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CHAPTER V
BRAIN TUMOR
DETECTION USING
HPACO
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CHAPTER 5
DETECTION OF BRAIN TUMOR REGION USING HYBRID
PARALLEL ANT COLONY OPTIMIZATION (HPACO) WITH FCM
(FUZZY C MEANS)
5.1 PREFACE
The Segmentation of Brain Tumor from Magnetic Resonance Image is an
important but time-consuming task performed by medical experts. The digital Image
processing community has developed several segmentation methods.
Four of the most common methods are:
1. Amplitude Thresholding
2. Texture Segmentation
3. Template Matching
4. Region-Growing Segmentation.
Segmentation is the second stage where Optimization forms an important part of
our day to day life. Many scientific, social, economic and engineering problems have
parameter that can be adjusted to produce a more desirable outcome. Over the years,
numerous techniques have been developed to solve such optimization. This study
investigates the most effective optimization method, known as Hybrid Parallel Ant
Colony Optimization (HPACO) is introduced in the field of Medical Image Processing.
Hybrid Parallel Ant Colony Optimization (HPACO) algorithm is a recent population-
based approach inspired by the observation of real Ant’s Colony and based upon their
collective behaviour.
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In HPACO, solutions of the problem are constructed within an iterative process,
by adding solution components to partial solutions. Each individual ant constructs a part
of the solution using an artificial pheromone, which reflects its experience accumulated
while solving the problem, and heuristic information dependent on the problem
FCM Algorithm is one of the popular Fuzzy Clustering algorithms which are
classified as constrained Soft Clustering algorithm. A Soft Clustering Algorithm finds a
soft partition of a given data set by which an element in the data set may partially belong
to multiple clusters.
The suspicious region is segmented using algorithm HPACO. A New CAD
System is developed for verification and comparison of brain tumor detection algorithm.
Hybrid Parallel Ant Colony Optimization determine the threshold value of given image
to select the initial cluster point then the clustering algorithm Fuzzy C Means calculates
the optimal threshold for the brain tumor segmentation.
5.2 FUZZY C MEANS
Segmentation is one of the first and most important tasks in image analysis and
computer vision. In the previous works, various methods have been proposed for object
segmentation and feature extraction, described in [67, 40]. However, the design of robust
and efficient segmentation algorithms is still a very challenging research topic, due to the
variety and complexity of images. Image segmentation is defined as the partitioning of
an image into nonoverlapped, consistent regions which are homogeneous in respect to
some characteristics such as intensity, color, tone, texture, etc.
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The image segmentation can be divided into four categories: (i) thresholding (ii)
clustering (iii) edge detection and (iv) region extraction. In this paper, a clustering
method for image segmentation will be considered.
Clustering is a process for classifying objects or patterns in such a way that
samples of the same cluster are more similar to one another than samples belonging to
different clusters. There are two main clustering strategies: the hard clustering scheme
and the fuzzy clustering scheme. The conventional hard clustering methods classify each
point of the data set just to one cluster. As a consequence, the results are often very crisp,
i.e., in image clustering each pixel of the image belongs just to one cluster.
However, in many real situations, issues such as limited spatial resolution, poor
contrast, overlapping intensities, noise and intensity in homogeneities reduce the
effectiveness o hard (crisp) clustering methods. Fuzzy set theory [75] has introduced the
idea of partial membership, described by a membership function. Fuzzy clustering, as a
soft segmentation method, has been widely studied and successfully applied in image
clustering and segmentation [53, 85, 90].
Among the fuzzy clustering methods, fuzzy c-means (FCM) algorithm
[89,150,151] is the most popular method used in image segmentation because it has
robust characteristics for ambiguity and can retain much more information than hard
segmentation methods [105,152]. Although the conventional FCM algorithm works well
on most noise-free images, it is very sensitive to noise and other imaging artifacts, since
it does not consider any information about spatial context.
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Smoothing step has been proposed in [124,130,146]. However, by using
smoothing filters important image details can be lost, especially boundaries or edges.
Moreover, there is no way to control the trade-off between smoothing and clustering.
Thus, many researchers have incorporated local spatial information into the original
FCM algorithm to improve the performance of image segmentation [109,136,153]
Noordam et al proposed a geometrically guided FCM (GG-FCM) algorithm, a
semi-supervised FCM technique, where a geometrical condition is used determined by
taking into account the local neighborhood of each pixel [93].
