STUDY AND DEVELOPMENT OF SOME NOVEL FUZZY IMAGE SEGMENTATION TECHNIQUEs

STUDY AND DEVELOPMENT OF SOME NOVEL FUZZY IMAGE SEGMENTATION TECHNIQUEs
STUDY AND DEVELOPMENT OF SOME
NOVEL FUZZY IMAGE SEGMENTATION
TECHNIQUEs
A thesis submitted in partial fulfillment of the
requirements for the degree of
MASTER OF TECHNOLOGY (Research)
In
ELECTRONICS AND COMMUNICATION ENGINEERING
By
KUMARI NIRULATA
Under the supervision
Of
DR. S. MEHER
Department Of Electronics and Communication Engineering
National Institute of Technology, Rourkela, India
August 2009
CertifiCate
This is to certify that the thesis titled “Study and Development of Some Novel
Fuzzy Image Segmentation Techniques”, submitted to National Institute of
Technology,Rourkela (INDIA) by Kumari Nirulata, roll no. 60609002 for the
award of the degree of master of Technology in Electronics and Communication
Engineering, is a bonafide record of the research work carried out by her under
my supervision and guidance.
The candidate has fulfilled all the requirements.
The thesis, which is based on candidate’s own work, has not been submitted
elsewhere for a degree/diploma.
In my opinion, the thesis is of standard required of a M.Tech (R) degree in
engineering.
To the best of my knowledge, Mrs. Nirulata bears a good moral character and
decent behavior.
Dr. Sukadev Meher
Asst. Professor
Department Of Electronics and Communication Engineering
National Institute of Technology,
Rourkela-769008(INDIA)
PREFACE
Digital Image Processing, developed during last two and half decades, has become a very
important subject in electronics and computer engineering. Computer vision and robotic
vision is one of the many areas it encompasses. Image object identification and
segmentation are the two sub-areas of image restoration.
The goal of image segmentation is partition of an image into a set of disjoint regions with
uniform and homogeneous attributes such as intensity, color, tone or texture etc. In many
real situations, for images, issues such as limited spatial resolution, poor contrast,
overlapping intensities, noise and intensity inhomogenities introduce fuzziness in the
object boundaries in the image. Due to this the fuzzy set theory was proposed, which
produced the idea of partial membership of belonging described by a membership
function.
Fuzzy rule based segmentation and various fuzzy clustering based segmentation has been
implemented and developed. The proposed FCM based segmentation methods are tested
extensively by subjective and objective evaluation. Under low noise conditions, though
many FCM based segmentation methods are very good in terms of objective evaluations,
the resulting output images of almost all methods give nearly equal visual quality. Hence
efforts are made here to develop efficient filters for suppression of a uniform random
noise under moderate and high noise conditions. The developed algorithm has also been
applied to biomedical image segmentation.
Therefore, the present research work may be treated as
(i)
developmental work; and
(ii)
applied research work.
I would be happy to see other researchers using the results reported in the thesis for
developing better image filters. Moreover, I will be contended to find these filters
implemented for practical applications in near future.
Kumari Nirulata
i
ACKNOWLEDGEMENT
I express my indebtedness and gratefulness to my teacher and supervisor Prof. Sukadev
Meher for his continuous encouragement and guidance. I needed his support, guidance
and encouragement throughout the research period. I am obliged to him for his moral
support through all the stages during this doctoral research work. I am indebted to him for
the valuable time he has spared for me during this work.
I am thankful to Prof. S. K. Patra, Head, Department of Electronics & Communication
Engineering who provided all the official facilities to me. I am also thankful to other DSC
members, Prof. G. Panda , Prof. K.K. Mahapatra and Prof. B. Majhi for their continuous
support during the doctoral research work.
I would like to thank all my colleagues and friends N. Bhoi, R. Kulkarni, C.S. Rawat,
Devi, Mamta, Satyasai and Sitanshu, for their company and cooperation during this
period.
I take this opportunity to express my regards and obligation to my parents whose support
and encouragement I can never forget in my life.
I would like to thank my husband Lalit for his patience and cooperation. I duly
acknowledge the constant moral support he provided throughout.
Lastly, I am thankful to all those who have supported me directly or indirectly during the
research work.
Kumari Nirulata
ii
BIO-DATA OF THE CANDIDATE
Name of the candidate
:
Kumari Nirulata
Father’s Name
:
Raghubansh Ku. Singh
Present Address
:
M.Tech( R) Scholar,
Dept. of Electronics and
Communication Engg.
National Institute of
Technology, Rourkela-769008
:
Permanent Address
Qr. No. B/7
N.I.T.Campus
Rourkela- 769008
:
ACADEMIC QUALIFICATION
(i) B. E. in Electronics and Instrumentation, Purushottam Institute of
Engg. and Technology
BPUT, Rourkela, Orissa, INDIA
PUBLICATION:
(i)
Published 02 papers in International Journals;
(ii)
Communicated 01 papers to International Journals;
(iii)
Published 03 papers in National and International Conferences.
iii
CONTENTS
Page No.
Certificate
Preface
Acknowledgement
Bio-data of the Candidate
Contents
Abstract
List of Abbreviations used
List of Symbols used
1.
1.1
1.2
1.3
1.4
1.5
1.6
2.
i
ii
iii
iv
vi
ix
xi
INTRODUCTION
Preview
Fundamentals of Digital Image Processing
Image Segmentation
Literature Survey of Fuzzy Techniques applied to
Segmentation
Problem Statement
Image Metrics
Conclusion
1
2
3
5
7
12
13
15
Basic Techniques of Image Segmentation
Preview
Region Based Segmentation
Segmentation Technique based on Discontinuity property
of pixels
16
17
17
22
29
3.3
Study and Implementation of Segmentation based on
Fuzzy Edge Detection
Preview
A FIS System for Edge Detection based Segmentation
An Efficient multilevel Fuzzy edge detector for Digital
Images
Edge Linking by Morphological Operators
45
4.1
4.2
Development of Algorithm for Segmentation of Color
Images using Fuzzy Clustering
Preview
Representation of Color Images
Selection of Color Space
2.1
2.2
3.
3.1
3.2
4.
iv
30
32
38
44
46
48
49
4.3
4.4
4.5
5.
5.1
5.2
5.3
5.4
5.5
Fuzzy c means Algorithm
Segmentation Method
Image Segmentation under Uneven Illumination of Objects
51
53
55
Development of Algorithm for Segmentation by
Incorporating Spatial Property of pixels in fuzzy
Clustering
Preview
FCM Related Extensions
Development of Algorithm for Incorporating Spatial
Spatial Relationship of Neighboring Pixels into FCM
Segmentation of noisy color images by using
neighborhood property of a digital image
Segmentation by using Morphological operator
Application of NAFCM algorithm in segmentation of
melanoma images
58
59
60
61
66
69
70
6.1
6.2
6.3
Simulation Results and Discussion
Preview
Simulation Results
Discussion
Conclusion
71
72
72
77
121
6.1
6.2
6.3
Conclusion
Preview
Comparative Analysis
Conclusion
Scope for Future Work
124
125
126
130
131
References
Contribution by the Candidate
132
6.
6.
v
Abstract
Some fuzzy technique based segmentation methods are studied and implemented and
some fuzzy c means clustering based segmentation algorithms are developed in this thesis
to suppress high and low uniform random noise. The reason for not developing fuzzy rule
based segmentation method is that they are application dependent
In many occasions, the images in real life are affected with noise. Fuzzy c means
clustering based segmentation does not give good segmentation result under such
condition. Various extension of the FCM method for segmentation are present in the
literature. But most of them modify the objective function hence changing the basic FCM
algorithm present in MATLAB toolboxes. Hence efforts have been made to develop
FCM algorithm without modifying their objective function for better segmentation .
The fuzzy technique based segmentation methods that are studied and developed are
summarized here.
(A) Fuzzy edge detection based segmentation: Two fuzzy edge detection methods
are studied and implemented for segmentation: (i) FIS based edge detection and (ii) Fast
multilevel fuzzy edge detector (FMFED).
(i): The Fuzzy Inference system (FIS) based edge detector consists of some fuzzy
inference rules which are defined in such a way that the FIS system output (“edges”) is
high only for those pixels belonging to edges in the input image. A robustness to contrast
and lightining variations were also taken into consideration while developing these
rules.The output of the FIS based edge detector is then compared with the existing Sobel,
LoG and Canny edge detector results. The algorithm is seen to be application dependent
and time consuming.
(ii) Fast Multilevel Fuzzy Edge Detector: To realise the fast and accurate detection of
edges, the FMFED algorithm is proposed. It first enhances the image contrast by means
of a fast multilevel fuzzy enhancement algorithm using simple transformation function
based on two image thresholds. Second, the edges are extracted from the enhanced image
by using a two stage edge detector operator that identifies the edge candidates based on
vi
local characteristics of the image and then determines the true edge pixels using edge
detector operator based on extremum of the gradient values.
Finally the segmentation of the edge image is done by morphological operator by edge
linking.
(B) FCM based segmentation: Two fuzzy clustering based segmentation methods
are developed: (i) Modified Spatial Fuzzy c-Means (MSFCM) (ii) Neighbourhood
Attraction Fuzzy c-Means (NAFCM). .
(i)
Contrast-Limited
Adaptive
Histogram
Equalization
Fuzzy
c-Means
(CLAHEFCM): This proposed algorithm presents a color segmentation process for low
contrast images or unevenly illuminated images. The algorithm presented in this paper
first enhances the contrast of the image by using contrast limited adaptive histogram
equalization. After the enhancement of the image this method divides the color space into
a given number of clusters, the number of cluster are fixed initially. The image is
converted from RGB color space to LAB color space before the clustering process.
Clustering is done here by using Fuzzy c means algorithm. The image is segmented based
on color of a region, that is, areas having same color are grouped together. The image
segmentation is done by taking into consideration, to which cluster a given pixel belongs
the most. The method has been applied on a number of color test images and it is
observed to give good segmentation results
(ii) Modified Spatial Fuzzy c-means (MSFCM): The proposed algorithm divides the
color space into a given number of clusters, the number of cluster are fixed initially. The
image is converted from RGB color space to LAB color space before the clustering
process. A robust segmentation technique based on extension to the traditional fuzzy cmeans (FCM) clustering algorithm is proposed. The spatial information of each pixel in
an image has been taken into consideration to get a noise free segmentation result. The
image is segmented based on color of a region, that is, areas having same color are
grouped together. The image segmentation is done by taking into consideration, to which
cluster a given pixel belongs the most. The method has been applied to some color test
images and its performance has been compared to FCM and FCM based methods to show
vii
its superiority over them. The proposed technique is observed to be an efficient and easy
method for segmentation of noisy images.
(iv)Neighbourhood Attraction Fuzzy c Means Algorithm: A new algorithm based on
the IFCM neighbourhood attraction is used without changing the distance function of the
FCM and hence avoiding an extra neural network optimization step for the adjusting
parameters of the distance function, it is called Neighborhood Atrraction FCM
(NAFCM). During clustering, each pixel attempts to attract its neighbouring pixels
towards its own cluster. This neighbourhood attraction depends on two factors: the pixel
intensities or feature attraction, and the spatial position of the neighbours or distance
attraction, which also depends on neighbourhood structure. The NAFCM algorithm is
tested on a synthetic image (chapter 6, figure 6.3-6.6) and a number of skin tumor
images. It is observed to produce excellent clustering result under high noise condition
when compared with the other FCM based clustering methods.
viii
List of Abbreviations used
Abbreviations
1.
FIS
Fuzzy Inference System
2.
FID
Fuzzification, Inference and de-fuzzification
3.
FCM
Fuzzy c-means
4.
sFCM
Spatial Fuzzy c means
5.
MSFCM
Modified spatial fuzzy c means
6.
FMFED
Fast Multilevel Fuzzy Edge Detection
7.
FMFE
Fast Multilevel Fuzzy Enhancement
8.
ANFIS
Adaptive Neuro Fuzzy Inference System
9.
FMMIS
10. DH
Fuzzy Min-Max Neural Network for Image
Segmentation
Result of applying hDH
11. DV
Result of applying hDV
12. E
Edge detected image
13. FRIST
14. GFRIS
Fuzzy Rules for Image Segmentation incorporating
Texture features
Generic Fuzzy Rule based Image Segmentation
15. PFCM
Penalized Fuzzy c-means
16. FMCM
Fuzzy Membership c means
17. SWFCM
Spatially Weighted Fuzzy c-means
18. k-NN
k-nearest neighbour
19. LoG
Laplacian of Gaussian
20. AHE
Adaptive Histogram equalization
ix
21. CLAHE
Contrast-Limited Adaptive Histogram Equalization
22. NC
Noisy Clustering
23. PCM
Possibilistic c-means
24. NAFCM
Neighbourhood Attraction Fuzzy c means
25. IFCM
Improved Fuzzy c means
26. HVS
Human Visual System
x
List of Symbols used
Symbols
1.
2.
R
R1,R2….Rn
Entire image region
N sub regions of R
3.
P(Ri)
Logical predicate defined over point in set Ri
4.
R’
Response of mask at any point in image
5.
w
Filtering mask
6.
z
Gray level of pixels
7.
TE
Execution Time
8.
9.
T
H s ( x, y )
Non negative threshold
Impluse response of Gaussian function
10. F(x,y)
Image in spatial domain
11. H(x,y)
LoG function
12. hDH
Sobel operator for derivative in horizontal direction
13. hDV
Sobel operator for derivative in vertical direction
14. hHP
15. hMF
3x3, High pass filter
5x5, arithmetic mean filter
16.
Output of applying hHP
H
17. M o
Mean value for object pixels
18.
19.
20.
21.
22. E ( ij )
Mean value for background pixels.
Sum of objects pixels
Sum of background pixels
Fuzzy membership function where i and j are row and
column value of image
Enhanced image using fuzzy enhancement operator
23. sij
24. l = 0,1..7
Edge sign
8 sub-windows
Mb
So
Sb
ij
xi
25.
26.
27.
28.
d l i, j
dij
c
m
29. d 2 ( xk , vi )
30.
31.
32.
33.
n
u ik
vi
U
Gradient value for pixel (i,j) in l sub-window
Final edge image
Number of clusters
the weighting exponents, 1 for ‘hard’ clustering, and
increasing for fuzzier clustering
The distance measure between object xk and cluster
center vi;
Total number of pixels in image;
Fuzzy membership value of pixel k in cluster i;
Cluster center for subset i in feature space
Fuzzy c-partition matrix
xii
CHAPTER1
Introduction
1
Chapter 1
Introduction
1
Preview
Digital image processing is the use of computer algorithms to perform image processing
on digital images. As a subfield of digital signal processing, digital image processing has
many advantages over analog image processing; it allows a much wider range of
algorithms to be applied to input data, and can avoid problems such as the build-up of
noise and signal distortion during processing. Image segmentation refers to the process of
partitioning a digital image into multiple regions (set of pixels). The goal of segmentation
is to simplify and/or change the representation of an image into something that is more
meaningful and easier to analyse. Image segmentation is typically used to locate objects
and boundaries (lines, curves, etc.) in an image.
In this thesis the various popular fuzzy techniques for image segmentation are studied.
Various methods for better clustering and segmentation have been developed. The
algorithms or methods developed are meant for online and real time applications like
television, camera phone, etc.
2
Chapter 1
Introduction
1.1 Fundamentals of Digital Image Processing
Digital image processing is a subset of the electronic domain wherein the image is
converted to an array of small integers, called pixels (derived from picture element),
representing a physical quantity such as scene radiance, stored in a digital memory, and
processed by computer or other digital hardware. Digital image processing, either as
enhancement for human observers or performing autonomous analysis, offers advantages
in cost, speed, and flexibility, and with the rapidly falling price and rising performance of
personal computers it has become the dominant method in use.
An image is denoted by two dimensional functions of the form f(x,y). The value or
amplitude of f at spatial coordinates (x,y) is a positive scalar quantity whose physical
meaning is determined by the source of the image. In a digital image, (x,y), and the
magnitude of f are all finite and discrete quantities.
It is a hard task to distinguish between the domains of image processing and any other
related area such as computer vision. But the two areas are quite different in the kind of
output we get from them. Computer vision is the science and technology of machines
that see. As a scientific discipline, computer vision is concerned with the theory for
building artificial systems that obtain information from images. The image data can take
many forms, such as a video sequence, views from multiple cameras, or multidimensional data from a medical scanner. In computer vision, the input is a digital image
and the output is some representation of its interesting features. Image processing is often
used in computer vision as a pre-processing step. Image processing is defined as an area
when both input and output are images.
As a technological discipline, computer vision seeks to apply the theories and models of
computer vision to the construction of computer vision systems.
The organization of a computer vision system is highly application dependent. Some
systems are stand-alone applications which solve a specific measurement or detection
problem, while other constitute a sub-system of a larger design which, for example, also
contains sub-systems for control of mechanical actuators, planning, information
databases, man-machine interfaces, etc. The specific implementation of a computer
3
Chapter 1
Introduction
vision system also depends on if its functionality is pre-specified or if some part of it can
be learned or modified during operation. There are, however, typical functions which are
found in many computer vision systems.
1.
Image acquisition: A digital image is produced by one or several image sensor
which, besides various types of light-sensitive cameras, includes range sensors,
tomography devices, radar, ultra-sonic cameras, etc. Depending on the type of sensor, the
resulting image data is an ordinary 2D image, a 3D volume, or an image sequence. The
pixel values typically correspond to light intensity in one or several spectral bands (gray
images or colour images), but can also be related to various physical measures, such as
depth, absorption or reflectance of sonic or electromagnetic waves, or nuclear magnetic
resonance.
2.
Pre-processing: Before a computer vision method can be applied to image data in
order to extract some specific piece of information, it is usually necessary to process the
data in order to assure that it satisfies certain assumptions implied by the method.
Examples are
(a) Re-sampling in order to assure that the image coordinate system is correct.
(b)
Noise reduction in order to assure that sensor noise does not introduce false
information.
(c ) Contrast enhancement to assure that relevant information can be detected.
(d) Scale space representation to enhance image structures at locally appropriate scales.
3.
Feature extraction: Image features at various levels of complexity are extracted
from the image data. Typical examples of such features are
(a) Lines, edges and ridges.
(b) Localized interest points such as corners, blobs or points.
More complex features may be related to texture, shape or motion.
4
Chapter 1
Introduction
4. Detection/Segmentation: At some point in the processing a decision is made about
which image points or regions of the image are relevant for further processing. Examples
are
(a) Selection of a specific set of interest points
(b) Segmentation of one or multiple image regions which contain a specific object of
interest.
5.
High-level processing: At this step the input is typically a small set of data, for
example a set of points or an image region which is assumed to contain a specific object.
The remaining processing deals with, for example:
(a) Verification that the data satisfy model-based and application specific assumptions.
(b) Estimation of application specific parameters, such as object pose or object size.
(c) Classifying a detected object into different categories
Hence it can be said that image segmentation forms an integral part of computer vision
systems and is more an area of computer vision than image processing.
1.2
Image Segmentation
1.2.1 Theory
Segmentation of an image entails the division or separation of the image into regions of
similar attribute. The basic attribute for segmentation is image amplitude- luminance for
a monochrome image and color components for a color image. Image edges and textures
are also useful attributes for segmentation. The result of image segmentation is a set of
regions that collectively cover the entire image, or a set of contours extracted from the
image.
Segmentation does not involve classifying each segment. The segmentor only subdivides
an image; it does not attempt to recognise the individual segments or their relationships to
one another.
There is no theory of image segmentation. As a consequence, no single standard method
of image segmentation has emerged. Rather, there are a collection of ad hoc methods that
5
Chapter 1
Introduction
have received some degree of popularity. Because the methods are ad hoc, it would
useful to have some means of assessing their performance. Haralick and Shapiro (1) have
established the
following qualitative guidelines for “good” image segmentation:
(a) Regions of the image segmentation should be uniform and homogeneous with respect
to some characteristic such as gray tone or texture.
(b) Region interiors should be simple and without many small holes
(c) Adjacent regions of segmentation should have significantly different values with
respect to the characteristic on which they are uniform.
(d) Boundaries of each segment should be simple, not ragged, and must be spatially
accurate.
1.2.2
Applications of segmentation
Some of the practical applications of image segmentation are:
1. Medical Imaging

