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Tumor Extraction from MRI of Human Head Scan using Genetic K-Means
Algorithm and Mean Absolute Percentage Error
T. Kalaiselvi1 and S. Karthigai Selvi2
Assistant Professor1, Research Scholar2
Department of Computer Science and Applications
The Gandhigram Rural Institute – Deemed University, Tamilnadu India.
kalaiselvi.gri@gmail.com, karthigachandru@gmail.com
Abstract
The proposed work uses Genetic K-Means algorithm
to extract brain tumor from magnetic resonance imaging
head scan. This paper introduces an error based fitness
function (Mean absolute percentage error) to obtain the
effectiveness in tumor extraction. The abnormal slices
automatically discriminated by the number of optimal
region from the output of Genetic K-Means algorithm.
Then the intensity based assumption extract the tumor
region separately. The fitness function selection avoids
the convergence of tumor with the normal brain pixels.
The results were compared with the existing conventional
algorithm which was used genetic K-Means for object
segmentation from images.
Keywords: Genetic K-Means, MRI, tumor.
1. Introduction
The Human brain is an incredibly complex organ. In
some situations, the brain cells will continue to divide
more numbers. It is known as primary brain tumor. The
frequent counting of tumor tissues helps to grade the
abnormality, tumor assessment and therapy [1]. For this
process, the physicians require imaging technique.
Magnetic resonance imaging (MRI) produces clear
images due to its excellent spatial resolution. It has
various imaging protocols. The fluid attenuated inversion
recovery (FLAIR) imaging protocol enables better
delineation of the tumor and its surrounding tissues [2]. It
plays an important role in the evaluation of tumor size
and pathology. The manual assessment of tumor tissues
from numerous slices of a patient makes tired the
physicians. That emerges an automatic computerized
method for tumor extraction. It can be potentially
reduced the diagnosing time of the physicians.
Recently, machine learning and clustering techniques
are used as the efficient models for brain image
segmentation [3]. The machine learning techniques
require, several learning rules, a considerable amount of
training and testing data. Sometimes, the training data are
not suitable for the unknown data set. Reza et al. used a
classical random forest for voxel classification with
texture features [4]. The model yielded 88% - 92% of
similarity measure for some set of data volumes, but the
algorithm provided 71% - 81% of similarity for some
other datasets [5].
In the clustering methods, the pixels of an image are
sorted according to the intensity values. Then the pixels
are clustered according to the predefined number of
clusters. Fuzzy C-means and K-means algorithms are
popular clustering techniques. However, the clustering
techniques require optimal centroid. Genetic algorithm
(GA) and ant colony optimizations are widely used to
detect the optimal centroid.
Generally, GA is used to generate valuable solutions
for hard optimization problems [6]. In nature, all
organisms consist of cells. In each cell, there is the same
set of chromosomes. Chromosome carries hereditary and
genetic information in long string of DNA called genes.
The gene frequencies tend to remain constant from
generation to generation when disturbing factors are not
present. Some habitatual processes disturb the natural
equilibrium of gene frequencies which is known as
mutation. It changes the DNA sequence. This natural
process was applied in optimization problems by Holland
in 1975 [7].
GA commenced with a set of solutions. Hierarchical
genetic algorithm and Fuzzy C-Means (FCM) have been
used to address the right number of regions in
meningioma subjects [8]. They selected the optimal
cluster centers using GA. Doborjeh used genetic K-
Means (GKM) algorithm to segment objects from an
image. The method used a new fitness function based on
length of the region and Euclidean distance between the
regions [9].
The intensity variation among various components of
brain in an MRI image depends on its tissue density and
MRI imaging modality [10]. In a 16-bit MRI scan, the
individual brain component may have more intensity
variation. Hence, the distance between each cluster and
number of pixels in a region are high in all regions.
Computational Methods, Communication Techniques and Informatics
ISBN: 978-81-933316-1-3 95
96
Hence, the proposed method uses a region error based
fitness function to avoid the region convergence.
