Mammogram image segmentation using rough

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 66
MAMMOGRAM IMAGE SEGMENTATION USING ROUGH
CLUSTERING
R. Subash Chandra Boss1
, K. Thangavel2
, D. Arul Pon Daniel3
1, 2, 3
Department of Computer Science, Periyar University, Salem-636 011, Tamilnadu, India
rmsubash_18@yahoo.co.in, drktvelu@yahoo.com, apdaniel86@yahoo.com
Abstract
The mammography is the most effective procedure to diagnosis the breast cancer at an early stage. This paper proposes mammogram
image segmentation using Rough K-Means (RKM) clustering algorithm. The median filter is used for pre-processing of image and it is
normally used to reduce noise in an image. The 14 Haralick features are extracted from mammogram image using Gray Level Co-
occurrence Matrix (GLCM) for different angles. The features are clustered by K-Means, Fuzzy C-Means (FCM) and Rough K-Means
algorithms to segment the region of interests for classification. The result of the segmentation algorithms compared and analyzed
using Mean Square Error (MSE) and Root Means Square Error (RMSE). It is observed that the proposed method produces better
results that the existing methods.
Keywords— Mammogram, Data mining, Image Processing, Feature Extraction, Rough K- Means and Image
Segmentation
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1. INTRODUCTION
Breast cancer is the most common type of cancer found among
women. It is the most frequent form of cancer and one in 22
women in India is likely to suffer from breast cancer [1]. This is
the second main cause of cancer death in women. Breast cancer
in India is in rise and rapidly becoming the leading cancer in
females and death toll is increasing at fast rate and no effective
way to treat this disease yet. So, early detection becomes a
critical factor to cure the disease and improving the surviving
rate. Generally the X-ray mammography is a valuable and most
reliable method in early detection.
Image segmentation refers to the process of partitioning a digital
image to multiple segments or set of pixels. The goal of
segmentation is to simplify the representation of an image into
different segments that is more meaningful and easier to
analyze. Image segmentation is typically used to locate objects
and boundaries in images. It is also the process of assigning
a label to every pixel in an image such that pixels with the
same label share certain visual characteristics. The result of
image segmentation is a set of segments that collectively
cover the entire image. Image segmentation is nothing but
the process of dividing an image into disjoint homogenous
regions [2]. These regions usually contain similar objects of
interest. The homogeneity of the segmented regions can be
measured using pixel intensity. Image segmentation techniques
can be broadly classiﬁed as into ﬁve main classes threshold
based, Cluster based, Edge based, Region based, and
Watershed based segmentation [3]. This paper focuses on
cluster based segmentation.
Data mining of medical images is used to collect effective
models, relations, rules, abnormalities and patterns from large
volume of data [4]. This procedure can accelerate the diagnosis
process and decision making. Different methods of data mining
have been used to detect and classify anomalies in mammogram
images such as K- means, FCM, wavelets, ant colony
optimization and neural network.
Clustering is defined as the optimal partitioning of a given set
of n data points into specified number of subgroups, such
that data points belonging to the same group are as similar to
each other as possible [5]. The data points from two different
groups share the maximum difference. Image segmentation is
also considered as a clustering problem where the features
describing each pixel correspond to a pattern, and each image
region corresponds to a cluster. Some hard clustering
approaches do not consider overlapping of classes which occur
in many practical image segmentation problems.
K-Means clustering generate a specific number of disjoints and
flat (non-hierarchical) clusters. It is well suited to generate
globular clusters. The K-Means method is numerical,
unsupervised, non-deterministic and iterative. Some of
disadvantages in K-Means algorithm are difficult in comparing
quality of the clusters produced (e.g. for different initial
partitions or values of K affect outcome), Fixed number of
clusters can make it difficult to predict what K should be, does
not work well with non-globular clusters. Different initial
partitions can result in different final clusters [6].