Locate tumors and other pathologies

Measure tissue volumes

Computer guided surgery

Diagnosis

Treatment planning

Study of anatomical structures
2. Locate objects in satellite images (roads, forests, etc.)
3. Face recognition
4. Fingerprint recognition
5. Automatic traffic controlling systems
6. Machine vision
6
Chapter 1
Introduction
1.3 Literature survey of fuzzy techniques applied for
segmentation
Fuzzy technique has been applied for various methods used for image segmentation.
Fuzzy image segmentation is increasing in popularity because of rapid extension of fuzzy
set theory, the development of various fuzzy set based mathematical modelling,
synergistic combination of fuzzy, genetic algorithm and neural network[50],[51], and its
successful and practical application in image processing, pattern recognition and
computer vision system.
In this work fuzzy edge detector and fuzzy clustering based image segmentation are
studied. Fuzzy based edge detection methods are extensively used for image
segmentation. Efficient fuzzy technique based edge detection method which would yield
good segmentation results on application of some edge tracking techniques and some
times even without application of edge tracking methods have been discussed.
Tood law, Hidenori Itoh and Hirohisa seki [1] characterized the problem of detecting
edges in images as a fuzzy reasoning problem. The edge detection problem is divided
into three stages: filtering, detection, and tracing. It was finally concluded in the paper
that the algorithm was able to assemble edge information in a meaningful way. Fuzzy
reasoning based edge detection has also been popular for edge detection of images
affected by noise [2- 4].
Olga Regina Pereira Bellon et al. [5] presented a methodology to perform edge detection
in range images in order to provide a reliable and meaningful edge map, which helps to
guide and improve range image segmentation by clustering technique. The obtained edge
map leads to three important improvements: (1) the definition of the ideal number of
regions to initialize the clustering algorithm; (2) the selection of suitable initial cluster
centers; and (3) the successful identification of distinct regions with similar features.
Xiaohan Yu, J. Yla-Jaaski et al. [6] proposed a new method for texture segmentation
based on edge detection. The new scheme is based on the idea that texture features
change abruptly near boundaries between different textures, and the segmentation can be
carried out by detecting the feature changes or so-called feature edges. In this algorithm,
7
Chapter 1
Introduction
the image is first projected onto a hyperplane called the characteristic image, in which the
value of each pixel is not a grey level but
a vector value of the local textural features. An edge detection algorithm is then extended
to the vector space and applied to the hyperplane to detect the feature edges.
Liu Yi, Chen Xue-quan [7] presented an improved edge detection algorithm for remote
sensing images, which is based on fuzzy logic theory and conventional Pal. King
algorithm. The membership function was redesigned, the method of fuzzy enhancement
was modified and an edge evaluation criteria was used to control the iterative procedure
automatically. The presented algorithm was found to be superior to other edge detectors
in edge detection of remote sensing images.
Jinbo Wu, Zhouping Yin, and Youlon Xiong [8] proposed a fast and accurate edge
detection method for blurry images. The algorithm called fast multilevel fuzzy edge
detection (FMFED) first enhances the image contrast by means of the fast multilevel
fuzzy enhancement (FMFE) algorithm using the simple transformation function based on
two image thresholds. Secondly, the
Edges are extracted from the enhanced image by a two-stage edge detection operator that
identifies the edge candidates based on the local characteristics of the image.
Cristiano Jacques Miosso and Adolfo Bauchspiess [9] evaluated the performance of a
fuzzy inference system in edge detection. It was concluded that despite the much superior
computational effort when compared to the Sobel operator, the implemented FIS system
presents greater robustness to contrast and lighting variations, besides avoiding obtaining
double edges. Further tuning of the weights associated to the fuzzy inference rules is still
necessary to reduce even more inclusion in the output image of pixels not belonging to
edges.
Image thresholding is another method which is used for image segmentation. Fuzzy
techniques are applied for this method.
Farrah wong HT, Ramachandran Nagaranjan et al. [10] presented an image segmentation
method by using a threshold value determined by fuzzy logic. The fuzzy based
segmentation reported in the paper is an automated threshold calculation. The threshold
value calculated by utilizing the histogram of the image and the measure of fuzziness
constitute the initial step in the proposed segmentation procedure. The threshold value is
8
Chapter 1
Introduction
then used as an input for the split and merge method of segmentation. Wen-Bing, Jin-Wn
Tian et al. [11] have presented a three level thresholding method for image segmentation
based on probability partition, fuzzy partition and entropy theory. The procedure for
finding the optimal combination of all the fuzzy parameters is implemented by a genetic
algorithm with appropriate coding method so as to avoid useless chromosomes. M.
Cheriet, J.N.Said et al.[12] presented a general recursive approach for image
segmentation by extending Otsu’s method. This approach segments the brightest
homogeneous objects after the last recursion. There are many thresholding based image
segmentation methods [13,14]. Most of these greyscale based segmentation methods
often assume that the image has a uniform and stationary or quasistationary distribution
of greyscale for various targets or background. So they are often not so effective for the
images with complex structure because of the complex distribution of the greyscale of
images. Some techniques [15] assume images to be mostly nonstationary with space
variant distribution. The segmentation methods based on this model are dependent on
local area. The performance of such local operator will degrade quickly as the noise
increases.
The most important fuzzy based approach to image segmentation are: fuzzy clustering
algorithms, fuzzy rule based approach and measure of fuzziness.
Lior Shamir[16] has described a human perception based approach to pixel color
segmentation. Fuzzy sets are defined on the H, S and V components of the HSV color
space and provide a fuzzy logic model that aims to follow the human intuition of color
classification. The knowledge-driven model allows simple modification of the
classification based on needs of a specific application, and the efficiency of the algorithm
in terms of the computational complexity makes the proposed method suitable for
applications where efficiency is a primary issue.
A. Borji and M. Hamidi [17] have proposed a new method for color image segmentation
using fuzzy logic where they automatically produce a system for color classification and
image segmentation with least number of rules and minimum error rate. A
comprehensive learning particle swarm optimization technique is used to find optimal
fuzzy rules and membership functions as it discourages premature convergence. Less
computational load is needed when using this method compared to other methods like
9
Chapter 1
Introduction
ANFIS. Large train data set and its variety makes the proposed method invariant to
illumination noise.
Estevez Pablo A., Flores Rodrigo J. et al. [18] proposed a method called FMMIS (fuzzy
min-max neural network for image segmentation). The FMMIS method grows boxes
from a set of seed pixels, to find the minimum bounded rectangle for each object present
in the images. The proposed method is very fast and it may be applied to real-time image
segmentation tasks.
G. Karmakar ,L. Dooley et al. [19] proposed a new algorithm called fuzzy rules for image
segmentation incorporating texture features (FRIST), which includes two additional
membership functions to those already defined in GFRIS( generic fuzzy rule based image
segmentation). FRIST incorporates the fractal dimension and contrast features of a
texture by considering image domain specific information. FRIST exhibits considerable
improvement in the results obtained compared with the GFRIS approach for many
different image types.
Tie Qi Chen and Yi Lu [20] developed a fuzzy clustering algorithm that iteratively
generates color clusters using a uniquely defined fuzzy membership function and an
objective function for clustering optimization. The region segmentation algorithm merges
clusters in the image domain based on color similarity and spatial adjacency. Martin
Tabakov [21] described a way of medical image segmentation using an appropriately
defined fuzzy clustering method based on a fuzzy relation. The considered relation is
defined in terms of Euclidean distance.
Ahmed Mohamed N., Yamany Sameh M. et al. [22] presented an algorithm for fuzzy
segmentation of MRI data and estimation of intensity inhomogenities using fuzzy logic.
The algorithm is formulated by modifying the objective function of the standard fuzzy cmeans algorithm to compensate for such inhomogenities and allow the labelling of a
pixel to be influenced by the labels in its immediate neighbourhood.
Y. Yang, Ch.Zheng and P. Lin [23] presented a novel penalized fuzzy c-means (PFCM)
algorithm for image segmentation. The algorithm is formulated by incorporating the
spatial neighbourhood information into the original FCM with a penalty term. The
penalty term is inspired by the neighbourhood expectation maximization algorithm and is
10
Chapter 1
Introduction
modified in order to satisfy the criterion of the FCM algorithm. The algorithm is found to
be more robust to noise than standard FCM.
Shan Shen,William Sandham et al. [24] presented an extension to the original FCM. The
algorithm is based on neighbourhood attraction, which is dependent on the relative
location and features of the neighbouring pixels. The degree of attraction is optimized by
a neural-network model.
Jiayin Kang, Lequan Min et al. [25] presented a novel method for image segmentation by
incorporating spatial neighbourhood information into the standard FCM. An adaptive
weighted averaging filter is given to indicate the spatial influence of the center pixel.
Li Ma and R. C. Staunton [26] proposed a novel FCM algorithm to be used when active
or structured lights are projected onto a scene. The recursive FCM algorithm is modified
to include biased illumination field estimation. New clustering center and fuzzy
clustering functions resulted based on the intensity and the average intensity of a pixel
neighbourhood based object function. A dilation operator was used in the end on the
initial segmented image for further refinement. The proposed method is found to be
effective for segmenting images illuminated by patterns containing underlying biased
intensity fields.
Yannis A. Tolias and Stavros M. Panas [27] presented the adaptive fuzzy
clustering/segmentation (AFCS). In AFCS, the nonstationary nature of the images is
taken into account by modifying the prototype vectors as function of sample location in
the image. A multiresolution model is utilized for estimating the spatially varying
prototype vectors for different window sizes. The segmentation of different resolutions is
combined using a data fusion process in order to compute the final fuzzy partition
matrix.The results provide segmentation having lower entropy.
N. A. Mohamed, M.N. Ahmed et al.[28] described the application of fuzzy set theory in
medical imaging. A fully automatic technique to obtain clusters is proposed. A modified
fuzzy c-means classification algorithm is used to provide a fuzzy partition. The method is
inspired by Markov random Field (MRF) and is found to be less sensitive to noise as it
filters the image while clustering it.
S R Kannan [29] presented a new method called fuzzy membership c-means(FMCM) for
segmentation of Magnetic Resonance Images(MRI). This work develops a specific
11
Chapter 1
Introduction
method to construct the initial membership matrix to clusters in order to improve the
strength of the clusters.
Y. Yong, Z. Chongxun et al. [30] presented a spatially weighted fuzzy c-means (SWFM)
clustering algorithm for image thresholding. Spatial neighbourhood information is taken
into account in this algorithm. Two improved implementations of the k-nearest
neighbour(k-NN) algorithm re introduced for calculating the weight in the SWFCM to
improve thresholding. To speed up FCM algorithm the iteration is carried out on
histogram of the image instead of all pixels of the image.
1.4 Problem Statement
In general, the classification of an image’s pixel belonging to one of the “objects” (i.e.,
classes) composing the image is based on some common feature(s), or resemblance to
some pattern. In order to determine which are the features that can lead to a successful
classification, some apriori knowledge or/and assumptions about the image are equally
required.
Classical, so-called “crisp” image segmentation techniques, while effective for images
containing well-defined structures such as edges, do not perform well in the presence of
ill-defined data. In such circumstances, the processing of images that posses ambiguity is
better performed using fuzzy segmentation techniques, which are more adept at dealing
with imprecise data. Fuzzy techniques may be broadly classified into five main
categories:
1. Fuzzy clustering based image segmentation
2. Fuzzy rule based image segmentation
3. Fuzzy geometry based image segmentation
4. Fuzzy thresholding based image segmentation
5. Fuzzy integral based segmentation techniques (Tizhoosh,1998).
Of all these methods mentioned, the most widely used are the fuzzy rule based and fuzzy
clustering based segmentation. The problem with fuzzy rule based image segmentation
techniques is that they are application dependent with the structure of the membership
functions being predefined and in certain cases, the corresponding parameters being
manually determined. Karmakar et al. [76] presented a contemporary review of fuzzy rule
12
Chapter 1
Introduction
based image segmentation techniques, and confirmed that despite being used in a wide
range of applications, both the structure of membership functions and derivation of their
relevant parameters were still very much application domain and image dependent. Fuzzy
c-means is an unsupervised technique that has been successfully applied to feature
analysis, clustering, and classifier designs in fields such as astronomy, geology, medical
imaging, target recognition, and image segmentation [21]-[28],[61],[62],[74],[75]. An
image can be represented in various feature spaces, and the FCM algorithm classifies the
image by grouping similar data points in the feature space into clusters. This clustering is
achieved by iteratively minimizing a cost function that is dependent on the distance of the
pixels to the cluster centers in the feature domain.
Unfortunately, the greatest shortcoming of FCM is its over-sensitivity to noise, which is
also a flaw of many other intensity based segmentation methods. In recent years, many
modification of the FCM algorithm have been reported to overcome the effect of noise.
Most of these methods inevitably introduce computation issues. In almost all methods
