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IJSRD - International Journal for Scientific Research & Development| Vol. 2, Issue 09, 2014 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 221
An Improved Way of Segmentation and Classification of Remote Sensing
Images using Kernel Induced Possiblistic C-Means Clustering Algorithm
with Statistical Measures
D. Napoleon1
Dr. E.Ramaraj2
1
Assistant Professor 2
Professor
1
Department of Computer Science
2
Department of Computer Science and Engineering
1
School of Computer Science and Engineering, Bharathiar University, Coimbatore, India 2
Alagappa
University, Karaikudi, India
Abstract— The Ultimate significance of Images lies in
processing the digital image which stems from two principal
application areas: Advances of pictorial information for
human interpretation; and dispensation of image data for
storage, communication, and illustration for self-sufficient
machine perception. The objective of this research work is
to define the meaning and possibility of image segmentation
based on remote sensing images which are successively
classified with statistical measures. In this paper kernel
induced Possiblistic C-means clustering algorithm has been
implemented for classifying remote sensing image data with
image features. As a final point of the proposed work is to
point out that this algorithm works well for segmenting and
classifying the image with better accuracy with statistical
metrices.
Key words: Image Processing, Image analysis, Statistical
Measures, Image Features
I. INTRODUCTION
An image can be defined as a two dimensional function in
spatial co-ordinates then its intensity or grey level of the
image at that point will be the amplitude f of the image at
that any pair of coordinates (x, y).when the coordinates pairs
x, y values and amplitude f values are finite, discrete
quantities then the image is known as digital image. Digital
images are being processed using the digital computers this
field of processing is called Digital Image processing.
Digital image is the collection of finite digits of elements,
where each element has a position and value. These
elements are called as pixels [5]. When the similar attributes
in the image are segmented into regions the process is
known as Segmentation. The extraction of important
features from image data for better interpretation and
description of the data is the reason of applying image
processing in various fields. Processing of remote sensing
images is an important task for the researchers but a time
consuming mission to be performed. The organization of
this paper is part II deals with the remote sensing image
segmentation analysis. Part III discusses about the related
work. Part IV illustrates the methodology while part V
focuses on the result and discussion and part VI deals with
conclusion of the paper.
II. RELATED WORK
A new algorithm is presented by Anjan Goswami, Ruoming
Jin, Gagan Agrawal where a few passes are only required
for the entire dataset to produce the same K-means
algorithm cluster centres. Initial clustering centres are based
on the sampling and to adjust cluster centres it takes one or
more passes for the whole dataset. Provides Theoretical
analyses of the clusters being computed are similar to the
original K-means algorithm. The results of real and
synthetic datasets are compared to K-means.
Herschel Boosting-Clustering algorithm is being
used to boost up the K-means algorithm for using it in the
remote sensing classification for acquiring better results.
There are two main objectives of this method 1) Choosing a
set of effectual features that is easily discriminated in feature
space. 2) Enhancing the performance of classifier for
classification. There are certain problems in the multi
clustering solution. An index is allotted to each category to
define the each iteration partitions and with the previous
iterations this indexing must be consistent. While running
the clustering based on the RGB value a rough training set is
being employed.
Leonardo Sant’anna Bins,Leila M. Garcia Fonseca,
Guaraci José Erthal, Fernando Mitsuo Ii Presented region
growing based segmentation which was implemented in
Geographic Information and Image Processing (SPRING)
which was developed by INPE. This approach is mainly
used in the assessment of land use changes in Amazon
region by segmenting the images. Landsat_TM images are
used in illustrating this technique.
Preetha, M.M.S.J., Suresh, L.P., Bosco, M.J Image
segmentation takes place when salient image regions are
clustered based on the pixels in which the regions
corresponds to the individual surfaces, natural parts of
objects or objects. In Image analysis and computer vision
applications segmentation process plays a very important
role. Various algorithms and techniques are developed in
image segmentation. Still Segmentation algorithm has not
satisfied the global application because when the region of
interest is segmented from the input image the segmentation
process is being stopped. So segmentation process still is a
challenging area for the researchers. This paper presents a
comparison of reviews based on colour image segmentation
is based on the region growing and merging algorithm.
Finally for segmenting of the colour images an automatic
seeded egion growing algorithm is being proposed.
