Image segmentation using advanced fuzzy c-mean algorithm [FYP @ IITR, obtained 'A+' ]

Project No.49
Image Segmentation using
Advanced Fuzzy c-means Algorithm
B.Tech Final Year Project Report
Submitted as requirement
for award of degree of
BACHELOR OF TECHNOLOGY
in
Electrical Engineering
Submitted By:
J Koteswar Rao Ankit Agarawal
Guided By:
Dr. R.P.MAHESHWARI
DEPARTMENT OF ELECTRICAL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
ROORKEE-247667(INDIA)
MAY,2012

Acknowledgement
We express our most sincere and heartfelt gratitude to Dr. R.P. Maheshwari for helping us
through every step of the project. Sparing time for us even through his extremely busy schedule,
his guidance was essential for the successful completion of this project. We would also like to
thank the research scholar, Mr. Subramaniam, for helping us and sharing his knowledge and
experience in the field of Digital Image Processing. We have gained good experience and
knowledge in the field of Digital Image Processing while doing this project and we are grateful to
everyone who has helped us in our endeavour.
Lastly we would like to thank God and our parents for their blessings and motivation throughout
this project.

ABSTRACT
K-means algorithm is still extensively used in various fields like image segmentation, data
mining, etc. for clustering data and retrieving information. To enhance its quality of output many
new concepts and algorithms have been developed like fuzzy c-means (fcm) which introduced
the concept of partial membership. Since then huge amount of research has been done on fcm
and many of its variants have been developed like Bias-corrected fuzzy c-means (BCFCM),
some kernel versions of FCM with spatial constraints, such as KFCM_S1 and KFCM_S2, to
solve those drawbacks of BCFCM. Then, a Gaussian kernel-based fuzzy c-means algorithm
(GKFCM) with a spatial bias correction was proposed to decrease the heavy effect of
parameters. In our project, we have implemented all these algorithms for image segmentation
which have been proved to give very good results and created a GUI. Later above our pre-stated
objectives, we developed an algorithm which improves them by automatically choosing the
number of clusters, better selection of initial cluster centres and tremendously increasing the
speed to enable their use in real-time video segmentation.
Segmentation of flowers

CHAPTER 1 INTRODUCTION
Due to ever increasing amount of visual data and need to retrieve the useful information out of it,
it has become very necessary to develop better image segmentation tools and methods which
enable retrieving desired information and that too fast. Huge amount of research has been and is
being done in this field and various algorithms have been developed. Clustering is one such
technique which helps not only in image segmentation but is also useful in various other fields
like data mining, pattern recognition, etc. K-means is the most common clustering algorithm
which is widely used due to its speed, simplicity and good output. It has been improved over the
years and many of its variants have been developed like fuzzy c-means, Bias corrected fuzzy c-
means, etc. which give better results and remove many drawbacks of K-means.
In our project we first implemented K-means algorithm for image segmentation to understand
the effect of clustering on an image and its segmentation results. We discovered that it suffers
from many drawbacks like non-convergence and is susceptible to effects from noise. Hence, we
implemented Fuzzy c-means algorithm which gives partial membership of each cluster to each
pixel and then its variant which was proposed to yield better results as it took into account the
effect of neighbouring pixels to decrease the effect of noise(BCFCM). Since it is
computationally time taking and lacks enough robustness to noise and outliers, some kernel
versions of FCM with spatial constraints, such as KFCM_S1 and KFCM_S2, were proposed to
solve those drawbacks of BCFCM. However, KFCM_S1 and KFCM_S2 are heavily affected by
their parameters. So,we implemented a Gaussian kernel-based fuzzy c-means algorithm
(GKFCM) with a spatial bias correction which was proposed to be more efficient and robust.
While implementing them, we noticed that we can improve the results of K-means algorithm by
hitting on its basic inputs and we realized research is being done in that direction as well. Inputs
to a K-means algorithm are number of clusters and the initial cluster centres. We noticed that
initial clusters were in general randomly chosen and the number of clusters was derived by
applying k-means a number of times and then comparing the results. So, we came up with the
idea that we can apply a moving average filter on the histogram of an image and take the number
of peaks as the number of clusters and those peaks as initial cluster centres. We found that this
way the problem of non-convergence was removed and the results were better as the initial
cluster centres were found to be close to final cluster centres. This way we also avoided the
input, number of clusters, from the user. Then, we happened to notice that we can apply the k-
means algorithm on the histogram of the image rather than the image itself which increased the
speed of the algorithm since the iterations became very fast. We incorporated an additional
feature which automatically varies the input to moving average filter and named it auto-pilot,
which depending on the application itself decides the value of n for moving average filter. As the
algorithm became very fast and didn’t require any input from the user we realized that we can
even try real-time video segmentation which is very difficult due to limitation of time.

We have developed a GUI(Graphic User Interface) to display all the algorithms implemented,
modifications which we are proposing, etc. so that the user can easily look through our work and
use it as well. We have some interesting features like report generation which makes a report of
the segmented results of an image in word file, live video segmentation, etc.
In the report starting with introduction to Digital Image Segmentation we have explained various
clustering algorithms implemented by us, then highlighted a few drawbacks of K-means and
Fuzzy c-means which we have removed by our proposed algorithm which is explained in the
next chapter along with auto-pilot and real-time video segmentation. At last we have explained
the features of GUI developed.
Segmentation using proposed algorithm (tumor got completely separated)

Chapter 2 Digital Image Segmentation
2.1 What is Digital Image Segmentation?
When acquiring an image, it might be interesting to know what parts of the image do belong to
each other. It could be a satellite image, where we wish to quantify and locate different types of
vegetation, or a medical MRI image where the doctors are interested to know how much of each
tissue type is present, and where it is located. Image segmentation techniques offer a method to
perform these tasks, and thus, can be regarded as the process of dividing an image into
groups of pixels which from a preset property are connected to each other. The goal of
segmentation is to simplify and/or change the representation of an image into something that is
more meaningful and easier to analyze.
Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in
images. More precisely, image segmentation is the process of assigning a label to every pixel in
an image such that pixels with the same label share certain common visual characteristics. These
characteristics or computed property may be, such as color, intensity or texture. Commonly this
means that pixels with almost the same intensity values are grouped together, or pixels with the
same colour code. There are techniques for finding for instance objects with closed contours,
convex objects and the boundaries of an object, etc.
Segmentation is a fundamental task of image processing because of its many areas
of application.
 Medical Imaging
 Locate tumors and other pathologies
 Measure tissue volumes
 Computer-guided surgery
 Diagnosis
 Treatment planning
 Study of anatomical structure
 Locate objects in satellite images (roads, forests, etc.)
 Face Recognition
 Iris Recognition
 Fingerprint Recognition
 Traffic Control Systems
 Brake Light Detection
 Machine Vision
Segmentation techniques have not been widely applied, partly because they are time consuming
and partly because there are no overall techniques that are suitable for all different types of
images. All intensity based segmentation techniques are sensible to the situation that different

objects have almost equal intensities. This will often lead to misclassification (wrongly classified
pixels) if the objects from the view of the human eye should not belong to the same class.
[In general all the segmentation techniques have to be based on intensity since the only data
available from an image is an array of numbers which signify the intensity. Then these numbers
are used in segmentation in various formats to represent just the intensity based(for gray level
images) or colour based(which uses three or more intensity matrices) or any kind of a pattern like
a texture(which again may use more than one parameter), etc. Here in our project we have
concentrated only on gray level images.]
2.2 Different ways of Image Segmentation
Image segmentation can proceed on three different ways,
1. Manually
2. Automatically
3. Semi-automatically
2.2.1 Manual Segmentation
The pixels belonging to the same intensity range could manually be pointed out, but clearly this
is a very time consuming method if the image is large. A better choice would be to mark the
contours of the objects. This could be done discrete from the keyboard, giving high accuracy, but
low speed, or it could be done with the mouse with higher speed but less accuracy. The manual
techniques all have in common the amount of time spent in tracing the objects, and human
resources are expensive. Tracing algorithms can also make use of geometrical figures like
ellipses to approximate the boundaries of the objects. This has been done a lot for medical
purposes, but the approximations may not be very good.
2.2.2 Automatic Segmentation
Fully automatic segmentation is difficult to implement due to the high complexity and variation
of images. Most algorithms need some a priori information to carry out the segmentation, and for
a method to be automatic, this a priori information must be available to the computer. The
needed a priori information could for instance be noise level and probability of the objects
having a special distribution. In computer vision it is required that computer is able to do
automatic segmentation and then take the required actions according to the segmentation results.
In our project we have made an attempt to go closer to automatic segmentation by requiring less
and less input from the user.
2.2.3 Semi-automatic Segmentation
Semiautomatic segmentation combines the benefits of both manual and automatic segmentation.
By giving some initial information about the structures, we can proceed with automatic methods.

