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CHAPTER I
ABSTRACT
Medical Image segmentation is an important tool in viewing and analyzing
magnetic resonance (MR) images and solving a wide range of problems in medical
imaging. The Fuzzy C means clustering algorithm performs well in the absence of noise
but considers only the pixel attributes and not its neighbors. This leads to accuracy
degradation with image segmentation. This was addressed by using Generalized spatial
Fuzzy C-means clustering algorithm, which utilizes both given pixel attributes and the
spatial local information which is weighted corresponding to neighbor elements based on
their distance attributes. Though GSFCM gives good output, the main drawback behind
this method is, it reaches only the local minima values of the objective function. To
improve the efficiency of clustering MR images, this paper proposes the genetic
algorithm (GA) based GSFCM. By using GA, the global minima of the clustering
objective function can be reached. Although GA has high computational complexity, it
greatly improves the accuracy of the segmentation on medical images.
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CHAPTER II
INTRODUCTION
Image segmentation is one of the first and most important tasks in image analysis
and computer vision. Image segmentation remains one of the major challenges in image
analysis, since image analysis tasks are often constrained by how well previous
segmentation is accomplished. Many existing image segmentation algorithms fail to
provide the satisfactory results when the boundaries of the desired objects are not clearly
defined by the image intensity information. Having good segmentations will benefit
clinicians and patients as they provide important information for 3-D visualization,
surgical planning and early disease detection. However, the design of robust and efficient
segmentation algorithms is still very challenging research topic, due to the variety and
complexity of images.
Many image processing techniques have been proposed for brain MRI
segmentation including Threshold, region growing and clustering. Fuzzy clustering is an
appropriate method in medical image segmentation. Its applications are very successful in
the area of image processing as well as medical imaging. The field of medicine has
become a very attribute domain for the application of fuzzy set theory. FCM is one of the
important clustering methods to segment the image. Fuzzy c-means (FCM) is a data
clustering technique in which a dataset is grouped into n clusters with every data point in
the dataset belonging to every cluster to a certain degree. For example, a certain data
point that lies close to the center of a cluster will have a high degree of belonging or
membership to that cluster and another data point that lies far away from the center of a
cluster will have a low degree of belonging or membership to that cluster.
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The Fuzzy Logic function performs FCM clustering. It starts with an initial guess
for the cluster centers, which are intended to mark the mean location of each cluster. The
initial guess for these cluster centers is most likely incorrect. Next, the fuzzy logic
function assigns every data point a membership grade for each cluster. By iteratively
updating the cluster centers and the membership grades for each data point, The Fuzzy
Logic function iteratively moves the cluster centers to the right location within a data set.
This iteration is based on minimizing an objective function that represents the distance
from any given data point to a cluster center weighted by that data point's membership
grade. Membership values of the FCM are renewed by considering the resistance of
neighbours or feature-weight learning to improve the performance of Fuzzy C-means
clustering. In the possibilistic approach that corresponds to the intuitive concept of degree
of belonging or compatibility and reduce trouble in noise environment.
To improve the possibilistic approach, a new Generalized Spatial Fuzzy C-
means(GSFCM) algorithm has improved. This method takes into account properties of
local neighborhoods because the membership of each pixel is caused by its membership
and the memberships of neighboring pixels which depend on their distances to the
considered pixel. This GSFCM algorithm results as a weighted sum of the pixel
membership and the membership of the pixels in the neighbouring pixels along with the
center pixel.
Finally, this GSFCM algorithm has to be implemented by the genetic algorithmic
approach. It utilizes a random initialization of the genomes. It implements this by
randomly choosing cluster centers from a uniform distribution over the data space.
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In this approach, the binary strings representing the cluster centers undergo
mutation. The incorporation of mutation enhances the ability of the genetic algorithm to
near optimal solutions. The role of the mutation operator is to introduce new genetic
material to the gene pool, thus preventing the inadvertent loss of useful genetic material
in earlier phases of evolution. The creation of new genomes from existing ones during
reproduction is the process of crossover. Parent genomes are selected with a probability
of Pcross
(Pcross=
0.8) using the roulette wheel selection scheme.
The genetic algorithm does not depend on any initial conditions, efficiently
escapes from the sensibility to initial value and improves the accuracy of clustering. It
proceeds in an incremental way attempting to optimally add one new cluster center at
each stage. This approach is very efficient to remove the noise also in the image. It is
unorthodox search or optimization algorithms.
