results with higher accuracy than HCM (hard C-means) and FCM (fuzzy C-means).
Ó 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an
open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction proposed from past few decades in the field of brain tumor seg-
mentation, but still this area plays important roles in the medical
The brain is the origin of the human body that has a very com- research field. No method has been found that can work well
plex structure due to the various shapes in nature. Abnormal (Menze et al., 2015) for all kinds of MRI datasets due to restriction
growth of brain tissues and uncontrolled cell division are the on image acquisition and biological variation. In the early days, the
causes of a brain tumor. Brain tumor segmentation (Menze et al., segmentation process was done manually by the clinical expert,
2015) from the MR images is a great attention to measure the utilizing the medical knowledge and delineating the region of
tumor growth as well as proper treatment planning depending interests (ROIs). Although manual segmentation provides the most
on the characteristics of the detected tumor. Magnetic resonance promising and accurate segmentation results, but it has the limita-
imaging (MRI) focuses on the organic anatomical structure in the tions in MRI data processing due to its complex structure, the
brain that is heavily used to measure the anatomical changes in quantity of clinical MRI datasets and variation of human
medical data. Although a fair amount of researches has been perception.
The general process of automated brain MR image segmenta-
tion requires removing bone and muscle tissues from the brain
⇑ Corresponding author. image which is called skull stripping. Then brain tissues are
E-mail address: abhisheknew1991@gmail.com (A. Bal). classified as gray matter, white matter, cerebrospinal fluid (CSF)
Peer review under responsibility of King Saud University. and suspicious tissues (Rogowska, 2000) through different types
of segmentation techniques. Image segmentation includes separat-
ing coherent regions of an image. However, the segmentation
becomes complicated when the pixel intensity is similar to the
Production and hosting by Elsevier average intensity value of its surrounding pixels and the process

https://doi.org/10.1016/j.jksuci.2018.11.001
1319-1578/Ó 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
2 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

will become difficult in the boundary of the region of interests 2006), possibilistic C-means (Krishnapuram and Keller, 1993),
(ROIs). The intensity variation within the same tissue region and rough C-means (Pawlak, 2012; Saha et al., 2016) and other can
the similarities between different tissues has raised potential chal- be the alternative way, where the tumor (Bal et al., 2018) can also
lenges in MR image segmentation. Most common segmentation be identified along with spatial characteristics like texture, shape,
methods are thresholding, edge-based segmentation, region- intensity, and others.
based segmentation, Markov random field methods, level set Fuzzy clustering (Phuong and Kreinovich, 2001) can be effi-
methods, and classification. ciently used as an unsupervised clustering in MRI medical datasets,
The common problem with the threshold based method is to because the MRI data elements are inherently fuzzy (Gordillo et al.,
handle multiple classes. Moreover, the thresholding process can 2013) in nature due to several constraints such as image acquisi-
not able to analyze the spatial characteristics of MRI dataset and tion and biological variation. Fuzzy C-means can efficiently handle
sensitive to noise and outliers. A threshold based 3D brain tumor the overlapping among the different tissues by assigning the fuzzy
segmentation method was proposed by Taheri et al. (2010), they membership values to all tissue types. Clark et al. (1998) proposed
used level set speed function. To handle intensity inhomogeneity knowledge-based fuzzy clustering by incorporating multispectral
and the presence of noise in MR image, Havaei et al. (2016) pre- histogram analysis for segmenting the brain tumor. Phillips et al.
sented an interactive (minimum user interaction) method for (1995) proposed a fuzzy C-means based brain tumor segmentation
MRI brain tumor segmentation. They also investigated that by add- and then incorporated the knowledge-based (Fathi Kazerooni et al.,
ing the spatial feature coordinates to the intensity features can sig- 2015) methods for better performance. Görlitz et al. (2007) pro-
nificantly improve the performance of different classification posed graph-cut based semi-supervised method for separating
methods such as SVM, KNN, and random forests. To estimate the the suspicious tissues from the normal brain tissues on MRSI data.
parameters of the tumor, such as volume and shape, an efficient For increasing the computational efficiency of the graph-cut
method was proposed by Gibbs et al. (1996) that integrates two method, a normalized-cut method has been proposed by Padole
methods, namely region growing and morphological edge detec- and Chaudhari (2012).
tion. Whereas, edge detection methods (Gonzales, 2002) perform In MRI data, uncertainty is a major artifact. The causes of uncer-
well on the good contrast image, but their performances are tainty may include lack of accuracy and distinctness in the class
reduced in low contrast image as well as the presence of noise. definition. Although the fuzzy membership function efficiently
An automated brain tumor segmentation method has been pro- deals with the overlapping partitions and uncertainty. However,
posed by Prastawa et al. (2004). The region growing method pro- the rough set-based approach may be considered as a better one,
posed by Shanthi and Kumar (2007) used an iterative approach because lower and upper bound in rough set significantly handle
for segmentation purpose. This process also suffers due to the uncertainty and inaccuracy in datasets during MR image segmen-
limitation in the spatial domain. Hamamci et al. (2012) proposed tation. Integration of these two methods called rough-fuzzy C-
a cellular automata (CA) based brain tumor segmentation on means (Mitra et al., 2006; Maji and Pal, 2007; Maji and Pal,
contrast-enhanced T1 weighted magnetic resonance (MR) images. 2008) can efficiently deal with uncertainty and overlapping parti-
They successfully applied CA-based segmentation to the graph- tions. Rough-fuzzy C-means can also avoid the problem of coinci-
theoretic methods to measure the shortest path solution. dent clusters. Each cluster in RFCM is represented by a set of
Hamamci et al. (2012) introduced a sensitivity parameter to deal three parameters (Maji and Pal, 2007), namely, a cluster prototype
with the heterogeneous tumor segmentation. To deal with com- centroid, a crisp lower approximation, and a fuzzy boundary. The
plex shapes and heterogeneous textures in MR image, Kwon lower approximation influences the fuzziness of the final partition.
et al. (2014) proposed a joint segmentation method for performing The cluster centroid depends on the weighting average of the crisp
the tumor segmentation on glioma patients. Using the random lower approximation and fuzzy boundary.
walk, they measured the prior shape of the tumor and incorporated Characterization of brain tumor is not straightforward due to
this shape into an EM framework to measure the mapping between the heterogeneous structure in surroundings of the tumor region
normal brain and the patient’s MRI. A hybrid of fuzzy C-means and sometimes overlaps with normal tissues. In order to handle
clustering algorithm (FCM) and cellular automata model (CA) is the uncertainty, heterogeneous structure, and overlapping tissues,
proposed by Sompong and Wongthanavasu (2016) for brain tumor present work proposes a hybrid method for brain tumor segmenta-
segmentation of MR image. tion on MR images that combines the advantages of rough set and
Apart from these traditional methods, supervised and unsuper- fuzzy set for clustering and shape based topological properties to
vised methods are widely used in MR image segmentation. Super- identify the exact tumor boundary region. Present work incorpo-
vised classification algorithms such as support vector machine rates the prior knowledge of the tumor’s shape based on shape fea-
(SVM) (Chaplot et al., 2006), neural networks (Shanthi et al., tures such as roundness and solidity. Several other shape-based
2010; Zhang et al., 2011; Rajini and Bhavani, 2011), and convolu- features are used to measure the performance of the proposed
tional neural network (CNN) (Soltaninejad et al., 2017; Hussain method with respect to the ground truth. A patch based K-means
et al., 2017; Urban et al., 2014; Beers et al., 2017; Shen and method is also implemented for skull stripping (brain tissue
Anderson, 2017; Isensee et al., 2017) requires the prior knowledge extraction) as a pre-processing step, which has an additional prop-
on an original dataset, which is treated as the training set. Depend- erty to classify an element depending on its neighborhood pattern.
ing on the training datasets, the algorithms take the decision to the After the skull stripping, the proposed method applied rough-fuzzy
experimental unlabeled test datasets for distinguishing between C-means clustering on extracted brain tissues, which separates
normal and abnormal tissues. Tustison et al. (2015) proposed a tumor region along with cerebrospinal fluid (CSF) into a single
supervised segmentation model based on multiple modality, cluster from the other brain regions. Finally, the exact tumor
asymmetry feature sets, and geometry. These feature sets drive boundary region is identified and extracted using shape-based fea-
the proposed supervised method based on random forest-derived tures analysis such as roundness and solidity. The details of the
probabilities. The probability maps from random forest models proposed method are described in Section 3. One of the major
refine the Markov random field regularized probabilistic segmen- issues in the rough-fuzzy C-means based brain tumor segmenta-
tation. Although supervised methods perform well, but it requires tion from MR images is how to choose the initial centroids because
more time and prior knowledge of the dataset. Unsupervised tech- it plays significant roles in the effectiveness of the algorithm. In
niques such as K-means, fuzzy C-means (Maitra and Chatterjee, this paper, an initial centroid selection method is introduced which
2008), self-organization feature map (SOFM) (Chaplot et al., requires less time as compared to random initial centroids during
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 3