III. FEATURE EXTRACTION
An object is uniquely identified by the features where this
identification is used in vision application to differentiate
one object and another object. The identification and
comparison process becomes ease by using the feature.
Colour, Shape and texture are the three basic features of
segmentation measurements [6]. This paper compares two
algorithms with the colour features. One of the most visually
used features is the colour feature. Colours are described in
a particular colour space [11]. Colour space is nearer to the
An Improved Way of Segmentation and Classification of Remote Sensing Images using Kernel Induced Possiblistic C-Means Clustering Algorithm with
Statistical Measures
(IJSRD/Vol. 2/Issue 09/2014/051)
All rights reserved by www.ijsrd.com 222
observation and is used in RBIR which includes RGB, LUV,
LAB, and HSV (HSL). Based on the segmentation results
the colour features are selected. The quality of visual
diffusion is enabled when the colour space is converted from
RGB colour to L*a*b [12]. Using the CIEXYZ tri stimulus
the L*a*b is derived. L*a*b denotes L for luminance, a for
colours in red-green axis and b for colours in blue-yellow
axis. The difference between the colours is measured using
the Euclidean distance.
IV. METHODOLOGY
The Methodology diagram of the proposed work is shown in
the figure1.
Input image (Landsat image, Quick Bird, Aster,
Modis) dataset is taken. Input image is Pre processed with
Image pre processing techniques which is a necessary one to
get better accuracy. After Pre processing techniques the
image has been inducted for Feature Extraction where the
features are segmented using this method. Main objective of
this research work is to classify the image based on basic
features and Modified Fuzzy Possiblistic C-means clustering
(KIPCM) is presented in this part.
Figure 1. Shows the present system in image
classification. This algorithm works well for the input image
and it performs well for Classification also.
Fig.1: System Architecture
The proposed System architecture as in fig 1.
Performs the above function in the way to extract the feature
so as to classify the image through effective segmentation
using Kernel Induced Possiblistic C-Means Algorithm.
V. KERNEL INDUCED POSSIBLISTIC C-MEANS CLUSTERING
ALGORITHM (KIPCM)
To convert the patterns to higher feature space the kernel
function is being used. This transforming allows the
partitioning of the distributed groupings more efficiently.
The transforming function specified need not be explicit
when the clustering is done based on the kernel. When the
dot product of two values is acquired by transforming
function into input space is known as the Kernel Function
[1]. The algorithm is described below
Algorithm:
STEP: 1 Initialization of memberships
Initialize fuzzier m, stopping criterion £, k=0;
Set initial uij (0) with memberships resulting from KIPCM
Set initial 
2
resulting from KIPCM;
STEP: 2 Minimization of objective function
REPEAT k k+1
Compute d2 (xi, vj) using the equation

 



 


 n
j
m
n
n
j
n
i
m
ij
n
j
m
ij
N
j
m
ij
u
u
u
u
xkxkk
1
1 1
1
1
2),(
Compute nij and uij (k)
UNTIL
 )()( kijkij uu
<€
VI. RESULTS AND DISCUSSION
Remote sensing image dataset has been used in this paper to
compute the basic image features by using various
techniques. The input image is given below
Landsat image Quick bird
Aster Modis
Fig.2: Remote Sensing Image Data Set
For this dataset green colour represents the
vegetation, dry land is represented by dark area, slightly
darker green represents the grass land and paddy field is
represented by deep darker colour. The degree of class
mixture is high in the vegetation area.
Exposed land is represented by brown colour.
Slightly brown colour represents the dry salt flats which is a
blocked by forest land and dry land which highly mixed.
This denotes the difficulty level of land cover clustering.
These images represent the image classification results after
using the proposed algorithm.
Fig.3: Result of KIPCM Using Landsat Dataset
An Improved Way of Segmentation and Classification of Remote Sensing Images using Kernel Induced Possiblistic C-Means Clustering Algorithm with
Statistical Measures
(IJSRD/Vol. 2/Issue 09/2014/051)
All rights reserved by www.ijsrd.com 223
Fig. 4: Result of KIPCM using Quick Bird Dataset
Fig. 5: Results of KIPCM Using MODIS Dataset
Fig. 6: Results in KIPCM using Aster Dataset
Table 1: Performance analysis of KIPCM Algorithm
Fig.7: Graph Analysis for KIPCM
VII. CONCLUSION
Image Classification and Segmentation is an important arena
in the field of Image Processing where numerous
information is hidden in Images. In this research work
Kernel Induced Possiblistic C-Means (KIPCM) clustering
algorithm is used to Segment and Classify the Remote
Sensing Images. Various remote sensing images have been
taken as input so as to perform segmentation and
Classification. Two parameters time and accuracy is
measured for the remote sensing image datasets. These
experimental results are carried out with different remote
sensing images, with Kernel Induced Possiblistic C-Means
(KIPCM) clustering algorithm which produces better results
in terms of time and accuracy. As a future work the Plan is
to improve the accuracy by combining clustering algorithms
with optimization techniques.