Pham modified the FCM objective function by including a spatial penalty on the
membership functions. The penalty term leads to an iterative algorithm, which is very
similar to the original FCM and allows the estimation of spatially smooth membership
functions [102,103,104].
Ahmed et al proposed FCM_S where the objective function of the classical FCM
is modified in order to compensate the intensity in homogeneity and allow the labelling
of a pixel to be influenced by the labels in its immediate neighborhood. One
disadvantage of FCM_S is that the neighborhood labelling is computed in each iteration
step, something that is very time-consuming [2, 3]. Chen and Zhang proposed FCM_S1
and FCM_S2, two variants of FCM_S algorithm in order to reduce the computational
time. These two algorithms introduced the extra mean and median-filtered image,
respectively, which can be computed in advance, to replace the neighborhood term of
FCM_S. Thus, the execution times of both FCM_S1 and FCM_S2 are considerably
reduced [19, 22].
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Szilagyi et al proposed the enhanced FCM (EnFCM) algorithm to accelerate the
image segmentation process. The structure of the EnFCM is different from that of
FCM_S and its variants. First, a linearly-weighted sum image is formed from both
original image and each pixel’s local neighborhood average gray level. Then clustering is
performed on the basis of the gray level histogram instead of pixels of the summed
image. Since, the number of gray levels in an image is generally much smaller than the
number of its pixels, the computational time of EnFCM algorithm is reduced, while the
quality of the segmented image is comparable to that of FCM_S [114,154]. More
recently, Cai et al. Proposed the fast generalized FCM algorithm (FGFCM) which
incorporates the spatial information, the intensity of the local pixel neighborhood and the
number of gray levels in an image. This algorithm forms a nonlinearly-weighted sum
image from both original image and its local spatial and gray level neighborhood. The
computational time of FGFCM is very small, since clustering is performed on the basis
of the gray level histogram. The quality of the segmented image is well enhanced [19].
Fuzzy C-Means (FCM) Algorithm
The fuzzy c-means (FCM) clustering algorithm was first introduced by
Dunn [40] and later extended by Bezdek [67]. The algorithm is an iterative
clustering method that produces an optimal partition by minimizing the
weighted within group sum of squared error objective function Jm .
( ) )1(2
1 1
ji
N
i
c
j
m
jim vxduJ -=åå= =
where thethi pixel is the center of the local window and the
thj pixel represents the
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set of the neighbors falling into the window around the thi pixel.
( )ji pp - are the coordinates of pixel i and ix is its gray level value. gsandll are two
scale factors playing a role similar to factor a in FCM, and is is defined
m
N IRxxxN =Ì= ),......,{ 21 is the data set in the m -dimensional vector space, N- is
the number of data items, c is the number of clusters with , jiNuc <£2 is the
degree of membership of ix in the thj cluster, m is the weighting exponent on each
fuzzy membership iv is the prototype of the center of cluster )(, 2
ji vxdj - is a
distance measure between object ix and cluster center jv A solution of the object
function mj can be obtained through an iterative process, which is carried as
follows
1) Set values for c, m ande .
2) Initialize the fuzzy partition matrix .)0(U
3) Set the loop counter 0=b .
4) Calculate the c cluster centers )(b
jv with )(bU .
( )
( ))2(
1
)(
1)(
å
å
=
==N
i
mb
ji
N
i
i
mb
ji
b
j
u
xu
v
5) Calculate the membership matrix)1( +bU .
)3(1
1
1/2
)1(
å=
-+
÷÷ø
öççè
æ=
c
k
m
ki
ji
b
j
d
du
6) If e<+ }max{ )1()( bb UU then stop, otherwise, set 1+= bb and go to step 4.
Figure 5.1 Fuzzy C Means Algorithm
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Figure 5.2 Flow Diagram for Fuzzy C Means Algorithm
Start
( )
( )å
å
=
==N
i
mb
ji
N
i
i
mb
jib
j
u
xu
v
1
)(
1)(
Initialize c, m ande
matrix .)0(U
)3(1
1
1/2
)1(
å=
-+
÷÷ø
öççè
æ=
c
k
m
ki
ji
b
j
d
du
max
{U(b)
U(b+1)
} < ɛ
Stop
Yes
No
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5.3 PREVIOUS WORK
Corina et al. studied Active Contour Model for segment the brain MRI images
successfully [27]. Mao et al. designed an automatic segmentation method using Fuzzy k-
means, Ant colony optimization for process the optimal labeling of the image pixels [78].