Pn  m1
RFCM. The performance of the proposed method is compared with lij xj
vi ¼
j¼1
the state-of-the-art algorithms on BraTS datasets. The usefulness of
Pn  m1 ð5Þ
the RFCM is also validated by comparing the results with hard C- j¼1 lij
means (HCM) and fuzzy C-means (FCM) on the standard MR
benchmark datasets using several volume metrics. In Eq. (4), dij denotes the normalized distance between data ele-
The rest of the paper is organized into six sections. Theoretical ments xj and ith cluster centroid v i .
preliminary in Section 2 briefly introduces the K-means (KCM),
dij ¼ kxj  v i k2
2
fuzzy C-means (FCM) and rough-fuzzy C-means (RFCM) clustering
ð6Þ
algorithms. The details of the proposed method for brain tumor The fuzzy (Bezdek, 2013) membership function must satisfy
segmentation, along with the selection of initial centroids are two conditions that are the sum of membership value of an ele-
described in Section 3. Section 4 provides the algorithm of the pro- ment in all clusters must be 1 (Eq. (7)) and the sum of membership
posed work. In Section 5, quantitative analysis of several shapes value of all elements in a single class must not be greater than the
based features and six-volume metrics are introduced. Experimen- number of cluster (Eq. (8)).
tal details are described in Section 6. The conclusion is presented in
Section 7.
X
c
lij ¼ 1; 8j ð7Þ
i¼1
2. Theoretical preliminary
X
n

2.1. K-means
0< lij 6 n; 8i ð8Þ
j¼1

The objective of K-means (Kanungo et al., 2002; Hartigan and The algorithm starts with the dataset X using randomly initial-
Wong, 1979) algorithm is to group the datasets of n elements into ized clusters centroid V fv 1 ; v 2 ; . . . ; v c g; m1 (fuzzifier) and threshold
c clusters by minimizing the sum of squares distance to the corre- value . After that, membership lij is calculated for all data ele-
sponding centroid. In K-means, each element belongs to exactly ments n using the Eq. (4). Then centroids V fv 1 ; v 2 ; . . . ; v c g are
one cluster. The objective function of K-means is formulated as: recalculated by memberships lij ði ¼ 1; 2; ::; c and j ¼ 1; 2; . . . ; nÞ
X
c X using the Eq. (5). The updating will continue until centroids are
J KCM ¼ kxi  v j k2 ð1Þ stabilized, that is j Vt  Vt1 jerr < .
j¼1 xi 2Bðbj Þ

2.3. Rough-fuzzy C-means

Each cluster bj is represented by the centroid value v j . In this algo-
rithm c number of centroids are initialized randomly. Then for every
Integration of rough set (lower and upper approximation)
element xi , the distance between xi and v j ð1 6 j 6 cÞ of cluster bj
(Pawlak, 2012) and fuzzy set (fuzzy membership) (Pal et al.,
ð1 6 j 6 cÞ is calculated. If the distance dji ð1 6 j 6 cÞ is the mini- 2005; Krishnapuram and Keller, 1993) provide a mathematical
mum distance, then the element xi is assigned to cluster the bj . framework to deal with uncertainties and overlapping pertitions
When all elements have been assigned, then the centroids are recal- of dataset called Rough-Fuzzy C-means (Mitra et al., 2006; Maji
culated using the Eq. (2) and continue this process until stopping and Pal, 2007, 2008) (Fig. 1).
criteria is satisfied that is j V t  V t1 j< , where  is the threshold In RFCM (Mitra et al., 2006; Maji and Pal, 2007), fuzzy member-
value. ship efficiently handles the overlapping partitions. The lower and
1 X  m1
upper approximation in rough set able to deal with incompleteness
vj ¼ lji xi ð2Þ and uncertainty in the class definition. Each cluster in RFCM is rep-
j bj j
xi 2Bðbj Þ resented by the crisp lower approximation that effects fuzziness of
cluster partition, cluster centroid (which is represented by the aver-
where j bj j is the number of elements (cardinality) in cluster bj . In age weight of the crisp lower approximation) and fuzzy boundary.
our proposed method, patch-based K-means is used, which has an RFCM partitions the datasets of n elements into c clusters by mini-
additional property that finds similar patches during segmentation. mizing the objective function (Maji and Pal, 2007) such as
The details about patch based K-means are described in Section 3.2. 8
< wl  P þ wb  Q ; if
> Aðbi Þ R £; Bðbi Þ R £
2.2. Fuzzy C-means J RF ¼ P; if Aðbi Þ R £; Bðbi Þ 2 £ ð9Þ
>
:
Q; if Aðbi Þ 2 £; Bðbi Þ R £
Let dataset X ¼ fx1 ; x2 ; . . . ; xn g, c is the number of cluster and
V ¼ fv 1 ; v 2 ; . . . ; v c g is the centroids. Fuzzy C-means partitions the where
dataset X into c number of clusters by minimizing the objective X
c X
function denoted by J ðU; V; X Þ in Eq. (3). P¼ kxj  v i k2 ð10Þ
i¼1 xj 2Aðbi Þ
X c 
n X m1
J ðU; V; X Þ ¼ lij kxj  v i k ð3Þ
X
c X  m1
kxj  v i k2
j¼1 i¼1
Q¼ lij ð11Þ
where m1 ð1 6 m1 < 1Þ is the fuzzifier, v i is the centroid of ith clus- i¼1 xj 2Bðbi Þ

ter and lij ð2 ½0; 1Þ is the fuzzy membership value of data element xj
The centroid (Maji and Pal, 2007) calculation of RFCM is formu-
to ith cluster. The fuzzy membership and centroid are calculated lated as
using the Eqs. (5) and (4) respectively. 8
 2 !1 < wl  X þ wb  Y; if
> Aðbi Þ R £; Bðbi Þ R £
c 
X dij m1 1 V i ¼ X; if Aðbi Þ R £; Bðbi Þ 2 £ ð12Þ
lij ¼ ð4Þ >
:
k¼1
dkj Y; if Aðbi Þ 2 £; Bðbi Þ R £