REFERENCES
[1]. D. Graves and W. Pedrycz, “Kernel-based fuzzy
clustering and fuzzy clustering: A comparative
experimental study,” Fuzzy Sets and Systems,vol.
161, no. 4, pp. 522–543, 2010.
[2]. Jiang-She Zhang and Yiu-Wing Leung,” Improved
Possibilistic C-Means Clustering Algorithms,”
IEEE Trans. on Fuzzy Systems, vol. 12, no. 2, pp.
209-217, April 2004.
[3]. Nikhil R. Pal,Kuhu Pal, James M. Keller, and
James C. Bezdek, “A Possibilistic Fuzzy c-Means
Clustering Algorithm,” IEEE Trans. On Fuzzy
Systems, vol. 13, no. 4, pp. 517-530, Aug. 2005.
[4]. T. Kanungo, D. M. Mount, N. Netanyahu, C.
Piatko, R. Silverman, & A. Y.Wu (2002) “An
efficient k-means clustering algorithm: Analysis
and implementation” Proc. IEEE Conf. Computer
Vision and Pattern Recognition, pp.881-892.
[5]. H. J. Zhang, Y. Gong, C. Y. Low and S. W.
Smoliar, „„Image Retrieval Based on Color
Feature: An Evaluation Study‟‟, SPIE - Digital
Image Storage and Archiving Systems, vol. 2606,
pp. 212-220, 1995.
[6]. Pooja Verma, Manish Mahajan, “Retrieval of better
results by using shape techniques for content based
retrieval”,IJCSC ,Vol. 3,No.2, January-June 2012,
pp. 254-257, ISSN: 0973-7391.
[7]. Jay Acharya, Sohil Gadhiya and Kapil Raviya,
“Segmentation Techniques for Image Analysis: A
Review”, International Journal of Computer
Science and Management Research, Vol 2 Issue 1,
January 2013, Pg. 1218-1221.
[8]. Rajesh Dass, Priyanka, Swapna Devi, “Image
Segmentation Techniques”, IJECT Vol. 3, Issue 1,
Jan. - March 2012.
[9]. Vishal B. Langote and Dr. D. S. Chaudhari,
“Segmentation Techniques for Image Analysis”,
International Journal of Advanced Engineering
Research and Studies (IJAERS)/Vol. I/ Issue
II/January-March, 2012.
[10]. Liu, Jian Guo & Mason, Philippa J.
(2009), “Essential Image Processing for GIS and
RemoteSensing”,Wiley- Blackwell. p. 4. ISBN
978-0-470-51032-2.
[11]. Sklansky, J., “Image Segmentation and
Feature Extraction,” IEEE Transactions on
Systems,Man, and Cybernetics, SMC-8, pp. 237-
247, 1978.
[12]. Hargreaves, D., and Robertson, B., 2001,
Review of Quickbird-1/2 and Orbview-3/4
An Improved Way of Segmentation and Classification of Remote Sensing Images using Kernel Induced Possiblistic C-Means Clustering Algorithm with
Statistical Measures
(IJSRD/Vol. 2/Issue 09/2014/051)
All rights reserved by www.ijsrd.com 224
Products from MacDonald Dettwiler Processing
Systems, Proceedings of the ASPRS Annual
Conference, St Louis, Missouri, USA, April 23-27,
(Bethesda, MD: ASPRS)
[13]. Malik, S. Belongie, J. Shi, and T. Leung.
Textons, contours and regions: Cue integration in
image segmentation. Seventh International
Conference on Computer Vision, Sept 1999.
[14]. N.Pal, S. Pal., “ A review on image
segmentation techniques, Pattern Recognition”,
Vol. 26. No. 9, 1993, pp 1277-1294.