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There are several methods for segmenting images based on two
fundamental properties of the pixel values: One of them is
“discontinuity” that uses the discontinuities between gray-level
regions to detect isolated points, edges and contours within an
image. The other is “similarity” that uses decision criteria to
separate an image into different group based on the similarity of
the pixel levels. Clustering is one of the methods of second
category. Clustering algorithms attempt to separate a dataset into
distinct regions of membership. Fuzziness occurs due to the
presence of pixels and use of fuzzy methods makes the results
more reliable. Integration of these two techniques (C-Means
clustering & Fuzzy methods) leads to Fuzzy C-Means clustering
(FCM) that consider each cluster as a fuzzy set. Computational
steps of FCM algorithm are: choosing the number of classes and
the initial value for the means, classify the image by defining
membership value for each class and assigning the pixels to the
class corresponding to the closest mean, Re-computing the
means of the class and at last, if the change in any of the means
is more than some pre-defined small positive value, then
stopping, else reclassifying the image based on membership
functions and iterating the algorithm.
This paper is organized as follows: Section 2 discusses the
Rough set theory. Section 3 discusses the Image as a rough set.
Section 4 discusses the Rough set in medical image
segmentation. Section 5 describes the Pre-processing work.
Section 6 discusses the Feature Extraction techniques. Section 7
explains the Clustering algorithms. Section 8 discusses
experimental results and Section 9 covers conclusion.
2. ROUGH SET THEORY
Rough set theory [7, 8] is a fairly recent intelligent technique for
managing uncertainty that is used for the discovery of data
dependencies, to evaluate the importance of attributes, to
discover patterns in data, to reduce redundancies, and to
recognize and classify objects. Moreover, it is being used for the
extraction of rules from databases where one advantage is the
creation of readable if-then rules. Such rules have the potential
to reveal previously undiscovered patterns in the data;
furthermore, it also collectively functions as a classifier for
unseen samples. Unlike other computational intelligence
techniques, rough set analysis requires no external parameters
and uses only the information presented in the given data. One
of the useful features of rough set theory is that it can tell
whether the data is complete or not based on the data itself. If
the data is incomplete, it will suggest that more information
about the objects is required. On the other hand, if the data is
complete, rough sets are able to determine whether there are any
redundancies and find the minimum data needed for
classification. This property of rough sets is very important for
applications where domain knowledge is very limited or data
collection is expensive because it makes sure the data collected
is just sufficient to build a good classification model without
sacrificing accuracy [7, 8].
In rough set theory, sample objects of interest are usually
represented by a table called an information table. Rows of an
information table correspond to objects and columns correspond
to object features. For a given set B of functions representing
object features and a set of sample objects X , an indiscernibility
relation B is a set of pairs (x, x′ ) ∈ X × X such that f (x) = f
(x′ ) for all f ∈ B. The relation ∼ B defines a quotient set X /
∼ B, i.e., a set of all classes in the partition of X defined by ∼ B.
Rough set theory identifies three approximation regions defined
relative to X / ∼ B, namely, lower approximation, upper
approximation and boundary. The lower approximation of a set
X contains all classes that are subsets of X, the upper
approximation contains all classes with non-empty intersections
with X, and the boundary is the set difference between the upper
and lower approximations.
Rough image processing can be defined as the collection of
approaches and techniques that understand represent and process
images, their segments and features as rough sets [9]. In images
boundaries between object regions are often ill-defined [10].
This uncertainty can be handled by describing the different
objects as rough sets with upper (or outer) and lower (or inner)
approximations.
3. IMAGE AS A ROUGH SET
In gray scale images boundaries between object regions are
often ill defined because of grayness and / or spatial ambiguities
[11]. Here, the concepts of upper and lower approximation can
be viewed, as outer and inner approximations of an image region
in terms of granules respectively.
Let the universe U be an image consisting of a collection of
pixels. Then if we partition U into a collection of non-
overlapping windows (of size m × n, say), each window can be
considered as a granule G. In other words, the induced
equivalence classes Im×n have m × n pixels in each non-over-
lapping window. Given this granulation, object regions in the
image can be approximated by rough sets.
Let us consider an object-background separation (a two class)
problem of an M × N, L level image. Let prop(B) and prop(O)
represent two properties (say, gray level intervals 0, 1, …, T and
T + 1, T + 2, …, L – 1) that characterize back-ground and object
can be viewed as two sets with their rough representation as
follows:
The inner approximation of the object ( rO ):






=∀>= Ui
jir n*m,...,3,2,1jT,P|GO .
Outer approximation of the object ( rO ):






>=∃= Ui
jjiT TPs.tn,*m,..,.3,2,1j,GO .