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CHAPTER III
LITERATURE SURVEY
Paper 1
Topic : A Generalized Spatial Fuzzy C-Means Algorithm for Medical Image
Segmentation
Author : Huynh Van Lung and Jong-Myon Kim, Member IEEE
Conference : Fuzz-IEEE 2009, Korea, August 20-24, 2009
Problem Description
3.1 Fuzzy C-Means Algorithm:
The FCM algorithm is an iterative algorithm of clustering technique that produce
optimal C partitions, centers V={v1,v
2,,v
c}which an exemplars, and radii which defines
these C partitions, let unlabelled data set X={x1,x
2,,x
c} be the pixel intensity. Where n
is the number of image pixels to determine their membership. The FCM algorithm tries to
partition the dataset X into C clusters. The standard FCM objective function is defined as
follows.
Jm(U,V)=
==
n
k
c
i 11 uik
md2(xk,v
i)-------------------------------------------------------(1)
Where d2(xk,v
i) represents the distance between the pixel x
kand centroid v
ialong with the
constraint
=
c
i 1 uik
= 1, and the degree of fuzzification m1. A data point xk
belongs to the
specific cluster vithat is given by the membership value u
ikof the data point to that
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1
1
)1(
1
2
2
),(
),(
=
=
c
j
m
jk
ikik
vxd
vxdU
cluster. Local minimization of the objective function Jm(U,V) is accomplished by repeatly
adjusting the values of uik
and viaccording to the following equations
-----------------------------------------------------------------(2)
Where Viis calculated by the following equation
=
n
k 0 uik
m xk
=
n
k 0 uik
m --------------------------------------------------------------------(3)
3.2 Generalized Spatial Fuzzy C Means Algorithm:
In the traditional FCM algorithm, for a pixel xk,
the clustering of xk
with class i
depends on the membership value uik.
Since the neighboring pixel xj
has an influential
function h of itself membership value uij
against pixel xk,
this degrades accuracy. To
overcome this problem, we take into the account the spatial information of correlated
neighboring pixels to impact the pixel xkbelonging to cluster I by a total function of P
ik
which is described as follows:
Pik
=
=
Nk
j 0 h(xk,x
j)g(u
ij) -------------------------------------------------------------------------(4)
=
Nk
j 0
h(xk,xj) = 1 and g(uij) are ranged in [0,1] with j
sk
If all pixels inside Sk
completely belong to cluster i, the function value Pik=1. This implies
that the pixel xk
is mostly impacted by its neighbours. Since the function g(uij) depends on
membership value of uij(The probability of pixel x
jbelonging to cluster i), the effective
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rate of g(uij) is between neighbor xj and the pixel xk. To determine the function
h(xk,x
j), assume that if u
ij=1, g(u
ij)=1.
As a result,
=
Nk
j 0 h(xk,x
j) = 1 when both the function value p
ikand function g(u
ij) are equal
to 1. This is sound if h(xk,x
j) is function of distances between neighbouring pixel x
jand
center pixel xk, Moreover the function h(x
k,x
j) should satisfy that the longer distance
between xk
and xj,
the smaller value of h(xk,x
j). These leads the following equation :
-1
h(xk,x
j) =
=
k
i 0 xi)d2(xk,
xj)d2(xk,
---------------------------------------------------------------------(5)
combine equation (1) and (2)
-1
Pik
=
=
Nk
j 0 g(uij)
=
k
i 0 xi)d2(xk,
xj)d2(xk,
---------------------------------------------------------------(6)
Pik
=
=
Nk
j 0 xi)d2(xk,1
=
k
i 0 xj)d2(xk,g(uij)
---------------------------------------------------------(7)
Where d2(xk,x
i)= d2(x
k,x
i)f(P
ik)----------------------------------------------------------------(8)
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3.2.1 Advantages of the GSFCM:
1. It considers the nearest neighbor pixels
2. It minimizes the value of the objective function
3. It degrades the difficulties of the FCM
4. It increases the accuracy of the image clustering
3.2.2 Limitations of the GSFCM:
1. Its convergence speed is low
2. High Computational Complexity than traditional FCM
3. It converges to the local minima value of the medical image.
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Paper 2
Topic : Robust Weighted Fuzzy C-Means Clustering
Author : A.H. Hadjahmadi, M.M. Homayounpour and S.M. Ahadi
Year : 2008
Problem Description
3.3 Robust Weighted Fuzzy C-Means Clustering (RWFCM):
FCM is the most famous clustering algorithm. However one of the greatest
disadvantages of this method is sensitivity for noises and outliers in the data. Since
the membership values of FCM for an outlier data is the same as real data, outliers
have a great influence on the centers of the clusters.