Dana et al. designed a method on 3D Variation Segmentation for process due to the high
diversity in appearance of tumor tissue from various patients [28,68]. Jayaram et al.
represented Fuzzy Connectedness and Fuzzy sets used to develop the concept of fuzzy
connectedness directly on the given image for facilitating the image segmentation
[60,61]. Hideki et al. specified a technique for Partition the image space into meaningful
regions [54].
Kabir et al. prescribed a method Markov random field model for segmenting
stroke lesions on MR Multi sequences [64]. Leung et al. presented Contour Deformable
Model for segmenting required region from MRI [76]. Marcel Prastawa said VALMET
Segmentation validation tool is used to detect intensity outliers and dispersion of the
normal brain tissue intensity clusters [79,80,81,82]. Tang et al. presented Multi
resolution image segmentation. For segmenting the brain tissue structure from MRI
[117]. Pierre et al. prescribed Atlas-based segmentation for Propagation of the labeled
structures on to the MRI [94,106]. Jayaram et al described a method on Evaluating
Image Segmentation Algorithm for segmenting objects from source image [60, 61].
Jaffrey et al designed a new method semi automatic segmentation method on volume
tracking for estimate tumor volume with process [62,63].
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5.4 SEGMENTATION BY HYBRID PARALLEL ANT COLONY
OPTIMIZATION ALGORITHM
The MRI image is stored in a two-dimensional matrix and a kernel is extracted
for each pixel. A unique label is assigned to the kernels having similar patterns. In the
labeling process, a label matrix is initialized with zeros. The size of the label matrix is
equal to the size of the MRI image. For each pixel in the image, the label value is stored
in the label matrix at the location corresponding to its central pixel coordinates in the
gray level image[26,36,37,38,39,46,146].
5.4.1 MARKVOV RANDOM FIELD
A pattern matrix is maintained to store the dissimilar patterns in the image. For
each pixel, a kernel is extracted and the kernel is compared with the patterns available in
the pattern matrix. Once it finds any matches the same label value is assigned to the
currently extracted kernel. .The labels are assigned integer values starting with one and
incremented by one whenever a new pattern occurs [71]. Finally the pattern matrix
contains all the dissimilar patterns in the image and the corresponding label values are
also extracted from the label matrix. For each pattern in the pattern matrix, the posterior
energy function value is calculated using the following formula.
( ) ( )9
å 2 2U x = { ([(y -μ) / (2*σ )]+ log(σ))+V x }i
i=1
Where, y is the intensity value of pixels in the kernel, m is the mean value of the
kernel, s is the standard deviation of the kernel, V is the potential function of the kernel
and x is the label of the pixel. If x1is equal to x2 in a kernel, then V (x) = b, otherwise 0,
where b is visibility relative parameter (b ≥ 0).
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The challenge of finding the Maximum A Posterior (MAP) estimate of the
segmentation is to search for the optimum label which minimizes the posterior energy
function U(x). In this section a new effective approach, HPACO is proposed for the
minimization of MAP estimation.
HPACO is applied to find the optimum label from the pattern matrix. Initially,
the dissimilar patterns, the corresponding labels and the MAP values are stored in a
solution matrix and the parameters such as number of iterations (NI), number of ants
(NA), initial pheromone value (T0) are assigned the values of 100, 20 and 0.005
respectively. Also the solution matrix contains separate columns for pheromone and flag
values of each ant. The flag value is used to indicate whether the kernel has been selected
previously or not. Initially all the flag values are set to zero and the pheromone values
are assigned T0. At the initial step, all the ants are assigned random kernels and the
pheromone values are updated.
The posterior energy function value for all the selected kernels from each ant is
extracted from the solution matrix. Compare the posterior energy function value for all
the selected kernels from each ant, to select the minimum value from the set, which is
known as ‘Local Minimum’ (Lmin) or ‘Iterations best’ solution. This local minimum
value is again compared with the ‘Global Minimum’ (Gmin). If the local minimum is
less than the global minimum, then the local minimum is assigned with the current global
minimum. Then the kernel that generates this local minimum value is selected and its
pheromone is updated.