Thresholding
If the distribution of intensities is known, thresholding divides the image into two
regions, separated by a manually chosen threshold value ‘a’ as follows:
if B(i; j) ¸ a; B(i; j) = 1 (object)
else B(i; j) = 0 (background)
for all i; j over the image B. This can be repeated for each region, dividing
them by the threshold value, which results in four regions etc. However, a successful
segmentation requires that some properties of the image is known beforehand. This
method has the drawback of including separated regions which correctly lie within
the limits specified, but regionally do not belong to the selected region. These pixels
could for instance appear from noise. The simplest way of choosing the threshold
value would be a fixed value, for instance the mean value of the image.
A better choice would be a histogram derived threshold. This method includes some
knowledge of the distribution of the image, and will result in less misclassification.
Isodata algorithm is an iterative process for finding the threshold value. First segment the image
into two regions according to a temporary chosen threshold value. Then calculate the mean value
of the image corresponding to the two segmented regions. Calculate a new threshold value from
thresholdnew = mean(meanregion1 + meanregion2)
and repeat until the threshold value does not change any more. Finally choose this value for the
threshold segmentation.
Various other thresholding methods are used like adaptive thresholding, Otsu algorithm,
Minimum error algorithm, Minimum entropy method, etc.
Boundary tracking
Edge-finding or edge-detection by gradients is the method of selecting a boundary manually, and
automatically follow this gradient until returning to the same point. Returning to the same point
can be a major problem of this method. Boundary tracking will wrongly include all interior holes
in the region, and will meet problems if the gradient specifying the boundary is varying or is very
small. A way to overcome this problem is first to calculate the gradient and then apply a
threshold segmentation. This will exclude some wrongly included pixels compared to the
threshold method only.
Zero-crossing based procedure is a method based on the Laplacian. Assume the boundaries of an
object has the property that the Laplacian will change sign across them. Assume the boundary is
blurred, and the gradient will have a shape like in Figure 2.2. The Laplacian will change sign just
around the assumed edge for position = 0.

For noisy images the noise will produce large second derivatives around zero crossings, and the
zero-crossing based procedure needs a smoothing filter to produce satisfactory results.
Various edge detection tools are used and huge development have been made in this like various
masks have been developed e.g. Robert operator, Sobel’s operator, Prewitt Operator, etc.
Neighbouring methods
Region growing is a statistical method for segmentation. We group the pixels into different
regions from the principles of proximity and homogeneity. The principle of proximity splits the
image into smaller regions and merges them again such that all pixels have neighbours similar to
themselves. This means that the intensities of the neighbours all lie within a certain threshold.
The principle of homogeneity compares the statistical probability of different combinations of
regions to belong to the same class. This requires some a priori information about the image we
are trying to segment. Various statistical measures like standard deviation, skewness, kurtosis
etc. are used for determining whether the regions are similar or different. But here also the input
for these measures to differentiate has to be given by the user based on a priori information.
Mathematical Morhphology
Mathematical morphology (MM) is a theory and technique for the analysis and processing of
geometrical structures. MM is most commonly applied to digital images, but it can be employed
as well on graphs, surface meshes, solids, and many other spatial structures.
Topological and geometrical continuous-space concepts such as
size, shape, convexity, connectivity, and geodesic distance were introduced by MM on both
continuous and discrete spaces. MM is also the foundation of morphological image processing,
which consists of a set of operators that transform images according to the above
characterizations.
Besides extending the main concepts (such as dilation, erosion, etc...) to functions, this
generalization yielded new operators, such as morphological gradients, and

the Watershed (MM's main segmentation approach). The watershed transformation considers the
gradient magnitude of an image as a topographic surface. Pixels having the highest gradient
magnitude intensities (GMIs) correspond to watershed lines, which represent the region
boundaries. Water placed on any pixel enclosed by a common watershed line flows downhill to a
common local intensity minimum (LIM). Pixels draining to a common minimum form a catch
basin, which represents a segment.
Clustering Methods
Clustering is the process of dividing data elements into classes or clusters so that items in the
same class are as similar as possible, and items in different classes are as dissimilar as possible.
Depending on the nature of the data and the purpose for which clustering is being used, different
measures of similarity may be used to place items into classes, where the similarity measure
controls how the clusters are formed. Some examples of measures that can be used as in
clustering include distance, connectivity, and intensity. Hence, clustering has been used as a very
useful tool in data mining, image segmentation, pattern recognition, information retrieval, etc.
Many clustering algorithms have been developed like K-means, Fuzzy c-means, etc. With
moderate processing time they give very good result and are very commonly used.
We’ll be discussing about clustering algorithms at length in the next chapter and discuss about
various clustering algorithms evolved and their drawbacks. Later in the report we’ll mention the
efforts made by us in trying to remove those drawbacks and getting better results.

Chapter 3 CLUSTERING METHODS
3.1 Introduction
Cluster analysis or clustering is the task of assigning a set of objects into groups
(called clusters) so that the objects in the same cluster are more similar (in some sense or
another) to each other than to those in other clusters.
Clustering is widely used in image analysis, pattern recognition, and many other fields,
including data mining, statistical analysis, machine learning, information retrieval
and bioinformatics. Its wide use can be attributed to the fact that they are very fast and simple
and give good results for unsupervised approaches.
In intensity based image segmentation for example clustering algorithms finds its use because an
object generally has same intensity, pattern or texture etc. for a particular orientation. Hence to
segment a particular object out of an image what we require to know is its intensity. Similarly
different objects can be segmented based on their intensity in the image. So by the process of
clustering we identify various groups of intensities which may refer to different objects and thus
segment the image into its constituting parts separately.
Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be
achieved by various algorithms that differ significantly in their notion of what constitutes a
cluster and how to efficiently find them. Popular notions of clusters include groups with
low distances among the cluster members, dense areas of the data space, intervals or particular
statistical distributions. Clustering can therefore be formulated as a multi-objective
optimization problem. The appropriate clustering algorithm and parameter settings (including
values such as the distance function to use, a density threshold or the number of expected
clusters) depend on the individual data set and intended use of the results. Cluster analysis as
such is not an automatic task, but an iterative process of knowledge discovery or interactive
multi-objective optimization that involves trial and failure. It will often be necessary to modify
preprocessing and parameters until the result achieves the desired properties.
3.2 CLUSTERS AND CLUSTERING
The notion of a "cluster" varies between algorithms and is one of the many decisions to take
when choosing the appropriate algorithm for a particular problem. At first the terminology of a
cluster seems obvious: a group of data objects. However, the clusters found by different
algorithms vary significantly in their properties, and understanding these "cluster models" is key
to understanding the differences between the various algorithms. There may be various cluster
models but we’ll be confining our discussion to centroid based models like K-means algorithm
and its variants in which a cluster is represented by a single mean vector.
A "clustering" is essentially a set of such clusters, usually containing all objects in the data set.
Additionally, it may specify the relationship of the clusters to each other, for example a hierarchy
of clusters embedded in each other. Clusterings can be roughly distinguished in:

 hard clustering: each object belongs to a cluster or not
 soft clustering (also: fuzzy clustering): each object belongs to each cluster to a certain
degree
In the next few sections of the chapter we would discuss various clustering algorithms which we
have implemented in our project.
3.3 K-Means Algorithm
K-means (MacQueen) is one of the simplest unsupervised learning algorithms that solve the well
known clustering problem. It is very popular because of its ability to cluster a kind of huge data,
and also outliers, quickly and efficiently. The procedure follows a simple and easy way to
classify a given data set through a certain number of clusters (assume k clusters) fixed a priori.
The main idea is to define k centroids, one for each cluster. Every pixel has to belong to only and
only one cluster. These centroids shoud be placed in a cunning way because different location
causes different result. So, the better choice is to place them as much as possible far away from
each other. The next step is to take each point belonging to a given data set and associate it to the
nearest centroid. When no point is pending, the first step is completed and an early groupage is
done. At this point we need to re-calculate k new centroids for the clusters resulting from the
previous step. After we have these k new centroids, a new binding has to be done between the
same data set points and the nearest new centroid. A loop has been generated. As a result of this
loop we may notice that the k centroids change their location step by step until no more changes
are done. In other words centroids do not move any more.
Finally, this algorithm aims at minimizing an objective function, in this case a squared error
function. The objective function
Where, is a chosen distance measure between a data point and the cluster
centre , is an indicator of the distance of the n data points from their respective cluster centres.
K-means has proved to be very useful algorithm for image segmentation being both simple and
fast is sometimes used as a pre-segmentation for other segmentation processes.

Place K points in
space one for each
cluster randomly.
Assign each pixel to
the cluster whose
centroid or centre is
closest
Calculate new
centres as the
centroid of the group
cj(new)-cj(old)<Є
Cluster centres have
been obtained
yes
No
figure: Flowchart for K-means algorithm

3.4 Fuzzy C-Means (FCM) Algorithm
Zadeh proposed fuzzy sets that introduced the idea of partial memberships described by
membership functions, it has been successfully applied in various areas. Especially, fuzzy sets
could allow membership functions to all clusters in a data set so that it is very suitable for cluster
analysis i.e. each pixel can have membership to all the clusters but the membership would be
defined. In contrast to K-means where each pixel is a member of only one cluster Ruspini first
proposed fuzzy c-partitions as a fuzzy approach to clustering. Later, the fuzzy c-means (FCM)
algorithms with a weighting exponent m = 2 proposed by Dunn , and then generalized by Bezdek
with m > 1 became popular.
Let X = {x1, . . .,xn} be a data set in an s-dimensional Euclidean space R. Let c be a positive
integer greater than one. A partition of X into c parts can be presented by a mutually disjoint set
X1, . . .,Xc such that X1 U….U Xc = X, or equivalently by the indicator functions µ1, . . .,µc
such that µij = µi(xj) = 1 if xj Є Xi and µij = 0 if xj ∉ Xi for i = 1,. . ., c and j = 1,. . .,n. The set
of indicator functions {µ1, . . ., µc} is known as a hard c-partition of clustering X into c clusters.
Ruspini first considered an extension to allow µij = -µi(xj) to be the membership functions of
fuzzy sets µi on X assuming values in the interval [0,1] such that ∑ µ for all xj in X.
In this fuzzy extension, {µ1, . . ., µc} is called a fuzzy c-partition of X.
The fuzzy c-partitions of X can be represented in a matrix form as follows:
µ = {µij}cxn Є Mfcn where Mfcn is a partition matrix with
Mfcn = {µ=[µij]cn | ∀ i, ∀j µij ≥0, ∑ µ , n> ∑ µ > 0 }
Dunn first embedded the fuzzy c-partitions into K-means and then proposed the fuzzy c-means
(FCM) objective function with
∑ ∑ µ
where µij Є Mfcn and {a1, . . .,ac} denote the cluster centres of the data set X. Bezdek extended
the weighting exponent m = 2 to any m > 1 with the FCM objective function Jm as
µ ∑ ∑ µ
Thus, the FCM algorithm is iterated through the necessary conditions for minimizing Jm(µ,a)
with the following update equations:
∑ µ
∑ µ
, i=1,2,…c (1)

µ ∑ , i=1,2,….c (2)
j=1,2,….n
Based on a sequence of execution for stage s using stage (s -1) according to the update Eqs. (1)
and (2), the FCM can be described as follows:
FCM procedure
Input:
(1) X = { ,…. }, Є R, the data set
(2) c, 2 ≤ c ≤ n, the number of clusters
(3) Ɛ > 0, the stopping criterion of algorithm
(4) ( ) the initials of cluster centers.
OUTPUT: a = { }, the final cluster centers
Algorithm:
Step 1: Let s = 1
Step 2: Compute µ using (2).
Step 3: Update the cluster centers with µ using (1).
Step 4: Compare to in a convenient matrix norm ||.||.
IF || || < Ɛ, STOP and OUTPUT.
ELSE s = s + 1 and return to step 2.
Fuzzy clustering has been widely studied and applied in a variety of areas, such as numerical
taxonomy, image processing, pattern recognition, medicine, economics, ecology, marketing,
artificial intelligence, data mining, engineering systems, and gene expression. In fuzzy
clustering, the fuzzy c-means (FCM) algorithm plays an important role.
3.5 Bias-corrected Fuzzy C-Means (BCFCM)
Although the FCM algorithm is the best known, it has several drawbacks. For example, the
points in the data set are supposed to be equally important, the number of points in the clusters is
almost equal, nearly all points do not have a membership value of one, and the outliers always
affect the clustering results. To overcome these drawbacks, many generalized FCM algorithms

have been proposed in the literature. Among them, Ahmed et al. (2002) first modified the FCM
algorithm as a bias-corrected FCM(BCFCM) with a spatial neighbourhood regularization term
by regularizing the following FCM objective function .
where Nj stands for the set of neighbours that exist in a window around xj and is the
cardinality of Nj. The effect of neighbouring terms is controlled by the parameter a. Thus, the
BCFCM algorithm is iterated through the necessary conditions for minimizing with the
following update equations:
However, Chen and Zhang (2004) pointed out a shortcoming of the BCFCM update equations
that computing the term of neighbourhoods Nj may take too much time than FCM. They then
proposed a modified objective function as
where is the sample mean within the window around xj where can be computed in advance.
The idea is that the term
Thus, the modified BCFCM algorithm is iterated through the necessary conditions for
minimizing with the following update equations:

3.6 Kernel based Fuzzy C-means (KFCM)
Chen and Zhang (2004) then replaced the Euclidean distance || || with a Gaussian kernel-
induced distance 1- K( =1 - exp(- / ). They gave the kernel version of
as
The necessary conditions for minimizing (µ,a)are the following update equations:
where K(x,y) =exp(- / ). Note that different kernels can be chosen by replacing the
Euclidean distance . for different purposes. However, a Gaussian kernel is suitable
for clustering in which it can actually induce the necessary conditions (7) and (8). They then
proposed the KFCM_S1 as follows:
KFCM_S1 procedure
Input:
(1) X = { ,…. }, Є R, the data set
(2) c, 2 ≤ c ≤ n,, the number of clusters