[15]. D. Q. Zhang and S. C. Chen, “A novel
kernelized fuzzy C-means algorithm with
application in medical image segmentation,” Artif.
Intell. Med., vol. 32, no. 1, pp. 37–50, Sep. 2004

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An Improved Way of Segmentation and Classification of Remote Sensing Images Using Kernel Induced Possiblistic C-Means Clustering Algorithm with Statistical Measures

  • 1. IJSRD - International Journal for Scientific Research & Development| Vol. 2, Issue 09, 2014 | ISSN (online): 2321-0613 All rights reserved by www.ijsrd.com 221 An Improved Way of Segmentation and Classification of Remote Sensing Images using Kernel Induced Possiblistic C-Means Clustering Algorithm with Statistical Measures D. Napoleon1 Dr. E.Ramaraj2 1 Assistant Professor 2 Professor 1 Department of Computer Science 2 Department of Computer Science and Engineering 1 School of Computer Science and Engineering, Bharathiar University, Coimbatore, India 2 Alagappa University, Karaikudi, India Abstract— The Ultimate significance of Images lies in processing the digital image which stems from two principal application areas: Advances of pictorial information for human interpretation; and dispensation of image data for storage, communication, and illustration for self-sufficient machine perception. The objective of this research work is to define the meaning and possibility of image segmentation based on remote sensing images which are successively classified with statistical measures. In this paper kernel induced Possiblistic C-means clustering algorithm has been implemented for classifying remote sensing image data with image features. As a final point of the proposed work is to point out that this algorithm works well for segmenting and classifying the image with better accuracy with statistical metrices. Key words: Image Processing, Image analysis, Statistical Measures, Image Features I. INTRODUCTION An image can be defined as a two dimensional function in spatial co-ordinates then its intensity or grey level of the image at that point will be the amplitude f of the image at that any pair of coordinates (x, y).when the coordinates pairs x, y values and amplitude f values are finite, discrete quantities then the image is known as digital image. Digital images are being processed using the digital computers this field of processing is called Digital Image processing. Digital image is the collection of finite digits of elements, where each element has a position and value. These elements are called as pixels [5]. When the similar attributes in the image are segmented into regions the process is known as Segmentation. The extraction of important features from image data for better interpretation and description of the data is the reason of applying image processing in various fields. Processing of remote sensing images is an important task for the researchers but a time consuming mission to be performed. The organization of this paper is part II deals with the remote sensing image segmentation analysis. Part III discusses about the related work. Part IV illustrates the methodology while part V focuses on the result and discussion and part VI deals with conclusion of the paper. II. RELATED WORK A new algorithm is presented by Anjan Goswami, Ruoming Jin, Gagan Agrawal where a few passes are only required for the entire dataset to produce the same K-means algorithm cluster centres. Initial clustering centres are based on the sampling and to adjust cluster centres it takes one or more passes for the whole dataset. Provides Theoretical analyses of the clusters being computed are similar to the original K-means algorithm. The results of real and synthetic datasets are compared to K-means. Herschel Boosting-Clustering algorithm is being used to boost up the K-means algorithm for using it in the remote sensing classification for acquiring better results. There are two main objectives of this method 1) Choosing a set of effectual features that is easily discriminated in feature space. 