proposed recently, the objective function of the FCM is changed. As most equations are
modified along with the modification of the objective function, these methods lose
continuity from FCM, which is well-realized with many types of software, such as
MATLAB.
1.5 Image Metrics
The quality of an image is examined by objective evaluation as well as subjective
evaluation. The subjective evaluation is the most widely used type of evaluation method,
in which the segmentation results are judged by a human evaluator. The disadvantage of
such methods is that visual or qualitative evaluation is inherently subjective. Subjective
evaluation scores may vary significantly from one human evaluator to another, because
each evaluator has their own distinct standards for assessing the quality of a segmented
image. The image metrics for fuzzy clustering based segmentation are discussed here. In
fuzzy clustering based method good clustering of the image amounts to good
segmentation. Hence in order to obtain a quantitative comparison, two types of cluster
validity functions, fuzzy partition and feature structure, are often used to evaluate the
performance of clustering in different clustering methods. The representative functions
13
Chapter 1
Introduction
for the fuzzy partition are partition coefficient V pc [31] partition entropy V pe [32]. They
are defined as follows:
n
c
u
V pc 
ik
k 1 i  1
(1.1)
n
and
n
c
   [ u ik log u ik ]
V pe 
k 1 i 1
The value of Vpc
(1.2)
n
is in the range [1/c,1]. An index close to 1 indicates good cluster
separation, while a low index value indicates fuzzier clustering. An index of Vpc =1/c
indicates that there is no clustering tendency. The value of Vpe is in the range [0,log c]. In
contrast to Vpc, a low value of Vpe indicates good cluster separation. The idea of these
validity functions is that the partition with less fuzziness means better performance. As a
result, best clustering is achieved when the value V pc is maximal or V pe is minimal.
The third image metric used for comparision of different algorithms present and proposed
is the percentage of misclassified pixels present in a class(cluster).To find the number of
misclassified pixels in each clusters first we find the number of pixels in each clusters
when noise is not added to the image. After that, we add noise to the image and calculate
the number of pixels which are misclassified i.e the number of pixels that have increased
in a cluster after adding noise or the missing pixels in a cluster after adding noise. Finally
the percentage of misclassified pixels is calculated using the formula :
Numberof misclassified pixels in a cluster
 100
Orignal number of pixels in thecluster
(1.3)
Another image metric used for comparison of different methods is the execution time.
Execution time is defined as the time taken for the simulation of an algorithm. The less
14
Chapter 1
Introduction
time an algorithm takes for execution the more efficient it is considered. The processesor
used is a Pentium IV core 2 duo processor, 2.4Ghz (clock), 2GB (RAM), Windows vista
64 bit operating system.
1.6 Conclusion
In this introductory chapter, the fundamentals of digital image processing, theory and
application of image segmentation, the existing image segmentation techniques and their
merits and demerits
and various image metrics are studied. The advantages and disadvantages of fuzzy rule
based segmentation and fuzzy clustering based segmentation have been discussed.
Hence, it is decided to study and develop various fuzzy rule based segmentation method
and fuzzy clustering based segmentation algorithms.
15
CHAPTER 2
Basic techniques of image
segmentation
16
Chapter 2
Basic techniques of image segmentation
2
Preview
Image segmentation algorithms are generally based on one of the two basic properties of
intensity values: discontinuity and similarity. In the first category, the approach is to
partition an image based on abrupt changes in intensity, such as edges in an image.
Segmentation based on discontinuity method is discussed in next chapter. The principal
approaches in the second category are based on partitioning an image into regions that are
similar according to a set of pre-defined criteria. Thresholding, region growing, and
region splitting and merging are examples of methods in this category. Segmentation
based on similarity property of intensity values that is region based segmentation
methods are described here.
2.1 Region-Based Segmentation
2.1.1 Basic formulation:
Let R represent the entire image region. Segmentation may be viewed as a process that
partitions R into n subregions, R1 , R2 ,..., Rn such that
17
Chapter 2
Basic techniques of image segmentation
n
(a )
R
i
= R
i 1
(b )
R i is a c o n n e c te d re g io n , i= 1 ,2 ,....,n .
(c )
R i R
(d )
P (R i ) = T R U E fo r a ll i = 1 ,2 ,....,n .
(e )
P (R i  R j ) = F A L S E fo r i  j
j
=  fo r a ll i a n d j, i  j
Here, P ( Ri ) is a logical predicate defined over the points in set Ri and  is the null set.
Condition (a) indicates that the segmentation must be complete; that is, every pixel must
be in a region. Condition (b) requires that points in a region must be connected in some
predefined sense. Condition (c) indicates that the regions must be disjoint. Condition (d)
deals with the properties that must be satisfied by the pixels in a segmented region- for
example P ( Ri ) = TRUE if all pixels in Ri have the same gray level. Finally, condition (e)
indicates that regions Ri and Rj are different in the sense of the predicate P [33].
2.1.2 Region growing
Region growing is a procedure that group’s pixels or subregions into larger regions based
on predefined criteria [34]. The basic approach is to start with a set of “seed” points and
from these grow regions by appending to each seed those neighboring pixels that that
properties similar to the seed ( such as specific ranges of gray level or color).
This approach has specific advantages over boundary based (pixel differences) methods:
1.
It is guaranteed (by definition) to produce coherent regions. Linking edges, gaps
produced by missing edge pixels, etc. are not an issue
2.
It works from the inside out, instead of the outside in. The question which object a
pixel belongs to, is immediate, not the result of point-in-contour tests.
However, it also has drawbacks:
1.
Decisions about region membership are often more difficult than applying edge
detectors.
18
Chapter 2
2.
Basic techniques of image segmentation
It can’t find objects that span multiple disconnected regions. (Whereas edge-based
method can be designed to handle “gaps” produced by occlusion—the Hough transform
is one example
The objectives of region-based approaches can be summarized as follows:
(a) Produce regions that are as large as possible (i.e., produce as few regions as
possible).
(b) Produce coherent regions, but allow some flexibility for variation within the region.
2.1.2.1 How to choose the seed(s) for region growing in practice?
1.
It depends on the nature of the problem.
2.
If target need to be detected using infrared images for example, choose the brightest
pixels
3. Without a-priori knowledge, compute the histogram and choose the gray-level values
corresponding to the strongest peaks.
2.1.2.2 How to choose the similarity criteria (predicates)?
The homogeneity predicate can be based on any characteristic of the regions in the image
such as
* Average intensity
* Variance
* Color
* Texture
* Motion
* Shape
* Size
Selecting a set of one or more starting points often can be based on the nature of the
problem. When a priori information is not available, the procedure is to compute at every
pixel the same set of properties that ultimately will be used to assign pixels to the regions
19
Chapter 2
Basic techniques of image segmentation
during the growing process. If the result of these computations shows clusters of values,
the pixels whose properties place them near the centroid of these clusters can be used as
seeds.
The selection of similarity criteria depends not only on the problem under consideration,
but also on the type of image data available. For example, the analysis of land-use
satellite imagery depends heavily on the use of color. This problem would be
significantly more difficult, or even impossible to handle without the inherent
information available in color images. When the images are monochrome, region analysis
must be carried out with a set of descriptors based on gray levels and spatial properties
(such as moments and texture).
Descriptors alone may yield misleading results if connectivity or adjacency information
is not used in the region-growing process.
Region growing should stop when no more pixels satisfy the criteria for inclusion in that
region. Criteria such as gray level, texture, and colour, are local in nature and do not take
into account the history of region growth. Hence the power of region growing algorithms
are increased by utilizing the concept of size, likeness between a candidate pixel and the
pixels grown so far (such as a comparison of the gray level of a candidate and the average
gray level of the grown region), and the region being grown.
2.1.3 Region split and merge
Split and merge image segmentation techniques are based on a quad tree data
representation whereby a square image is broken (split) into four quadrants if the original
image segment is nonuniform in attribute. If four neighboring squares are found to be
uniform, they are replaced (merge) by a single square composed of the four adjacent
squares.
Subdivide an image initially into a set of arbitrary, disjoint regions and then merge
and/or split the regions in an attempt to satisfy the necessary conditions
Let R represent entire image region and select a predicate P
(1) Split into four disjoint quadrants any region Ri for which P(Ri) = FALSE
(2) Merge any adjacent regions Rj and Rk for which P(Rj ∪ Rk) = TRUE
20
Chapter 2
Basic techniques of image segmentation
(3) Stop when no further merging or splitting is possible
Several variations of this theme are possible
2.1.3.1 Quadtrees for region extraction
Important data structures which is used in split and merge algorithms is the quadtree.
Figure 2.1 shows a quadtree and its relation to the image. Note that in graphics the
quadtree is used in a region splitting algorithm (Warnock's Algorithm) which breaks a
graphical image down recursively from the root node, which represents the whole image,
to the leaf nodes where each leaf node represent a coherent region, which can be rendered
without further hidden line elimination calculations[14]. The same use is made of
quadtrees for vision. Quadtrees impose one type of regular decomposition onto an image.
To complete the segmentation process this must be followed by a merging phase. Thus
the problem of finding adjacent neighbours to a given node has been studied in figure 2.2.
The problem is one of tree search and efficient algorithms have been published.
Figure 2.1 Quadtree decomposition
21
Chapter 2
Basic techniques of image segmentation
Figure 2.2 Splitting and merging with quadtrees
2.2 Segmentation technique based on discontinuity
property of pixels.
2.2.1 Detection of Discontinuities
In this category, the approach is to partition an image based on abrupt changes in
intensity, such as edges in an image. Three basic types of gray-level discontinuities that
are mostly detected in a digital image are: points, lines and edges. The most common way
to look for discontinuities is to run a mask through the image. For the 3x3 mask shown in
fig. 3.1 , this procedure involves computing the sum of products of the coefficient with
the gray level contained in the region encompassed by the mask. That is, the response of
the mask at any point in the image is given by
R '  w 1 z1  w 2 z 2  ...  w 9 z 9
9


(2.1)
wi zi
i1
22
Chapter 2
Basic techniques of image segmentation
Figure 2.3 Point detection mask
where zi is the gray level of the pixel associated with mask coefficient wi . As usual, the
response of the mask is defined with respect to its center location.
2.2.1.1 Point detection
Using the mask shown in Fig. 2.3, we say that a point has been detected at the location on
which the mask is centered if
| R ' | T
(2.2)
where T is a nonnegative threshold and R’ is given by (2.1).
2.2.1.2 Line detection
Consider the masks in Fig. 2.4. If the first mask were moved around an image, it would
respond more strongly to lines (one pixel thick) oriented horizontally. With a constant
background, the maximum response would result when the line passed through the
middle row of the mask. Similarly, the second mask in Fig. 2.4 responds to lines oriented
0
at 45 ; the third mask to vertical lines; and the fourth mask to lines oriented at 45
0
direction.
Let R1’, R2’, R3’, and R4’ denote the responses of the masks in Fig. 2.4, from left to
right, where R’s are given by equation 2.1. Let the four masks be run through an image
23
Chapter 2
Basic techniques of image segmentation
individually. If, at a certain point in the image, |Ri’|>|Rj’|, for all j  i, that point is said to
be more likely associated with a line in the direction of the mask i.
Figure 2.4. Line detector masks
2.2.1.3 Edge detection
Edge detection is an important step for image segmentation. The goal of edge detection
process in a digital image is to determine the frontiers of all represented objects based on
automatic processing of the color or gray level information in each present pixel.
To extract the edges from the images, derivative edge detection operators or gradient
operator, such as Sobel operator, Prewitt operator, Roberts operator, and Laplacian
operators are commonly used. A 3x3 mask is used for edge detection using the mentioned
operators. The various masks and the result of applying them on the image are shown in
fig. 2.4 and fig. 3.5 respectively.
The reasons that Prewitt and Sobel edge detectors visually appear to better delineate
object edges than the Roberts edge detector is attributable to their larger size, which
provides averaging of small luminance fluctuations. The Sobel edge detector uses a
weight of 2 in the center coefficient. A weight of 2 is used to achieve some smoothing by
24
Chapter 2
Basic techniques of image segmentation
giving more importance to the center point. The Prewitt masks are simpler to implement
than the Sobel masks, but the latter have slightly superior noise-suppression
characteristics, an important issue when dealing with derivatives. Note that the
coefficients in all masks shown in Fig. 2.5 sum to 0, indicating that they give a response
of 0 in areas of constant gray levels, as expected of a derivative operator.
Roberts
Prewitt
Sobel
Figure 2.5. Line detection
masks
(A) Laplacian of Gaussian edge detector
Marr and Hildreth [35] have proposed the Laplacian of Gaussian (LoG) edge detection
operator operator in which Gaussian-shaped smoothing is performed prior to application
of the Laplacian. The continuous domain LoG gradient is
G ( x, y )   2  F ( x, y )  H s ( x, y )
(2.3)
25
Chapter 2
Basic techniques of image segmentation
where
Hs (x, y)  g(x, s)g ( y, s)
(2.4)
is the impulse response of the Gaussian smoothing function as defined by
g ( x, s)  2 s 2 
1/ 2
exp 1/ 2( x / s)2 
(2.5)
where s is standard deviation
As a result of the linearity of the second derivative operation and of the linearity of
convolution, it is possible to express the LoG response as
G(x, y)  F(x, y) H(x, y)
(2.6)
where
H ( x, y )   2  g ( x, s ) g ( y , s )
(2.7)
Upon differentiation one obtains
 x2  y2   x2  y2 
1
H( x, y)  4 g( x, s) 1
exp 
2 
2 
s
2
s