There exist different method to overcome this problem. Among them, three
well-known robust clustering algorithms, namely Fuzzy Possibilistic C-Means
(FPCM), Credibilistic Fuzzy C-Means (CFCM) and Density weighted Fuzzy C-
Means (DWFCM) were proposed in this paper. This paper decreased the noise
sensitivity in fuzzy clustering by using different kinds of weights in objective
function, in order to decrease the effect of noisy samples and outliers on centroids.
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3.3.1. A fuzzy Possibilistic C-Means Clustering (FPCM):
FPCM is a mixed c-means technique which generated both probabilistic
membership and typically for each vector in the dataset. FPCM minimizes the objective
function
Jfcm=
= =
c
i
N
k1 1 (Uik
m+tik
n) dik
2 , dik =
vixk-----------------------------------------(9)
Where is a parameter for controlling the effect typically on clustering and the
constraints
=
c
i 1 uik= 1 and
=
c
i 1 tik= 1.--------------------------------------------------------(10)
This algorithm provided the matrices U,T and V. The conditions for local minima
on the following equations
Tik= [
=
N
j 1 (dik/d
ij)2/(n-1) ] -1 ----------------------------------------------------(11) and
Due to the constraint (10), if the number of input samples (N) in a dataset is large,
the typically of samples will degrade and then the FPCM will not be insensitive to
outliers. So the modified version of FPCM was used. This is known as MFPCM which is
the sum of typically values of a cluster i, for all the input samples are equal to the number
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of data that belongs to this cluster.
Vi=
= =
c
i
N
k1 1 (Uik
m+tik
n) xi
=
N
k 1 (Uik
m+tik
n) ------------------------------------------(12)
3.3.2. The Credibilistic Fuzzy C-Means Clustering (CFCM):
This algorithm is decreased the noise sensitivity in fuzzy clustering by modifying
the probabilistic constraint uij=1. So that the algorithm generates low memberships for
outliers. To distinguish an outlier from a non-outlier, a new variable was introduced, that
is called as credibility. It is a vector represents its typically to the data set, not to any
particular cluster. If a vector has a low value of credibility, it is a typical to the data set
and is considered an outlier. Thus the credibility kof a vector x
kis defined as
k
= 1-(1-)k/max(
j) where j=1n and 0 1-------------------------(13)
Here k
is the distance of vector xk
from its nearest centroid. The parameter controls
the minimum value of vk
so that the noisiest vector gets credibility equal to . So the
CFCM partitions X by minimizing the FCM objective function.
=
c
i 1 uik
= k--------------------------------------------------------------------------(14)
like wise Uik
is calculated as follows
uik
= k
=
N
j 1 (dik/d
ij)2/(m-1)-----------------------------------------------------(15)
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3.3.3. The Density Weighted Fuzzy C-Means Clustering (DWFCM):
This algorithm modify the FCM to convergence process of clustering. The
equation of DWFCM is
J===
n
k
c
i 11 uik
md2(xk,v
i)w
k------------------------------------------------------------(16)
Where Wk =
=
N
y 1 exp(-h x xk-x
y/ ) for which h is a resolution parameter
and is a standard deviation of input data.
Like wise the following update equations for U and V for DWFCM
Vi=
=
n
k 1 Wk
(Uik
m) xi
=
N
k 1 Wk(U
ikm)-----------------------------------------(17)
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3.3.4 Advantages of the RWFCM:
1. This algorithm has 3 well known clustering algorithms namely FPCM,CFCM
and DWFCM
2. All algorithms attempt to decrease the noise sensitivity
3. The FPCM algorithm attempt to minimize the objective function than FCM
4. The CFCM is decreasing the noise sensitivity in fuzzy clustering by
modifying the probabilistic constraint
5. By using CFCM may result in oscillations for noise-free data and for
overlapped clusters, but the original update equation will not
6. The DWFCM has different density parameters
3.3.5 Limitations of the RWFCM:
1. All the three algorithms computational complexity is very high
2. It is hard to measure the density parameter
3. All these 3 algorithms are not particularly suited for medical image
segmentation.