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
4 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

Fig. 1. Lower approximation, upper approximation, and fuzzy boundary of rough-fuzzy C-means (RFCM) for cluster bi .

where performance of RFCM is reduced as because of corresponding clus-

X ter can not be able to handle the elements of boundary region and
1
X¼ xj ð13Þ the movement of the centroid will be stuck.
j Aðbi Þ j x 2Aðb Þ
j i The performance of RFCM significantly depends on the value of
d, because RFCM can separate the dataset into lower approxima-
1 X  m1 tion and boundary region of the cluster depending on the value
Y¼ l xj ð14Þ
ni x 2Bðb Þ ij of d. d denotes the average difference of two highest memberships
j i
considering all elements of the dataset. The high value of d (Maji
X  m1 and Pal, 2007) will generate better clustering results. The value
ni ¼ lij ð15Þ of d (Maji and Pal, 2007) is calculated as:
xj 2Bðbi Þ

n o 1 X 
Aðbi Þ; Aðbi Þ and Bðbi Þ ¼ Aðbi Þ n Aðbi Þ denote lower approxima- d¼ lij  lkj ð17Þ
n
tion, upper approximation and boundary region of cluster bi
where n is the total number of elements. lij and lkj are the highest
respectively. According to the definition of rough set, if an element
and second highest membership of the element xj to the cluster bj
xj 2 Aðbi Þ, then definitely xj R Bðbi Þ; 8j and xj R Aðbk Þ; 8k – i. The
point xj belongs to Aðbi Þ depending upon the threshold value d, and bk respectively.
which is given in Eq. (17). In RFCM, membership lij of the element
xj that belongs to crispy lower approximation of cluster bi should 3. Proposed method
be 1, whereas the membership in the boundary region is same as
FCM membership. The proposed work is described in the built-in diagram in Fig. 2.
The parameter wl and wb ð¼ 1  wl Þ are important for the lower The major steps of the proposed method are as follows and each
approximation and the boundary region respectively. Hence, cen- step is explained in the following subsections.
troids of the clusters depend on the parameter wl and
wb ð¼ 1  wl Þ. The value of wl and wb are set experimentally. Differ- – Pre-processing such as noise removal and bias correction (sec-
ent values of wl and wb are used by Mitra et al. (2006), Maji and Pal tion 3.1) on original MR image.
(2007, 2008), which should follow the Eq. (16). – Perform patch based K-means (section 3.2) for skull stripping
on preprocessed MR image.
0 < wb < wl < 1; where wl þ wb ¼ 1 ð16Þ
– Apply RFCM on brain tissues to segment tumor region (section
If an element xj belongs to the lower approximation in cluster 3.3) along with CSF into a single cluster region.
bi , then wl is larger as compared to wb for the elements that belong – Perform shape based features analysis (section 3.4) on that seg-
to the boundary region of cluster bi . If wl ¼ 1 and wb ¼ 0 then the ment to identify the exact tumor boundary region.

Fig. 2. Block diagram of the proposed model.

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 5

3.2. Patch based K-means for skull stripping

3.1. Pre-processing

3.1.1. Noise removal In order to remove the skull from preprocessed MR image bI, the
Noise in MRI data can cause severe bias and the huge variation present work implements a patch based K-means method, which is
in physiological parameters in diagnosis that can affect the further described as follows:
processing and analysis, such as segmentation (Bal and Saha, 2016, At fast, the present work separates 3  3 neighborhood window
 
2018). Several researchers (Chang et al., 2000; Mateo and for each pixel of the preprocessed MR image bI and stored it in
Fernández-Caballero, 2009; Sanches et al., 2008; Yousuf and each row of a 2D patch matrix (Fig. 4(b)). Let us consider, middle
Nobi, 2010) proposed a number of various techniques to remove rectangle (light gray color) of Fig. 4(a) denotes the preprocessed
as per as possible noise. In the present work, BayesShrink (Chang image. To separate the patches, at first zero padding (dark gray
et al., 2000) denoising method is applied to collected MRI datasets. color) is performed around the image, then separate 3  3 patches
BayesShrink is a soft adaptive, data-driven thresholding technique, for all pixels that belong to the preprocessed image. Here, patches
where the distinct threshold is used for different subbands. The are selected using 3  3 sliding window that moves from the top
details about the BayesShrink are described in the article proposed
left pixel to bottom right pixel of the image bI by one position from
by Chang et al. (2000).
left to right. As a result, each 3  3 patch converted to 1  9 vector
and stored into each row of a 2D patch matrix (Fig. 4(b)). In Fig. 4
3.1.2. Bias correction (b), each row holds gray scale neighborhood values of a pixel
Intensity inhomogeneity in MR images may arise due to several including the pixel itself (middle pixel in each row) and total num-
factors, such as qualities of MR machine and the acquisition proto- ber of rows indicates the number of 3  3 patches in the prepro-
col. Due to the intensity inhomogeneity in MRI dataset, the inten- cessed image. Gray scale values in 1st, . . ., 4th, 6th,. . ., 9th columns
sity variation within the same tissue region and the similarities (Fig. 4(b)) represent the neighborhood of 5th column. Then this
between different tissues has raised potential challenges in MR patch matrix is treated as an input of K-means clustering that con-
image segmentation, which may cause misclassification of tissues. tains all possible neighborhood windows (patches). Apply hard
So, it is very much essential to remove the intensity inhomogeneity clustering (K-means) on patch matrix with two clusters that sepa-
before analyzing the MR images. To handle such issue, the present rate the patches into two distinct clusters. Here, each element in
method applied the bias field correction method (Li et al., 2014) on 5th column of patch matrix is clustered depending on its neighbor-
denoised MR images in order to remove intensity inhomogeneity. ing pixels (1st, . . ., 4th, 6th, . . ., 9th). The patch based K-means
In the bias field correction method (Li et al., 2014), MR images method works well to separate the brain regions in the presence
are decomposed into two multiplicative components, namely, the of noise because it considers the neighborhood characteristic of
true image that characterizes a physical property of the tissues each pixel.
and the bias field which accounts for the intensity inhomogeneity. The outcome of patch-based K-means clustering is converted to
The bias field is iteratively optimized by using efficient matrix a binary image by initializing the cluster elements by 1, which con-
computations. More details of the bias field correction technique tains brain tissues and remaining cluster elements by 0. After bina-
are described in the article proposed by Li et al. (2014) (Fig. 3). rization, the 4-connected components are measured and filled if
there is any hole in the 4-connected components. Then the largest
connected component is extracted which has the solidity (Eq. (27))
>0.75 and roundness (Eq. (28)) >0.6, that represents the brain mask
(Fig. 5(b)). The solidity and roundness value for identifying the
brain mask is set experimentally. Finally, depending on the brain
mask (Fig. 5(b)), brain tissues (Fig. 5(c)) are extracted from the pre-
processed MR image ðwidehatIÞ.

3.3. Rough-fuzzy C-means for tumor region identification

Once the skull stripping is done using patch-based K-means

Fig. 3. Bias correction on the MR image. (a) MR image before bias correction, (b) MR method, rough-fuzzy C-means (RFCM) (Section 2.3) is applied on
image after bias correction. extracted brain tissues to separate the tumor region along with

Fig. 4. Patch creation for K-means based skull stripping. (a) Original image (light gray color) with zero padding (dark gray color), (b) patch matrix.
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
6 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

Fig. 5. Patch based brain mask segment. (a) MR image, (b) brain mask (outcome of patch based K-means), (c) segmented brain tissues.