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The pheromone value for the remaining kernels is updated. Thus the pheromone
values are updated globally. This procedure is repeated for all the image pixels. At the
final iteration, the Gmin has the optimum label of the image. The corresponding kernel is
selected from the pattern matrix. The intensity value of the center pixel in the kernel is
selected as optimum threshold value for segmentation. In the MRI image, the pixels
having lower intensity values than the threshold value are changed to zero. The entire
procedure is repeated for any number of times to obtain the more approximated value.
Step 1: Read the brain image or the stored in a two dimensional matrix.
Step 2: Divide the image to 3x3 labels (cells).
Step 3: For each label in the image, calculate the posterior energy U (x) value.
U(x)={Σ[(y-μ)2
/(2*σ2
)]+Σ log(σ)+ΣV(x)} Where
y = intensity value of pixels in the kernel, μ = mean value of the kernel,
σ = standard deviation of the kernel, V = potential function of the kernel, and
x = center pixel of the label. If x1 is equal to x2 in a kernel, then
V(x) = β, otherwise 0, where β is visibility relative parameter (β≥0).
Step 4: The posterior energy values of all the labels are stored in a separate matrix.
Step 5: HPACO System is used to minimize the posterior energy function. The
procedure is as follows:
Step 6: Initialize the values of number of iterations (N), number of ants (K) for colonies,
initialize number of colonies (M), initial pheromone value (T0), a constant value for
pheromone update (ρ). [Here, we are using N=20, K=10, M= 10, T0=0.001 and ρ=0.9].
Step 7: initliasition for each colonies. {
Step 8: slave colonies systems
{ colony 1, colony 2…. Colony M-1 }
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Algorithm of colony 1
Mij¬ Original Image
for each pixel in Mij
G ¬ kernel of the border pixel of size 3´3 from M
U ¬ fitness value; the posterior energy U (x) is calculated.
U (x) ={å[( y-m )2 / ( 2 * s2
)] +å log(s) + å V(x)}
end
N ¬ 50; K¬ 10; T0¬ 0.001; r ¬ 0.9
S ¬ {U(x),T0, flag} flag column mentions whether the pixels is selected by the ant
or not. Store the energy function values in S. Initialize all the pheromone values
with
T0=0.001. repeat for N times
for each pixel in Mij
for each ant
gi¬ a random kernel for each ant, which is not selected previously.
Tnew ¬ (1–r) * Told + r * T0 for gi
End Lmax ¬ max(Ui(x))
if (Lmax < Gmax) then Gmax = Lmax
g¬ Select the ant, whose solution is equal to local maximum
Tnew ¬ (1 – a) * Told + a * DTold, only for g
End , End
Similarly this algorithm is used to M-1 slave ant colonies and also master ant
colonies system
}
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Step 8: The final highest global value derived from slave ant colony system.
Step 9: Master colony system
Step 10: The master colony yield global optimum value
Step 11: compare to 8 and 10, the highest global optimum value treated as a
optimum threshold value.
The Gmin has the optimum label which minimizes the posterior energy function.
Step 12: The optimal value HPACO is used to select the initial cluster point.
FCM- HPACO Algorithm is the following:
Step 13: Calculate the cluster centers.
C = (N/2)1/2
Step 14: Compute the Euclidean distances
Dij = CCp – Cn
Step 15: Update the partition matrix
æ öç ÷è ø
å ij
kj
ij 2/(m-1)c
k=1
d
d
1U = (Repeat step 4) Until Max[ │Uij(k+1)-Uijk│] < € is
satisfied
Step 16: Calculate the average clustering points.
c c nn 2
iji i ij
i=1 i=1 j=1
C = J = U då åå
Step 17: Compute the adaptive threshold
Adaptive threshold =max (Adaptive threshold, ci ) i=1...n
Figure 5.3 HPACO with FCM
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In the MRI image, the pixels having lower intensity values than the adaptive
threshold value are changed to zero. The entire procedure is repeated for in the MRI
image, the pixels having lower intensity values than the adaptive threshold value are
changed to zero. The entire procedure is repeated for any number of times to obtain the
more approximated value.