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Inner approximation of the background ( TB ):






=∀≤= Ui
jiT n*m,.,.3,2,1j,TP|GB .
Outer approximation of the background ( TB ):






≤=∃= Ui
jiT TPs.t.n*m,..,3,2,1jj,GB
Therefore, the rough set representation of the image (i.e., object
OT and background BT) for a given Im×n depends on the value of
T. Let the roughness of object OT and background BT be
defined as
T
TT
T
T
O
O
OO
O
O
1R T
−
=−=
T
TT
T
T
B
B
BB
B
B
1R T
−
=−= ,
Where TO and TO are the cardinality of the sets TO and
TO , and TB and TB are the cardinality of the sets TB and
TB , respectively.
4. ROUGH SETS IN MEDICAL IMAGE
SEGMENTATION
One of the most important tasks in medical imaging is
segmentation as it is often a pre-cursor to subsequent analysis,
whether manual or automated. The basic idea behind
segmentation-based rough sets is that while some cases may be
clearly labeled as being in a set X (called positive region in
rough sets theory), and some cases may be clearly labelled as
not being in X (called negative region), limited information
prevents us from labeling all possible cases clearly. The
remaining cases cannot be distinguished and lie in what is
known as the boundary region. Kobashi et al. [12] introduced
rough sets to treat nominal data based on concepts of
categorization and approximation for medical image
segmentation. The proposed clustering method extracts features
of each pixel by using thresholding and labeling algorithms.
Thus, the features are given by nominal data. The ability of the
proposed method was evaluated by applying it to human brain
MRI images. Peters et al. [13] presented a new form of
indiscernibility relation based on k-means clustering of pixel
values. The end result is a partitioning of a set of pixel values
into bins that represent equivalence classes. The proposed
approach allows introducing a form of upper and lower
approximation specialized relative to sets of pixel values.
An improved clustering algorithm based on rough sets and
entropy theory was presented by Chena and Wang [14]. The
method avoids the need to pre-specify the number of clusters
which is a common problem in clustering based segmentation
approaches. Clustering can be performed in both numerical and
nominal feature spaces with a similarity introduced to replace
the distance index. At the same time, rough sets are used to
enhance the algorithm with the capability to deal with vagueness
and uncertainty in data analysis. Shannon’s entropy was used to
refine the clustering results by assigning relative weights to the
set of features according to the mutual entropy values. A novel
measure of clustering quality was also presented to evaluate the
clusters. The experimental results confirm that both efficiency
and clustering quality of this algorithm are improved
An interesting strategy for colour image segmentation using
rough sets has been presented by Mohabey et al. [15]. They
introduced a concept of encrustation of the histogram, called his
ton, for the visualization of multi-dimensional colour
information in an integrated fashion and study its applicability in
boundary region analysis. The his ton correlates with the upper
approximation of a set such that all elements belonging to this
set are classified as possibly belonging to the same segment or
segments showing similar colour value. The proposed
encrustation provides a direct means of separating a pool of
inhomogeneous regions into its components. This approach can
then be extended to build a hybrid rough set theoretic
approximations with fuzzy c-means based colour image
segmentation. The technique extracts colour information
regarding the number of segments and the segment centers of
the image through rough set theoretic approximations which
then serve as the input to a fuzzy c-means algorithm.
Widz et al. [16] introduced an automated multi-spectral MRI
segmentation technique based on approximate reducts derived
from the theory of rough sets. They utilised T1, T2 and PD MRI
images from a simulated brain database as a gold standard to
train and test their segmentation algorithm. The results suggest
that approximate reducts, used alone or in combination with
other classification methods, may provide a novel and efficient
approach to the segmentation of volumetric MRI data sets.
Segmentation accuracy reaches 96% for the highest resolution
images and 89% for the noisiest image volume. They tested the
resultant classifier on real clinical data, which yielded an
accuracy of approximately 84%.
5. PRE-PROCESSING
Pre-processing is an important issue in low-level image
processing. It is possible to filter out the noise present in
image using filtering. A high pass filter passes the frequent
changes in the gray level and a low pass filter reduces the
frequent changes in the gray level of an image. That is; the low
pass filter smoothes and often removes the sharp edges. A
special type of low pass filter is the Median filter. The Median