  2s 
(2.8)
This function is commonly referred to as the Laplacian of a Gaussian (LoG) because
Eq.2.8 is in the form of a Gaussian function. A 5x5 mask that approximates H ( x, y ) is
shown in Fig.2.6(c). This approximation is not unique. Its purpose is to capture the
essential shape of H ( x, y ) ; that is, a positive central term, surrounded by an adjacent
negative region that increases in value as a function of distance from the origin, and a
zero outer region. The coefficients must also sum to zero, so that the response of the
mask is zero in areas of constant gray level. Due to its shape, the Laplacian of Gaussian is
called the Mexican hat function.
26
Chapter 2
Basic techniques of image segmentation
(a)
(b)
(c)
Figure 2.6 Laplacian of a Gaussian (LoG). (a) 3-D plot. (b) Image (black is negative, gray is the zero plane,
and white is positive). (c) 5x5 mask approximation to the shape of (a)
(B) Canny edge detector
The Canny edge detection operator was developed by John F. Canny [57] in 1986 and
uses a multi-stage algorithm to detect a wide range of edges in images. The method can
be summarized as follows:
1. The image is smoothed using a Gaussian filter with a specified standard deviation, s,
to reduce noise.
2. The local gradient, g ( x, y )  [Gx2  G y2 ]1/ 2 , and edge direction,  ( x, y )  tan 1 (Gx / Gy ) ,
are computed at each point. Any of the first three techniques Prewitt, Sobel or LoG edge
27
Chapter 2
Basic techniques of image segmentation
detector can be used to compute Gx and G y . An edge point is defined to be a point whose
strength is locally maximum in the direction of the gradient.
3. The edge points determined in (2) give rise to ridges in the gradient magnitude image.
The algorithm then tracks along the top of these ridges and sets to zero all pixels that are
not actually on the ridge top so as to give a thin line in the output, a process known as
nonmaximal suppression. The ridge pixels are then thresholded using two thresholds, T1
and T2, with T1<T2. Ridge pixels with values greater than T2 are said to be “strong”
edge pixels. Ridge pixels with values between T1 and T2 are said to be “weak” edge
pixels.
4. Finally, the algorithm performs edge linking by incorporating the weak pixels that are
8-connected to the strong pixels.
The gradient-based edge detection method has been widely applied in practice and a
reasonable edge map is obtained for most images. Nevertheless, they suffer from some
practical limitations.
First, they need a smoothing operation to alleviate the effect of high spatial frequency in
estimating the gradient. Usually this smoothing is applied to all pixels in the image
including the edge regions, and so the edge is distorted and missed in some cases, in
particular at junctions or corners. Secondly, the gradient magnitude alone is insufficient
to determine meaningful edges because of the ambiguity caused by the underlying pixel
pattern, especially in complex natural scenes. Thirdly, the gradient-based edge detection
methods increase the computational complexity because calculations, such as square root
and arctangent, to produce the gradient vector are required. Finally, for edge thresholding
conventional gradient methods use one or two global edge thresholds for an input image.
For example, the hysteresis thresholding proposed by Canny in many practical
applications require not only the trial and error adjustment of two thresholds to produce a
satisfactory edge result for each different input image, but also the validity of the preadjusted thresholds.
The simulation results and conclusion of this chapter are in chapter 6.
28
CHAPTER 3
Study and Implementation of
Segmentation based on Fuzzy Edge
Detection
29
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
3
Preview
The goal of edge detection in image processing is to determine the frontiers of all
represented objects, based on automatic processing of color or gray level information
contained in each pixel. This procedure has many applications in image processing,
computer vision and biological and robotic vision [46], [47], and [48].
Edge detection of real world images is a challenging task as there are a number of objects
and huge variations between them which makes it difficult to approximate all objects
using a general frame. Segmentation based on edge detection mostly consists of two
steps:
1. Edge detection
2. Edge linking
30
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
Most real world images posses a certain amount of ambiguity and hence their
segmentation produces fuzzy regions. For such images, fuzzy image segmentation
techniques are more adept for processing their uncertainties. The importance of the fuzzy
sets for analyzing complex natural
systems has been determined in several application domains. Digital images, which are
mappings of natural scenes, are always accompanied by some degree of uncertainty
(fuzziness) mainly due to:
i)
Imprecision of gray values of the pixels;
ii)
Ambiguity resulting from the image acquisition and mapping mechanism;
iii) Vague information in the region boundaries.
This fact justifies the development of algorithms based on fuzzy sets for several tasks of
image analysis.
Recent techniques have characterized edge detection as a fuzzy reasoning problem [37],
[38], [40], [41], [42]. These techniques have presented good and, therefore, promising
results in the areas of image processing and computational vision. Fuzzy techniques
allow a new perspective to model uncertainties due to the uncertainty of gray-values
present in the images. Thus, instead of assigning gray-values to the pixels in the image,
fuzzy membership may be used to the gray-values in the image.
Fuzzy approaches for image segmentation may be classified as approaches based on
fuzzy rules; fuzzy classification algorithms; fuzziness measurements and image
information and fuzzy geometry [39]. The approach based on rules treats image
characteristics as linguistic variables and, therefore, uses IF-THEN fuzzy rules to
segment images in different regions [36], [40], [41]. Fuzzy classification is the oldest
approach for image segmentation. Algorithms such as the c-means fuzzy and possibilistic
c-means may be used to build classes (segments) [40], [41], [27]. Fuzziness
measurements (fuzzy entropy) and image information (fuzzy divergence) may also be
used to segment images [38], [44].
31
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
3.1 A Fuzzy Inference System for Edge Detection based
Segmentation
A nonlinear image filtering technique is developed here which is based on fuzzy
inference systems (FIS) [45]. During input image processing, three kinds of linear filters
are applied to it:
1. Sobel operators, used to estimate its derivative in horizontal and vertical directions
( hDH and hDV filters)
2. A low-pass filter and
3. A high-pass filter.
Here the gray level associate to pixel (i,j) in the output image E depends not only on the
pixel (i,j) in each pre-processed image but also on some neighbor pixels, as depicted in
Figure 3.1. Besides, each image DH and DV that results from applying Sobel operators is
passed to the FIS system, and not only the image composition D  DH 2  DV 2 .
The purpose of proposed fuzzy system is to determine if pixel (i,j) evaluated is or is not
present in one of the edges of the image, given the information explicit in the input
filtered images.
DH(i,j), DH(i,j+1),
DH(i+1,j), DH(i-1,j)
hDH
DV(i,j), DV(i,j+1),
DV(i+1,j), DV(i-1,j)
hDV
I
F/I/D
H
Threshold
E
hHP
hM
M
Figure 3.1. FIS applied to edge detection in image I. hDH and hDV are Sobel operators to estimate 1st derivative
of I in horizontal and vertical directions. hHP & hM are masks of a high pass and low pass filters. F,I,D refer to
fuzzification, inference and deffuzification stages.
32
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
3.1.1 Implementation of the FIS system
During input image pre-processing step, four linear filters were employed. Sobel operator
hDH and hDV are masks of size 3x3 and are given by
hDH
=
hDV
=
The high pass filter mask is given by:
hHP =
1/16
1/8

1/16
1/8
3/4
1/8
1/16
1/8 
1/16
The low pass filter mask is selected in such a way that the gray level in each pixel of the
output image is the arithmetic mean of the gray levels in a 5x5 neighbourhood of the
same pixel in the input image.
The mask for low pass filter is given as
33
Chapter 3
hMF
=
Study and implementation of segmentation based on fuzzy edge detection
1
1
1 
. 1
25 
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

1
1
Given the masks associated with each filter, the filtered images may be computed through
a bi-dimensional convolution operation.
DH  hDH  I
DV  hDV  I
HP  hHP  I
M  hMF  I
3.1.2 Fuzzy sets and fuzzy membership functions
The system implementation was carried out considering that the input image and the
output image obtained after defuzzification are both 8-bit quantized; this way, their gray
levels are always between 0 and 255. These values define the working interval of the
output variable and the input variable M (the other input variables are not guaranteed to
be less than 255). Besides, three fuzzy sets were created to represent each variable’s
intensities; these sets were associated to the linguistic variables “low”, “medium” and
“high”.
The Gaussian membership function is adopted for the fuzzy sets (“low , medium and
high”)
associated with input M and the output. The mean value for the Gaussian
membership function is taken as 0, 127.5 and 255 as shown in figure 3.2(a). For the fuzzy
set associated with inputs DV,HP and output, Gaussian functions were also adopted for
linguistic variables “low” and “medium”. The membership function for linguistic
34
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
variable “high” is chosen to be a sigmoid function, since in this case we can not
guarantee that the input values will be restricted to the interval [0,255].
3.1.3 Fuzzy logical operations and defuzzification method
definitions
The functions adopted to implement the “and” and “or” operations were the minimum
and maximum functions, respectively. The Mamdani method was chosen as the
defuzzification procedure, which means that the fuzzy sets obtained by applying each
inference rule to the input data were joined through the add function; the output of the
system was then computed as the centroid of the resulting membership function [52,
pages 2-20 to 2-23].
3.1.4 Inference rules
The fuzzy inference rules were defined in such a way that the FIS system output
(“Edges”) is high only for those pixels belonging to edges in the input image.
The first three rules were defined to represent the general notion that in pixels belonging
to an edge there is a high variation of gray level in the vertical or horizontal direction:
1.
( DH low ) AND ( DV low )
(“Edges” low).
2.
( DH medium ) AND (DV medium)
(“Edges” high).
3.
( DH high ) OR ( DV high )
(“Edges” high).
To guarantee that edges in regions of relatively low contrast can be detected, the two
following rules were established to favour medium variations of the gray level in a
specific direction in regions of low frequency of the input image (HP “low”):
4.
(DH medium ) AND ( HP low )
( “ Edges” high).
5.
(DV medium ) AND ( HP low )
( “ Edges” high).
35
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
To avoid including in the output image, pixels belonging to regions of the input where the
mean gray level is lower, the following two rules were established. These regions are
proportionally more affected by noise, supposed it is uniformly distributed over the
whole image. The goal here
is to design a system which makes it easier to include edges in low contrast regions, but
which does not favour false edges by effect of noise.
6.
(DV medium) AND (M low)
(“Edges” low).
7.
(DH medium) AND (M low)
(“Edges” low).
To avoid forming double edges in the output image that tend to appear due to shadows in
the natural images, following four rules were developed. Considering that high variations
in gray level in horizontal direction correspond to vertical edges, it is concluded that high
values of DH(i,j) and DH (i,j  1) do not imply edge pixels in (i,j) and (i,j  1)
simultaneously. High values of DV(i,j) and DV(i  1,j) do not correspond to edge pixels
in (i,j) and (i  1,j).
8.
(DV high) AND (DV (i + 1, j) high)
(“Edges” medium).
9.
(DH high) AND (DH (i, j + 1) high)
(“Edges” medium).
10.
(DV medium) AND (DV (i+1,j) high)
(“Edges” low).
11.
(DH medium) AND (DH (i, j+1) high)
(“Edges” low).
Finally, rule 12 was defined to avoid including isolated pixels in the output image,
favouring only continuous lines. It also avoids including points by effect of noise, since
this tends to generate isolated pixels in the image which represents the input’s edges.
12.
(DV (i, j + 1) low) AND (DH(i + 1, j) low) AND
(DV (i, j - 1) low) AND (DH(i -1, j) low)
36
(“Edges” low).
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
(a)
(b)
Figure 3.2 Membership function of fuzzy sets associated to (a) output E (edges) and input
M and (b) to inputs DH , DV , HP
37
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
3.2 An Efficient Multilevel Fuzzy Edge Detector for
Digital Images
The traditional fuzzy edge detection algorithm introduces the fuzzy enhancement method
and is suitable for edge detection up to some extent [53]-[54]. The algorithm first
enhances the image by means of mapping transformations, fuzzy enhancement operator,
and inverse mapping transformation and then extracts the edge information from the
enhanced image using “min” or “max” operator. This algorithm is computationally
complex because the mapping transformation involves the exponential calculation and it
will lead to loss of low intensity pixel.
Many improved algorithms have been proposed by various authors with simplified
mapping transformation and optimized fuzzy enhancement operator [55],[56]. In this
method the image is enhanced by dividing it into various levels and then edge detection is
done by using two stages. The two- stage detection first determine the pixels which are
potential edge candidate by means of local characteristic of the image and in the second
step it determines true edges.
3.2.1 Overview of the fuzzy algorithm
Step 1. Computing the Threshold
The first step before fuzzification is image thresholding. Here thresholding is done by
global thresholding [33] method. The reason for applying global thresholding as a
method of thresholding in this case is its simple implementation. This is an iterative
process given as follows
1. Select initial estimate for threshold T.
2. Segment the image into two groups g1 and g2. Where g1 is intensity values greater
than or equal T and g2 is intensity values less than T.
3. Compute a new threshold
T = 0.5*(mean (g1) +mean (g2));
4. Repeat steps 2 through 3 until the difference in T in successive iterations is smaller
than a predefined parameter T0.
38
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
Based on the threshold value, all the pixels in the image can be classified into two sets,
namely Fo containing high gray level value greater than or equal to T and another Fb
containing low gray level value less than threshold T. The mean value Mo for set Fo and
Mb for set Fb can be computed as follows:

Mo 
(3.1)
So

Mb 
f ij
f ij  Fo
f ij
f ij  Fb
(3.2)
Sb
where So and Sb are sum of object pixels and the sum of background pixel.
Step 2. Computing the Fuzzy Membership value
The membership function as defined by Pal. King algorithm is given as:
f  f ij 

 ij  G ( f ij )   1  max

Fd


 Fe
(3.3)
where Fd and Fe are reciprocal and exponential fuzzy factor respectively.
There is a large amount of calculation with exponential form for fuzzy membership
function. Therefore the equation is redesigned as following:
39
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
 fij  f min

 M o  f min
 M o  M b  2 fij

 M o  Mb
 ij  G ( fij )  
 2 fij  M o  M b
 Mo  Mb

 f max  fij
 f M
o
 max



M  Mb 
M b  fij  o

2


Mo  Mb
 fij  M o 

2


fij  M o


fij  M b
(3.4)
i  1, 2...., M ; j  1, 2..., N
where fmax and fmin denote the maximum and minimum gray value of image. M and N
denote the rows and columns of the image respectively.
Step 3. Fuzzy Enhancement
After changing the image from spatial domain to fuzzy domain, the fuzzy enhancement
operator Er is applied to get the enhanced image as follows:
 'ij  E r (  ij )  E ( E r 1 (  ij ))
(3.5)
  ij 2

 t
E (  ij )  
(1   ij ) 2

1  1  t
(3.6)

0   ij  t 



t   ij  1 

where r denotes the number of iterations, and to enhance the image moderately it is
usually chosen as 2 or 3. t denotes fuzzy characteristic threshold, and its value can be
chosen flexibly between 0 and 1. For the images considered here the results were mostly
obtained for a t value varying in the range 0.5 to 1.
Step 4. Inverse transform of step 2
After enhancement in fuzzy domain, the inverse mapping is done to change the image
from fuzzy domain into the spatial domain as follows:
40
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
hi, j  G1(ij' )
(Mb  fmin )ij'  fmin

'
 Mo  Mb  (Mo  Mb )ij

2
 
'
(Mo  Mb )ij  Mo  Mb

2

'
 fmax  ( fmax  Mo )ij


Mo  Mb 
Mb  fij 

2 

Mo  Mb

 fij  Mo 
2

fij  Mo

fij  Mb
(3.7)
i  1,2...., M; j  1,2...., N
3.2.2. Edge detection in two stages
1. First Stage Edge Detection: The first stage edge detections aim is to determine pixels
which are probable edge candidates.
For any one pixel (i,j) with its gray value equal to fij, the 3x3 window centered around
(i,j) is chosen. The mean value Mij of the gray values of all the pixels in the window is
computed. The edge sign is determined according to relationship between Mij and fij as
follows:
 1,
s ij  
 0 ,
f ij  M
f ij  M
ij
ij



(3.8)
where sij=0 indicates that pixel(i,j) is not an edge pixel, while sij=1 indicates pixel (i,j)
will be edge candidate.
2. Second-Stage Edge Detection Operator:
For the pixel (i,j) with sij=1,the 5x5 window centered around (i,j) is chosen, and it is
divided into eight sub-windows as shown in Fig 1. Let the four pixels included in the lth
(l=0….7) sub window be ( r0l , c0l ), (i , j ), ( r1l , c1l ) and ( r2l , c 2l )
The gradient values for the pixel (i,j) and the two neighbouring pixels in this sub window
can be defined as follows:
41
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
d r l ,cl  abs( gi , j  gr l ,cl )
0
0
0
0
d il, j  g r l , c l  g i , j
1
(3.9)
1
drl ,cl  abs( grl ,cl  grl ,cl )
1
1
2
2
1
1
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
x
x
o
o
o
o
o
x
x
o
o
o
o
x
o
o
x
o
o
o
o
o
o
o
x
x
x
x
o
o
x
o
o
o
o
x
o
o
o
o
x
o
o
o
o
o
o
o
o
x
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x
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x
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x
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x
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o
x
o
o
o
o
o
o
x
Figure.3.6. The eight partition of the detection window
The additional edge sign for every pixel (i,j) in every sub window is determined as
follows:
 1, sij  1 and dil, j  dr l ,cl and dil, j  dr l ,cl 
0
0
1 1
s 

 0, otherwise

l
ij
All the gradient values for pixel (i,j) with

s ijl  1

Dij  d ijl | sijl  1, l  0.....7
(3.10)
in the sub windows constitute
(3.11)
42
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
The maximal gradient value in Dij will be used as the ultimate gradient value for the pixel
(i,j) in the 5x5 detection window and the edge image will be produced when the gradient
values of all the pixels in the enhanced image have been calculated as following:
 m a x ( D i j ) ,
d ij  
 0 ,
D i j   

D i j   
(3.12)
where  denotes null set
3.3 Edge linking by morphological operators
The methods discussed in the previous section should result in pixels lying only on edges.
However, practically this set of pixels seldom characterizes edge completely because of
nose, breaks in the edge from nonuniform illumination, and other effect that introduce
spurious intensity discontinuities. Thus edge detection algorithms are normally followed
by edge linking procedures to bridge gaps in region boundary.
We apply simple morphological tools for the edge linking problem. The results of
applying edge linking by morphological operators, on the edge detected image is shown
in chapter 6 (Fig.6.15). The edge detection method considered for all these images is
FMFED algorithm. The reason for not applying FIS based edge detector is its poor
quality of edge detection compared to some older techniques like canny edge detector.
The various morphological operators used for edge linking of these images are described
below:
Cleaning – This operation removes isolated foreground pixels from the binary edge
image.
Dilation – Dilation is an operation that “grows” or “thickens” objects in binary image.
The specific manner an extent of this thickening is controlled by a shape referred to as a
structuring element.
Mathematically, dilation is defined in terms of set operations. The dilation of A by B,
denoted A  B, is defined as
43
Chapter 3
Study and implementation of segmentation based on fuzzy edge detection
A  B  {z | ( Bˆ ) z  A   |}
Where
 is the empty set
B is the structuring element and
B̂ is reflection of set B, defined as
Bˆ  {w | w  b, for b  B}
Closing
–
Dilation and erosion are often applied to image in concatenation. Dilation
followed by erosion is called a close operation. It is mathematically defined as
f  b  ( f  b)  b
Where erosion is defined as a process that “shrinks” or “thins” objects in an binary
image. The manner and the extent of shrinking is controlled by a structuring element.
Mathematically, erosion is defined as
A  B  {z | ( B ) z  Ac  }
Where Ac is the complement of set A.
The simulation results and conclusion of the chapter are in chapter 6.
44
CHAPTER 4
Development of Algorithm for
Segmentation of Color Images using
Fuzzy Clustering
45
Chapter 4
Development of algorithm for segmentation of color images using fuzzy clustering
4
Preview
Advances in cognitive psychology over the past decades have revealed that visual data, in
the form of scenes and pictures, are often mentally processed in visual terms alone,
without any corresponding translation or recording into verbal labels or representation,
and humans often respond strongly to color cues within image contents. In the past
decade, color imaging and printing devices has become more affordable and computer
power has been ever increasing. As a result color imaging has become very popular in
many applications including object classification and recognition, video surveillance,
image indexing and retrieval in image databases, feature based video compression, etc. In
this chapter we discuss about color image segmentation, which is often a necessary
computational process for color-based image retrieval and object recognition.
Image segmentation is a process of partitioning image pixels based on selected image
features. The pixels that belong to the same region must be spatially connected and have
the similar image features. If the selected segmentation feature is color, an image
segmentation process would separate pixels that have distinct color feature into different
46
Chapter 4
Development of algorithm for segmentation of color images using fuzzy clustering
regions, and simultaneously, group pixels that are spatially connected and have the
similar color into the same region. Every pixel in the image must be assigned to a region
when any segmentation algorithm terminates. In image processing two terms are usually
seen very frequently close to each other: clustering and segmentation. When analyzing
the color information of an image, for example and trying to separate regions or ranges of
color components having same characteristics, the process is called clustering. Mapping
the clusters onto the spatial domain and physically separating regions or surfaces in the
image is called segmentation.
The objective of color clustering is to divide a color set into c homogeneous color
clusters. Color clustering is used in a variety of applications, such as color image
segmentation and recognition.
Color clustering is an inherently ambiguous task because color boundaries are often
blurred. For example, consider the task of dividing a color image into color objects. In
color images, the boundaries between objects are blurred and distorted due to the imaging
acquisition process. Furthermore, object definitions are not always crisp, and knowledge
about the objects in a scene may be vague. Fuzzy set theory and fuzzy logic are ideally
suited to deal with such uncertainties. Fuzzy clustering models have proved a particularly
promising solution to the color clustering problem. Such unsupervised models can be
used with any number of features and clusters. In addition, they distribute membership
values across the clusters based on natural groupings in feature space (Bezdek, 1999). In
fuzzy clustering, the uncertainty inherent in a system is preserved as long as possible
before decisions are made. Of the fuzzy clustering algorithms proposed to date, the fuzzy
c-means (FCM) algorithm proposed by Bezdek is the most widely used in image
segmentation because it has robust characteristics for ambiguity and can retain much
more information than hard segmentation methods. Fuzzy c-means is an unsupervised
technique that has been successfully applied to feature analysis, clustering, and classifier
designs in fields such as astronomy, geology, medical imaging, target recognition, and
image segmentation. An image can be represented in various feature spaces, and the
FCM algorithm classifies the image by grouping similar data points in the feature space
into clusters. This clustering is achieved by iteratively minimizing a cost function that is
dependent on the distance of the pixels to the cluster centers in the feature domain.
47
Chapter 4
Development of algorithm for segmentation of color images using fuzzy clustering
4.1 Representation of Color Images
4.1.1 The colour data: vector representation
A. Bitmaps
The original and basic way of representing a digital colored image in a computer’s
memory is obviously a bitmap. A bitmap is constituted of rows of pixels, contraction of
the words ‘Picture Element’. Each pixel has a particular value which determines it’s
appearing color. This value is qualified by three numbers giving the decomposition of the
color in the three primary colors Red, Green and Blue. Any color visible to human eye
can be represented this way. The decomposition of a color in the three primary colors is
quantified by a number between 0 and 255. For example, white will be coded as R = 255,
G = 255, B = 255; black will be known as (R,G,B) = (0,0,0); and say, bright pink will be :
(255,0,255). In other words, an image is an enormous two dimensional array of color
values, pixels, each of them coded on 3 bytes, representing the three primary colors. This
allows the image to contain a total of 256x256x256 = 16.8 million different colors. This
technique is also know as RGB encoding, and is specifically adapted to human vision.
With cameras or other measure instruments we are capable of ‘seeing’ thousands of other
‘colors’, in which cases the RGB encoding is inappropriate. The range of 0-255 was
agreed for two good reasons: The first is that the human eye is not sensible enough to
make the difference between more than 256 levels of intensity (1/256 =0.39%) for a
color. That is to say, an image presented to a human observer will not be improved
byusing more than 256 levels of gray (256 shades of gray between black and white).
Therefore 256 seems enough quality. The second reason for the value of 255 is obviously
that it is convenient for computer storage. Indeed on a byte, which is the computer’s
memory unit, can be coded up to 256 values.
As opposed to the audio signal which is coded in the time domain, the image signal is
coded in a two dimensional spatial domain. The raw image data is much more straight
forward and easy to analyse than the temporal domain data of the audio signal. This is
why we will be able to do lots of stuff and filters for images without transforming the
source data, this would have been totally impossible for audio signal.
48
Chapter 4
Development of algorithm for segmentation of color images using fuzzy clustering
B. Vector representation of colors
As we have seen, in a bitmap, colors are coded on three bytes representing their
decomposition on the three primary colours. It sounds obvious to a mathematician to
immediately interpret colors as vectors in a three dimension space where each axis
stands for one of the primary colors. Therefore we will benefit of most of the geometric
mathematical concepts to deal with our colors, such as norms, scalar product, projection,
rotation or distance. Figure 4.1, illustrates this new interpretation:
Figure 4.1. vector representation of color
4.2 Selection of Color Space
Sometimes it is necessary to adjust computer vision to human vision. Especially it is
necessary when we are segmenting images, which were segmented by people and we try
to replace people with computers or when we want to help people in segmentation of
images. For this purpose we are using the L*a*b* color space. The L*a*b* color space
consists of a luminosity layer ‘L*’, chromaticity-layer ‘a*’ indicating where color falls
along the red-green axis and chromaticity-layer ‘b*’ indicating where the color falls
along the blue-yellow axis. The non linear relationships for L* a* and b* are the same as
49
Chapter 4
Development of algorithm for segmentation of color images using fuzzy clustering
for CIE XYZ (1931) and is another attempt to linearise the perceptibility of unit vector
color differences. Again, it is in non-linear, and the conversions are still reversible.
Colouring information is referred to the color of the white point of the system. The non
linear relationships for L* a* and b* are the same as for CIELUV and are intended to
mimic the logarithmic response of the eye.
The color space used in the initialization is of great importance because the shapes and
distribution of clusters depend on the color space (Tominaga, 1992). Typically, raw color
data are expressed in the RGB color space. However, RGB is not a perceptually uniform
space. The CIELAB color space, adopted as an international standard in the 1970’s,
provides perceptually uniform space, which means the Euclidean distance between two
color points in the CIELAB color space corresponds to the perceptual difference between
the two colors by the human vision system (Wyszecki and Stiles, 2000). This property
has made the CIELAB color space to be attractive and useful for color analysis, and the
CIELAB color space has shown its superior performance than other color spaces in many
color image applications (Paschos, 2001; Gong et al., 1998; Chang and Wang, 1996; Li
and Yuen, 2000; Shafarenko et al., 1998). Based on these reports, the CIELAB color
apace has been chosen for color clustering. The transformation from RGB to CIELAB is
performed as followed.
The L parameter has a good correlation with perceived lightness. The LAB cube root
color coordinate system was developed to provide a computationally simple measure of
color in agreement with Munsell color system[58]. The color coordinates are
1/ 3

Y
L  25 100 
Yo 

  X 1/ 3
A  500    
  X o 
 X 
B  200   
  X o 
(4.1)
 16
Y 
 
 Yo 
1/ 3



1/ 3
Z 
 
 Zo 
(4.2)



(4.3)
50
Chapter 4
Development of algorithm for segmentation of color images using fuzzy clustering
where Xo, Yo, Zo are the tristimulus values for the reference white and X, Y, Z are the
tristimulus value of the image pixels. We approximate these tristimulus values from
(RGB) by the linear transformation:
 X   0.607 0.174 0.200   R 
  