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Paper 3
Topic : The Global Fuzzy C-Means Clustering Algorithm
Author : Weina Wang, Yunjie Zhang, Yi Li and Xiaona Zhang
Year : 2006
Problem Description
3.4 The Global Fuzzy C-Means Clustering (GFCM):
For a set of unlabeled data X={x1,x2,xn}, where N is the number of data
points. Its constrained fuzzy C-partition can be briefly described as follows : given
that the membership function of the ith (i=1N) vector to the jth (j=1,2,C)
cluster is denoted as Uij. The membership values are often constrained as
i,
=
c
i 1 uik
= 1; i, j, uij[0,1]; j,
=
N
i 1 uij > 0
The most widely used clustering criterion is the weighted within-group sum of
squared errors as follows:
Jm ===
n
k
c
i 11 uik
md2(xk,v
i) -------------------------------------------------------------(18)
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Where V is the vector of the cluster centers and m is the weighting component.
The FCM is a local search procedure with respect to the clustering criterion. Its
performance heavily depends on initial starting conditions and always converges to a
local minimum. To find the global minimum value, this paper proposed the global fuzzy
C-Means Clustering algorithm.
More specifically, we start with fuzzy 1-partition and find its optimal position
which corresponds to the centroid of the data set X. For fuzzy -2 partition problem, the
first initial cluster center is placed at the optimal position for fuzzy -1 partition, while the
second initial center at execution n is placed at the position of the data point xn(n=1..N).
Then we perform the FCM algorithm from each of these initial partitions respectively, to
obtain the best solution for Fuzzy-2 partition. In general, let (V1(c) ,.,V
c(c)) denote the
final solution for Fuzzy C-means partition. If we have found the solution for the fuzzy (c-
1) partition problem, we perform the FCM algorithm with C clusters from each of these
initial state (V1(c-1) ,.,V
c-1(c-1),x
n)(n=1,2,3N) respectively.
The main advantage of the algorithm is that it does not depend on any initial
conditions and improves the accuracy of clustering.
3.4.1 Algorithm :
1. Perform the FCM algorithm to find the optimal clustering centers V (1) of the
fuzzy 1-partition problem and let obj-1 be its corresponding value of the objective
function found by 18
2. Perform N runs of the FCM algorithm with c clusters where each run n starts
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from the initial value (V1(c) ,.,V
c(c),x
n) and obtain their corresponding values of the
objective function and clustering centers.
3. Find the minimal value of the objective function obj(c+1) and its corresponding
clustering centers V(c+1) from step 2. Let V(c+1)be the final clustering centers for fuzzy c+1
partition.
4. if c+1=C stop; otherwise set c=c+1 and go to step 2.
3.4.2 The Fast Global Fuzzy C-Means Clustering (FGFCM):
The global Fuzzy C-Means algorithm requires N executions of the FCM
algorithm for each value of c (c=1,2,.,C), in order to improve the convergence speed of
the global Fuzzy C-means algorithm we proposed the fast global FCM clustering
algorithm. For each of the N initial states(V1(c-1),Vc-1(c-1),xn) we do not execute the
FCM to obtain the final clustering error Jm. Instead we straightforward compute the
value of the objective function for all initial state, find the center corresponding to the
minimum value of objective function to be the initial center, and then execute the FCM
algorithm to obtain the solution with c clusters. The steps for the fast global Fuzzy C-
means clustering algorithms can be described as follows:
Step 1:
Perform the FCM to find the optimal clustering center V(1) of the Fuzzy 1-
partition and let obj_1 be the corresponding value of the objective function found by 18.
Step 2:
Compute the value of the objective function for all initial state (V1(c-1),.,Vc-
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1(c-1),xn) by using Jm =
= =
N
i
C
c1 1
(
xi-v
c2(1-m))1-m, x
i-v
c 0 (i=1,,N;c=1,2,3,,C)
Step 3:
Find the minimal value of the objective function obj_(c+1) and the corresponding
initial state V0
(c+1) and obtain the final clustering center V(c+1) for fuzzy c+1 partition
Step 4:
Perform FCM algorithm with c+1 clusters from the initial state V0(c+1) and
obtain the final clustering center V(c+1) for fuzzy c+1 partition.