(4) and , the values of parameters
(5) ( ) the initials of cluster centres.
Output: a = { }, the final cluster centres
Algorithm:
Step 1: Let s = 1
Step 2: Compute µ using (8).
Step 3: Update the cluster centres with and µ using (7).
Step 4: IF || || < Ɛ, STOP and OUTPUT.
If ̅ is taken as the median of the neighbours within the window around , then the
algorithm is called KFCM_S2 by Chen and Zhang(2004) where they compare the KFCM_S1
and KFCM_S2 with FCM and BCFCM. However, the parameter in BCFCM, KFCM_S1 and
KFCM_S2 heavily affects the final clustering results. For estimating the parameter and
learning the parameter , we propose a generalized type of BCFCM, KFCM_S1 and KFCM_S2
where the parameters and can be automatically estimated and learned from the data in the
next section.
3.7 Gaussian kernel-based FCM (GKFCM)
We know that Chen and Zhang (2004) considered a kernel version of FCM by replacing the
Euclidean distance || || with the kernel substitution as
( )
where / is a nonlinear map from the data space into the feature space with its corresponding
kernel K. They specially assumed K(x,y) = 1 and then proposed the kernel-type objective
function with
µ ∑ ∑ µ
Thus, the update equations for the necessary conditions for minimizing µ are as follows:

∑ µ ( )
∑ µ ( )
i = 1,2,…,c (9)
µ
( )
∑ ( )
, i = 1,2,…c; (10)
j=1,….,n
We point out that the necessary conditions for minimizing µ are update Eqs. (9) and (10)
only when the kernel function K is chosen to be the Gaussian function with K( ) = exp(-
).
µ ∑ ∑ µ ∑ ∑ µ ̅
Where, K(x,y) =exp(- / ) is taken. Thus, the necessary conditions for minimizing
µ are Eqs. (7) and (8) as shown in Section 2.We mention that the parameter is used to
control the effect of the neighbors for adjusting the spatial bias correction term. In fact, the
parameter heavily affects the clustering results of BCFCM, KFCM_S1 and KFCM_S2.
Intuitively, it would be better if we can adjust each spatial bias correction term separately for
each cluster i. That is, the overall parameter is better replaced with that is correlated to each
cluster i. In this sense, we will consider the following modified objective function with
µ ∑ ∑ µ ∑ ∑ µ ̅ (11)
where K(x,y) =exp(- / ).
Based on the concept of machine learning with a learning capability to improve the performance
of clustering results, an exponential-type distance is bounded and monotone increasing. Hence it
can be robust to noise and outliers when = 1- exp(- ) is used to
replace the Euclidean distance . However, there are parameters and in the
proposed objective function . Since is presented as a dispersion, we use the sample
variance to estimate with
∑ ̅ with ̅ ∑ (12)
On the other hand, because the parameter controls the effect of the neighbouring term for each
cluster i, a ratio of the two distance-based influence terms, and
̅ , can be used as a learning scheme for . This is because the term
presents the separation of data set for the cluster i. If the value of is larger,
then the cluster i will be more isolated so that the value of should be larger. However, the
scale of for each data set may depend on the total separation of the data set in
which it can be measured by the term ̅ . Thus, the ratio of the two terms

and ̅ can be well used as a standardized separation strength of
cluster i. Moreover, we also consider these influencing factors simultaneously in replacing the
Euclidean distance with the exponential-type distance 1- K(x,y) = 1-exp(- / ).
Therefore, the parameter is estimated as follows:
̅
, i = 1,2,…c (13)
Thus, the update equations for the necessary conditions of minimizing µ are
∑ µ ( ) (̅̅̅ )̅̅̅
∑ µ ( )
, i = 1,…c (14)
µ
( ( )) (̅̅̅ )
∑ ( ( )) (̅̅̅ )
, i = 1,…,c; j = 1,…,n (15)
where K(x,y) = exp(- / ).
We see that the KFCM objective function µ is a special case of µ when =
for all i. Thus, we have the GKFCM as follows:
GKFCM procedure
Input:
(1) X = { ,…. }, Є R, the data set
(2) c, 2 ≤ c ≤ n, the number of clusters
(4) ( ) the initials of cluster centres.
Output: a = { }, the final cluster centers
Algorithm:
Step 1: Let s = 1and estimate using (12).
Step 2: Compute using (13).
Step 3: Compute µ and using (15).
Step 4: Update the cluster centres with , and µ using (14).
Step 5: IF || || < Ɛ, STOP and OUTPUT.

If ̅ in Eqs. (14) and (15) is considered as the sample mean within the window around , then
we call the algorithm as GKFCM1. If ̅ in Eqs. (14) and (15) is replaced with the median within
the window around , then the algorithm is called GKFCM2. Note that the parameters and
in BCFCM, KFCM_S1 and KFCM_S2 are priori assigned by users where they heavily affect the
clustering results. But in our proposed GKFCM1 and GKFCM2, the parameter is estimated by
Eq. (12) and the parameter i
is updated at each iteration using Eq. (13) based on the data and
learning schemes.

CHAPTER 4 Drawbacks of K-means and FCM Algorithms
4.1 Introduction
The K-means and FCM algorithms are having many drawbacks due to which their results are not
good and hence the algorithms which have k-means as their starting point or are from its
variations have to suffer from various drawbacks. These are drawbacks are:
1. No. of clusters has to be a human input
2. May not converge (K-means)
3. Different initial cluster centres may yield different final cluster centres hence sometimes
the result may be completely erroneous
4. Slow (FCM)
In the next few sections we discuss these drawbacks along with some methods which were
proposed to modify and improve it. They also have suffered from the drawbacks of their own so
we have suggested a new method in the next chapter and its certain features have been discussed
along with the drawbacks of previously proposed algorithms.
4.2 Number of clusters
The first issue is that the number of clusters k needs to be determined in advance as an input to
clustering algorithms. In a real data set, k is usually unknown. In practice, different values
of k are tried, and cluster validation techniques are used to measure the clustering results and
determine the best value of k, see, for instance, [9]. In [10], Li et al. presented an agglomerative
fuzzy k-means clustering algorithm for numerical data, an extension to the standard fuzzy k-
means algorithm by introducing a penalty term to the objective function. The algorithm can
determine the number of clusters by analyzing the penalty factor. For categorical data, a bottom-
up hierarchical algorithm ACE was proposed in [11], which uses entropy as an index function to
capture the candidates for the number of clusters.
All these methods are time consuming and computation expensive to apply. For example, [9] for
instance requires whole K-means algorithm to be applied multiple times to gain the no. of
clusters to divide the image. In [10] the algorithm needs to randomly select a subset from data set
as initial cluster centers, which results in an uncertainty and then suffers with the problem as
stated in the next drawback. [11] is very time consuming and is dependent on the size of the
image because if the size of the image is very large, the ACE algorithm is not efficient due to its
computational burden of O(n2
log2n) with n being the number of data points.
Hence, we would like to propose a method to find out the number of clusters for clustering of an
image for the purpose of segmentation which is lot simpler, fast and gives good results. First, the
histogram of the image is developed and on the histogram of the image a moving average filter is
applied whose size can be decided by the user depending upon the image. Then this moving