In the proposed work, initial solutions are obtained by
using K-Means segmentation which is more popular and
a hard segmentation. It groups each pixel in a class [11].
The initial population is given as input to GA to detect
optimal number of regions. Then the tumor cluster is
extracted by a knowledge based technique.
The remaining part of the paper is organized as three
sections. Section 2 describes the proposed method,
section 3 discusses and compares the performance of the
proposed method with the existing GKM and finally the
section 4 concludes the results.
I. Method
The proposed method carries a six stage process such
as pre-processing, K-Means clustering, population
generation, parent selection, reproduction and tumor
extraction.
Stage 1: Pre-processing
Stage 2: Population Initiation by K-Means
Stage 3: Population Generation
Stage 4: Selection of parents
Stage 5: New generation estimation
Stage 6: Tumor extraction
2.1 Pre-processing
The varying scanner technology, acquisition speed
and signal to noise ratio cause noise in MRI images [12].
On account of this, pre-processing is required before
segmentation. In this method, the pre-processing stage
encompasses two phases. The first phase deals denoising
and the second phase deals image smoothening for each
2D slice. A wavelet based method performs well for
denoising without making artifacts [13]. It is employed
for denoising in the proposed method. Then a non local
means filter (NLM) is applied to minimize intra region
variability [14]. It compares pixel‘s intensity with its
neighbour and then adjusts the intensity of the pixel. It is
also crafted based on an anisotropic filter that helps in
preserving the edge details.
2.2 Population Initiation by K-Means
In order to cluster the entire pixels of an image into
several regions, K-Means clustering algorithm is used
here. In the slices, which contain brain ending part, the
pixel count is very less and also all pixels are
approximately of the same intensity. For such images, k-
means clusters all pixels in a group and leaves other
groups as empty. By using a few regions, some optimal
region detection is difficult. Hence, object segmentation
from a minimum number of pixel set is hard to achieve.
To overcome such difficulties, the proposed method
considers the slices with a hundred or more brain pixel
count. For clustering these pixels into nine groups using
K-Means algorithm, all non zero pixels are sorted in the
ascending order and considered as an array. Then nine
pixels were chosen from equal distance in the pixel array
as cluster centre (v).
A pixel x is chosen as the cluster member j, if the
intensity (xg) distance between this pixel and its center vj
is smaller than the distance between the other cluster
center vi. It is represented as
j i and1,2,...k ifor x x if , gg ijj vvcx
(1)
where k represents the number of clusters. Then
recalculate the cluster center vk for all clusters ck
(2)
where the norm |.| represents the number of members in
ck, sg represents the gray value of pixel ‗s‘ and ‗g‘ is a
member of ck . It will be processed iteratively until the
cluster center is constant. Finally, it gives ten clusters
such as nine brain pixels (foreground) and one
background. In order to ignore inappropriate clusters, the
genetic algorithm is employed. It converges and finalizes
the optimal number of regions.
2.3. Population Generation
2.3.1. Encoding
It represents the clusters as a chromosome. Each
gene of the chromosome indicates a separate cluster. K-
Means algorithm yields nine foreground clusters (r2-r10)
and one background clusters (r1). The K-Means
algorithm selects multiple seed points in the ascending
order of intensity value. Due to this fact, the successive
clusters may be the member of similar region. By
merging the successive clusters, more population can be
generated. Each cluster is considered as DNA (gene) of a
chromosome. Then the result of the merging clusters r2
and r3 (R= r2 U r3) and R is copied in the locations of
r2 and r3 to form a new chromosome called
chromosome 2. In the same manner, the clusters r4 and
r5 are merged and copied to form chromosome 3, the
clusters r6 and r7 are merged and copied to form
chromosome 4, the clusters r8 and r9 are copied and
merged to form chromosome 5. The last cluster r10
contains hyper intense pixels such as tumor. It may have
less dispersion. Hence, r10 is left without merging like
other clusters. Each cluster and its mean value are taken
for the remaining process. Finally, five chromosomes are
taken as initial population.