Step 5:
If c+1 = C stop; otherwise set c=c+1 and go to step 2
Obviously, the global Fuzzy C-Means clustering algorithms requires performing
C X N executions of the FCM algorithm, the fast global FCM clustering algorithms only
requires performing C executions of the FCM algorithm. Therefore it improves the
convergence speed of the former.
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3.4.3 Advantages of the GFCM & FGFCM:
1. It converges to the global minima
2. GFCM accuracy is very high compared to the FCM
3. FGFCM algorithm improves the convergence speed of the GFCM
4. The converging speed of the FGFCM did not significantly affect the solution
quality
3.4.4 limitations of the GFCM & FGFCM:
1. GFCM converging speed is very low
2.
Paper 4
Topic : A Genetic Fuzzy C-Means Clustering Algorithm
Author : M.A.Egan
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Year : 1998
3.5 Genetic c-means fuzzy clustering algorithm:
Most FCM minimize the fitness function. The FCM is an iterative technique that
refines the cluster centers, sizes and weights at each iteration. The genetic c-means fuzzy
clustering algorithm GFCM uses non-overlapping populations in which each generation
creates an entirely new population of individuals.
Genetic operators are initialization, mutation, and crossover. GFCM utilizes a
random initialization of the genomes. It implements this by randomly choosing cluster
centers from a uniform distribution over the data space. In GFCM, the binary strings
representing the cluster centers undergo mutation. The incorporation of mutation
enhances the ability of the genetic algorithm to find near optimal solutions. The role of
the mutation operator is to introduce new genetic material to the gene pool, thus
preventing the inadvertent loss of useful genetic material in earlier phases of evolution.
The mutation operator in GFCM flips each bit of the bit string with a small probability,
Pmut
(Pmut
=0.01).
The creation of new genomes from existing ones during reproduction is the
process of crossover. Parent genomes are selected with a probability of
Pcross(Pcross=0.8) using the roulette wheel selection scheme. After a partner string is
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chosen randomly, the two-point cross over operator is applied to these two parents.
The implementation of two point cross over is as follows: two integer random numbers, i
and j, between 1 and 2c are generated. Both strings are cut into three portions at positions
I and j and the portions between these crossover points are mutually interchanged. The
following figure demonstrates this two-point cross over on a binary-to-decimal
representation. It shows the two parent genomes, the crossover points, i and j and their
resulting offspring.
Parent 1: 122 23 35 56 89 81 67 65 124 176
Parent 2: 67 98 76 53 76 86 54 34 65 45
1st crossover 2rd crossover
point i point j
Offspring1: 122 98 76 56 89 86 67 65 124 176
Offstring2: 67 23 35 53 76 81 54 34 65 45
CHAPTER IV
PROBLEM DEFINITION:
4.1 Fuzzy Applications in Medicine:
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Medicine is one of the field in which the applicability of fuzzy set theory was
recognized quite early, in the mid-1970. Within this field, it is uncertainty found in the
process of diagnosis of disease that has most frequently been the focus of applications of
fuzzy set theory. With the increased volume of information available to physicians from
new medical technologies, the process of classifying different sets of symptoms under a
single name and determining appropriate therapeutic actions becomes increasingly
difficult. A single disease may manifest itself quite differently in different patients and at
different disease stages. Furthermore, a single symptom may be indicative of several
different diseases, and the presence of several diseases in a single patient may disrupt the
expected symptom pattern of any one of them.
Although medical knowledge concerning the symptom-disease relationship
constitutes one source of imprecision and uncertainty in the diagnostic process, the
knowledge concerning the state of the patient constitutes another. The physician
generally gathers knowledge about the patient from the past history, physical
examination, laboratory test results, and other investigative procedures such as X-rays
and ultrasonic. The knowledge provided by each of these sources carries with it varying
degrees of uncertainty. The past history offered by the patient may be subjective,
exaggerated, underestimated, or incomplete. Mistakes may be made in the physical
examination, and symptoms may be overlooked. The measurements provided by
laboratory test are often of limited precision, and the exact borderline between normal
and pathological is often unclear. X-rays and other similar procedures require correct
interpretation of the results. Thus, the state and symptoms of the patient can be known by
the physician with only a limited degree of precision. In the face of the uncertainty
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concerning the observed symptoms of the patient as well as the uncertainty concerning
the relation of the symptoms to a disease entity, it is nevertheless crucial that a physician
determine the diagnostic label that will entail the appropriate therapeutic regimen. The
desire to better understand and teach this difficult and important process of medical
diagnostics has prompted attempts to model it with the use of fuzzy sets.