 
CSF. Present work considers the fixed number of clusters ðc ¼ 4Þ 4. For normalized feature F j ¼ f 1j ; f 2j ; . . . ; f nj , compute maxi-
during the RFCM, because four clusters (Maji and Pal, 2007) can mum feature value F max , minimum feature value F min , range
efficiently partition the brain regions into the background ðRB Þ,  j   j
range max min
gray matter ðRG Þ, white matter ðRW Þ and tumor along with CSF Fj ¼ Fj  Fj , and DIF ¼ F max
j  F min
j =NC. Then ini-
ðRTC Þ. The initial centroids are chosen depending on the algorithm tialize the centroids using the Eqs. (19) and (20).
which is shown next subsection.
The complete tumor regions are mostly hypermetabolic in CLðmÞ j ¼ F min
j þ DIF; where m ¼ 1 ð19Þ
nature in FLAIR modality. Due to this characteristic, the class
that contains hypermetabolism has higher centroid value than
CLðmÞ j ¼ CLðm  1Þ j þ DIF; where 2 6 m 6 NC ð20Þ
others in FLAIR modality, which is tested experimentally. So,
the cluster RTC has the highest centroid value in gray scale 5. Once centroids initialization is done, the Euclidean distance
image is selected for further shape-based analysis to identify (similar to K-means) is calculated between data point
the tumor region. Proposed work also noticed that not so much xi ð1 6 i 6 nÞ and all the centroids CLðmÞj , where 1 6 m 6 NC.
significant changes have been found with additional features 6. For each data point xi ð1 6 i 6 nÞ, choose the closest centroid
(Haralick and Shanmugam, 1973; Soh and Tsatsoulis, 1999), CLðmÞj , and assign the data point xi to mth cluster.
other than the intensity-based method in tumor boundary 7. Once the data points have been assigned to the various clus-
regions. ters, then for each cluster m ð1 6 m 6 NC Þ, recompute the
centroids value using the step 8.
8. For the data points within the cluster bm ð1 6 m 6 NC Þ, com-
3.3.1. Initial centroids selection pute the mean of mth cluster and the centroid CLðmÞj is
The optimum result of C-means algorithm significantly depends assigned by the mean value.
on the initial centroids selection. If the initial centroids are not well
9. After recomputing the centroids CLðmÞj ; 1 6 m 6 NC value,
enough, then the centroid movement will be stuck. To overcome
the weakness of random centroids, present work introduces a sim- repeat the steps 5 to 9 until j CLðmÞtj  CLðmÞjt1 j< , where
ple initial centroids selection method. The proposed initial cen- t and  is the iteration number and threshold value
troids selection method is tested on MR images and found that respectively.
to achieve the promising solution, it takes lesser time than the ran- 10. Once the centroids calculation is done for all the features
dom initial centroids. The steps of the proposed initial centroids with the datasets X, then CL is used as the initial centroids
method are as follows: for the C-means algorithm.

1. The dataset X ¼ fx1 ; x2 ; . . . ; xn g are the set of data points, 3.4. Measurement of shape-based features for exacting tumor region
 
F j ¼ f 1j ; f 2j ; . . . ; f nj is the jth feature for the dataset X.
2. At first, features set of all data points are normalized. Sup- Since there are a variety of shapes and no fixed intensity distri-
 
pose, the range of the jth features F j ¼ f 1j ; f 2j ; . . . ; f nj in bution model in the tumor region, it is essential to measure shape
h i based properties to estimate the exact tumor boundary region.
the dataset X is F min j ; F max
j , then each feature f ij ð1 6 i 6 nÞ
Tumor shape is one of the most important parameters for charac-
of data point xi ð1 6 i 6 nÞ is normalized using the Eq. (18). terization of the tumor. Inter-patient tumor heterogeneity can be
quantified by the size and shape of the tumor. In this paper, prior
f ij  F min knowledge of tumor shapes (George et al., 2015; Bharath, 2018;
j
f ij ¼ ð18Þ Srivastava et al., 2011) is used to distinguish the tumor boundary
F max
j  F min
j region from CSF.
  To measure the threshold value of shape parameters, roundness
3. For each normalized feature F j ¼ f 1j ; f 2j ; . . . ; f nj , (Eq. (28)) and solidity (Eq. (27)) of manually segmented (ground
1 6 j 6 NOF continue the following steps 4 to 9 and gener- truth) tumor regions are computed on the standard benchmark
ates the centroids CLð jÞ ¼ fC 1 ; C 2 ; . . . ; C NC g as an initial pro- datasets. The range of solidity and roundness value is [0, 1]. More
totypes of the RFCM algorithm, where NOF and NC about the shape based features are described in Section 5. From the
represent number of features and number of clusters outcome, we observed that minimum roundness (Eq. (28)) and
respectively. solidity (Eq. (27)) value of expected tumor regions is more than
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 7

0.3 and 0.78 respectively. These values are treated as a threshold 5. Quantitative analysis
for automated tumor detection. It is also found that cerebrospinal
fluid (CSF) has distinct roundness and solidity value as compared In this section, we present few quantitative indices for the eval-
to the tumor region due to its structural nature. uation of the proposed automated tumor segmentation method.
For the cluster containing CSF and tumor ðRTC Þ, measure the 4- The quantitative indices are presented in two parts. In the first part
connected components and perform hole filling within the 4- (Section 5.1), we describe the different shape based features that
connected components. Then, the 4-connected components within are used to measure the shape based properties of the proposed
the cluster RTC are compared with the estimated threshold (solidity segmented results and ground truth. In the next part (Section 5.2),
>0.78 and roundness >0.3) value of the shape based properties to volume metrics are briefly described that are used during the
distinguish the tumor mask from the CSF. At last, tumor region is comparison.
delineated and segmented depending on tumor mask.
To validate the performance of the proposed method, we com- 5.1. Shape based features
pare the proposed segmented tumor areas with manually seg-
mented tumor areas using several shapes based properties and 5.1.1. Area
volume metrics that are described in Section 6. It denotes the number of elements in the region of interest (ROI)
represented by
4. Algorithm T Area ¼j X j ð21Þ

The algorithm of the proposed method is as follows. where X denotes the region of interest (ROI) and j X j is the cardinal-
ity of X.
Algorithm 1: Rough-fuzzy C-means and shape features based
brain tumor segmentation on MR images 5.1.2. Centroid
It represents the center of mass of the region of interest (ROI).
Procedure: RFTS (IMRI)
INPUT: 5.1.3. Eccentricity
– Original MR image, IMRI It specifies the eccentricity of the ellipse that has same second-
OUTPUT order moments as the region of interest (ROI), formulated by Eq.
–Segmented Tumor, STumor (22). It denotes the ratio of the distance between the foci of the
Steps ellipse and its major axis length.
1: Apply BayesShrink based noise removal method on sffiffiffiffiffiffiffiffiffiffiffiffiffiffi
original MR ðIMRI Þ image to estimate denoised image ðID Þ. B2
2: To remove the intensity inhomogeneity on the denoised E¼ 1 2 ð22Þ
A
MR image, the bias correction method is applied to
 
obtain preprocessed MR image bI . where A and B are the semi-major and semi-minor axis length.