2) Enhancing the performance of classifier for classification. There are certain problems in the multi clustering solution. An index is allotted to each category to define the each iteration partitions and with the previous iterations this indexing must be consistent. While running the clustering based on the RGB value a rough training set is being employed. Leonardo Sant’anna Bins,Leila M. Garcia Fonseca, Guaraci José Erthal, Fernando Mitsuo Ii Presented region growing based segmentation which was implemented in Geographic Information and Image Processing (SPRING) which was developed by INPE. This approach is mainly used in the assessment of land use changes in Amazon region by segmenting the images. Landsat_TM images are used in illustrating this technique. Preetha, M.M.S.J., Suresh, L.P., Bosco, M.J Image segmentation takes place when salient image regions are clustered based on the pixels in which the regions corresponds to the individual surfaces, natural parts of objects or objects. In Image analysis and computer vision applications segmentation process plays a very important role. Various algorithms and techniques are developed in image segmentation. Still Segmentation algorithm has not satisfied the global application because when the region of interest is segmented from the input image the segmentation process is being stopped. So segmentation process still is a challenging area for the researchers. This paper presents a comparison of reviews based on colour image segmentation is based on the region growing and merging algorithm. Finally for segmenting of the colour images an automatic seeded egion growing algorithm is being proposed. III. FEATURE EXTRACTION An object is uniquely identified by the features where this identification is used in vision application to differentiate one object and another object. The identification and comparison process becomes ease by using the feature. Colour, Shape and texture are the three basic features of segmentation measurements [6]. This paper compares two algorithms with the colour features. One of the most visually used features is the colour feature. Colours are described in a particular colour space [11]. Colour space is nearer to the
  • 2. An Improved Way of Segmentation and Classification of Remote Sensing Images using Kernel Induced Possiblistic C-Means Clustering Algorithm with Statistical Measures (IJSRD/Vol. 2/Issue 09/2014/051) All rights reserved by www.ijsrd.com 222 observation and is used in RBIR which includes RGB, LUV, LAB, and HSV (HSL). Based on the segmentation results the colour features are selected. The quality of visual diffusion is enabled when the colour space is converted from RGB colour to L*a*b [12]. Using the CIEXYZ tri stimulus the L*a*b is derived. L*a*b denotes L for luminance, a for colours in red-green axis and b for colours in blue-yellow axis. The difference between the colours is measured using the Euclidean distance. IV. METHODOLOGY The Methodology diagram of the proposed work is shown in the figure1. Input image (Landsat image, Quick Bird, Aster, Modis) dataset is taken. Input image is Pre processed with Image pre processing techniques which is a necessary one to get better accuracy. After Pre processing techniques the image has been inducted for Feature Extraction where the features are segmented using this method. Main objective of this research work is to classify the image based on basic features and Modified Fuzzy Possiblistic C-means clustering (KIPCM) is presented in this part. Figure 1. Shows the present system in image classification. This algorithm works well for the input image and it performs well for Classification also. Fig.1: System Architecture The proposed System architecture as in fig 1. Performs the above function in the way to extract the feature so as to classify the image through effective segmentation using Kernel Induced Possiblistic C-Means Algorithm. V. KERNEL INDUCED POSSIBLISTIC C-MEANS CLUSTERING ALGORITHM (KIPCM) To convert the patterns to higher feature space the kernel function is being used. This transforming allows the partitioning of the distributed groupings more efficiently. The transforming function specified need not be explicit when the clustering is done based on the kernel. When the dot product of two values is acquired by transforming function into input space is known as the Kernel Function [1]. The algorithm is described below Algorithm: STEP: 1 Initialization of memberships Initialize fuzzier m, stopping criterion £, k=0; Set initial uij (0) with memberships resulting from KIPCM Set initial  2 resulting from KIPCM; STEP: 2 Minimization of objective function REPEAT k k+1 Compute d2 (xi, vj) using the equation            n j m n n j n i m ij n j m ij N j m ij u u u u xkxkk 1 1 1 1 1 2),( Compute nij and uij (k) UNTIL  )()( kijkij uu <€ VI. RESULTS AND DISCUSSION Remote sensing image dataset has been used in this paper to compute the basic image features by using various techniques. The input image is given below Landsat image Quick bird Aster Modis Fig.2: Remote Sensing Image Data Set For this dataset green colour represents the vegetation, dry land is represented by dark area, slightly darker green represents the grass land and paddy field is represented by deep darker colour. The degree of class mixture is high in the vegetation area. Exposed land is represented by brown colour. Slightly brown colour represents the dry salt flats which is a blocked by forest land and dry land which highly mixed. This denotes the difficulty level of land cover clustering. These images represent the image classification results after using the proposed algorithm. Fig.3: Result of KIPCM Using Landsat Dataset