These models vary in the degree to which they attempt to deal with different
complicating aspects of medical diagnostics such as relative importance of symptoms, the
varied symptom patterns of different disease stages , relations between diseases
themselves, and the stages of hypothesis formation, preliminary diagnostics, and final
diagnostics within the diagnostics process itself. These models also form the basis for
computerized medical expert systems, which are usually designed to aid the physician in
the diagnostics of some specified category of diseases.
A fuzzy set framework has been utilized in the several different approaches to
modeling the diagnostics process. In the approach formulated by Sanchez (1979), the
physicians medical knowledge is represented as a fuzzy relation between the symptoms
and diseases.
4.2 Existing System
4.2.1 Fuzzy C-Means Clustering Method:
Clustering is one of the most fundamental issues in medical image segmentation.
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It plays a key role in searching for structures in data. Given a finite set of data X, the
problem of clustering in X is to find several cluster centers that can properly characterize
relevant classes of X. In classical cluster analysis, these classes are required to form a
partition of X such that the degree of association is strong for data within blocks of the
partition and weak for data in different blocks. However, this requirement is too strong in
many practical applications, and it is thus desirable to replace it with the weaker
requirement. When the requirement crisp partition of X is replaced with the weaker
requirement of a fuzzy partition or a fuzzy pseudo partition on X, we refer to the
emerging problem area as Fuzzy Clustering. Fuzzy pseudo partitions are often called
Fuzzy C-Partitions, where c designates the number of fuzzy classes in the partition. Both
of them are generalizations of classical partitions.
There are two basic methods of fuzzy clustering. One of them, which are based on
Fuzzy C-Partitions, is called a Fuzzy C-Means clustering method. The other method,
based on fuzzy equivalence relations is called a Fuzzy equivalence relation-based
hierarchical clustering method.
The traditional FCM algorithm based on pixel attributes lead to accuracy
degradation with segmentation because medical images are limited spatial resolution,
poor contrast, noise and non-uniform intensity variation. To overcome this GSFCM was
introduced that incorporates both given pixel attributes and spatial local information
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put: Clustered image
Step 8: otherwise calculate the J objective function.
Cluster the image according to the value U
is greater than 0.01 then repeat the step 4 to 6.
e of the current pixel and centroid valueep 2: Determine the Number of clusters & set the m value as >=1
Step 6: Assume e= difference between previous center and curren5 : Centroid value is calculated by sum((U)m) X current pixel / sum((U)m)
Input : Medical Image
Step 3: Generate the fuzzification Matrix U (Uniform Distributio
which is weighted correspondingly to neighbor elements based on their distance
attributes.
The problem architecture of the FCM and GSFCM is given in the following
diagram.
FCM Algorithm
4.1.2 Generalized Spatial Fuzzy C-Means Method:
1. Distributed the pixels of the input image into data set X and initiate centers
V(0)=(v1
(0),v2
(0),,vc(0))
2. Compute all membership values Uik
of each pixel against c centroids in
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Step 3: Generate the fuzzification Matrix U (Uniform Distributionep 2: Determine the Number of clusters & set the m value as >=1 Input : Medical Image
fuzzification matrix.
3. Compute new membership values wik
by manipulating g(uij) and f(p
ik), in
which we used g(uij)=u
ijand f(p
ik)=1/p
ikfor an efficient trade-off among the cluster
validity functions.
4. Calculate new centroid values visuch as
vi=
=
n
k 1 wik
mXk
=
n
k 1 wik
m
5. Evaluate the threshold of information condition max(vi(t)-vi(t-1)) < 0.01. stop if
it is satisfied, otherwise go to step 2.
6. Assign all pixels to belong to clusters by using the maximum membership
value of every pixel.