3: Apply patch based K-means for skull stripping 5.1.4. Exetent

(Section 3.2) on preprocessed MR image bI and extract It represents the ratio between the elements in the region of
brain tissues ðBmask Þ. interest (ROI) and elements in the total bounding box.
4: Go through step 4 to 8 for performing the RFCM on brain
tissues ðBmask Þ. 5.1.5. Major axis and minor axis length
5: Initial parameters of RFCM are assigned such as the Major axis and minor axis length represent the length of the
number of clusters ðc ¼ 4Þ, centroids v i ; 1 6 i 6 c major and minor axis of an ellipse respectively that have same nor-
(Section 3.3.1), fuzzifier m1 (Section 3.3), and threshold d malized second central moments as the region of interest (ROI).
(Section 3.3). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
6: Calculate membership value lij (Eq. (4)) for n elements AMajor ¼ ðp þ qÞ2  f ð23Þ
by considering c number of clusters.
7: Find two highest memberships lij and lkj for the AMinor ¼ p þ q ð24Þ
 
element xj . If lij  lkj 6 d, then xj 2 Aðbi Þ and where f represents the distance between foci. p and q are the dis-
xj 2 Aðbk Þ, and xj R Aðbi Þ and xj R Aðbk Þ. Else xj 2 Aðbi Þ tances from each focus to any point on the ellipse.

and xj 2 Aðbi Þ.
5.1.6. Perimeter
8: Modify membership lij of element xj to 1 that belongs to
It represents the distance around the boundary of the seg-
crisp lower approximation ðAðbi ÞÞ of cluster bi . mented region of interest (ROI).
9: Recalculate the centroids using the Eq. (12) and continue Z p=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
the steps 4 to 8 until j V t  V t  1 j< . Peri ¼ 4a 1  E2 cos2 hdh ð25Þ
10: Once RFCM is done, extract the cluster RTC that contain 0

tumor along with CSF based on the centroid value. where a and E are the major axis length and the eccentricity of the
11: Measure the connected components and perform hole ellipse respectively. The integral called elliptic integral.
filling within the connected components of the cluster
RTC to obtain RCHTC . 5.1.7. EquivDiameter
12: Perform shape based statistical analysis on RCHTC based It measures the diameter of the circle with the same area as the
on prior knowledge of tumor shapes (Section 5.1) and region of interest (ROI) and formulated as
distinguished the tumor region ðRTumor Þ from CSF. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4  Area
ED ¼ ð26Þ
p

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
8 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

5.1.8. Convex area 5.2.5. Sensitivity (true positive rate)

It represents the total number of elements in a convex image Sensitivity measures the proportion of positives that are cor-
within the region of interest (ROI). rectly identified as such and useful to evaluate the true positive
rate. It is formulated as
5.1.9. Solidity jX^Y j
It represents the proportion of the elements in the convex hull,
Sensitiv ity ¼ ð33Þ
jYj
which are also in the region of interest (ROI).

Area 5.2.6. Specificity (true negative rate)

S¼ ð27Þ
Conv exArea Specificity measures the proportion of negatives that are cor-
rectly identified as such and useful to evaluate the true negative
rate. It is formulated as
5.1.10. Roundness
Roundness measures the shape of the region of interest (ROI) j X0 ^ Y 0 j
Specificity ¼ ð34Þ
and formulated as j Y0 j

4  Area where X 0 and Y 0 represent the pixels predicted as negatives for the
R¼ 2
ð28Þ tumor region.
Perimeter

The range of roundness is [0, 1]. The value closer to 1 denotes the 6. Experiment results
object is circle shape and lower value indicate the object looks like
the line shape or curve. 6.1. MRI datasets

5.2. Volume metrics The proposed method was tested on BraTS 2013, BraTS 2017,
dataset from ‘‘eHealth laboratory” and ‘‘Whole Brain Atlas (WBA)”.
5.2.1. False positive volume function (FPVF) MICCAI BraTS 2013 dataset is provided by Virtual Skeleton
It signifies the error that occur due to the misclassification in Database (VSD) ( https://www.smir.ch/BRATS/Start2013) (Kistler
the region of interest (ROI) and represented as et al., 2013). BraTS 2013 dataset includes the multicontrast 3D
MRI data. Each patient’s MR image has four modalities such as
jX jjX^Y j T1, T1C, T2, and FLAIR along with expert annotation for ground
FPVF ¼ ð29Þ
jYj truth. In BraTS 2013 ground truth dataset, the whole tumor is sub-
divided into edema, enhancing tumor, non-enhancing tumor and
where X and Y denote the region of interest (ROI) segmented by the necrotic.
proposed method and manual method (ground truth) respectively. The BraTS 2017 dataset contains T1, T1 contrast-enhanced, T2,
j X j and j Y j represent the number of elements within X and Y and FLAIR images for a total of 243 patients. Five segmentation
respectively. labels are provided in ground truth, namely non-tumor, necrosis,
edema, enhancing tumor and non enhancing tumor. The expert
5.2.2. False negative volume function (FNVF) board certified neuroradiologists manually-revised the ground
It represents the error that occurs due to the loss of the desired truth labels of BraTS 2017 (Menze et al., 2015; Bakas et al.,
elements in the region of interest (ROI) and formulated as 2017a,b). The dataset has been already skull-removed, registered
and interpolated by the BraTS challenge organizers. The images
jY jjX^Y j in the BraTS dataset have a consistent shape of 240  240  155
FNVF ¼ ð30Þ
jYj voxels.
The dataset of ‘‘eHealth laboratory” and ‘‘Whole Brain Atlas
Note that, lower value of FPVF and FNVF denote better
(WBA)” are download from http://www.medinfo.cs.ucy.ac.cy/
segmentation.
and http://www.med.harvard.edu/aanlib/ respectively. More
details about these datasets are available on the corresponding
5.2.3. Similarity index (SI) websites.
Similarity index is a statistic that is used to compare the simi-
larities between two regions of interests (ROIs) and formulated as 6.2. Results

jX^Y j
SI ¼ 2  ð31Þ The performance of the proposed method is described in five
jXjþjY j subsections. In the first subsection, we have applied the proposed
The range of SI is [0, 1] and value >0.8 denotes excellent method on standard benchmark MRI datasets collected from
matches. BraTS2013, BraTS 2017, ‘‘eHealth laboratory” and ‘‘Whole Brain
Atlas (WBA)”. In the present work, more than 500 brain MR images
with different sizes have been used for evaluation. For pre-
5.2.4. Jaccard index (JI) processing, noise removal and bias correction methods are applied
Jaccard index is used to compare the elements of two objects to to the original MR images. The performance of the proposed
measure which elements are shared by both objects and which ele- method has been validated by the outcome of the manual segmen-
ments are distinct within a range of [0, 1]. JI is formulated as tation (ground truth) done by the neurologist. The second subsec-
tion describes the inter-dataset cross-validation to validate the
jX^Y j
JI ¼ ð32Þ proposed method. In the third subsection, the performance of the
jX_Y j
RFCM is compared with HCM and FCM with respect to ground
The higher value indicates more similarities between two truth (manual segment) using several shapes based properties
objects. and four-volume metrics (SI, FPVF, FNVF, and JI). In the fourth sub-
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 9