2.4. Selection of Parents
The objective is to minimize the disjoint clusters in
order to obtain the actual number of regions in an image.
k
c
k
kc
v
1
cs g
s
1
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A good pair of chromosome is selected to reproduce the
next generation. It is analyzed with the fitness function.
2.4.1. Fitness function
A variety of fitness functions have been proposed for
different object segmentation from images. However, the
universal objective function for brain tissue segmentation
is difficult. In all types of MR images, the tumor tissues
are different based on their intensity characteristics
instead of shape and size and such clusters are obtained
by mean based clustering technique. Hence, the mean
absolute percentage error is taken as fitness function (Ei).
Then the error is calculated as:
100
N
1
1
Np
i
i
p
iM
BM
E
(3)
where M represents the mean of genes (clusters) in a
chromosome, B represents the actual intensity of each
gene and Np is the number of pixels in a gene. |M-Bi|
achieves the absolute distance between each pixel in a
cluster and its mean. It produces the absolute mean
deviation error Ei of a gene. The maximum error in a
chromosome Fj is taken as:
1,2,...5j 1,2,...9,i where)( ij EMaxF
(4)
The maximum error represents the chromosome
containing inhomogeneous clusters. The Fj value of all
chromosomes is passed to the parent selection process.
2.4.2. Parent Selection
RWS approach is an ancient and popular method for
chromosome selection. In this approach, each individual
chromosome occupies a portion of the roulette wheel,
with respect to its fitness value. The larger portion of the
wheel has the highest priority to be selected. The fitness
value Fi is implemented in Eqn.(5) to get proportionate Pi
for each individual chromosome.
N
jj
i
iF
F
P
1
(5)
where N represents the number of the population, in this
method N=5. The better fitness value takes the higher
portion of the Roulette wheel. But the fitness function
calculates the error measure that recommends taking the
last two low priority chromosomes as two best parents
(P1 and P2) for next generation estimation.
The fitness value of P1 determines the continuity of
the process. If the fitness value of P1 is higher than the
previous iteration‘s best fitness value, the iteration will
be stopped abruptly.
2.5. New Generation Estimation
A new generation creation is the sequential process of
crossover and mutation.
2.5.1. Crossover
It distinguishes GA from other optimized techniques.
It ensures the information exchange takes place in such a
way that it selects genes from parent chromosomes and
creates a new offspring.
The crossover differs by determining the crossover
point [15]. Two crossover points (c1 and c2) are chosen
randomly. It splits the parental chromosomes P1 and P2
from the crossover points c1 to c2. Subsequently, a new
child genotype is created by appending the selected part
of the first parent with the selected part of the second
parent [15]. The regions between the crossover points in
P1 are appended to the parent P2 in the same location
that yields child 2. In the same manner, the genes
between the crossover points in P2 are appended to P1
that yields child1. These children are passed to mutation
operation.
2.5.2. Mutation
The mutation operation causes to change the region
label into one of its neighbours. Two genes were
randomly selected from a chromosome and merged with
its one of the neighbours. The neighbours were selected
using the region adjacency graph. It is given in Fig. 1.
Each region of a chromosome is considered as a node.
The Euclidean distance between the nodes is representing
its edges. The node which is in minimum distance is
taken as its neighbor. Then the selected neighbor is
merged with the gene. In Fig.1, the regions r6 and r7 have
less distance. Hence, the regions r6 and r7 are merged and
labeled as r6. In the same manner two regions were
mutated.
Figure 1. Mutation process: Region adjacency graph
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2.6 Tumor Extraction
The GA provides optimal number of regions in a brain
image as separate clusters. Among those clusters tumor
cluster is extracted from its mean value. In FLAIR
images, tumor region shows in hyper intense. Hence, the
clusters mean value is taken for this task. The cluster
which gives higher mean value is chosen as tumor
region.
2.7 Materials Used
For this experiment, 5 real high grade (HG) tumor
data sets were collected from the database which is
maintained by Dr. Kalaiselvi, T. and her team at The
Gandhigram Rural Institute Deemed University, India.