Problem Architecture of GSFCM:
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Output: Clustered Image00000000003000400000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000Step 6: Find the different between new centroid and old centr
0000000000000000000000000000000000000000000000000000000000000000000000000
Yes No
GSFCM algorithm
4.2 Proposed System (Genetic approach):
This paper takes the advantages of genetic algorithm which is used to find the
global optimum solution and degrades the disadvantages of the traditional FCM and
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GSFCM algorithm. These two algorithm proposes the gradient local minimum optimum
solution. But these two methods are not successful for finding the global optimum
solution. So this paper propose, Genetic approach apply to this two algorithms FCM and
GSFCM for medical image segmentation. The following diagram shows the architecture
of the Genetic approach on medical image segmentation by GSFCM.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000430
0000001000000000000005802000025000000372e90010000020f0502020204030204ef0
200a07b20004000000000000000009f00000000000000430061006c00690062007200000
0000000000000d09b120010232e3130be0f32309f12003c9b1200ca3927310b0000000100
0000789b1200789b1200087a25310b000000a09b12008c1dfc0064760008000000002500
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CHAPTER V
ALGORITHM
5.1 Genetic Algorithm :
There are basically two ways of fuzzifying classical genetic algorithms. One way
is to fuzzify the gene pool and the associated coding of chromosomes. The other one is to
fuzzify operations on chromosomes. To illustrate this possibility, let us consider the
example of determining the maximum of function f(x) = 2x-x2 / 16 within the domain
[0,31]. Numbers in this domain are represented by chromosomes whose components are
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numbers in [0,1]. For example, the chromosome {0.1,0.5,0,1,9} represents the number
8.5 = 0.1 x 24 + 0.5 x 23 + 0 x 22 + 1 x 21 + 0.9 x 20
in [0,31]. It turns out that this reformulation of classical genetic algorithms tends to
converge faster and is more reliable in obtaining the desired optimum. To employ it,
however, we have to find an appropriate way of coding alternatives of each given
problem by chromosomes formed from the gene pool [0,1].
To illustrate this issue, let us consider a travelling salesman problem with fourcities C
1, C
2, C
3and C
4. The alternative routes that can be taken by the salesman may be
characterized by chromosomes {X1, X
2, X
3, X
4} in which x
icorresponds to city c
i(i N4)
and represents the degree to which the city should be visited early.
Thus for example,{ 0.1,0.9,0.8,0} denotes the route C2,C3,C1,C4,C2. Although the
extension of the gene pool from {0, 1} to [0, 1] may be viewed as a fuzzification of the
genetic algorithms, more genuine fuzzification requires that the operations on
Chromosomes also be fuzzified.
5.2 Genetic Algorithm in fuzzy systems:
There are basically two ways of fuzzifying classical genetic algorithms. One way
is to fuzzify the gene pool and the associated coding of chromosomes. The other one is to
fuzzify operations on chromosomes. In classical genetic algorithms
To illustrate this possibility, let us consider the example of determining the
maximum of function f(x) = 2x-x2 / 16 within the domain [0,31]. Numbers in this domain
are represented by chromosomes whose components are numbers in [0,1]. For example,
the chromosome {0.1,0.5,0,1,9} represents the number
8.5 = 0.1 x 24 + 0.5 x 23 + 0 x 22 + 1 x 21 + 0.9 x 20
in [0,31]. It turns out that this reformulation of classical genetic algorithms tends to
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converge faster and is more reliable in obtaining the desired optimum. To employ it,
however, we have to find an appropriate way of coding alternatives of each given
problem by chromosomes formed from the gene pool [0,1].
To illustrate this issue, let us consider a travelling salesman problem with four
cities C1, C
2, C
3and C
4. The alternative routes that can be taken by the salesman may be
characterized by chromosomes {X1, X
2, X
3, X
4} in which x
icorresponds to city c
i(i N4)
and represents the degree to which the city should be visited early.
Thus for example,{ 0.1,0.9,0.8,0} denotes the route C2,C
3,C
1,C
4,C
2. Although the
extension of the gene pool from {0, 1} to [0, 1] may be viewed as a fuzzification of the
genetic algorithms, more genuine fuzzification requires that the operations on
chromosomes also be fuzzified.
Consider chromosomes X = {x1,x
2,..,x
n} and Y={y
1,y
2,y
n} , whose components
are taken from a given genepool. Then, the simple crossover with the crossover position
iNn-1
can be formulated in the terms of a special n-tuple.
t = {tj|tj=1 for j Ni and tj=0 for Ni+1,n} referred to as a template, by the formulas
X=(x t) (x t)
Y=(x t) (x t),
Where and are min and max operations on tuples and t = .