__________________________________________________________________________________________
filter takes an area of image (3 x 3, 5 x 5, 7 x 7 etc),
observes all pixel values in that area and puts it into the array
called element array. Then, the element array is sorted and
the median value of the element array is found out. We
have achieved this by sorting the element array in the
ascending order using bubble sort and returning the middle
elements of the sorted array as the median value. The output
image array is the set of all the median values of the element
arrays obtained for all the pixels. Median filter goes into a series
of loops which cover the entire image array [13].
Some of the important features of the Median filter are: It is a
non-linear digital filtering technique. It works on a
monochrome color image. It reduces “speckle” and “salt and
paper” noise. It is easy to change the size of the Median filter.
It removes noise in image, but adds small changes in noise-free
parts of image. It does not require convolution. Its edge
preserving nature makes it useful in many cases.
The selected median value will be exactly equal to one of the
existing brightness value, so that no round-off error is
involved when we take independently with integer brightness
values comparing to the other filters [13, 14].
6. FEATURE EXTRACTION
The idea is to calculate the co-occurrence matrix for small
regions of the image and then use this matrix to find statistic
values, for instance Contrast, Correlation, Uniformity,
Homogeneity, Probability, Inverse and Entropy. The distance
and angle is converted to a vertical and a horizontal offset in
pixels according to the following list of angle offset.
Gray-Level Co-occurrence Matrix (GLCM) is one of the texture
descriptors most used in the literature. Starting to summarize
different researches we can find works by Bovis and Singh [19]
studying how to detect masses in mammograms on the basis of
textural features using five co-occurrence matrices statistics
extracted from four spatial orientations, horizontal, left diagonal,
vertical and right diagonal corresponding to (00, 450, 900 and
1350) and four pixel distance (d = 1, 3, 6 and 9). Hence, a
classification is performed using each feature vector and linear
discriminate analysis. According to Marti et al. [20], GLCMs
are frequently used in computer vision obtaining satisfactory
results as texture classifiers in different applications. Their
approach uses mutual information with the purpose to calculate
the amount of mutual information between images using
histograms distributions obtained by grey-level co-occurrence
matrices. Blot and Zwiggelaar [21, 22] proposed two approaches
based in detection and enhancement of structures in images
using GLCM. The purpose is to compare the difference between
these two matrices obtaining a probability estimate of the
abnormal image structures in the ROI. Finally, another study
based on background texture extraction for classification of Blot
and Zwiggelaar [23] presented their work where there is a
statistical difference between GLCM for image regions that
include image structures and regions that only contain
background texture which is provided by a classification in
mammograms. In 2003, different approaches based on co-
occurrences matrix as a feature descriptors extraction were
developed. Houssay et al. [24] presented a neuro-fuzzy model
for fast detection of candidate circumscribed masses in
mammograms and texture features are estimated using co-
occurrence matrices which are used to train the neuro-fuzzy
model. On the other hand, Marti et al. [25] proposed a
supervised method for the segmentation of masses in
mammographic images using texture features which present a
homogeneous behaviour inside the selected region.
Jirari [26] proposes an intelligent Computer-Aided Detection
system (CAD) by constructing five co-occurrence matrices at
different distances for each suspicious region. A different
number of statistical features are used to train and test the Radial
Basis neural network. Another work is presented by Lena et al.
[27] with the study of a multi-resolution texture feature of
second order statistics were extracted from spatial GLCM using
different orientations and distances.
Recent studies, Karahaliou et al. [28] investigate whether texture
properties of the tissue surrounding micro-calcifications using a
wavelet transform. Thirteen textural features were calculated
from four GLCMs. Finally, Lyra et al. [29] study how to
identify breast tissue quality data quantification using a CAD
system, where images categorized using the BIRADS breast
density index. The texture features were derived for each sub-
region from an averaged gray- level co-occurrence matrix
(GLCM). Karahaliou et al. [30] Gray-level texture and wavelet
coefficient texture features at three decomposition levels are
extracted from surrounding tissue regions of interest.
6.1 Grey-Level Co-Occurrence Matrices:
The Statistics of grey-level histograms give parameters for each
processed region but do not provide any information about the
repeating nature of texture. According to Beichel and Sonka
[31], the occurrence of gray-level configuration may be
described by matrices of relative frequencies, called co-
occurrence matrices. Hence, the GLCM is a tabulation of how
often different combinations of pixel brightness values (grey
levels) occur in an image. GLCM are constructed by observing
pairs of image cells distance d from each other and incrementing
the matrix position corresponding to the grey level of both cells.
This allows us to derive four matrices for each given distance: 0,
P (450, d), P (900, d), and P (1350, d). For instance, P (00; d) is
defined as follows:
P ((00
), d (a, b)) = | {((k, l), (m, n)) ∈D:
k – m = 0, |l – n| = d, f(k, l) = a, f(m, n) = b}|
Where each P value is the number of times that: f(x1, y1) = i,
f(x2, y2) = j, |x1 - x2| = d and y1 = y2 append simultaneously in