section, the performance of the different C-means algorithms is laboratory” and ‘‘Whole Brain Atlas (WBA)” respectively using dif-
tested with respect to proposed and random initial centroids selec- ferent shape based features such as area, centroid, eccentricity,
tion. In the last subsection, we compare the performance of the extent, major axis and minor axis length, perimeter, equivDiame-
proposed method with existing tumor segmentation methods ter, convex area, solidity and roundness. The results in Tables 1
(Soltaninejad et al., 2017; Hussain et al., 2017; Sompong and and 2 signify that shape based features value of the proposed seg-
Wongthanavasu, 2016; Saha et al., 2016; Urban et al., 2014; mented tumors are closer to manual segmentation. Table 3 pre-
Havaei et al., 2016; Hamamci et al., 2012; Kwon et al., 2014; sents the comparative performance analysis of the proposed
Tustison et al., 2015; Beers et al., 2017; Shen and Anderson, method with respect to manual segmentation using four-volume
2017; Isensee et al., 2017) based on BraTS 2013 and BraTS 2017 metrics such as SI, FPVF, FNVF and JI considering c ¼ 4 (back-
datasets. The proposed method was implemented in the Matlab ground, gray matter, white matter and CSF-tumor). The volume
8.6 version on a PC with CPU Intel Core i7 and RAM 16 GB with metrics in Table 3 signify that the results of the proposed segmen-
Windows platform. tation method achieve good quantitative measures with respect to
manual segmentation.
6.2.1. Comparative performance analysis between proposed method The performance of the proposed method on BraTS 2013 and
and ground truth BraTS 2017 datasets for the whole (complete) tumor segmentation
The performance of the proposed algorithm on benchmark is shown in Figs. 8–15. Whole tumor region depicts the collection
datesets is reported for clusters c ¼ 4. In Ref. (Maji and Pal. of all sub-regions of tumor. In this proposed method FLAIR and T2
2007), it was shown that four clusters ðc ¼ 4Þ can efficiently seg- modalities are used for identifying the whole tumor region. Each
ment the MR images into background, gray matter, white matter, figure in Figs. 8–15 shows the segmentation results by the pro-
and cerebrospinal fluid. In RFCM, we consider m1 ¼ 2:0; wl ¼ 0:9, posed method and manual segmentation on multiple consecutive
and wb=0.1, which are tested experimentally. The value of d (thresh- MRI slices for a single patient. The numerical results of the pro-
old) is computed using the Eq. (17), which is data dependent. During posed method on BraTS 2013 datasets are shown in Table 4 with
RFCM, centroid calculation is affected by the value of wl and wb as it respect to SI, JI, FPVF, FNVF, sensitivity and specificity. The details
control lower bound and boundary region of that cluster. of the performance comparison between the proposed method and
Note that, if wb=0, then RFCM can not able to handle the cluster other methods are described in the last sub-section on both BraTS
boundary region. Original MR images, tumor mask, and delineated 2013 and BraTS 2017 datasets. Present work also highlights the
tumor regions by proposed method (yellow color) and manual seg- performance of the proposed method (using similarity index) on
mentation (red color) are shown in Figs. 6 and 7 respectively. the complete tumor region by varying the tumor size, which is
Tables 1 and 2 depict the performance of the proposed method shown in Fig. 16. The curve in Fig. 16 depicts the complete picture
with respect to manual segmentation on the datasets of ‘‘eHealth of the effectiveness of the proposed method. The proposed method

Fig. 6. Performance of the proposed RFCM based whole tumor segmentation on brain MR dataset (I-01, I-02, I-03, I-04 and I-05) of ‘‘eHealth laboratory”. First column denotes
original images, second column denotes segmented tumors mask and third column denotes tumors delineated by the proposed method (yellow) and manual segmentation
(red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
10 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

Fig. 7. Performance of the proposed RFCM based whole tumor segmentation on brain MR dataset (I-06, I-07 and I-08) of ‘‘Whole Brain Atlas (WBA)”. First row denotes
original images, second row denotes tumors along with CSF, third row denotes segmented tumors mask and forth row denotes tumors delineated by the proposed method
(yellow) and manual segmentation (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 1
Shape based features analysis of proposed and manual segmentation method on MR dataset (I-01, I-02, I-03, I-04, I-05 and I-06).

I-01 I-02 I-03

Properties Proposed Manual Proposed Manual Proposed Manual
Area 2565 2446 2630 2513 2787 2769
Centroid-X 94.516 95.153 147.869 148.379 147.421 148.539
Centroid-Y 168.408 168.671 181.685 182.709 180.287 179.657
Eccentricity 0.795 0.756 0.764 0.774 0.738 0.736
EquivDiameter 57.148 55.806 57.867 56.565 59.569 59.377
Extent 0.737 0.705 0.751 0.743 0.785 0.738
MajorAxisLength 77.385 72.322 72.617 71.795 73.893 74.587
MinorAxisLength 46.956 47.363 46.866 45.499 49.881 50.475
Perimeter 245.615 228.431 198.740 198.467 205.562 210.748
Solidity 0.834 0.849 0.950 0.943 0.961 0.930
ConvexArea 3074 2881 2769 2665 2900 2977
Roundness 0.534 0.589 0.837 0.802 0.829 0.783
I-04 I-05 I-06
Properties Proposed Manual Proposed Manual Proposed Manual
Area 671 709 3052 2817 2136 2118
Centrod-X 112.114 112.035 173.739 173.806 359.435 358.900
Centroid-Y 172.119 172.577 137.222 137.885 323.302 322.800
Eccentricity 0.418 0.618 0.861 0.857 0.500 0.559
EquivDiameter 29.229 30.045 62.337 59.889 52.150 51.930
Extent 0.799 0.767 0.535 0.523 0.781 0.791
MajorAxisLength 30.873 34.216 92.630 88.695 56.294 57.507
MinorAxisLength 28.043 26.900 46.989 45.651 48.745 47.672
Perimeter 91.716 96.397 314.746 314.019 166.057 168.339
Solidity 0.974 0.966 0.807 0.792 0.976 0.965
ConvexArea 689 734 3752 3558 2188 2195
Roundness 0.9895 0.9588 0.3660 0.3590 0.9734 0.9392

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 11

Table 2
Shape based features analysis of proposed and manual segmentation method on MR dataset (I-07 and I-08).

I-07 I-08
Properties Proposed Manual Proposed Manual
Area 2497 2494 674 661
Centroid-X 356.493 357.225 195.641 196.398
Centroid-Y 325.354 324.513 297.519 298.062
Eccentricity 0.737 0.749 0.588 0.621
EquivDiameter 56.385 56.351 29.294 29.011
Extent 0.739 0.742 0.801 0.734
MajorAxisLength 68.817 69.594 32.827 33.264
MinorAxisLength 46.541 46.145 26.544 26.080
Perimeter 186.310 187.593 91.997 94.933
Solidity 0.966 0.955 0.977 0.959
ConvexArea 2586 2611 690 689
Roundness 0.9040 0.8906 0.9823 0.9217

Table 3
Evaluation of the segmentation results by employing four volume metrics (SI, FPVF, FNVF and JI). VMF denotes volume metrics function.

VMF I-01 I-02 I-03 I-04 I-05 I-06 I-07 I-08

SI 0.92 0.96 0.95 0.93 0.93 0.95 0.95 0.95
FPVF 0.101 0.061 0.051 0.034 0.111 0.045 0.050 0.057
FNVF 0.087 0.045 0.044 0.062 0.072 0.037 0.048 0.037
JI 0.86 0.92 0.90 0.88 0.87 0.92 0.90 0.90

Fig. 8. Performance of the proposed method on BraST 2013 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 1 are shown. Delineation by red
and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of
this article.)