To ensure the performance of a segmentation task, the
algorithmic predicted result S is to be mapped with the
expert‘s annotation (ground truth) T with Dice similarity.
Dice is the measure of similarity between the predicted
result and the ground truth. It is defined as,
||||
|T S|2
11
11
TS
Dice
(6)
where |.| represents the number of pixels in the set.
3. Result and Discussion
The proposed method and GKM are coded using
Matlab R2013a in a Dual core2 laptop machine. The
experimental results are analysed in terms of qualitative
and quantitative measures such as Dice.
For complete tumor extraction, the performance of
genetic algorithm is very much important for obtaining
optimal clusters in FLAIR image. After applying the
genetic K-Means, the final decision about tumor region is
taken by considering the tumor appearance in FLAIR
images. A cluster, which quotes maximum mean value is
declared as tumor region.
During the experiment, four difficulties were
experienced. They are intensity variations in a tumor
region, low contrast, narrow and sharpen tumor region
and partial volume effect (PVF). A few sample images
are given in Fig. 2. In Fig. 2, the input FLAIR images are
given ro1, the experts results are given row 2, the results
of GKM and the proposed method are given in row 3 and
row 4 respectively. The column1 image is a low contrast
images. In this image, the neighbouring tumor tissues
original image Truth Segmented
original image Truth Segmented
original image Truth Segmented
Figure 2. Segmented results. Row1 shows the input FLAIR image, row2 shows the ground truth, row 3 and row 4 shows
the output of GKM and the proposed method.
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have the nearly same intensity of the tumor. The method
used the region adjacency graph in mutation process that
avoided the merging of neighbouring normal pixels with
the tumor cluster. The GKM method cannot avoid some
normal pixels close to the tumor boundary.
The Fig. 2, column 2 image has the tumor with ramp
edges and not having a perfect closed region. In the
experiment, the mutation process merged the normal
pixels with the tumor region after some iterations. In
such situtation, the chromosome rose higher error during
the fitness value calculation. Then the proposed method
immediately stopped the iteration and provided previous
iteration‘s result. Hence, the proposed method could be
avoided the cluster, which contains the tumor pixels
along with some other brain pixels. Next advantage is the
proposed method can perfectly cluster the tumor with its
ramp edges with the help of error based fitness function.
The Fig. 2, column 3 image is one of the samples of
PVE which shows the neighbouring pixels of the tumor
as tumor and have heterogeneity in the tumor region.
Initially, the tumor is clustered into separate regions,
finally it is merged and resulted as a single region in both
methods. The GKM method extracted the partial volume
pixels as tumor pixel, but the proposed method avoided
the erroneous pixel region and gave better result.
The Fig. 2, column 4 image has the heterogeneous
tumor region. The GKM method cannot extract tumor
completely due to its length based fitness function. The
region error differences were very low. Hence, the
proposed method can extract the tumor. In every
iteration, the crossover operation interchanged the
clusters between parent chromosomes. It also increased
the region error (fitness value) in all chromosomes.
Among the erroneous chromosomes, lower error
chromosome was selected after some iteration and the
tumor extracted significantly.
The quantitative results reveal the accurate
performance of the methods. The Dice value for some
sample images are given in Fig. 3. The image number is
given in x-axis, the Dice measures are given in y-axis.
The line chart shows that the proposed method gives
linear result for all images and also the Dice is higher
than the GKM for all images. However, complete tumor
extraction from entire volume is more challenging. The
complete tumor extraction for five volumes are given in
Fig. 4. In Fig. 4, y-axis represents the Dice measure. The
proposed method provided good result in all volumes.
The both quantitative and qualitative results ensure
the selection of the fitness function. In some ending
slices, the proposed method extracts tumor with normal
pixels it will be avoided in future.
4. Conclusion
The proposed-work used genetic K-Means
algorithm for tumor extraction from 16-bit MRI scan. It
used conventional method and introduced a error based
fitness function. The performance of the proposed work
was analyzed in terms of qualitative and quantitative
measures. It is also compared with the recent genetic K-
Means algorithm. The proposed method provided good
result in both measures.
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