__________________________________________________________________________________________
the image. P (450
, d), P (900
, d), P (1350
, d) are defined
similarly:
P ((450
), d (a, b)) = |f ((k, l); (m, n)) ∈D:
(k - m = d, l - n = - d) OR (k - m = d; l - n = d), f (k, l) = a,
f (m, n) = b}|
P ((900
), d (a, b)) = | {((k, l), (m, n)) ∈D:
|k – m| = d, l - n = 0, f (k, l) = a, f (m, n) = b}|
P ((1350
), d (a, b)) = | f ((k, l); (m, n)) ∈D:
(k - m = d, l - n = d) OR (k - m = - d, l - n = -d), f (k, l) = a, f
(m, n) = b}|
A co-occurrence matrix contains the frequency of a certain pair
of pixels repetition in an image. According to the previous
formulas the parameters needed are the follows:
Number of grey levels: Normally, it is used a grayscale image of
256 grey levels, which means a high computational cost because
all possible pixel pairs must be taken into account. The solution
is to generate the matrix reducing the number of grayscales, and
so the number of possible pixel combinations. The co-
occurrence matrix is always square with the same
dimensionality as the number of grey-levels chosen.
Distance between pixels (d): the co-occurrence matrix stores the
number of times that a certain pair of pixels is found in the
image. Normally the pair of pixels are just neighbors, but the
matrix could also be computed analyzing the relation between
non consecutive pixels. Thus a distance between pixels must be
previously defined.
Angle (θ ): Similarly to the distance it is necessary to define the
direction of the pair of pixels. The most common directions are
00, 450, 900, 1350 and its symmetric equivalents. Figure 1
shows an example of how we can construct a co-occurrence
matrix with eight grey levels, computed using one for distance
between pixels and zero degrees for the direction. In this case,
the element (1, 1) of C matrix is equivalent to 1 because it has
been found only one occurrence in the original image f. Another
example is shown in the Figure 1. On the element (6, 2), where
there are three occurrences because a pixel with a value of 6 has
a pixel valued 2 immediately to its right. The other elements of
C are computed in the same way.
Figure1. How to generate a co-occurrence matrix
The co-occurrence matrix has some properties about the spatial
distribution of the gray levels in the texture image. Haralick [31]
proposed descriptors used for characterizing co-occurrence
matrices of size K x K. The term Pij is the ijth term of C divided
by the sum of the elements C.
7. CLUSTERING ALGORITHM
The main objective in cluster analysis is to group objects that are
similar in one cluster and separate objects that are dissimilar by
assigning them to different clusters. One of the most popular
clustering methods is K-Means clustering algorithm. It classifies
object to a pre-defined number of clusters, which is given by the
user (assume K clusters). The idea is to choose random cluster
centres, one for each cluster. These centres are preferred to be as
far as possible from each other. In this algorithm mostly
Euclidean distance is used to find distance between data points
and centroids [7]. The Euclidean distance between two multi-
dimensional data points X = (x1, x2, x3, ..., xm) and Y = (y1,
y2, y3, ..., ym) is described as follows:
( )∑=
−=
n
i
ji yxYXD
0
2
),(
The K-Means method aims to minimize the sum of squared
distances between all points and the cluster centre. This
procedure consists of the following steps, as described below.
7.1 K-Means Algorithm:
Require: D = {d1, d2, d3, ..., dn } // Set of n data points.
K - Number of desired clusters
Ensure: A set of K clusters.
Steps-1: Arbitrarily choose k data points from D as initial
centroids;
Steps-2: Repeat: Assign each point di to the cluster which has
the closest centroid;
Calculate the new mean for each cluster;
Steps-3: Until convergence criteria is met.
Though the K-Means algorithm is simple, it has some
drawbacks of quality of the final clustering, since it highly
depends on the arbitrary selection of the initial centroids. Data
clustering is the process of dividing data elements into classes or
clusters so that items in the same class are as similar as possible,
and items in different classes are as dissimilar as possible.
Depending on the nature of the data and the purpose for which
clustering is being used, different measures of similarity may be
used to place items into classes, where the similarity measure
controls how the clusters are formed. Some examples of
measures that can be used as in clustering include distance,
connectivity, and intensity.