Fig. 9. Performance of the proposed method on BraST 2013 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 2 are shown. Delineation by red
and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of
this article.)

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
12 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

Fig. 10. Performance of the proposed method on BraST 2013 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 3 are shown. Delineation by
red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version
of this article.)

Fig. 11. Performance of the proposed method on BraST 2017 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 4 are shown. Delineation by
red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version
of this article.)

Fig. 12. Performance of the proposed method on BraST 2017 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 5 are shown. Delineation by
red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version
of this article.)

further applied to identify the core tumor region, which is basically core tumor region are shown in Figs. 17–19 for the patient number
hypometabolic in nature in T1C modality as compared to T1 4, 6 and 8 respectively, where the complete tumor region segmen-
modality. Here, T1C and T2 modalities are used during the tation of same patients are shown in Figs. 11, 13 and 15
identification of core tumor region. The segmentation results of respectively.

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 13

Fig. 13. Performance of the proposed method on BraST 2017 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 6 are shown. Delineation by
red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version
of this article.)

Fig. 14. Performance of the proposed method on BraST 2017 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 7 are shown. Delineation by
red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version
of this article.)

Fig. 15. Performance of the proposed method on BraST 2017 dataset for the segmentation of complete tumor region. Eight MRI slices of patient 8 are shown. Delineation by
red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version
of this article.)

6.2.2. Inter-dataset cross-validation amount of proper medical image datasets are very rare, so, cross-
To measure the accuracy of the proposed method, inter-dataset validation technique is very useful in medical image analysis. The
cross-validation is applied. It acquires knowledge from a known datasets of ‘‘eHealth laboratory” and ‘‘Whole Brain Atlas (WBA)”
task and reuses it to solve the next unknown task. The large are significantly smaller as compared to the BraTS dataset. To

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
14 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

Table 4 BraTS datasets is used on the dataset of ‘‘eHealth laboratory”. The

Results obtain by different metrics on BraST 2013 test dataset. segmentation results in Fig. 20 achieve promising performance.
Metrics Complete tumor
Similarity Index (SI) 0.91
6.2.3. Comparative performance analysis of different C-means with
Jaccard Index 0.87
False positive volume function (FPVF) 0.06 ground truth
False negative volume function (FNVF) 0.07 Original MR image (I-07), along with the corresponding tumor
Sensitivity 0.90 segmented results by HCM, FCM, RFCM, and ground truth (manual
Specificity 0.92 segmentation) are shown in Fig. 21. The comparative results of
HCM, FCM, and RFCM, along with ground truth on image I-07 is
reported in Table 5 with respect to different shape based proper-
ties. The results in Table 5 show that the performance of RFCM is
validate the performance of the proposed method, we acquire the more closer to the ground truth (manual segmentation) as com-
shape based knowledge from the larger BraTS dataset, then reuse pared to the HCM and FCM.
the prior knowledge of the shape on datasets of ‘‘eHealth labora- Finally, Table 6 depicts the performance of different C-means
tory” and ‘‘Whole Brain Atlas (WBA)”. Fig. 20 shows the example algorithms on several MR images with respect to ground truth
of inter-dataset cross-validation, where prior knowledge from (manual segmentation) using two volume metrics namely SI and

Fig. 16. Area versus similarity index (SI) value of proposed segmentation for different size of tumor.

Fig. 17. Performance of the proposed method on BraST 2017 dataset for the segmentation of core tumor region. Eight MRI slices of patient 4 (Fig. 11) are shown. Delineation
by red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)

Fig. 18. Performance of the proposed method on BraST 2017 dataset for the segmentation of core tumor region. Eight MRI slices of patient 6 (Fig. 13) are shown. Delineation
by red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 15

Fig. 19. Performance of the proposed method on BraST 2017 dataset for the segmentation of core tumor region. Eight MRI slices of patient 8 (Fig. 15) are shown. Delineation
by red and yellow colors are done by manually and proposed method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)

JI. The results depicted in Table 6 confirm that overall performance

of RFCM with respect to ground truth is better than the HCM and
FCM.

6.2.4. Proposed initialization versus random initialization of centroid

in different C-means
Table 7 provides the performance of HCM, FCM, and RFCM for
proposed initial centroids and random initial centroids selection
methods on several MR images (Figs. 6 and 7) with respect to
the requirement of the average execution time. Better performance
is obtained using the presented centroids selection method as
compared to random initial centroids. The execution time (in sec-
Fig. 20. Inter-dataset cross-validation for complete tumor region. Prior shape ond) mentioned in Table 7 refers the time to compute the C-means
knowledge from BraTS datasets is applied on datasets of ‘‘eHealth laboratory”. (a) algorithms excluding the input–output (I/O) operations. Although
MR image from ‘‘eHealth laboratory”, (b) delineated tumor by the proposed method the time requirement of RFCM is higher than the HCM, but RFCM
(yellow color) and manual segmentation (red color). (For interpretation of the
overperformed with respect to ground truth, which shown in
references to colour in this figure legend, the reader is referred to the web version of
this article.) Table 6.

6.2.5. Comparative performance analysis of different tumor

segmentation algorithms
In order to measure the performance of the proposed method,
the present work is compared with the other existing methods.
For the comparison, BraTS 2013 and BraTS 2017 datasets are used.
Similarity index and sensitivity are considered as performance
measurement metrics, because these two are the common metrics
which are used by most of the segmentation methods.
The average similarity index (SI) and sensitivity values in Table 8
demonstrate a competitive performance of the proposed method
over other methods on BraTS 2013 dataset. In Soltaninejad et al.
(2017), learning-based automated brain tumor segmentation is
proposed by Soltaninejad et al., where learned features of CNN
are applied to random forests to classify each MR image into nor-
mal brain tissues and tumor. An automated brain tumor segmenta-
tion method using deep convolutional neural networks (DCNN) is
proposed by Hussain et al. (2017) on BraST 2013 dataset. In their
proposed method bias field correction is used as a preprocessing
step to handle intensity inhomogeneity. Sompong and
Wongthanavasu (2016) proposed a hybrid of fuzzy C-means
(FCM) and cellular automata model (CA) for brain tumor segmen-
tation on MR images. In this method, features are obtained from
gray level co-occurrence matrix (GLCM). Saha et al. (2016) pro-
posed rough set based brain tumor segmentation method along
with Quadtree and K-means. Their method applied on BraTS
Fig. 21. Segmentation performance of different C-means algorithms and ground
truth on I-07 MR image. (a) Delineated tumor by HCM, (b) delineated tumor by
2013 dataset and efficiently handles the boundary region of the
FCM, (c) delineated tumor by RFCM, and (d) delineated tumor by manual tumor using the advantages of the rough set. A 3D CNN architec-
segmentation. ture for the multi-modal MRI glioma segmentation task is pro-
Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
16 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

Table 5
Performance of different C-means algorithms with manually segmented result for MR image I-07.

Properties HCM FCM RFCM Manual

Area 2395 2402 2497 2494
Centroid-X 356.3428 356.3455 356.4926 357.2249
Centroid-Y 325.4697 325.4580 325.3536 324.5128
Eccentricity 0.7339 0.7329 0.7366 0.7486
EquivDiameter 55.2215 55.3021 56.3851 56.3512
Extent 0.7188 0.7209 0.7385 0.7423
MajorAxisLength 67.3167 67.3510 68.8171 69.5941
MinorAxisLength 45.7222 45.8232 46.5411 46.1452
Perimeter 183.8790 183.8790 186.3100 187.5930
Solidity 0.9565 0.9570 0.9656 0.9552
ConvexArea 2504 2510 2586 2611
Roundness 0.8901 0.8927 0.9040 0.8906

Table 6
Performance of different C-means algorithms using proposed initial centroids selection method.