average filter will do the smoothing of the filter and give rise to some smooth peaks and valleys.
In general, it has been noticed that the intensity of an object in an image is clustered in one
particular region which forms a peak and the peaks of two different objects (or the object from
the background) are separated by a valley. So, this feature of a digital image is made use of to
determine the number of clusters. It is proposed that for intensity based segmentation each peak
will refer to a separate segment of the image. Hence, the number of peaks is our required number
of clusters. As such it can be said that this can easily be known by just viewing the histogram of
an image. But, for the purpose of computer vision and machine learning it is important that
computer itself identifies the number of clusters. This particular method aids computer in
identifying the number of cluster on its own. Though it can be said that the size of the moving
average filter is to be an input which cannot be done by computer, but later in the project we’ve
tried to sort that problem as well.
4.3 INITIAL cluster centres
Through the iterative partitioning, k-means algorithm minimizes the sum of distance from each
data to its clusters. However, one of the biggest drawbacks of the k-means algorithm is, it is
very sensitive to the designated initial starting points as cluster centers because they have direct
impact on final cluster centres. K-Means does not guarantee unique clustering as we get different
results with randomly chosen initial cluster centres. The final cluster centroids may not be the
optimal ones as the algorithm can converge into local optimal solutions. An empty cluster can be
obtained if no points are allocated to the cluster during the assignment step. Thus, computer
vision and machine learning practitioners find it difficult to rely on the results thus obtained.
Therefore, it is quite important for k-means to have good initial cluster centers.
Several methods proposed to solve the cluster initialization for k-means algorithm.
Since clusters are separated groups in a feature space, it is desirable to select initial centers which
are well separated. So the image is first divided into k parts on the basis of its intensity and then
the centre of each part is taken to be the initial cluster centres. But, the clustering of the data can
be in any region and need not be spread throughout the range and it is dangerous to select
outliers as initial centers, since they are away from normal samples. This will not only take time
for reaching to the final cluster centres there may be the problem of convergence as is discussed
in next section as well.
For the initial cluster center, Jain and Dubes (1988) applied the k-means with several times by
randomly selected initial values and selected the average of these final cluster centers.
Bradley and Fayyad (1998) proposed the refinement algorithm that builds a set of small random
sub-samples of the data, then clusters data in each sub-samples by k-means. All centroids of all
sub-samples are then clustered together by k-means using the k-centroids of each sub-sample as

initial centers. The centers of the final clusters that give minimum clustering error are to be used
as the initial centers for clustering the original set of data using k-means algorithm.
Penã et al. (1999) presented a comparative study for different initialization methods for the K-
means algorithm. The result of their experiments illustrate that the random initialization method
outperforms the rest of the compared methods as they make the K-means more effective and
more independent on initial clustering and on instance order.
This clearly showed that the methods developed till then were not giving effective but
the need to find better initial cluster was there in order to get better final cluster centres
and also to avoid any problem of convergence which may occur due to inappropriate
selection of initial cluster centres.
Hence, more research was being done to find better initial cluster which are closer to the
final cluster centres which would make the results better and along with that would be
speedy since convergence will be faster and number of iterations required will be less.
Likas et al. (2003) proposed the global k-means algorithm which is an incremental approach to
clustering which dynamically adds one cluster center at a time through a deterministic global
search procedure consisting of N (with N being the size of the dataset) executions of the k-means
algorithm from suitable initial positions. But it is a very long and time consuming process as
error finding method is run about (K-1)*N times in this.
Khan and Ahmad (2004) proposed Cluster Center Initialization Algorithm (CCIA) to solve
cluster initialization problem. CCIA is based on two observations, which some patterns are very
similar to each other. It initiates with calculating mean and standard deviation for data attributes,
and then separates the data with normal curve into certain partition. CCIA uses k-means and
density-based multi scale data condensation to observe the similarity of data patterns before
finding out the final initial clusters. The experiment results of the CCIA performed the
effectiveness and robustness this method to solve the several clustering problems.
Deelers and Auwatanamongkol (2007) proposed an algorithm to compute initial cluster centers
for k-means algorithm. They partitioned the data set in a cell using a cutting plane that divides
cell in two smaller cells. The plane is perpendicular to the data axis with the highest variance and
is designed to reduce the sum squared errors of the two cells as much as possible, while at the
same time keep the two cells far apart as possible. Also they partitioned the cells one at a time
until the number of cells equals to the predefined number of clusters, k. In their method the
centers of the k cells become the initial cluster centers for k-means algorithm.

Presently research is being done to make use of many attributes of the data set to find initial
cluster centres but this is again very time consuming and computation expensive process for just
finding the initial cluster centres as all the other methods mentioned above though they might
give very good result but if the data set is large and the processing time available for segmenting
images (or in that case any other kind of data) is less i.e. there is huge amount of images or video
data which has to be segmented then they would not fulfill the requirement.
Our proposed algorithm calculates the initial cluster centers that are quite close to the desired
cluster centers. The peaks which are obtained by using a moving average filter on the histogram
of the image are taken to be our initial cluster centres and they may not be the modes of the
histogram. This method is really fast in comparison to other methods as explained above in
finding the initial cluster centres (and is almost completed by the end of the process to find the
number of clusters) and better as well.
Firstly, it is not based on any kind of random choice for initial cluster centres which may lead to
the problem of non-convergence or may give erratic results(it will be very difficult to get unique
final cluster centres) for different initial centres which are chosen randomly and we can’t even
have any kind of control over them.
Secondly, since the initial cluster centres are found to be close to the final cluster centres the
whole clustering algorithm becomes fast as the number of iterations required to converge will
decrease whereas if the initial cluster centres are equally spaced throughout the intensity range
and the data is confined only to one section of intensity range, then unnecessarily more iterations
will be required and the cluster centres may also get trapped in local clustering of data.
Thirdly, it is independent of the size of the image. Only while making the histogram we require
going through all the pixels of the image otherwise all the calculations can be conducted on the
histogram itself which saves a lot of computation time [and is kind of uniform for different
image sizes].
Fourthly, it can be used on histogram and doesn’t require any other attribute to find the initial
cluster centres though there may be compromise with quality. The ones which use many
attributes to find the initial cluster centres are very calculation intensive and would make the
algorithm slow.
4.4 Convergence
There is a problem of convergence which may occur in K-means algorithm if care is not taken
and when random selection of initial cluster centres is done then since there is no control over
the process the algorithm may not even converge to final cluster centres. This may happen if the
initial cluster is put in a region where there are no data points. So when the new cluster centres
will be calculated in the next step then since there are no data points in that cluster the
denominator will become zero, hence there will be the problem of convergence.

A way was devised to avoid this problem by assigning the initial cluster centres between the
minimum and the maximum values of the data points. But still this problem may arise if cluster
centre drops in a region where there are no points pertaining to the data i.e. data need not be
spread throughout uniformly. So, this problem is also resolved by choosing correct initial cluster
centres and having some control over it.
4.5 Speed
Speed is always a factor which determines the applicability of a particular method. Simple K-
means algorithm applied on images is very slow because it is iteratively applied on the image
and as the size of the image increases its time of evaluating cluster centres will increase
proportionately as the computer will have to peruse all the pixels again. Though K-means is still
very fast in comparison to other methods for clustering as the computation is less. But it can be
made faster if it is applied on the histogram of the image rather than the image pixels.
Hence, as we have mentioned earlier we can work on the histogram of the image. The initial
cluster centre rather than being a pixel and iteratively measuring the distance of intensity of each
pixel from the intensity of the cluster centre pixel what can be done is we can take the intensities
of the peaks as the initial cluster centres and then cluster the intensities on the basis of their
nearness to respective cluster centre. Then using their frequency in the image as their weight and
calculate the new cluster centres. This way the number of data points is reduced from any
number depending on the size of the image to 255(if 8-bit representation). So the iterations
become faster and hence the same result can be obtained in lesser time.