 
 Y    0.299 0.587 0.114   G 
 Z   0.000 0.066 1.116   B 
  
 
(4.4)
The reference white is (Ro,Go,Bo) = (255,255,255).
Basically, ‘L’ is correlated with brightness, ‘A’ approximates redness - greenness, and
‘B’ with yellow – blueness. These coordinates are used to construct a Cartesian color
space where the Euclidean distance is used that is,
2
2
2
*
 Eab
  L*   a*   b*
(4.5)
4.3 Fuzzy c-means Algorithm
Clustering is a process for classifying objects or patterns in such a way that samples of
the same group are more similar to one another than samples belonging to different
groups. Many clustering strategies have been used, such as the hard clustering scheme
and the fuzzy clustering scheme, each of which has its own special characteristics. The
conventional hard clustering method restricts each point of the data set to exclusively just
one cluster. As a consequence, with this approach the segmentation results are often very
crisp, i.e., each pixel of the image belong to exactly just one class. However, in many real
situations, for images, issues such as limited spatial resolution, poor contrast, overlapping
intensities, noise and intensity inhomogeneities variations make this hard (crisp)
segmentation a difficult task. Due to this fuzzy set theory was proposed, which produced
the idea of partial membership of belonging described by a membership function.
Fuzzy clustering as a soft segmentation method has been widely studied and successfully
applied to image segmentation [59-63].The fuzzy c-means (FCM) algorithm, proposed by
Dunn and generalized by Bezdek[64],
has the function to describe the fuzzy
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Development of algorithm for segmentation of color images using fuzzy clustering
classification for the pixels by calculating the fuzzy membership value. Fuzzy c-means
algorithm is a data clustering algorithm in which each data point belongs to a cluster to a
degree specified by a membership grade. It minimizes an objective function, with respect
to fuzzy membership U, and set of cluster centroids V
n
c
J (U , V )  
 (u
ik
) m d 2 ( x k , vi )
(4.6)
k 1 i 1
where
X  { x1 , x 2 , ..., x n }  R
p
c - the number of cluster centers or data subsets
m - the weighting exponents, 1 for ‘hard’ clustering, and increasing for fuzzier
clustering;
d 2 ( xk , vi ) - the distance measure between object xk and cluster center vi;
n - the total number of pixels in image;
uik - the fuzzy membership value of pixel k in cluster i;
vi - the cluster center for subset i in feature space;
U – the fuzzy c-partition
The above fuzzy c-mean algorithm uses iterative operation to get U and V and finally
minimizes the objective function. The algorithm is achieved as following:
1.
Fix the number of cluster c, 2<c<n;
Fix m, 1<m< 
2.
Initialize the fuzzy c-partition U[0] ;
3. Assume the steps b = 1, 2 ,…. ;
4. Calculate the c cluster centers { Vi(b) } with U (b) , the cluster center for cluster i is .
n
 (u
vi 
ik
)m xk
k=1
n
 (u
ik
)
(4.7)
m
k =1
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Development of algorithm for segmentation of color images using fuzzy clustering
5. Update U (b) , calculate the membership U (b+1) :
(a) Calculate Ik and Tk
I k  {i
1<i<c};
d ik  abs(x i - v k )  0 ;
Tk  {1,2, ...,c} - I k ;
(b) For data set k, calculate the new membership values:
(i) if I k = 0
1
u ik =
 d ik


d jk
j = 1
c



2
m 1
(4.8)
(ii) else
u ik = 0,  i  T k and
u
Ik
1
i I k
6. Compare U (b) and U (b+1) in a convenient matrix norm,
If U (b)  U (b+1)  L , stop;
Otherwise, set b = b+1 and go to step 4.
Here U (0) is the initial partition and can be randomly set or by an approximation method.
L is the convergence threshold. The introduction of the term m makes the segmentation
flexible, m = 1 for ‘hard’ clustering. The increase of the values of m stresses the fuzzy
properties. The FCM process is guaranteed to converge for m >1.
4.4 Segmentation Method:
The Segmentation process consists of several steps. The first step is the conversion of the
input image to chosen feature space, which may depend on the clustering method used. In
53
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Development of algorithm for segmentation of color images using fuzzy clustering
our case the input image is converted from RGB colour space to LAB colour space. The
L, A and B values are used as input to the clustering method.
Next step after the conversion of input image color is the application of clustering
algorithm. In our case we use fuzzy c- mean clustering as described in the section above.
After these two steps the segmentation process is followed as described:
Assumptions: Image transformed into feature space, number of clusters is c, stop
condition is  , fuzziness parameter m = 2.
Step 1: Convert the given RGB image into desired feature space (LAB colour space in
this case).
Step 2: Cluster image in feature space, with given conditions: number of clusters is c,
fuzziness index is m=2 and stop condition is  .
Step 3: The FCM iteration is stopped when the maximum difference between two
objective functions at two successive iterations is less than or equal to that of a fixed
value.
Step 4: For every pixel I(r,c) of image I, where ‘r’ is number of row and ‘ c’ is number
of column, the following steps are followed.
Step 4.1: All the pixels were considered belonging to one of the predetermined regions or
clusters. The number of cluster should be chosen carefully.
Step 4.2: The defuzzification process [23] takes place in order to convert the fuzzy
partition matrix U to crisp partition. A number of methods have been developed to
defuzzify the partition matrix, among which the maximum membership procedure is the
most important. The procedure assigns the object k to the class c with the highest
membership
ck  argi {max(uik )}
(4.9)
Step 4.3: The decision on how to assign the pixel I(i,j) to various clusters was based on
wining
uik
having highest value among the clusters.
Step 5: The pixel I(i,j) would be painted the same colour as the cluster to which it
belongs the most.
54
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Development of algorithm for segmentation of color images using fuzzy clustering
4.5 Image segmentation under uneven illumination of
objects
Image degradation is inevitable during the transmission and conversion of images. For
example, the quality of an image shot by a camera is sometimes low due to the distortion
of camera’s optics system, low light conditions, the relative motion of the photographed
object and the camera, the environmental change and the random disturbance. If we
perform clustering operation on such images we are likely to get wrong classification of
objects present in the image due to distortion of the image. Hence an enhancement
operation has to be carried out as a preprocessing step on such images before clustering
operation is performed on them. The enhanced image avoids wrong classification to great
extent. The image enhancement is an important technique that can improve the quality of
the degraded image and provide some interested image features selectively. Image
enhancement algorithms have been designed to process a given image so the results are
better than the original image for their applications.
When the objective is to improve perceptual aspects, desirable image enhancement can
be performed by the contrast and dynamic range modification.
Processing techniques for image enhancement can be classified into spatially uniform
operators and spatially non-uniform operators. Linear contrast stretch, histogram
equalization are two of the most widely used spatially uniform technique. Adaptive
histogram-equalization (AHE) [67], contrast-limited adaptive histogram equalization
(CLAHE) [68] belongs to the second class of image-contrast enhancement methods.
While the spatially uniform methods use a transformation applied to all the pixels of the
image, the later methods use an input–output transformation that varies adaptively with
the local characteristics of the image. Spatially non-uniform operators usually provide a
better performance than spatially uniform operators. The linear contrast-stretch method
can hardly enhance all parts of the image simultaneously. Histogram equalization tends to
over-enhance the image contrast if there are high peaks in the histogram. Adaptive
histogram equalization applies locally varying gray-scale transformation each small
region (block) of the image, thus requiring the determination of the block size. An
improvement on this technique is represented by the CLAHE method. In contrast-limited
55
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Development of algorithm for segmentation of color images using fuzzy clustering
adaptive histogram equalization, the local contrast-gain is limited by restricting the height
of local histograms. This method provides for local enhancement of region in an image. It
reduces undesired noise amplification and reduces boundary artefacts.
4.5.1. Contrast limited adaptive histogram equalization
Contrast Limited Adaptive Histogram Equalization (CLAHE) is an extension to Adaptive
Histogram Equalization (AHE) which limits the maximum contrast adjustment that can
be made to any local histogram. This limitation is useful so that the resulting image does
not become too noisy (which is a problem with AHE). The limitation is performed by
allowing a set maximum number of pixels within each gray level associated with a local
histogram. After clipping the histogram, the pixels that were clipped are equally
redistributed over the whole histogram to keep the whole histogram count unchanged. It
operates on small data regions (tiles) rather than the entire image. Each tiles contrast is
enhanced so that the histogram of each output region approximately matches the
specified histogram (uniform distribution in this case).
4.5.2 Segmentation method
The algorithm developed is a contrast limited adaptive histogram equalization based
FCM. Hence, it is called CLAHEFCM. The segmentation process consists of several
steps. The first step is the conversion of the input image to chosen feature space, which
may depend on the clustering method used. In our case the input image is converted from
RGB color space to LAB color space. The L, A and B values are used as input to the
clustering method.
Next step after the conversion of input image color space is the application of
enhancement method, followed by clustering algorithm. In our case we use fuzzy c- mean
clustering as described in the section above.
After these two steps the segmentation process is followed as described:
Assumptions: Image transformed into feature space, number of clusters is c, stop
condition is  , fuzziness parameter m = 2.
Step 1: Covert the given RGB image into desired feature space (LAB color space in this
case).
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Development of algorithm for segmentation of color images using fuzzy clustering
Step 2: Next we normalize the brightness layer L, by dividing by 100. After that we
apply the contrast limited adaptive histogram enhancement (CLAHE) algorithm to the
luminosity layer.
Rest of the steps are same as the step 3- step 5 in section 4.4.
The simulation results and conclusion of the chapter are in chapter 6.
57
CHAPTER 5
Development of Algorithm for
Segmentation by Incorporating Spatial
Property of Pixels in Fuzzy Clustering
58
Chapter 5
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
5
Preview
Fuzzy c-means clustering is an unsupervised technique that has been successfully applied
to feature analysis, clustering, and classifier designs in fields such as astronomy, geology,
medical imaging, target recognition, and image segmentation. An image can be
represented in various feature spaces, and the FCM algorithm classifies the image by
grouping similar data points in the feature space into clusters. This clustering is achieved
by iteratively minimizing a cost function that is dependent on the distance of the pixels to
the cluster centers in the feature domain.
The pixels on an image are highly correlated, i.e. the pixels in the immediate
neighbourhood posses nearly the same feature data. Therefore, the spatial relationship of
neighbouring pixels is an important characteristic that can be of great aid in imaging
segmentation. General boundary detection techniques have taken advantage of this spatial
information for image segmentation. However, the conventional FCM does not fully
utilize this spatial information.
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Development of algorithm for segmentation by incorporating spatial property of pixels in
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5.1 FCM-Related Extensions
The most direct way to compensate for the drawback of FCM is to smooth the image
before segmentation. However, standard smoothing filters lead to a loss of important
image details. Various extensions of the FCM algorithm with attempt to accommodate
noise have been presented by many researchers. Tolias and Panas post-processed the
membership function to smooth the noise effect [69]. Acton and Mukherjee incorporated
multiscale information to enforce spatial constraints [70].
The most popular approach for increasing the robustness of FCM to noise is to modify
the objective function directly. Dave proposed the idea of a noise cluster to deal with
noisy clustering data in the approach known as NC [71]. Noise is effectively clustered
into a separate cluster which is unique from from signal clusters. However, it is not
suitable for image segmentation, since noisy pixels should not be separated from other
pixels, but assigned to the most appropriate clusters in order to reduce the effect of noise.
Another similar method, developed by Krishnapuram and Keller [72], is called
possibilistic c-means (PCM), which interprets clustering as a possibilistic partition.
Instead of having one term int the objective function, a second term is included, forcing
the membership to be as high as possible without a maximum limit constraint of one.
However, it caused clustering being stuck in one or two clusters.
Pedrycz and Waleztzky [73] took advantage of the available classified information and
actively applied it as a part of their optimization procedures. Ahmed et al. [22] modified
the objective function of the standard FCM by introducing a term that allowed the
labelling of a pixel to be influenced by the labels in its immediate neighbourhood. Zhang
Yang , Fu-lai Chuang et al.[75] developed a robust fuzzy clustering- based segmentation
method for noisy images. A robust modified FCM in the sense of a novel objective
function is derived. The applicability of the proposed modified FCM is also explored.
Jiayin Kang et al.[25] proposed another such modified FCM where objective function
was modified by incorporating the spatial neighbourhood information into the standard
FCM algorithm. Y. Yang et al. proposed a novel penalized fuzzy c-means (PFCM)
algorithm for image segmentation, the penalty term acts as a regularizer in the algorithm
which is inspired by neighbourhood maximization (NEM) algorithm and is modified in
order to satisfy criterion of FCM algorithm [23].
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Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
S.Shen,W.Sandham et al. [24] presented an algorithm called IFCM. A neighbourhood
attraction, which is dependent on relative location and features of neighbouring pixels, is
used to improve the segmentation results. This method changed the distance function
used in FCM which is the distance between pixel intensity and the cluster intensities and
a neural network optimization technique was used to adjust parameters in the modified
distance function. But problem with this method is that it requires an extra neural
network optimization step for adjusting parameters of the distance function. Hence, this
makes the algorithm complex.
Keh-Shih Chuang, Hong-Long Tzeng, et al. [74]
presented a fuzzy c-means (FCM) algorithm that incorporated spatial information into the
membership function for clustering, and the membership weighting of each cluster is
altered after the cluster distribution in the neighbourhood is considered. The problem
with this method is that it does not produce smooth edges.
All these methods except the last two methods inevitably introduce computation issues,
by modifying most equations along with the modification of the objective function, and
have to lose the continuity from FCM, which is well-realized with many types of
software, such as MATLAB.
5.2 Development of algorithm for incorporating spatial
relationship of neighbouring pixels into FCM
5.2.1 Method
This proposed method is based on the FCM incorporating spatial function [74] proposed
by K-S Chuang et al. One of the important characteristics of an image is that its
neighbouring pixels are highly correlated to each other. The probability that a pixel
neighbourhood will belong to same cluster is very high. This property of the pixels is
quite helpful when the image is affected by noise. As the spatial relationship among
pixels is not considered in the standard FCM algorithm a spatial function is introduced to
take into account the neighborhood property.
For finding the spatial function, the membership information of each pixel of a cluster is
converted to its spatial domain to get the complete image. Then we calculate the spatial
function, using the following definition
61
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Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
M