SI (Similarity Index) JI (Jaccard Index)

Dataset HCM FCM RFCM HCM FCM RFCM
I-01 91.5165 91.4818 92.5165 85.0750 85.7613 86.0750
I-02 93.6403 95.6403 96.3251 92.4990 92.4990 92.9107
I-03 92.2124 94.4099 95.2124 87.8622 89.4118 90.8622
I-04 92.4703 92.7681 93.7681 87.7410 87.8674 88.2674
I-05 93.2320 93.3720 93.3720 86.1268 86.8679 87.5679
I-06 94.0156 94.9981 95.9097 91.7465 91.9504 92.1409
I-07 94.3751 94.4036 95.0912 89.4004 89.3493 90.6417
I-08 94.0541 94.9651 95.2809 89.1344 89.4130 90.9871

Table 7
Performance analysis between proposed and random initial centroids selection method with respect to the average time requirement.

HCM (time in second) FCM (time in second) RFCM (time in second)

Dataset Random Ini Proposed Ini Random Ini Proposed Ini Random Ini Proposed Ini
I-01 0.0970 0.0390 0.1464 0.0988 0.1253 0.0639
I-02 0.0890 0.0310 0.1586 0.0901 0.1248 0.0688
I-03 0.0980 0.0490 0.1239 0.0957 0.1111 0.0692
I-04 0.1220 0.0470 0.1422 0.0946 0.1241 0.0776
I-05 0.0790 0.0300 0.1870 0.0994 0.1160 0.0658
I-06 0.1040 0.0410 0.1440 0.0894 0.1261 0.0728
I-07 0.0750 0.0320 0.1524 0.0863 0.1205 0.0764
I-08 0.0980 0.0540 0.1430 0.0909 0.1213 0.0747

Table 8
Performance comparison of various MRI brain tumor segmentation techniques (results are obtained using dataset of BRATS 2013 benchmark). – denotes not reported result.

Complete tumor Core tumor

Authors Level of interaction Similarity Index Sensitivity Similarity Index Sensitivity
Soltaninejad et al. (2017) Fully automatic 0.88 0.89 0.80 0.77
Hussain et al. (2017) Fully automatic 0.80 0.82 0.67 0.63
Sompong and Wongthanavasu (2016) Semi-automatic 0.84 0.79 – –
Saha et al. (2016) Fully automatic 0.84 0.93 0.73 0.63
Urban et al. (2014) Fully automatic 0.87 – 0.77 –
Havaei et al. (2016) Semi-automatic 0.86 0.78 0.77 0.68
Kwon et al. (2014) Semi automatic 0.88 0.86 0.83 0.81
Tustison et al. (2015) Fully automatic 0.87 0.89 0.78 0.88
Proposed Fully automatic 0.91 0.90 0.82 0.88

posed by Urban et al. (2014), where patches are extracted from the dom walk and utilizes multiple tumor seeds as initial foreground
different MRI modalities and classified using the convolutional information. Tustison et al. (2015) proposed supervised brain
neural network (CNN). Havaei et al. (2016) proposed a semi- tumor segmentation method based on multiple modality intensity,
automatic framework for interactive brain tumor segmentation, geometry, and asymmetry feature sets. Tustison et al. used asym-
which segments a brain tumor by training and generalizing within metry and first order statistical features to train concatenated ran-
that brain only, based on minimum user interaction. Kwon et al. dom forests (RFs) by introducing the output of the first random
(2014), proposed a new method for brain tumor segmentation of forest (RF) as an input to the another. In order to handle the uncer-
glioma patients, which generates a tumor shape prior via the ran- tainty, heterogeneous structure and overlapping tissues in tumor

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx 17

Fig. 22. Performance evaluation of different methods on BraTS 2013 dataset.

region, present work combines the advantages of rough set and

fuzzy set for clustering along with shape-based topological proper-
ties to identify the exact tumor boundaries and able to deal with
the various size of the tumor at different position of the brain.
The comparison results in Table 8 (Fig. 22) show that the proposed
method achieves better performance based on similarity index (SI)
and sensitivity metrics.
The average similarity index (SI) and Sensitivity values in
Table 9 (Fig. 23) demonstrate a competitive performance of the
proposed method over other methods (Beers et al., 2017; Shen
and Anderson, 2017; Isensee et al., 2017) on BraTS 2017 dataset.
Beers et al. (2017) presented multiple deep neural networks based
brain tumor segmentation method with a 3D U-Net architecture in
a tree structure to separate the brain tumor from the background
on BraTS 2017 dataset. A novel CNN-based architectures for glioma
segmentation from the BraTS 2017 dataset is proposed by Shen and Fig. 23. Performance evaluation of different methods on BraTS 2017 dataset.
Anderson (2017). They also explored transfer learning between the
BraTS 2017 dataset and other neuroimaging datasets. Isensee et al.
(2017) proposed convolution neural network based brain tumor – Time requirement of HCM, FCM, and RFCM using proposed ini-
segmentation method which modified U-Net architecture. This tial centroids selection is lesser than the random initial cen-
method (Isensee et al., 2017) achieved very promising results on troids selection for achieving the promising results.
BraTS 2015 and BraTS 2017 datasets, and got third ranking in BraTS – However RFCM requires higher time as compared to HCM, but
2017 challenge. From the comparison results in Table 9, it is seen still, it achieved very promising results for clinical point of view
that present work achieves better results over other methods as well as ROIs segmentation.
based on similarity index (SI) and sensitivity except the method – It is also observed that the performance of FCM is between the
proposed by Isensee et al. (2017). The performance of the proposed performance of HCM and RFCM.
method is approximately same with the method proposed by – The performance of the proposed method is compared with
Isensee et al. (2017). state-of-the-art algorithms based on the segmented results of
The following conclusions can be drawn from experimental tumor regions and achieves better performance than other
results that are reported in this paper: algorithms.

– Integration of rough set and fuzzy set efficiently deal uncer- 7. Conclusion and future work
tainty and overlapping boundary regions of the expected brain
tumor. In the present work, an automated brain tumor segmentation
– It is observed that RFCM overperformed than the HCM and FCM method is proposed using rough-fuzzy C-means and shape based
with respect to the SI and JI. topological properties to quantify tumor region. A patch based

Table 9
Performance comparison of various MRI brain tumor segmentation techniques (results are obtained using dataset of BraTS 2017 benchmark). – denotes not reported result.

Complete tumor Core tumor

Authors Level of interaction Similarity Index Sensitivity Similarity Index Sensitivity
Beers et al. (2017) Fully automatic 0.88 0.91 0.73 0.78
Shen and Anderson (2017) Fully automatic 0.86 – – –
Isensee et al. (2017) Fully automatic 0.89 0.89 0.82 0.83
Proposed Fully automatic 0.89 0.90 0.81 0.84

Please cite this article as: A. Bal, M. Banerjee, A. Chakrabarti et al., MRI Brain Tumor Segmentation and Analysis using Rough-Fuzzy C-Means and Shape
Based Properties, Journal of King Saud University –
Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001
18 A. Bal et al. / Journal of King Saud University – Computer and Information Sciences xxx (xxxx) xxx

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Computer and Information Sciences, https://doi.org/10.1016/j.jksuci.2018.11.001