Segmentation of Brain MR Images for Tumor Extraction by Combining Kmeans Clustering and Perona-Malik Anisotropic Diffusion Model

M. Masroor Ahmed & Dzulkifli Bin Mohammad
International Journal of Image Processing, Volume (2) : Issue(1) 27
Segmentation of Brain MR Images for Tumor
Extraction by Combining Kmeans Clustering and
Perona-Malik Anisotropic Diffusion Model
M. Masroor Ahmed masroorahmed@gmail.com
Faculty of Computer Science & Information System
University Teknologi Malaysia
Johor Bahru, 81310, Malaysia
Dzulkifli Bin Mohamad dzulkifli@utm.my
Faculty of Computer Science & Information System
University Teknologi Malaysia
Johor Bahru, 81310, Malaysia
Abstract
Segmentation of images holds an important position in the area of image
processing. It becomes more important while typically dealing with medical
images where pre-surgery and post surgery decisions are required for the
purpose of initiating and speeding up the recovery process [5] Computer aided
detection of abnormal growth of tissues is primarily motivated by the necessity of
achieving maximum possible accuracy. Manual segmentation of these abnormal
tissues cannot be compared with modern day’s high speed computing machines
which enable us to visually observe the volume and location of unwanted tissues.
A well known segmentation problem within MRI is the task of labeling voxels
according to their tissue type which include White Matter (WM), Grey Matter
(GM) , Cerebrospinal Fluid (CSF) and sometimes pathological tissues like tumor
etc. This paper describes an efficient method for automatic brain tumor
segmentation for the extraction of tumor tissues from MR images. It combines
Perona and Malik anisotropic diffusion model for image enhancement and
Kmeans clustering technique for grouping tissues belonging to a specific group.
The proposed method uses T1, T2 and PD weighted gray level intensity images.
The proposed technique produced appreciative results
Keywords: White Matter (WM), Gray Matter (GM), Cerebrospinal Fluid (CSF)
1. INTRODUCTION
The developments in the application of information technology have completely changed the
world. The obvious reason for the introduction of computer systems is: reliability, accuracy,
simplicity and ease of use. Besides, the customization and optimization features of a computer
system stand among the major driving forces in adopting and subsequently strengthening the
computer aided systems. In medical imaging, an image is captured, digitized and processed for
doing segmentation and for extracting important information. Manual segmentation is an alternate
method for segmenting an image. This method is not only tedious and time consuming, but also

produces inaccurate results. Segmentation by experts is variable [16]. Therefore, there is a strong
need to have some efficient computer based system that accurately defines the boundaries of
brain tissues along with minimizing the chances of user interaction with the system [3].
Additionally, manual segmentation process require at least three hours to complete [1] According
to [2] the traditional methods for measuring tumor volumes are not reliable and are error
sensitive.
2. PREVIOUS WORK
Various segmentation methods have been cited in the literature for improving the segmentation
processes and for introducing maximum possible reliability, for example:
2.1 Segmentation by Thresholding
Thresholding method is frequently used for image segmentation. This is simple and effective
segmentation method for images with different intensities. [6] The technique basically attempts for
finding a threshold value, which enables the classification of pixels into different categories. A
major weakness of this segmentation mode is that: it generates only two classes. Therefore, this
method fails to deal with multichannel images. Beside, it also ignores the spatial characteristics
due to which an image becomes noise sensitive and undergoes intensity in-homogeneity
problem, which are expected to be found in MRI. Both these features create the possibility for
corrupting the histogram of the image. For overcoming these problems various versions of
thresholding technique have been introduced that segments medical images by using the
information based on local intensities and connectivity [7]. Though this is a simple technique, still
there are some factors that can complicate the thresholding operation, for example, non-
stationary and correlated noise, ambient illumination, busyness of gray levels within the object
and its background, inadequate contrast, and object size not commensurate with the scene. [8].
[9] introduced a new image thresholding method based on the divergence function. In this
method, the objective function is constructed using the divergence function between the classes,
the object and the background . The required threshold is found where this divergence function
shows a global minimum.
2.2 Region Growing Method
According to [10] Due to high reliability and accurate measurement of the dimensions and
location of tumor, MRI is frequently used for observing brain pathologies. Previously, region
growing and shape based methods were heavily relied upon for observing the brain pathologies.
[11] Proposed a Bayes-based region growing algorithm that estimates parameters by studying
characteristics in local regions and constructs the Bayes factor as a classifying criterion. The
technique is not fully automatic, i.e. it requires user interaction for the selection of a seed and
secondly the method fails in producing acceptable results in a natural image. It only works in
homogeneous areas. Since this technique is noise sensitive, therefore, the extracted regions
might have holes or even some discontinuities [7] Shape based method provides an alternative
approach for the segmentation of brain tumor. But the degree of freedom for application of this
method is limited too. The algorithm demands an initial contour plan for extracting the region of
interest. Therefore, like region growing approach, this method is also semi automatic. Both of
these methods are error sensitive because, an improper or false description of initial plan and
wrong selection of the seed image will lead to disastrous results. Statistical methods and fuzzy
logic approaches seems to be reliable and are the best candidates for the replacement of the
above mentioned techniques.
2.3 Supervised and Un-Supervised Segmentation Methods.
Supervised and un-supervised methods for image processing are frequently applied [3] [14]. [12]
Presents a technically detailed review of these techniques. [13] Attempted to segment the volume
as a whole using KNN and both hard and fuzzy c-means clustering. Results showed, however,
that there appears to be enough data non-uniformity between slices to prevent satisfactory