CHAPTER 5 PROPOSED ALGORITHMS
5.1 optimum cluster centers and optimum number of clusters
Clustering algorithms like k-means and fuzzy c-means , although appears very simple, we get
long time or short time to converge depending upon initial cluster centers chosen and sometimes
it so happens that it doesn’t converge at all. For computer vision, we need a reliable algorithm
producing fast and sure shot convergence.
Number of clusters and initial cluster centers are human input in k-means algorithm. So, there is
a (n+1) degrees of freedom to get a particular segmentation, which causes inconsistency in
results, and there is known charge against k-means algorithm that it doesn’t have spatial
coherence.
Keeping these two things in mind, We propose a new concept of finding initial cluster centers as
a function of size of filter used to filter the histogram. Using this concept, degree of freedom
reduces to one i.e. size of the filter instead of number of clusters and it accounts for spatial
coherence too. Convergence becomes faster as initial cluster centers are somewhat near final
cluster centers.
We propose two methods of finding such optimum cluster centers using filtered histogram of the
image.
METHOD-1
Step 1: Apply moving average filter of size ‘t’ on histogram and obtain Histogram-1
Step 2: Apply moving average filter of size ‘round(t/2)’ on Histogram-1 and obtain Histogram-2
Step 3: Intensities having local maxima in the Histogram-2 can be taken as optimum initial
cluster centers. Since Histogram-2 is a filtered histogram, there are only very few local maximas
METHOD-2
Step 1: Apply moving average filter of size ‘t’ on histogram and obtain Histogram-1
Step 2: Apply moving average filter of size ‘round(t/2)’ on Histogram-1 and obtain Histogram-2
Step 3: Intensities having minima in the histogram can be taken as separating criteria for dividing
the original histograms into sub-histograms.
Step 4: Within those sub histograms, intensities having maximum frequency can be taken as
optimum initial cluster centers.

Although, choosing initial cluster centers at equal distance has been in practice so far. But by
using this method, we account for spatial coherency and speed increases very significantly as the
initial cluster centers obtained are somewhat near final cluster centers.
It is observed that greater the size of filter, lesser is the number of clusters obtained to start with.
And there is a high degree of consistency in final cluster centers obtained by same number of
cluster within certain range of size of filter used.
Whole idea is that input is size of the filter not number of clusters we want to divide the image
into, forcibly.
5.2 Proposed Algorithms for clustering
5.2.1 K-means using histogram
Step 1: Divide histogram into sub histograms by criteria of mid-point between cluster centers.
Step 2: perform k-means on histogram using these cluster centers to obtain new cluster centers
by finding the weighted average of intensities within the corresponding histogram. Weights are
calculated by dividing corresponding frequency of intensity with sum of all frequencies within
the sub histogram. This weighted average becomes the new cluster center
Step 3: Check if error between consecutive iterations is less than maximum error allowed
If Yes, final cluster centers are obtained and intensities within corresponding histogram belong to
corresponding cluster
Otherwise, Go to step 1
5.2.2 Fuzzy c-means using histogram
Equation for calculating membership remains same but while calculating average membership
term is multiplied with corresponding frequency of that intensity.
5.2.3 FCM +k-means
In FCM, while segmenting finally maximum an intensity falls in the cluster in which it has
maximum intensity.Finding maximum membership consumes lot of time. This can be easily
avoided by dividing in the way we divide in k-means (an intensity value belongs to the cluster if
it falls in sub-histogram of that particular cluster)
5.2.4 kf-means
K-means is fast whereas fuzzy c-means ensures sure shot convergence, therefore we propose a
method of combining these two to find the final cluster center in optimum time and with sure
shot convergence. We carry on iterations as we do in k-means, recalling the (sum of sub-

histogram) criteria discussed above can be used to call a single iteration of fuzzy c-means to
place the cluster centers in such a manner that convergence will happen as the criteria doesn’t
sense the problem of convergence once FCM is called.
5.3 Effect of using initial cluster centers proposed by two theorems
Original Image
Normal Initial cluster centers: 32 96 159 223
Final cluster centers: 19 77 137 237
Time taken: 1.59 secs
Optimum initial cluster centers by theorem 1(t=22): 33 78 123 255
Time Taken: 0.445 secs

Optimum initial cluster centers by theorem 1(t=22): 14 65 111 255
Time Taken:0.703 secs
Original Histogram
0
500
1000
1500
2000
2500
0 50 100 150 200 250

Filtered Histogram
One may ask what about time taken for finding these initial cluster centers. But finding normal
cluster centers also takes time as range of image need to be calculated as if by chance cluster
center outside the range is chosen, algorithm doesn’t converge.
0 50 100 150 200 250 300
0
200
400
600
800
1000
1200
1400
1600
1800
2000

5.4 Addressing problem of convergence in clustering algorithms
In spite of choosing optimum cluster centers, we cannot ensure convergence because of inherent
nature of the image. One of the reason might be discontinuous histogram. So we propose a
solution of using histogram based k-means algorithm. By which speed increases drastically. We
can have a constant check in every iteration, if algorithm can converge for given number of
cluster centers. Especially in computer vision, predefined number of clusters based on training
but still there are problems of convergence encountered.
We propose a flexible number of clusters method based on histogram.
Use optimum initial cluster centers obtained from METHOD-1.
Step 1: Divide histogram into sub histograms by criteria of mid-point between cluster centers.
Step 2: Check if sum of all frequencies in the sub histogram is greater than 0
If yes, continue.
Otherwise, delete this cluster center and merge the left part of sub histogram to left cluster center
and right part of sub histogram to right cluster center.
Original image with segmented edge Segmented image with segmented edge

Step 3: perform k-means on histogram using these cluster centers to obtain new cluster centers
by finding the weighted average of intensities within the corresponding histogram. Weights are
calculated by dividing corresponding frequency of intensity with sum of all frequencies within
the sub histogram.
Step 4: Check if difference between consecutive iteration is less than criterion predefined.
If yes, obtained cluster centers are final cluster centers.
Otherwise, go to step1.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 50 100 150 200 250

Now if we use normal initial cluster centers=32 96 159 223, algorithm doesn’t converge.
Because 3rd
initial cluster center (159) can’t have any pixel in his cluster.
if we use cluster centers obtained by theorem 1=44 88 125 237
Final cluster centers=14 59 104 215
Time taken=0.0911 secs
if we use cluster centers obtained by theorem 2=14 75 200 255
Final cluster centers=23 91 201 250
Time taken=0.09 secs

So, using these cluster centers, algorithm converges.
In spite of using these cluster centers we cannot ensure sure shot convergence , so reduction in
number of clusters remains as only solution as discussed above when it is encountered that
algorithm cannot converge using sub-histogram criteria
Main reason behind using histogram instead of image is to have some criteria for checking if
convergence is possible and take described action.
Thus the advantages of the proposed algorithms are:
1. It automatically finds the number of clusters for segmentation which used to be a
human input, thus, heading to automatic segmentation.
2. The initial cluster centres are obtained in a simple and refined way which removes the
problems which are created due to random selection of initial cluster centres like non-
convergence, improper clustering results, etc. , and is faster than other algorithms
which use many attributes to calculate initial cluster center though the result may be a
bit poor.
3. The problem of convergence has also been removed.
4. The speed has been increased manifold as is shown in next section containing results
because of various reasons:
a. Use of histogram for iterations rather than applying it on the image itself.
b. Number of clusters is chosen faster.
c. Initial cluster centres are also chosen very fast and they are found to be near
final cluster centre which decreases the overall number of iterations.
But there is a drawback in this method of segmentation that it is susceptible to noise because
noise can bring heavy shift in the final cluster centres and thus degrade the segmentation
result. The effect of noise can be removed by using a filter before segmenting the image to
get better result.