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In hard clustering, data is divided into distinct clusters, where
each data element belongs to exactly one cluster. In fuzzy
clustering (also referred to as soft clustering), data elements can
belong to more than one cluster, and associated with each
element is a set of membership levels. These indicate the
strength of the association between that data element and a
particular cluster. Fuzzy clustering is a process of assigning
these membership levels, and then using them to assign data
elements to one or more clusters.
7.2 Fuzzy C-Means Algorithm
Input: Dataset X of n objects with d features, value of K and
fuzzification value m >1
Output: Membership matrix Uij for n objects and K clusters
Procedure:
Step-1: Declare a membership matrix U of size Kn× .
Step-2: Generate K cluster centroids randomly within the range
of the data or select K objects randomly as initial
cluster centroids. Let the centroids be c1, c2,…, cK.
Step-3: Calculate the distance measure jiij cxd −= using
Euclidean distance, for all cluster
centroids jc , , K,,j K21= and data
objects , n,,ixi K21, = .
Step-4: Compute the Fuzzy membership matrix ijU















≠∈=
∉
=
=
∑
∑∀
∈
=
−
−
≤≤
≤≤
Ij
iiij
i
i
K
i
m
ij
m
ij
ij
Kj
ni
IIjU
Ij
I
d
d
U
φ
φ
,,1
,0
,
)(
)(
1
1
1
1
1
1
1
where
{ }0;1
1
=≤≤=
≤≤∀
ij
ni
i dKjjI
Step-5: Compute new cluster centroids jc
∑
∑
=
=
≤≤
=∀ n
i
m
ij
n
i
i
m
ij
j
Kj
U
xU
c
1
1
1
)(
)(
Step-6: Repeat steps 3 to 5 until convergence.
7.3 Rough K-Means Clustering
Lingras proposed Rough K-Means (RKM) algorithm
by incorporating rough sets into K-Means
algorithm
RKM algorithm does not verify all the properties of
rough set theory, but uses the following basic
properties:
Property-1: a data object can be a member of one lower
approximation at most.
Property-2: a data object that is a member of the lower
approximation of a cluster is also member of the
upper approximation of the same cluster.
Property-3: a data object that does not belong to any lower
approximation is a member of at least two upper
approximations.
According to the above three properties, the lower
approximation is a subset of the upper approximation
The difference between upper and lower approximation is called
boundary region, which contains objects in multiple clusters
The membership of each object in lower and upper
approximation is determined by three parameters Wl,
Wu and ε
The parameters Wl and Wu correspond to the relative
importance of lower and upper bounds, and Wl + Wu =
1
The ε is a threshold parameter used to control the size
of boundary region
Input: Dataset of n objects with d features, number of clusters
K and values of parameters Wlower, Wupper, and
epsilon.
Output: Lower approximation U (K) and Upper
approximation )(KU of K Clusters.
Procedure:
Step1: Randomly assign each data object one lower
approximation U (K). By property 2, the data object
also belongs to upper approximation )(KU of the
same Cluster.
Step 2: Compute Cluster Centroids Cj
If φ≠)(KU and φ=− )()( KUKU
)(
)(
KU
xj
C
KUx
j
∑
=
ε
Else
If φ≠)(KU and φ=− )()( KUKU

__________________________________________________________________________________________
Pre-Processing
Feature Extraction
Clustering
Image Segmentation
Image Database
)()(
))()((
KUKU
x
C
KUKUx j
j
−
=
∑ −ε
Else
)()()(
))()(()(
KUKU
x
W
KU
x
WC
KUKUx j
u
KUx
j
lj
−
×+×=
∑∑ −εε
Step 3: Assign each object to the lower approximation U (K)
or upper approximation )(KU of cluster i cluster
respectively. For each object vector x, let d(x, cj) is
the distance between itself and the centroid of cluster
cj. Let d(x, cj) is min 1≤j≤K d(x, cj). The ratio d(x,
ci) /d(x, cj), 1≤i, j≤K is used to determine the
membership of x as follows:
Step 4: Repeat Steps 2 and 3 until convergence.
8. EXPERIMENTAL RESULTS
In this paper, the image samples are taken from the benchmark
MIAS database analyzing for analyzing the proposed method.
14 Haralick features were extracted using Gray level Co-
occurrence Matrix (GLCM). The sub-matrices of size 5 x 5 is
used for constructing GLCM at different angle with distance d =
1 and then feature are extracted. Further feature are clustered
into five groups by RKM algorithm, each groups is partition into
one segment, the segmented image show in Figure 3. The same
features are used to cluster using K- Means and FCM algorithms
with five groups each groups is partition into one segment, the
segmented image shown in Figure 4 and Figure 5. The quality of
segmentation result are measured using MSE and RMSE if the
error value becomes low means that the better results. Figure2
shows the proposed system.
Figure2. Proposed system
The MSE and RMSE values for the RKM segmentation, FCM
segmentation and K-Means segmentation are tabulated in table
I, table II, table III, table IV, table V and table VI respectively.
According to the segmentation errors means square error (MSE)
and root mean square error (RMSE) the GLCM at distance 1
and angle 450 gives the best result for all tested image. These
are demonstrated in Figure 5.
MDB01
7
MDB0
72
MDB0
18
MDB
0114
MDB
213
MDB
290
OriginalAngle00Angle450Angle900Angle1350
Figure3. Segmented Results in Rough K-Means Algorithm
MDB01
7
MDB0
72
MDB0
18
MDB
0114
MDB
213
MDB
290
OriginalAngle00Angle450