sik 
uij
(5.1)
kNB( xk )
where
NB(xk )
represents a square window centered on pixel xk (1<k<n, where n is the
total number of pixels in the image) in the spatial domain image containing the
membership information of each pixel to a particular cluster ‘i ‘. A 5x5 window was
used for this work. Just like the membership function uij the spatial function sik gives the
membership of the kth pixel to a particular cluster ‘i ‘.
The spatial function is modified in order to take into account the properties of a local
neighborhood in a way that the membership of each pixel results as a weighted sum of
the pixels in the 5x5 neighborhood. This enables smoothening of the edges or boundaries
of objects present in an image. Assuming M as the 5x5 neighborhood of the pixel j, the
membership function to a cluster i is modified as follows:
hik 
(hik  sik )
25
(5.2)
Hence the new algorithm developed is named Modified spatial fuzzy c means (MSFCM)
The spatial function is then introduced in the membership function as follows:
'
ik
u 
u ikp hikq
c
u
p
jk
h qjk
(5.3)
j 1
where p and q are parameters which control the relative importance of both functions. If
the pixels in an image are not affected by noise then spatial function will only fortify the
62
Chapter 5
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
original membership, and the clustering result remains unchanged. However, for a noisy
pixel, this formula reduces the weight of a noisy cluster by the labels of its neighboring
pixels. As a result, misclassified pixels from noisy regions or spurious blobs can easily
be corrected.
The clustering is a two-pass process. In the first pass we use the standard FCM to
calculate the membership value for each pixel. The membership value for each pixel to
different clusters is then mapped to spatial domain and the spatial function is calculated
from that.
In the second pass, the FCM iteration proceeds with the new membership function that is
incorporated with the spatial function. The iteration of spatial FCM algorithm stopped
when the difference between the present and the previous objective function is less than
or equal to a certain value ( 105 ).
After the convergence, defuzzification is applied to assign each pixel to a specific cluster
for which the membership is maximal.
5.2.2 Segmentation method
The Segmentation process consists of several steps. The various steps involved in the
method are shown in Fig. 5.1. The first step is the conversion of the input image to
chosen feature space, which may depend on the clustering method used. In our case the
input image is converted from RGB color space to LAB color space. The L, A and B
values are used as input to the clustering method.. In our case we use fuzzy c- mean
clustering as described in the section above.
After these two steps the segmentation process is followed as described:
Assumptions: Image transformed into feature space, number of clusters is c, stop
condition is  , fuzziness parameter m = 2.
Step 1: Convert the given RGB image into desired feature space (LAB color space in this
case).
Step 2: Cluster image in feature space, with next conditions: number of clusters is c,
fuzziness index is m=2 and stop condition is  .
Step 3: The membership information of each pixel is mapped to the spatial domain, and
the spatial function is calculated.
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Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
Step 4: The new membership function is calculated using equation (4).
Step 5: The FCM iteration proceeds with the new membership function. The iteration is
stopped when the maximum difference between two objective functions, at two
successive iterations, is less that a fixed value.
The next steps are same as steps 4-5 in segmentation method of section 4.4
Input
Color image
+
Noise
CL1
Convert image
from RGB to
L*a*b* color
space
Fuzzy clustering in
L*a*b* domain and
converting partition
matrix to spatial
domain
Find modified spatial
function of the images
in spatial domain and
give it as input for FCM
CL2
Map initial
clusters to
image
domain
Apply
defuzzification
rule
Fig. 5.1. Block diagram of the various steps used for
segmentation using standard FCM along with input
and output
CL3: A set
of color
regions
Output
The ‘hand’ image was divided into three clusters, the three clusters consists of the hand,
green ring and the background. The membership function of each of these three clusters
with respect to ‘A’and ‘B’ values of image pixels, calculated by standard FCM and
proposed method called modified spatial FCM (MSFCM) is shown in Fig. 5.2.The
membership function for both sFCM and proposed method are same.
64
Chapter 5
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
(a)
(b)
(c)
(d)
Fig. 5.2. (a) Membership function of first, second and third cluster with respect to a* values of
image pixels using FCM. (b) Membership function of first, second and third cluster with
respect to b* values of image pixels using FCM. (c) Membership function of first, second and
third cluster with respect to b* values of image pixels using MSFCM. (d) Membership function
65
Chapter 5
5.3
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
Segmentation
of
noisy
colour
images
using
neighbourhood property of a digital image
5.3.1
Method
A new algorithm based on the IFCM (Improved Fuzzy c- means) [24] neighbourhood
attraction is proposed. The algorithm does not change the distance function of the FCM,
hence avoiding an extra neural network optimization step for the adjusting parameters of
the distance function; it is called Neighbourhood Attraction FCM (NAFCM). During
clustering, each pixel attempts to attract its neighbouring pixels towards its own cluster.
This neighbourhood attraction depends on two factors: the pixel intensities or feature
attraction, and the spatial position of the neighbours or distance attraction, which also
depends on neighbourhood structure.
The first parameter, feature attraction, is given by the function
S

H

ij
u ik g
jk
k 1
S

(5.4)
g
jk
k 1
Where g jk is the intensity difference between study pixel j and its neighbour pixel k.
g
jk

x j  xk
u ik is the membership of the neighboring pixel k to the ith cluster, and S is the number of
neighboring pixels.
The distance attraction function is given by
S

F ij 
u i2k q
2
jk
k 1
S

q
(5.5)
2
jk
k 1
The neighbourhood structure is of the form
K j   k  N | 0  ( a j  a k ) 2  ( b j  bk ) 2  Q 
66
(5.6)
Chapter 5
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
Where (a j ,b j ),(ak , bk ) denote the coordinates of the pixel j, k. Q is a constant, equal to
2(L-1), and L is the level of the neighbourhood. Fig.5.7 shows the neighbourhood for
different levels. We consider L =2.
qjk in (5) can be described as follows:
q jk  ( a j  a k ) 2  (b j  bk ) 2
(5.7)
After getting the functions Hij and Fij each of these matrixes are converted into spatial
domain and perform the smoothing operation on them using averaging filters. This
operation is done in order to reduce the effect of noise in the image.
M
w ij 
N

i 1
H ij
j 1
hij  (hij  wij ) / 25
M
m ij 
N

i 1
(5.8)
F ij
j 1
fij  ( f ij  mij ) / 25
(5.9)
h i j and f i j are given as input to the FCM algorithm. We take the number of cluster
according to object of interest for a particular problem.
67
Chapter 5
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
Figure. 5.7. Neighborhood structure definitions. (A higher level includes pixels labeled as the number of
the level and pixels in all lower levels).
5.3.2 Segmentation method
The Segmentation process consists of several steps. The first step is the conversion of the
input image to LAB color space. Next step is finding the two attraction features for the
image, followed by clustering algorithm. In our case we use fuzzy c- mean clustering as
described in the section above.
After these two steps the segmentation process is followed as described:
Assumptions: Image transformed into feature space, number of clusters is c, stop
condition is  , fuzziness parameter m = 2.
Step 1: Take the desired noisy colour image (Skin tumor images in this case) and convert
the image to LAB color space.
Step 2: Find the feature attraction and distance attraction function as defined by equation
(5.4) and (5.5).
Step 3: Convert the feature attraction and distance information into spatial domain, and
perform smoothing operation using averaging filters on the image matrix formed in
spatial domain. The smoothed images formed from the two matrixes are found by
equation (5.8) and (5.9).
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Chapter 5
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
Step 4: The data from equation (5.8) and (5.9) are used as input for the FCM algorithm.
Step 5: The FCM iteration is stopped when the maximum difference between two
objective functions at two successive iterations is less than or equal to that of a fixed
value.
Rest of the steps are same as steps 4-5 in section 4.4.
5.4 Segmentation by using morphological operator
Apart from the segmentation method described in previous section for segmenting tumor
images, morphological operators can also be used for segmentation. The results of
applying morphological operators for segmentation after clustering is shown in figure
6.40- figure 6.41. The steps involved for segmentation by using morphological operators
are as follows.
Step 1: First the cluster images are converted to black and white images by thresholding
and then the regions in the images are filled using morphological tool
Step 2: Fill the holes (hole is an area of dark pixels surrounded by lighter pixels) inside
the region of the black and white cluster images.
Step 3: Perform morphological opening on the image with a structuring element (square
mask of size 3x3). This is done to smooth the contour of the object, break narrow
isthumuses and eliminates thin protrusions.
Step 4: Remove from the binary segmented imgaes all connected components (objects)
that have less than 200 pixels. We select 200 pixels as it is sufficient to remove object
which do not belong to region of interest, i.e the affected region.
Step 5: Finally find the perimeter of the objects in binary image and overlay them on the
original image.
69
Chapter 5
Development of algorithm for segmentation by incorporating spatial property of pixels in
fuzzy clustering
5.5 Application of NAFCM algorithm in segmentation of
melanoma images:
Segmentation of Melanoma images using the above algorithm:
Melanoma, the most serious type of skin cancer, develops in the cells that produce
melanin — the pigment that gives the skin its color. Melanoma can also form in eyes and,
rarely, in internal organs, such as intestines.
The exact cause of all melanomas isn't clear, but exposure to ultraviolet (UV) radiation
from sunlight or tanning lamps and beds greatly increase risk of developing melanoma.
Avoiding excessive sun exposure can prevent many melanomas. And making sure you
know the warning signs of skin cancer can help ensure that cancerous changes are
detected and treated before they have a chance to spread. Melanoma can be successfully
treated if it is caught in early stages.
The first melanoma symptoms often are: a change in an existing mole, or the
development of a new, unusual-looking growth on the skin. But melanoma can also occur
in otherwise normal looking skin.
Unusual moles that may indicate melanoma:
Characteristics of unusual mole that may indicate melanoma or other skin cancer follow
the A-B-C-D guide developed by the American Academy of Dermatology:

A is for asymmetrical shape. Look for moles of irregular shapes, such as two very
different-looking halves.
 B is for irregular border. Look for moles irregular, notched or scalloped borders – the
characteristics of melanoma.
 C is for changes in color. Look for growths that have many colors or an uneven
distribution of color.