  • 3. An Improved Way of Segmentation and Classification of Remote Sensing Images using Kernel Induced Possiblistic C-Means Clustering Algorithm with Statistical Measures (IJSRD/Vol. 2/Issue 09/2014/051) All rights reserved by www.ijsrd.com 223 Fig. 4: Result of KIPCM using Quick Bird Dataset Fig. 5: Results of KIPCM Using MODIS Dataset Fig. 6: Results in KIPCM using Aster Dataset Table 1: Performance analysis of KIPCM Algorithm Fig.7: Graph Analysis for KIPCM VII. CONCLUSION Image Classification and Segmentation is an important arena in the field of Image Processing where numerous information is hidden in Images. In this research work Kernel Induced Possiblistic C-Means (KIPCM) clustering algorithm is used to Segment and Classify the Remote Sensing Images. Various remote sensing images have been taken as input so as to perform segmentation and Classification. Two parameters time and accuracy is measured for the remote sensing image datasets. These experimental results are carried out with different remote sensing images, with Kernel Induced Possiblistic C-Means (KIPCM) clustering algorithm which produces better results in terms of time and accuracy. As a future work the Plan is to improve the accuracy by combining clustering algorithms with optimization techniques. REFERENCES [1]. D. Graves and W. Pedrycz, “Kernel-based fuzzy clustering and fuzzy clustering: A comparative experimental study,” Fuzzy Sets and Systems,vol. 161, no. 4, pp. 522–543, 2010. [2]. Jiang-She Zhang and Yiu-Wing Leung,” Improved Possibilistic C-Means Clustering Algorithms,” IEEE Trans. on Fuzzy Systems, vol. 12, no. 2, pp. 209-217, April 2004. [3]. Nikhil R. Pal,Kuhu Pal, James M. Keller, and James C. Bezdek, “A Possibilistic Fuzzy c-Means Clustering Algorithm,” IEEE Trans. On Fuzzy Systems, vol. 13, no. 4, pp. 517-530, Aug. 2005. [4]. T. Kanungo, D. M. Mount, N. Netanyahu, C. Piatko, R. Silverman, & A. Y.Wu (2002) “An efficient k-means clustering algorithm: Analysis and implementation” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp.881-892. [5]. H. J. Zhang, Y. Gong, C. Y. Low and S. W. Smoliar, „„Image Retrieval Based on Color Feature: An Evaluation Study‟‟, SPIE - Digital Image Storage and Archiving Systems, vol. 2606, pp. 212-220, 1995. [6]. Pooja Verma, Manish Mahajan, “Retrieval of better results by using shape techniques for content based retrieval”,IJCSC ,Vol. 3,No.2, January-June 2012, pp. 254-257, ISSN: 0973-7391. [7]. Jay Acharya, Sohil Gadhiya and Kapil Raviya, “Segmentation Techniques for Image Analysis: A Review”, International Journal of Computer Science and Management Research, Vol 2 Issue 1, January 2013, Pg. 1218-1221. [8]. Rajesh Dass, Priyanka, Swapna Devi, “Image Segmentation Techniques”, IJECT Vol. 3, Issue 1, Jan. - March 2012. [9]. Vishal B. Langote and Dr. D. S. Chaudhari, “Segmentation Techniques for Image Analysis”, International Journal of Advanced Engineering Research and Studies (IJAERS)/Vol. I/ Issue II/January-March, 2012. [10]. Liu, Jian Guo & Mason, Philippa J. (2009), “Essential Image Processing for GIS and RemoteSensing”,Wiley- Blackwell. p. 4. ISBN 978-0-470-51032-2. [11]. Sklansky, J., “Image Segmentation and Feature Extraction,” IEEE Transactions on Systems,Man, and Cybernetics, SMC-8, pp. 237- 247, 1978. [12]. Hargreaves, D., and Robertson, B., 2001, Review of Quickbird-1/2 and Orbview-3/4
  • 4. An Improved Way of Segmentation and Classification of Remote Sensing Images using Kernel Induced Possiblistic C-Means Clustering Algorithm with Statistical Measures (IJSRD/Vol. 2/Issue 09/2014/051) All rights reserved by www.ijsrd.com 224 Products from MacDonald Dettwiler Processing Systems, Proceedings of the ASPRS Annual Conference, St Louis, Missouri, USA, April 23-27, (Bethesda, MD: ASPRS) [13]. Malik, S. Belongie, J. Shi, and T. Leung. Textons, contours and regions: Cue integration in image segmentation. Seventh International Conference on Computer Vision, Sept 1999. [14]. N.Pal, S. Pal., “ A review on image segmentation techniques, Pattern Recognition”, Vol. 26. No. 9, 1993, pp 1277-1294. [15]. D. Q. Zhang and S. C. Chen, “A novel kernelized fuzzy C-means algorithm with application in medical image segmentation,” Artif. Intell. Med., vol. 32, no. 1, pp. 37–50, Sep. 2004