__________________________________________________________________________________________
Angle900Angle1350
Figure4. Segmented Results in Fuzzy C-Means Algorithm
MD
B017
MDB
072
MDB
018
MDB0
114
MDB
213
MDB
290
OriginalAngle00Angle450Angle900Angle1350
Figure5. Segmented Results in K-Means Algorithm
Performance Analysis on RKM segmentation in-order to error
rate (MSE)
Sample
Image
MSE
mdb0
17
mdb0
72
mdb0
18
mdb1
14
mdb2
13
mdb29
0
Angle
00
9.75e+
003
7.65e+
003
6.27e
+003
8.23e
+003
5.63e
+003
7.38e+
003
Angle
450
8.05e+
003
9.17e+
003
6.34e
+003
8.26e
+003
5.77e
+003
7.31e+
003
Angle
900
9.82e+
003
8.09e+
003
6.02e
+003
8.06e
+003
5.79e
+003
8.06e+
003
Angle
1350
9.11e+
003
7.15e+
003
5.74e
+003
1.10e
+004
6.18e
+003
6.91e+
003
Performance Analysis on RKM segmentation in-order to error
rate (RMSE)
Sample
Image
RMSE
mdb0
17
mdb07
2
mdb0
18
mdb1
14
mdb2
13
mdb29
0
Angle
00
98.76 87.51 79.19 90.73 75.04 85.91
Angle
450
89.17 95.77 79.63 90.91 75.97 85.54
Angle
900
99.15 89.97 77.60 92.75 76.13 89.79
Angle
1350
100.9
1
84.59 75.77 104.9
6
78.65 83.13
Performance Analysis on FCM segmentation in-order to error
rate (MSE)
Sa
mpl
e
Ima
ge
MSE
mdb0
17
mdb0
72
mdb0
18
mdb11
4
mdb2
13
mdb2
90
An
gle
00
1.08e+
004
1.18e+
004
1.41e+
004
8.77e+
003
8.84e
+003
1.10e
+004
An
gle
450
8.11e+
003
1.06e+
004
1.01e+
004
8.41e+
003
7.94e
+003
9.43e
+003
An
gle
900
1.11e+
004
1.30e+
004
1.19e+
004
9.97e+
003
9.86e
+003
1.07e
+004
An
gle
135
0
1.16e+
004
1.29e+
004
1.10e+
004
1.17e+
004
1.01e
+004
1.09e
+004
Performance Analysis on FCM segmentation in-order to error
rate (RMSE)
Sa
mpl
e
Ima
ge
RMSE
mdb0
17
mdb0
72
mdb0
18
mdb11
4
mdb2
13
mdb2
90
An
gle
00
104.17 109.00 118.99 93.68 94.05 105.9
9
An
gle
450
90.08 102.99 100.92 91.75 89.10 97.11
An
gle
900
105.78 114.08 109.20 99.89 99.31 103.7
1
An
gle
135
0
107.83 113.58 105.20 108.32 100.6
1
104.6
6

__________________________________________________________________________________________
Performance Analysis on K-Means segmentation in-order to
error rate (MSE)
Sa
mpl
e
Ima
ge
MSE
mdb0
17
mdb0
72
mdb0
18
mdb11
4
mdb2
13
mdb2
90
An
gle
00
1.24e+
004
1.61e+
004
1.56e+
004
1.31e+
004
1.15e
+004
1.18e
+004
An
gle
450
1.18e+
004
1.24e+
004
1.20e+
004
1.05e+
004
1.03e
+004
1.08e
+004
An
gle
900
1.19e+
004
1.82e+
004
1.27e+
004
1.07e+
004
1.06e
+004
1.18e
+004
An
gle
135
0
1.25e+
004
1.86e+
004
1.24e+
004
1.28e+
004
1.15e
+004
1.24e
+004
Performance Analysis on K-Means segmentation in-order to
error rate (RMSE)
Sa
mpl
e
Ima
ge
RMSE
mdb0
17
mdb0
72
mdb0
18
mdb11
4
mdb2
13
mdb2
90
An
gle
00
111.61 127.26 119.82 114.64 107.2
7
108.9
1
An
gle
450
108.97 111.41 109.81 102.23 101.8
5
104.2
6
An
gle
900
109.34 135.16 112.85 103.77 103.2
9
108.9
3
An
gle
135
0
111.99 136.69 111.66 113.55 107.3
8
111.5
8
Mdb017 Mdb072 Mdb018 Mdb114 Mdb213 Mdb290
5,000
6,000
7,000
8,000
9,000
10,000
11,000
Images
Errorrate(MSE)
0
45
90
135
(a)
Mdb017 Mdb072 Mdb018 Mdb114 Mdb213 Mdb290
70
75
80
85
90
95
100
105
110
115
120
Images
Errorrate(RMSE)
(b)
Mdb 017 Mdb 072 Mdb 018 Mdb 114 Mdb 213 Mdb 290
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
x 10
4
Images
ErrorRate(MSE)
0
45
90
135
(c)
85
90
95
100
105
110
115
120
Images
Errorrate(RMSE)
0
45
90
135
(d)