5.5 IMPLEMENTATION OF HPACO WITH FCM
After completing all the process the generated output is given to the FCM as
input. The optimal value of HPACO through MRI Brain Image is given as an input for
FCM. The aim of FCM is to find cluster centres (centroids) that minimize dissimilarity
function.
The membership matrix (U) is randomly initialized as
c
ij
i=1
U =1;å
Where i is the number of cluster
j is the image data point
The dissimilarity function can be calculated with this equation
c c nn 2
iji i ij
i 1 i 1 j 1
C J U d= = =
= =å åå
Where
Uij - is between 0 and 1
Ci - is the centroid of cluster i
dij - is the Euclidean distance between ith and centriod (Ci ) and jth data
point
M - is a weighting exponent.
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To calculate Euclidean distance (dij)
Euclidean distance (dij) = Cluster center pixels - current neuron
dij = CCp – Cn
where
CCp - is the Cluster center pixels
Cn - is the current neuron
i.e. Number of clusters is computed as
C = (N/2)1/2
where
N= no. of pixels in image
To find the Minimum dissimilarity function can be computed as
ij
kj
ij 2/(m-1)c
k=1
d
d
1U =
æ öç ÷è ø
å
where
dij=|| xi -cj|| and dkj=|| xi –ck||
xi - is the ith of d- dimensional data
cj - is the d-dimensional center of the cluster x
so these iteration will stop when the condition
Max ij {│Uij(k+1)
-Uijk│} <€ is satisfied
where
€ - is a termination criterion between 0 and 1
K - is the iteration step
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The step of the FCM Algorithm has been listed
Step 1: Initialize U = Uij matrix
Step 2: At K step initialize centre vector C (k)
= C j taken from HPACO Clustering
Algorithm
Step 3: Update U (k)
, U (k+1)
, then compute the dissimilarity function
ij
kj
ij 2/(m-1)c
k=1
d
d
1U =
æ öç ÷è ø
å
If || U (k+1)
- U (k)
|| < € then stop. Otherwise return to step3.
Figure 5.4 FCM Algorithm
5.6 EXPERIMENTS AND RESULTS
The sliding window of 3×3, 5×5, 7×7, 9×9 and 11×11 are analyzed. In that 3×3
window is based on the high contrast value than 5×5, 7×7, 9×9, and 11×11. The
following table shows the adaptive threshold value, no. of pixels in the tumor region,
execution time and weight vector. The execution time in HPACO with FCM, the 3x3 is
14, 5x5 is 28, 7x7 is 25, 9x9 is 23 and 11x11 is 18 ,Adaptive threshold for HPACO with
FC M is 3x3 is 185, 5x5 is 164, 7x7 is 160, 9x9 is 148 and 11x11 is 139, the number of
segmented pixel in HPACO with FC M of 3x3 is 1000, 5x5 is 1995, 7x7 is 2285, 9x9 is
3445and 11x11 is 8881,Weight vector for HPACO with FCM is 3x3 is 14, 5x5 is 28, 7x7
is 25, 9x9 is 23 and 11x11 is 18 are shown in Fig 5.5.