CHAPTER 6 Auto-segmentation/auto-pilot
Introduction
In a step to go further to automatic segmentation, to be more useful for computer vision and
machine learning, we made an effort wherein we don’t even require giving the input to the
moving average filter used in our proposed algorithm. Thus, we have been able to advance
further in our research to make the algorithm more user-friendly and faster.
The program itself applies the moving average filter on the histogram of the image for different
values of ‘t’ in steps of 2. This way a number of filtered outputs will be obtained and the number
of peaks obtained from the histogram may keep on decreasing due to more and more smoothing
of the histogram. And hence the number of clusters or the value of k may also keep on changing
according to our algorithm. The program will then see what are the values of k which is/are
stable, i.e. when the size of the moving average filter is varied which value of k occur
repetitively. Then, only for those values of k the segmentation is done and the results are shown.
This way we have been able to avoid any kind of human intervention and made the program
easier and faster. Presently, if a biomedical practitioners or some other professional interested in
segmentation uses K-means algorithm, he/she would have to try various values of k and then see
which value is suitable for him/her or is giving good results, which can be tedious, but here
he/she can just give one input to the program i.e. the image to be segmented, then the program
itself will find the stable values of k and show the segmented image only for those values of k.
Auto pilot
Auto pilot is a concept of finding all stable segmentations of an image.
Initialize t=3, s=maximum clusters you want, sm=minimum clusters you want
Step 1: increment ‘t’ in step of 2
Step 2: find initial cluster centers,
Step 3: if number of clusters<’s’. s=number of clusters. Segment the image
Otherwise, go to step 1
Step 4: s<=sm, autopilot has finished its job,break

Inverse auto pilot
Initialize t=80,sm=minimum clusters you want, s=maximum clusters you want
Step 1: decrement ‘t’ in step of 1
Step 2: find initial cluster centers,
Step 3: if number of clusters>=’sm’. sm=number of clusters. Segment the image
Step 4: sm>=s, autopilot has finished its job,break.
Original image
This image has been segmented into 4,3,2 clusters by auto pilot as shown below

clusters=4
clusters=3
clusters=2

CHAPTER 7
Fast Video Segmentation with automatic
change of number of clusters
Real-time Video-segmentation
Introduction
A video is made up of many images called frames which are linked together and these frames are
displayed at such a high speed that it appears to us as if it is one single component(one video).
But, it is not so, hence, video segmentation is similar to image segmentation only major
difference being that we segment each frame of the video in order to segment it. But various
other aspects come into picture while segmenting a video since it is not random images which
are to be segmented they are all linked in a manner.
Several video segmentation algorithms have been proposed. They can be classified into three
types:
1. edge information based video segmentation,
2. image segmentation based video segmentation and
3. change detection based video segmentation.
1. Edge information based algorithms, first apply edge detector algorithms to find edge
information of each frame and then keep tracking these edges. A morphology motion
filter is also applied to find edges belonging to foreground objects. Next, a filling
technique can connect edge information to generate final object masks. This method can
deal with both still camera and moving camera situations; however, the computation load
is very large.
2. Image segmentation based algorithms first apply image segmentation algorithms, such
as watershed transform and colour segmentation on each frame to separate a frame into
many homogeneous regions. By combining motion information derived with motion
estimation, or frame difference, regions with motion vectors different from the global
motion are merged as foreground regions. These algorithms often can give segmentation
results with accurate boundaries, but the computation load for image segmentation and
motion information calculation is also high, and the region merging process often has
many parameters to set. Both these two kinds of algorithms are too complex to be
integrated into a real-time system.
3. Change detection based segmentation algorithms, threshold the frame difference to
form change detection mask. Then the change detection masks are further processed to
generate final object masks. The processing speed is high, but it is often not robust. The
segmentation results are suffered from the uncovered background situations; still object
situations, light changing, shadow, and noise. The robustness can be promoted by a lot of
post-processing algorithms; however, complex post-processing will make the efficiency
of less computation lost. The threshold of change detection is very critical and cannot be
automatically decided. These reasons make this kind of algorithms not practical for real
applications.

All these algorithms have their own specific areas of excellence like image segmentation type
algorithms can give very good segmentation results but are too heavy to be used for real-time
applications, and change detection algorithms being light are often used for real-time
applications though a compromise on quality of segmentation is to be made.
Real time video segmentation is a very difficult task since the segmentation of the frame has to
be done very fast i.e. before the next frame arrives. Though the speed of arrival of frames can be
varied but still it has to be fast enough so that it doesn’t appear as a collection of images but a
video. In general, a speed of 25frames/second is found to be sufficient but that too requires the
segmentation algorithm to be really fast.
Proposed real-time video segmentation algorithm
We noticed that since our proposed algorithm is very fast in comparison to regular K-means
algorithm we thought that we can go one more step forward and try real-time video
segmentation. Our method would qualify as the second category of segmentation i.e. image
segmentation based algorithm, wherein we segment each frame of the video separately till the
next frame arrives. These types of algorithms are famous for their segmentation quality and poor
time efficiency, but our proposed method has not only improved the quality but also has
increased the speed large enough to be used for real-time purposes which earlier was not possible
for other image segmentation type algorithms.
By using moving average filter to find the number of clusters we have been able to break the
video into variable number of clusters for each frame i.e. each frame will have its own number of
clusters. If general K-means algorithm is applied to segment a video (not even real time) in
which the number of clusters is given as an input, it cannot be given for each frame as it will be
very difficult, so K will be given for a complete video. Hence, the program will try to break
every frame into equal number of clusters. For example, if the value of k is given as 4 then the
program will try to break each frame into 4 clusters even if in a frame there is only one intensity
value. This will give rise to the problem of non-convergence since the rest of the three clusters
won’t be able to find final cluster centres and it will give error. But by our method if any of the
frame has many objects of different intensities then it will be appropriately broken into many
clusters and if there is only one intensity then it will have only one cluster.
The additional feature of auto-pilot which has been incorporated so that the program itself
decides the value of n for moving average filter to give the number of clusters brings it closer to
being unsupervised. We just need to give the input that how much detail do we require from the
video i.e. If we require good amount of detail then we can keep number of clusters to be the
maximum value of n which comes out to be stable or if we require only crude discrimination
then we can have minimum stable value of n as number of clusters.

In video segmentation, clustering has been used only for video summary, but not for
segmentation of video frame itself, because of large computing time. By using autopilot as
discussed, segmentation of video is possible with automatic change in number of clusters when
there is introduction of new object in the image. This automatic change becomes a crucial point
of consideration in computer vision.
This can be established by using the auto pilot by choosing proper limits of clusters and breaking
the autopilot at first possible segmentation itself.
This fastest video segmentation algorithm as speed can go even up to 100 frames per second
based on limits of clusters whereas speed of previous algorithms is limited to only 25 frames per
second.
In applications like where we are concerned about only watching the video segmentation we can
just use color map to give the effect of segmentation without actually getting into the image and
cause increased computation time. This makes algorithm time independent of size of frame.
Uses,
 We can also use this algorithm for lossy video compression in internet video chating or
live streaming etc.
 In algorithms having to segment large database of images. This can save lot of time.
Frames of same video with change in number of clusters by introduction of object in the
video

CHAPTER 8 GRAPHIC USER INTERFACE
Layout of GUI
Divided into 7 panels:
1. Loader Panel
2. Error and Selection Panel
3. Viewer Panel
4. Interaction Panel
5. Initialization Panel
6. Segmentation Panel
7. Results Panel
Loader Panel
 Used for loading the image in the software
 Image name should be written in ‘file name.file format’
 Image is loaded as soon as Load Image button is pressed

 Software works only for 2 dimensional images. Therefore Image should be first
converted into 2 dimension and then it can be loaded
Error & Selection Panel
 Used for error selection & Theorem selection
 Error is the minimum error allowed between consecutive iteration to stop the iterations. It
acts as breaking criteria
 10 Algorithms have been loaded in the software. User can select any one of them for
segmenting the image
 First 6 Algorithms are already existing and last 4 Algorithms are proposed ones
 Existing Algorithms:
1. K-means
2. Fuzzy-cmean
3. Fcm for image with salt and pepper noise
4. Fcm for image with Gaussian noise
5. GKFCM
6. Modified GKFCM
 Proposed Algorithms
1. K-means using histogram
2. Fuzzy c-means using histogram
3. F+k means
4. Kf-means
Viewer Panel