__________________________________________________________________________________________
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
x 10
4
Images
Errorrate(MSE)
0
45
90
135
(e)
85
90
95
100
105
110
115
120
125
130
135
140
Images
Errorrate(RMSE)
0
45
90
135
(f)
Figure6. Performance Analysis on Error rates in (a) MSE (b)
RMSE RKM algorithm (c) MSE (d) RMSE FCM Algorithm, (e)
MSE (f) RMSE K-Means Algorithm
CONCLUSIONS
In this paper, Rough K-Means algorithm (RKM) is proposed for
mammogram image segmentation. The 14 Haralick features are
extracted from mammogram image using Gray Level Co-
occurrence Matrix (GLCM) for different angles. The features
are clustered by K-Means, Fuzzy C-Means (FCM) and RKM
algorithms inorder to segment the region of interests for further
classification. The performance of the RKM segmentation is
evaluated using MSE and RMSE measures. The proposed
segmentation algorithm is compared with K-Means algorithm
and FCM algorithm. It was observed that RKM segmentation
algorithm out performs the benchmark K-Means algorithm and
FCM algorithm. Further the resultant mammogram can be used
for the detection of abnormalities in human breast like
calcification, circumscribed lesions etc. This is the direction for
further research.
ACKNOWLEDGMENTS
The second author immensely acknowledges the UGC, New
Delhi for partial financial assistance under UGC-SAP (DRS)
Grant No. F.3-50/2011
The first and third authors immensely acknowledge the partial
financial assistance under University Research Fellowship,
Periyar University, Salem
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BIOGRAPHIES
Subash Chandra Boss Rajaraman was born
in 1985 at Villuppuram District, Tamilnadu,
India. He is received the Master of Science in
Computer Science in 2009 from Pondicherry
University, Pondicherry, India. He obtained his
M.Phil (Computer Science) Degree from
Periyar University, Salem, Tamilnadu, India in 2010. Currently
he is doing fulltime Ph.D., Periyar University, Salem,
Tamilnadu, India. His area of interests includes Medical Image
Processing, Data Mining, Neural Network, Fuzzy logic, and
Rough Set.
Thangavel Kuttiyannan was born in 1964 at
Namakkal, Tamilnadu, India. He received his
Master of Science from the Department of
Mathematics, Bharathidasan University in 1986,
and Master of Computer Applications Degree
from Madurai Kamaraj University, India in
2001. He obtained his Ph.D. Degree from the Department of
Mathematics, Gandhigram Rural Institute-Deemed University,
Gandhigram, India in 1999. Currently he is working as
Professor and Head, Department of Computer Science, Periyar
University, Salem. He is a recipient of Tamilnadu Scientist
award for the year 2009 and Sir C.V.Raman award for the year
2013. His area of interests includes Medical Image Processing,
Data Mining, Artificial Intelligence, Neural Network, Fuzzy
logic, and Rough Set.

__________________________________________________________________________________________
Arul Pon Daniel Thiyoder was born at
Tuticorin District, Tamil Nadu, India, in 1986.
He received the Master of Computer
Applications degree from the Bharathidasan
University, Tiruchirapally, TN, India, and
Master of Business Administrations in Human
Resource degree from the Periyar University, Salem, TN, India,
in 2009. He is currently pursuing the Ph.D. degree with the
Department of Computer Science, Periyar University, Salem,
TN, India. His research interests include data mining, image
processing, array processing, signal processing and artificial
intelligence.

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