We can see that the template t defines an abrupt change at the crossover
position i. This is characteristic of the usual, crisp operation of simple crossover.
The change can be made gradual by defining the crossover position
approximately. This can be done by a Fuzzy template,
f=< fi|i Nn, f1=1, fn=0, i < j fi fj >.
For example, f= is a fuzzy template for some n.
Assume that chromosomes X = {x1,x
2,..,x
n} and y={y
1,y
2,y
n}are given, whose
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components are, in general, numbers in [0,1]. Assume further that a fuzzy template f =
is given. Then the operation of fuzzy simple crossover of mates x and y
produces offstrings x and y defined by the formulas
X=(x f) (x f)
Y=(x f) (x f),
These formulas can be written, more specifically as
X = ,
Y = ,
The operation of a double crossover as well as the other operations on
chromosomes can be fuzzified in a similar ways. Experience with fuzzy genetic
algorithms seems to indicate that they are efficient, robust, and better attuned to
some applications than their classical, crisp, counterparts.
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Compare and find the optimal solutionFind the Cross over value of the chromosomeGenerate the chromosome fitness function
segmentad2(xk,xi)d2(xk,xi)
Set the centroid matrix as a chromosomeFind the centroid value using GSFCM and FCMsegmentation d2(xk,xi)d
2(xk,xi)
Input MRI image for
segmentation d2(xk,xi)d2(xk,xi)
5.2 Architecture of Genetic Algorithm :
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Clustered Image
Chapter VI
EXPECTED OUTCOME
This section evaluates the performance of the proposed GSFCM algorithm and
compares the GSFCM with the FCM and MFCM algorithms
Table 1
Performance comparison of FCM, MFCM and GSFCM in terms of Cluster Validity
Functions
Image
Number
of
clusters
Technique The value of validity functions
Vpc
Vpe
Vxb
Vfs[x106]
Image 1 3 FCM0.89052
5
0.10165
6
0.23995
5
-288.221096
MFCM
0.94904
3
0.07276
3
0.28326
8
-299.651287
GSFCM
0.97702
7
0.02199
1
0.12106
0
-324.535968
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4 FCM
0.94080
4
0.10401
5
0.16145
4
-322.930972
MFCM
0.95382
4
0.08752
6
0.16569
1
-321.925050
GSFCM0.96543
4
0.03043
0
0.09695
0
-329.502357
5 FCM
0.91684
4
0.13712
8
0.17282
5
-335.425575
MFCM
0.78408
9
0.17558
2
0.29602
0
-307.483034
GSFCM
0.96776
5
0.02826
7
0.07696
5
-353.473182
Image 2 3 FCM0.83368
3
0.10395
6
0.03777
2
-316.408642
MFCM
0.90960
1
0.08299
2
0.03785
6-318.056959
GSFCM
0.95008
9
0.03770
6
0.03395
7-335.892399
Image
Number
of
clusters
Technique The value of validity functions
Vpc
Vpe
Vxb
Vfs[x106]
Image 2 4 FCM
0.86566
0
0.12636
2
0.06004
9
-305.583680
MFCM
0.88933
1
0.10616
1
0.05690
2-305.905533
GSFCM
0.93569
1
0.04851
8
0.04751
5-314.344920
5 FCM
0.86540
7
0.15523
0
0.18440
7-292.620881
MFCM
0.82069
8
0.18405
9
2.05156
0-254.728798
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GSFCM
0.91525
2
0.06385
2
0.07858
7
-301.709628
Image 1 Image 2
Chapter VII
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IDL TECHNOLOGICAL MAP
Randomu(seed, dimension of matrix):
-To generate the random numbers for the given input matrix
Reform(Array,size):
Reform the matrix that is change the row and column of the matrix
Fltarr() : To declare the float array
Intarr() : to declare the int array
For i=0,n-1 do beginendfor Iteration loop
Chapter VIII
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MILES STONES
March first week : Find the Segmentation related IEEE Papers
March last week : Understood Existing System
April First week : Find the Proposed system
May first week : Implementation of Existing System
May Last week : Problem of Proposed System defined and understood the problem
June First Week : Implementation of Proposed System
June Last week : Documentation
Chapter IX
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REFERENCES
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