 Axes 11 for showing image with initial cluster centers(to give an idea about
segmentation)
 Axes 6 for showing original image
Initialization panel
 Axes 1 is used for showing original histogram and filtered histogram
 Slider is used for giving size of moving average filter as user input
 Popup menu to select algorithm for finding initial cluster centers
 Provision for starting with normal cluster centers as ‘Normal’

 KHT and FHT for speeding up the segmentation of images that can use only image based
algorithms like image with noise
 Crop and Zoom In buttons for cropping the images and finding the pixel values
respectively.
Interaction Panel
 Used for snapshot
 Live segmentation demo(for computer vision )
 Chating demo
 User input: No. of frames
Segmentation Panel

 Display and editing of initial cluster centers
 Starting Segmentation
 Choosing color map and color of edge
 For choosing variables controlling neighborhood effect
 Choosing Auto Pilots:
1. Auto pilot using k-means
2. Auto Pilot using fuzzy c-means
Results Panel
 Display of final cluster centers.
 Display of time taken for segmentation algorithm.
 Display of number of iterations carried out.

CHAPTER 9 Experimental Results
Original Image
Original Histogram

Filtered Histogram
Comparision between speeds for initial cluster centers found with different theorems
(Algorithm used is simple k-means).
Normal Initial cluster centers for number of clusters as 3= [24 73 122]
Final cluster centers= [19 47 91], Time=0.3773 secs, iterations=12
Initial cluster centers using theorem 1 for ‘t’ as 15= [19 39 99]
Initial cluster centers using theorem 2 for ‘t’ as 15= [0 27 86]
Observe the reduction in no. of iterations required to get the result.

Since, we have found fastest results with theorem-1, Segmentation results in that case are being shown:
Comparision between results obtained by different algorithms(using initial cluster centers
of theorem -1):

Initial Cluster centers:[34 94 128]
k-means:
Fuzzy c-means:
k-means using proposed method:

Fcm using propsed method:
F+k means:
kf-means
Segmentations results obtained by kf-means:

Segmentation of noisy images:
(i)Salt & Pepper noise:
BCFCM_S2 is used

Initial Cluster Centers: [32 78 123 255]
‘t’=28
‘af’=10
‘sig’=20

cluster1 cluster2
cluster3 cluster4
Original Image with segmented edge Segmented Image with segmented edge

Edge obtained by matlab Edge obtained by propesed method

(ii)Gaussian Noise
Algorithm used=BCFCM_S1
Initial cluster centers=[57 77 255]
‘t’=41
‘af’=60
‘sig’=20

cluster1 cluster2 cluster3
Original Image with segmented edge Segmented Image with segmented edge

GKFCM:
Edge obtained by matlab Edge obtained by propesed method

Cropping
Sometimes detail required in the mage may be very small portion of entire image. In that case cropping
is necessary to obtain useful results so that the detail plays a significant role in the segmentation
Cropped image
To be able to see the tumor clearly

Tumor has got separated in cluster 5.
cluster1 cluster2 cluster3
cluster4 cluster5

CHAPTER 10 ACCOMPLISHMENTS, FUTURE RESEARCH AND APPLICATIONS
Accomplishments:
1. We have been able to implement six different algorithms for clustering K-means, Fuzzy
C-means, BCFCM, KFCM_S1, KFCM_S2 and GKFCM.
2. We have been able to make modifications to already existing algorithms to remove the
problem of number of clusters, initial cluster centres and non-convergence.
3. Four new methods have been proposed by us.
4. By speeding-up of the algorithms we have been able to do real-time image segmentation.
Future research or development:
1. Better selection of number of clusters can be done, though auto-pilot gives decent results
and is fast but it can be further improved depending upon the applications.
2. The algorithm is much faster than required to do 25frames/second so the work can be
done on improving the quality of the segmented video.
3. A further research can be done on choosing better membership function and relationship
between pixel and its neighbours that removes more noise gives better segmentation
results.
Applications:
1. For many segmentation algorithm K-means is pre-processing step on which other
segmentation tools are used so our method can speed-up segmentation and quality of
output as well , and can speed-up other processes requiring clustering like data mining,
information retrieval, etc.
2. By using the auto-pilot option the K-means algorithm has been made more unsupervised
and can be useful in computer vision and machine learning.
3. Real-time video segmentation can be useful in video-surveillance where data size is large
and time to survey it is less or in on-line chatting when the speed of transmission is poor
then the segmented image can be compressed more for fast transmission and retrieval.

References
1. Digital Image Processing using MATLAB, by Gonzalez, Woods and Eddins, 2009
2. Miin-Shen Yang, Hsu-Shen Tsai, 2008, ‘A Gaussian kernel-based fuzzy c-means
algorithm with a spatial bias correction’
3. Erlend Hodneland ,July, 2003, ‘Segmentation of Digital Image’
4. Ursula Gonzales-Baron, Francis Butler, March 2005, ‘A comparison of seven
thresholding techniques with the k-means clustering algorithm for measurement of bread-
crumb features by digital image analysis’
5. D.A. Clausi, 2002, K-means Iterative Fisher (KIF) unsupervised clustering algorithm
applied to image texture segmentation
6. Likas, Nikos Vlassis, Jakob J. Verbeek, 2003, The global k-means clustering algorithm
7. Sadullah Sakallioglu, Murat Erisoglu, Nazif Calis ,2011, ‘A new algorithm for initial
cluster centers in k-means algorithm 2011’
8. Liang Bai, Jiye Liang, Chuangyin Dang, 2011, ‘An initialization method to
simultaneously find initial cluster centers and the number of clusters for clustering
categorical data’
9. Fuyuan Cao, Jiye Liang, Guang Jiang, 2009, ‘An initialization method for the K-Means
algorithm using neighborhood model’
10. A.K. Jain, R.C. Dubes, Algorithms for Clustering Data
11. K.K. Chen, L. Liu, 2008, ‘Best K: critical clustering structures in categorical datasets’
12. J.J. Li, M.K. Ng, Y.M. Cheng, Z.H. Huang, 2008, ‘Agglomerative fuzzy k-means
clustering algorithm with selection of number of clusters’
13. J.M Peña, J.A Lozano, P Larrañaga, 1999, An empirical comparison of four initialization
methods for the K-means algorithm
14. Yasira Beevi and Dr. S. Natarajan, Dec 2009, An efficient Video Segmentation
Algorithm with Real time Adaptive Threshold Technique

Accomplishments:
5. We have been able to implement six different algorithms for clustering
Future research or development:
4. Better selection of number of clusters can be done, though auto-pilot gives decent results
and is fast but it can be further improved depending upon the applications.
5. The algorithm is much faster than required to do 25frames/second so the work can be
done on improving the quality of the segmented video.
6. A further research can be done on choosing better membership function and relationship
between pixel and its neighbours that removes more noise gives better segmentation
results.
Applications:
4. For many segmentation algorithm K-means is pre-processing step on which other
segmentation tools are used so our method can speed-up segmentation and quality of
output as well , and can speed-up other processes requiring clustering like data mining,
information retrieval, etc.
5. By using the auto-pilot option the K-means algorithm has been made more unsupervised
and can be useful in computer vision and machine learning.
6. Real-time video segmentation can be useful in video-surveillance where data size is large
and time to survey it is less or in on-line chatting when the speed of transmission is poor
then the segmented image can be compressed more for fast transmission and retrieval.

Image segmentation using advanced fuzzy c-mean algorithm [FYP @ IITR, obtained 'A+' ]

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Image segmentation using advanced fuzzy c-mean algorithm [FYP @ IITR, obtained 'A+' ]