CA
D S
YS
TE
M F
OR
AU
TO
MA
TIC
DE
TE
CT
IO
N O
F B
RA
IN
TU
MO
R T
HR
OU
GH
MR
I
BR
AIN
TU
MO
R D
ET
EC
TIO
N U
SIN
G H
PA
CO
162
Tab
le 5
.1 P
erfo
rm
an
ce
Evalu
ati
on
s of
HP
AC
O w
ith
FC
M
Val
ue/
Nei
ghb
orh
ood p
ixel
s 3x
3
5x
5
7x
7
9x
9
11x
11
Adap
tive
Thre
shold
185
164
160
148
139
Num
ber
of
Seg
men
ted
1000
1995
2285
3445
8881
Ex
ecuti
on T
ime
14
28
25
23
18
Wei
ght
14
28
25
23
28
CA
D S
YS
TE
M F
OR
AU
TO
MA
TIC
DE
TE
CT
IO
N O
F B
RA
IN
TU
MO
R T
HR
OU
GH
MR
I
BR
AIN
TU
MO
R D
ET
EC
TIO
N U
SIN
G H
PA
CO
163
Fig
ure
5.5
Per
form
an
ce E
va
luati
on
s of
HP
AC
O w
ith
FC
M
CA
D S
YS
TE
M F
OR
AU
TO
MA
TIC
DE
TE
CT
IO
N O
F B
RA
IN
TU
MO
R T
HR
OU
GH
MR
I
BR
AIN
TU
MO
R D
ET
EC
TIO
N U
SIN
G H
PA
CO
164
Tab
le 5
.2 C
om
para
tiv
e A
naly
sis
of
Exis
tin
g A
pp
roach
es
Auth
or
Typ
es o
f R
epre
senta
tion
Sli
din
g
win
dow
Val
ue
of
Wei
ght
Vec
tor
Tota
l N
o. of
Tum
or
val
ue
(pix
el)
Ex
ecuti
on
Tim
e
Ex
isti
ng A
pp
roac
h
HS
OM
- F
CM
3x
3
8
795
13.0
98
Ex
isti
ng A
pp
roac
h
GA
- F
CM
3x
3
13.6
1913
40
Pro
pose
d A
pp
roac
h
BL
OC
K B
AS
ED
TE
CH
NIQ
UE
5x
5
14
1000
14
Pro
pose
d A
pp
roac
h
HP
AC
O-
FC
M
5x
5
14
1000
14
Pro
pose
d A
pp
roac
h
PS
O-
FC
M
5x
5
14
1000
14
CA
D S
YS
TE
M F
OR
AU
TO
MA
TIC
DE
TE
CT
IO
N O
F B
RA
IN
TU
MO
R T
HR
OU
GH
MR
I
BR
AIN
TU
MO
R D
ET
EC
TIO
N U
SIN
G H
PA
CO
165
Fig
ure
5.6
C
om
para
tiv
e A
naly
sis
of
Exis
tin
g A
pp
roach
es
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The comparative analysis shows that proposed system has a much lower tumor
value and lesser execution time when compared to existing approach. The following
graph shows the performance analysis of HSOM, GA, HPACO with Fuzzy. It is clear
from the graph that the tumor and the execution time are much better when compared to
existing approach.
CA
D S
YS
TE
M F
OR
AU
TO
MA
TIC
DE
TE
CT
IO
N O
F B
RA
IN
TU
MO
R T
HR
OU
GH
MR
I
BR
AIN
TU
MO
R D
ET
EC
TIO
N U
SIN
G H
PA
CO
167
Fig
ure
5.7
Sel
ect
th
e H
PA
CO
wit
h F
CM
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Fig
ure
5.8
Seg
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Fig
ure
5.9
Ou
tpu
t Im
ag
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ved
to t
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lder
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Fig
ure
5.1
0 C
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firm
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of
HP
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er
CAD SYSTEM FOR AUTOMATIC DETECTION OF BRAIN TUMOR THROUGH MRIE
PERFORMANCE ANALYSIS
185
5.7 SUMMARY
In this work, a novel approach was applied to MRI Brain Image segmentation
based on the Hybrid Parallel Ant Colony Optimization (HPACO) with Fuzzy Algorithm
have been used to find out the optimum label that minimizes the Maximizing a Posterior
estimate to segment the image. The HPACO search is inspired by the foraging behaviour of
real ants. Each ant constructs a solution using the pheromone information accumulated by the
other ants. In each iteration, local minimum value is selected from the ants’ solution and the
pheromones are updated locally. The pheromone of the ant that generates the global
minimum is updated. At the final iteration global minimum returns the optimum label for
image segmentation. In the above 3×3, 5×5, 7×7, 9×9, 11×11 windows are analyzed the
HPACO with Fuzzy of 3×3 window is chosen based on the high contrast than 5×5, 7×7, 9×9,
and 11×11.
The detection of brain tumor region using Hybrid Parallel Ant Colony Optimization
with Fuzzy C Means is investigated. A New CAD System is developed for verification and
comparison of brain tumor detection algorithm. HPACO with FCM automatically determines
the adaptive threshold for the brain tumor segmentation.
CAD SYSTEM FOR AUTOMATIC DETECTION OF BRAIN TUMOR THROUGH MRIE
PERFORMANCE ANALYSIS
186
CHAPTER VI
CLASSIFICATION