segmentation. Supervised classification enables us to have sufficient known pixels to generate
representative parameters for each class of interest. In an un-supervised classification pre hand
knowledge of classes is not required. It usually employees some clustering algorithm for
classifying an image data. According to [14] KNN, ML and Parzen window classifiers are
supervised classification algorithm. Whereas, un-supervised classification algorithm includes: K-
Means, minimum distance, maximum distance and hierarchical clustering etc.
3 METHODOLOGY
A brain Image consists of four regions i.e. gray matter (GM), white matter (WM), cerebrospinal
fluid (CSF) and background. These regions can be considered as four different classes.
Therefore, an input image needs to be divided into these four classes. In order to avoid the
chances of misclassification, the outer eleptical shaped object should be removed. By removing
this object we will get rid of non brain tissues and will be left with only soft tissues. In this
experiment we have used T1, T2 and PD weighted brain MRIs. These images posses same size
and same pixel intensity values. The pixels from the image under consideration is supposed to be
grouped in any one of the aforementioned class. Finally, by applying certain post processing
operations, the tumerous region can be extracted. Figure 1 shows the methodology of this work.
The process uses Kmeans algorithm for solving clustering problem this algorithm aims at
minimizing an objective function, in this case a squared error function. Mathematically, this
objective function can be represented as:
J = ( ) 2
1 1
k x
j
i j
j i
x c
= =
−∑∑P P
where
( ) 2j
i jx c−P P is a chosen distance measure between a data point xi
(j)
and the cluster
centre cj, is an indicator of the distance of the n data points from their respective cluster centres.
Image is read from database. The image contains the skull tissues. These tissues are non brain
elements. Therefore, they should be removed in the preprocessing step. The presence os these
tissues might lead to misclassification.
Figure 2 shows an image of the brain with skull seen as an outer eliptical ring. In figure 3 this
elitical ring is removed and we are left with only soft tissues. This is done by employing the
following morphological function, i.e. erosion and dilation. Mathematically, these functions can be
expressed as:
AӨ B = { w : Bw ⊆ A}
A⊕ B = x
x B
A
∈
U

FIGURE 1: Methodology.
FIGURE 2: Image with Outer Ring (Skull) FIGURE 3: Removing Skull Tissues
To test the algorithm, white guassian noise is added to the input image. This image is then
processed for enhancement. Perona and Malik [17] model is used for this purpose. This model
uses partial differential equation for image denoising and enhancement. The model smooths the
image without loosing important details with the help of following mathematical reation [15].
Read Image Database
Image Enhancement
Skull Stripping
Classification
Preprocessing
Extracting WM, GM,
CSF and Tumor
Morphological
Operations
Accumulation of
Tumor Volume
Post processing

.[ ( , , ) ] ( ( , , ) )It f x y t I div f x y y I=∇ ∇ = ∇
I(x, y, t) is the intensity value of a pixel at sampling position (x, y) and scale t and f(x, y, t) is the
diffusivity acting on the system. The diffusivity function in Peronan and Malik mode is given by the
folwing mathematical relation
2
2 2
1
( , , ) ( )
1 /
f x y t f
k
= ∇ =
+ ∇
P P
P P
FIGURE 4: Noisy Image FIGURE 5: Enhanced Image
4 RESULTS AND CONSLUSION
It has been observed that when Perona and Malik model is combined with Kmeans algorithm, it
produces reliable results. Due to un-supervised nature of the approach, the proposed system is
efficient and is less error sensitve.
a b c d e
f g h i j
FIGURE 6 (a) Original Image (b) Skull Removed (c) Segmented mage (d) Extracting WM (e) WM after Intensity Correction (f)
Extracting GM (g) GM after Intensity Correction (h) Removing Tumor (i) Tumor Volume (j) Erosion
It can be deduced from the results that un-supervised segmentation methods are better than the
supervised segmentation methods. Becuase for using supervised segmentation method a lot of
pre-processing is needed. More importantly, the supervised segmentation method requires
considerable amount of training and testing data which comparitively complicates the process.
Whereas, this study can be applied to the minimal amont of data with reliable results. However, it
may be noted that, the use of K-Means clustering method is fairly simple when compared with

frequently used fuzzy clustering methods. Efficiency and providing simple output are fundamental
features of K-Means clustering method [18].To check the accuracy of the proposed method,
mean and standard deviations of clean image, noisy image containing white guassian noise and
enhanced image is drawn in Figure 7.
a b c
d e f
Figure 7: (a) Deleting normal tissues from enhanced MRI slice (b)
Segmentation of enhanced MRI slice (c) Extraction of tumor (d) Noisy
image showing only normal tissues (e) Segmentation of noisy image (f)
Deleting normal tissues and retaining tumor cells.
a b
c d
Figure 8: (a) Mean and Standard Deviations of Clean, Noisy and Enhanced Image (b) Mean and Standard
Deviations of Noisy and Enhanced Image (c) Mean and Standard Deviations of clean and Enhanced Image
(d) Mean and Standard Deviations of clean and Noisy Image
Figure 7 shows some results from an image enhanced by Perona-Malik anisotropic
diffusion model and results from an image corrupted with with guassian noise. There is a
significant difference in both the results. Tumor extracted from a noisy image marks
various portions of the MR slice which even contain the normal tissues. The results
obtained from enhanced image and the clean image are almost similar. The accuracy of

the proposed method can be deduced from Figure 8 in which mean and standard
deviations of MR image in various combinations is shown. Due to very less amount of
noise, mean and standard deviations plotted in Figure 8 (d) shows almost the same range.
5. ACKNOWLWDGEMENTS
We would like to extend our thanks to “ Whole Brain Atlas“ for MR images.
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