D is for diameter. Look for new growth in a mole larger than about ¼ inch (6 mm.).
For every symptom listed above, we take one example into consideration. The
examination of growth on skin is done automatically by use of the proposed NAFCM
algorithm. The simulation results are present in Fig. 6.32-Fig. 6.35.
The simulation results and conclusion of the chapter are in chapter 6.
70
CHAPTER 6
Simulation Results and
Discussion
71
Chapter 6
Simulation results and discussion
6
Preview
The simulation results of all the chapters and their conclusion is presented in the chapter.
The image metrics like partition coefficient Vpc, partition entropy Vpe and the percentage
of misclassified pixels are used in the chapter to compare between the various existing
and proposed algorithms. Extensive qualitative and quantitative analysis is done for
comparing the clustering and segmentation results obtained using the different
algorithms, under increasing noise condition. The algorithms are tested on synthetic
image, real world image and biomedical image.
6.1 Simulation Results
The algorithms are implemented on Matlab 7.0 (The Mathworks Inc.). The processesor
used is a Pentium IV core 2 duo processor, 2.4Ghz (clock), 2GB (RAM), Windows vista
64 bit operating system.
Fig. 6.1(a) is an infrared image of an aluminium weld with porosity or crack. Fig 6.1(b)(d) shows the result of applying region growing for segmentation of the crack in the weld.
72
Chapter 6
Simulation results and discussion
Fig. 6.2 shows a scenery image and the result of applying region growing for segmenting
a particular field region. Figure 6.3 shows the result of applying region split and merge
on the weld crack image of Fig. 6.1(a). Fig. 6.4(a) shows image of Saturn planet with a
distant isolated star near its right bottom side. Fig. 6.4(b) shows the result of applying a
point detector mask shown in Fig.2.3. Fig. 6.5(a) shows a pill set image. Fig. 6.5(b)-(c) is
the result of running a horizontal mask (Fig.2.4) on the image and thresholding it. Fig 6.6
(a) shows lena image and Fig.6.6(b)-(f) shows the result of applying Roberts, Prewitt’s,
Sobel, LoG and Canny edge detector.
The FIS based edge detection described in section 3.1 is tested on different images, its
performance being compared to that of the other derivative based popular edge detectors
like, Sobel operator and Canny edge detector. Fig. 6.7(a) shows a block image which has
varying gray levels on its two faces that are visible. Fig.6.7 (b)-(d) shows the result of
applying Sobel and Canny edge detector and FIS system respectively. Fig, 6.8(a) depicts
the image of digital cameras calibration pattern, in which there is a high contrast
variation. Fig.6.8 (b)-(d) shows the result of applying Sobel and Canny edge detector and
FIS system respectively. Fig. 6.9(a) shows a 230  325  8 bits standard image that is
used for the calibration in the visual system. Fig.6.9 (b)-(d) shows the result of applying
Sobel and Canny edge detector and FIS system respectively. The edge detection
performance of the methods Sobel operator, Canny edge detector and Fuzzy Inference
system are compared in terms of the image quality.
The FMFED algorithm described above has been tested on some test images and its
qualitative performance is compared to two popular edge detectors – Sobel and Canny
edge detectors [57]. The fuzzy enhancement operator is tuned to allow good results while
extracting edges of the image. For the images considered here the value of the fuzzy
enhancement operator is mostly varied between the ranges 0.5 to 1. The first test image
(Fig. 6.10) considered for comparison of the simulation results is a bird image, the second
image (Fig. 6.11) is a tire image where the object of interest and the background have
same gray level values. The third test image (Fig. 6.12) is a MRI image and the fourth
(Fig. 6.13) and fifth (Fig. 6.14) test images are X-ray images. The qualitative comparison
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between Sobel edge detector, Canny edge detector and the FIS algorithm on the different
test images is shown in Fig. 6.10(b)-(d) to Fig. 6.14 (b)-(d).
The results of applying morphological operators described in the section above is shown
in Fig. 6.15 .The figure shows three edge detected image by applying FMFED algorithm
in Fig. 6.15(a)-(c). The result of applying morphological operators is shown in figure
6.15(d)-(f). By observing the results it can be said that morphological operators are not
the best way to fill the gaps in the edge images and hence there is scope for applying
some other edge linking algorithm.
The FCM based segmentation described in chapter 4, section 4.4 has been tested on some
colour test images in LAB and their results are shown. The number of cluster was chosen
in such a manner that we are able to segment the region of interest based on color
completely from the image provided. Selecting large values for number of cluster m,
would lead to not so good generalization of the image. If too low values for the number
of cluster are selected, the neighbourhood colours may be confused. Fig. 6.16 and Fig.
6.17, show comparison between segmentation in RGB color space and LAB color space.
The quantitative comparison between the two color spaces is done in Table 6.1 and Table
6.2. The effect on partition coefficient Vpc and partition entropy Vpe for increasing noise
has been studied in these tables.
The images considered as test images
for applying FCM algorithm are shown in
Fig.6.18 (a) – Fig.6.21 (a). Fig.6 .18(a) is an image of some vegetation in desert area. Fig
6.18(b)-(d) shows the two clusters formed by using c=2 and the segmented image
respectively. Fig. 6.19(a) is the image of an woman. Fig 6.19(b)-(e) shows the three
clusters formed by choosing selecting c = 3 and the segmented image. Fig. 6.20(a) is a
biomedical image showing hyper pigmentation of skin of an old lady. The cheek region
shows dark patches due to hyperpigmentation. Fig 6.20(b)-(d) shows the two clusters
formed by selecting c=2 and the segmented image. Fig. 6.21(a) is an image containing a
bird flying in sky. Fig 6.21(b)-(d) shows the two clusters formed by selecting c=2 and the
segmented image.
The CLAHE based FCM algorithm described in section 4.6 has been tested on some
color test images in LAB color space and their results are shown in Fig 6.22-6.25. Fig.
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6.22(a) is a close aerial view of a landscape, which has a water body along with some dry
areas. Fig 6.22(b) shows the enhanced image. Fig 6.22(c)-(d) shows the segmentation
results for Fig. 6.22(a) and Fig. 6.22(b) respectively. Fig. 6.23(a) is the image of a
person’s cheek region suffering from hyper-pigmentation. Fig. 6.23(b) is the enhanced
image. Fig 6.23(c)-(d) shows the segmentation results for Fig. 6.22(a) and Fig. 6.22(b)
respectively. Figure 6.24(a) is the image of a woman. Fig. 6.24(b) is the enhanced image.
Fig 6.24(c)-(d) shows the segmentation results for Fig. 6.24(a) and Fig. 6.24(b)
respectively. Fig. 6.25(a) is the image of a stork bird in a field. Fig. 6.25(b) is the
enhanced image. Fig 6.25(c)-(d) shows the segmentation results for Fig. 6.25(a) and Fig.
6.25(b) respectively.
The MSFCM algorithm described in section 5.2 and the NAFCM algorithm described in
section 5.3 has been tested in LAB color space on a synthetic image, a grayscale image
and some color test images, and their results are shown in Fig. 6.26-6.35.
A synthetic image shown in fig. 6.26(a) is used to show how the three classes of the
image, having intensity values 0, 255 and 128, are affected while clustering the image
using various clustering method such as FCM, sFCM, MSFCM, and NAFCM when the
noise is increased from (-40,40) to (-90,90). The effect of increasing noise is shown in the
Fig. 6.26- Fig. 6.28. From the images in Fig.6.26 - Fig.6.28, the percentage of
misclassified pixels in each three clusters present in the synthetic image is calculated.
Fig. 6.29 shows the comparison of segmentation results of region based segmentation,
edge based segmentation and FCM clustering based segmentation under a low noise
varying between (-25,25) on a grayscale image(weld crack image).
The color images considered as test images are shown in Fig. 6.20- Fig.6.35. Fig. 6.30(a)
shows an woman’s image with a uniform random noise with magnitude varying between
(-35,35), in this image our region of interest is the skin color. Fig. 6.30(b)-6.30(e) shows
the output of applying FCM, sFCM, MSFCM and NAFCM respectively on the input
image. Fig. 6.30(f)-6.30(i) are the segmented images after applying FCM, sFCM,
MSFCM and NAFCM algorithm respectively. The second test image in Fig.6.31(a) is the
aerial view of a cross-road with a uniform random noise varying between (-35,35). The
clustering result of applying FCM,sFCM, MSFCM and NAFCM is shown in Fig.
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6.31(b)-6.31(e) respectively. Fig.6.31 (f)-(i) shows the segmented result of the four cases
respectively. The test image in Fig.6.32 (a) is that of a human hand with a huge green
color plastic ring. The image is corrupted with a noise of (-45,45). The green color plastic
ring is our object of interest in this image. The segmentation result of all the algorithms
has been shown in fig.6.32 (f)-6.32(i).The test image shown in Fig. 6.33 (a) is that of
bacteria with a noise of (-90,90). The bacteria image is separated using all the four
methods and the segmentation results are shown in Fig 6.31(f)-(i). The test image in Fig.
6.33(a) is image of a stork bird in a field with a noise of (-60,60).The image is first
enhance using CLAHE algorithm as in Fig.6.25(b). The bird is separated from its
background (field) using all the four clustering methods and the results are shown in Fig.
6.30(f)-(i).The test image in Fig. 6.35(a) is that of a woman. The skin color is clustered
using the four algorithms under a random noise varying between (-90,90). The image is
enhanced first using CLAHE algorithm as in Fig.6.24 (b) and then the four clustering
algorithms are applied in Fig. 6.35(b)-6.35(e). The segmentation results are shown in Fig.
6.35(f)-6.35(i).
Fig. 6.36-Fig 6.39 shows an application of the NAFCM algorithm in detecting the tumor
growth by observing tumor images showing different symptoms as discussed in section
5.2.4. Fig. 6.36(b) shows an example of asymmetrical shape of the mole with a noise of (60,60) in which one half is different from the other may indicate melanoma. Here, the
left side of the mole is dark and a little raised, whereas the right side is lighter in color
and flat. Fig. 6.36(c)-(d) are the results of using FCM for clustering of the image. The
clusters formed by using NAFCM algorithm is shown in Fig.6.36(g)- 6.36(i). Fig. 6.37(b)
is an example of a growth with irregular border having a noise of (-60,60). The clusters
formed by using NAFCM algorithm is shown in Fig.6.36(f)- 6.36(g). Fig. 6.38(b) is an
example of changes in colour of a mole with a noise of (-90,90).Fig.6.38(c)-6.38(l) shows
the various clusters and segmented image using FCM and NAFCM respectively.
Fig.6.39(b) is a case where we take the diameter of the mole into consideration to know
whether it can develop into skin cancer. Here the image has a noise of (-90,90).
Fig.6.39(c)-6.39(h) shows the various clusters and segmented image using FCM and
NAFCM respectively.
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Table 6.3 shows the quantitative analysis of all the algorithms. A high Vpc and a low Vpe
gives good clustering result. Table 6.4 shows the percentage of misclassified pixels in
each cluster for increasing noise condition.
Fig. 6.39 and Fig 6.40 shows the result of applying morphological operators for
segmentation of tumor images as described in section 5.2.3. Table 6.5 shows that
NAFCM gives good clusters (high Vpc and low Vpe) while using it for segmentation of
melanoma images.
6.2 Discussion
Two examples for region growing have been shown in Fig 6.1 and Fig 6.2. In the first
case, Fig. 6.1, the seed point under consideration is single pixel intensity. In the second
case, Fig. 6.2, an array of seed points has been considered, where pixels are added to a
region if any of the pixels in its four neighbourhood satisfies a predefined condition. The
first test image is an infrared image of an aluminium weld with porosity or crack. A
threshold value of 65 and pixel intensity of 255(brightest pixels signify crack) are taken
as condition for region growing. The second test image is a scenery image. The region is
iteratively grown by comparing all unallocated neighbouring pixels to the region.The
distance between a pixel's intensity value and the region's mean,is used as a measure of
similarity. The pixel with the smallest distance measured this way is allocated to the
respective region.This process stops when the intensity difference between region mean
and new pixel become larger than a certain threshold.Region maximum distance is taken
as 0.3. Figure 6.3 shows how the weld crack is segmented by using region split and
merge with a standard deviation greater than 10 and mean intensity greater than 15. In
Fig. 6.4 (b) it is observed that we are able to detect the isolated star using point detector
mask. In Fig. 6.5(b)-(c) it is observed that the horizontal lines in the image are easily
recovered. By observing Fig 6.6(b)-(f) it can be said that, Canny operator performs the
best in detecting all edges, but the problem with it is that it gives false edges also. The
Canny edge detector also requires the set of two threshold every time by the user.
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The FIS based edge detection described in section 3.1 is tested with different images, its
performance being compared to that of the other derivative based edge detectors like,
Sobel operator and Canny edge detector. It is observed in Fig. 6.7 that the Sobel operator
does not allow edges to be detected in the region where the transition from high gray
level values of image pixels to low gray level values of image pixels is blurred. The
Canny edge detector is able to detect all edges but it also gives some false edges along
with the true edges. The FIS system in turn, allows edges to be almost detected even in
the low contrast regions without the output image being much affected by noise. But still
it is unable to detect true edge completely. In case of Fig. 6.8 we observe that again the
Sobel operator is not able to detect edges in the low contrast region. The Canny edge
detctor is able to detect some edge pixels in the low contrast regions of the image but it is
unable to detect any eges in high contrast region. The FIS system is able to detect edge
pixels in the low contrast region and some pixels even in the high contrast regions.In Fig.
6.9 it is seen that the original image is quite blurred in nature. The Sobel edge detector is
again unable to detect edges in the regions where the image starts getting more blurred.
The Canny edge detector is the best performer here as it detects edges even in the blurred
region, even though it has a disadvantage of detecting false edges.
The FMFED algorithm described above has been tested on some test images and its
qualitative performance is compared to two popular edge detectors – Sobel and Canny
edge detectors[57]. By the visual comparison of all the algorithms results Fig. 6.10- 6.14
(b-d), it is observed that the sobel edge detector operator performs the worst among all as
it is unable to detect true edge pixels in certain areas. The Canny edge detector on the
other hand is able to detect all the edge pixels but the problem with this method is that it
detects false edges too. These false edges give wrong information about the original
objects approximate shape. False edges are also a liability in cases where edge detection
is used for image compression. In case of all test images considered here it is seen that we
get too many edge pixels in the cases where Canny edge detector is applied to the original
image. Whereas, when Sobel operator is applied to the same images, certain important
edge information has been lost. The FMFED algorithm is a good. By observing the result
of applying morphological operators on the edge detcted images [Fig. 6.15(a)-6.15(c)]
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shown in Fig. 6.15(d)-6.15(f), it can be said that morphological operators are not the best
way to fill the gaps in the edge images and hence there is scope for applying some other
edge linking algorithm.
The FCM based segmentation described in chapter 4, section 4.4 has been tested on some
colour test images in LAB color space and their results are discussed here. Apart from
the reason that CIELAB color space provides perceptually uniform space, it is also
observed that using RGB color space the clusters that are formed are not correct as shown
in Fig. 6.16 and Fig. 6.17, here comparison is made between segmentation in RGB color
space and LAB color space. The same results are proved by observing quantitative
comparison between the two color space is done in Table 6.1 and Table 6.2 as the LAB
color space shows high Vpc and low Vpe value (condition for good clustering).
The images considered as test images for applying FCM algorithm are shown in Fig.6.18
(a) – Fig.6.21 (a). Fig.6.18(a) is an image of some vegetation in desert area. Fig. 6.18(b)(d) by using just c=2, the sand and the green vegetation has been segmented
satisfactorily. Figure 6.19(a) is the image of a women, here we want to segment the skin
color, which can be done easily by choosing selecting c = 3. Fig. 6.20(a) is a biomedical
image showing hyper pigmentation of skin of an old lady. The cheek region shows dark
patches due to hyperpigmentation. By selecting c=2, the affected skin which is brown or
dark in color is separated from the pink skin which is unaffected by hyperpigmentation.
Fig. 6.21(a) is an image containing a bird flying in sky. Selecting c = 2 we are able to
separate the bird from the sky.
The CLAHE based FCM algorithm described in section 4.6 has been testedin LAB color
space on some color test images and their results are discussed. The CLAHE algorithm is
applied only to the luminosity layer L. This is because the enhancement of the image
depends on the brightness level of the image pixels. The images considered as test images
here are shown in Fig 6.22-6.25(a). Fig. 6.22(a) is a close aerial view of a landscape,
which has a water body along with some dry areas. Taking c=3, segments the water area
(dark blue color in the segmented image) from the dry area. Figure 6.23(a) is the image of
a person’s cheek region suffering from hyper-pigmentation. The extent of affected skin
(shown by dark blue color in the segmented image) is known more accurately in the case
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when segmentation is done after image enhancement. Figure 6.24(a) is the image of a
woman. Taking the number of clusters c=3, the skin is correctly classified and segmented
(yellow color in segmented image) after enhancement of the image. Fig. 6.25(a) is the
image of a stork bird in a field. Taking the number of clusters c=3, the stork bird is
almost correctly classified and segmented after enhancement of the image [sky blue color
Fig. 6.25(d)].
The MSFCM algorithm described in section 5.2 and the NAFCM algorithm described in
section 5.3 have been tested on a synthetic image, a greyscale image, and some color test
images in LAB color space, and their results are discussed. In Fig. 6.26- Fig. 6.28 it is
observed that under low noise condition the best clusters are formed for MAFCM
algorithms and NAFCM gives the best clusters under high noise condition. From the
images in Fig.6.26 - Fig.6.28, the percentage of misclassified pixels in each three clusters
present in the synthetic image is calculated.
In Fig. 6.29 (weld crack image) it is observed that the proposed method MSFCM
performs the best under low noise condition. The region growing based segmentation
method completely fails to recognise regions under noisy conditions. The split and merge
based segmentation too fails to identify the weld crack correctly.
The color images considered as test images are shown in Fig. 6.30- Fig.6.35. In Fig. 6.30
it is observed that the edges of the clustered output are better preserved in case of the
MSFCM algorithm as compared to the case when FCM, sFCM and NAFCM algorithms
have been applied for a noise of (-35,35). In Fig.6.31 it is observed that the clustering
result obtained by applying FCM gives the worst result as it is not able to reduce the
noise present in the image during clustering operation for a noise of (-35,35). In case of
Fig.6.31(d) we observe that the edges of inner circle and inner triangle of the road is
smoother as compared to Fig.6.31(b), Fig. 6.31(c) and Fig. 6.31(e) where FCM, sFCM
and NAFCM algorithms are applied. The test image in Fig.6.32 (a) is that of a human
hand with a huge green color plastic ring. The image is corrupted with a noise of (45,45). The green color plastic ring is our object of interest in this image. The MSFCM
algorithm is able to cluster the object of interest accurately and the edges are also
preserved well as compared to the other algorithms. Fig. 6.33 (a) is that of bacteria with a
noise of (-90,90). The bacteria is separated from its background using all the three
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methods. It is observed that the NAFCM algorithm is able to retain the boundary of
bacteria more effectively as compared to other methods.
Fig. 6.34(a) is image of a stork bird in a field with a noise of (-60,60).The image is first
enhanced using CLAHE algorithm as in Fig.6.25(b). The bird is separated from its
background (field) using all the four clustering methods. It is observed the edges are well
preserved using NAFCM algorithm.
Fig. 6.35(a) is that of a woman. The skin color is clustered using the four algorithms
under a random noise varying between (-90,90). The image is enhanced first using
CLAHE algorithm as in Fig.6.24(b) and then the four clustering algorithms are applied.
The NAFCM algorithm is seen to perform the best clustering to segment the skin of the
woman.
Fig. 6.36-Fig 6.39 shows an application of the NAFCM algorithm in detecting the tumor
growth by observing tumor images showing different symptoms as discussed in section
5.2.4. Fig. 6.36(b) shows an example of asymmetrical shape of the mole with a noise of (60,60) in which one half is different from the other may indicate melanoma. Here, the
left side of the mole is dark and a little raised, whereas the right side is lighter in color
and flat. Fig. 6.36(c)-(d) are the results of using FCM for clustering of the image. By
observing these images we cannot say anything about the irregularity of the growths
shape. But using the NAFCM algorithm we observe in Fig.6.36(g) and Fig. 6.36(h) that
the two halves of the growth are very different from each other hence it has chances of
developing into melanoma. Fig. 6.37(b) is an example of a growth with irregular border
having a noise of (-60,60). The irregular border can be very easily determined using
proposed method as shown in Fig. 6.37(h). Fig. 6.38(b) is an example of changes in
colour of a mole with a noise of (-90,90). The different colours present in the growth are
not easily observed using naked eyes or standard FCM method of clustering, whereas by
using the NAFCM method we observe more than two color or uneven distribution of
color present in the affected area. Fig.6.39(b) is a case where we take the diameter of the
mole into consideration to know whether it can develop into skin cancer. Here the image
has a noise of (-90,90). For measuring the diameter of the growth the border of the
growth has to be known accurately but because of noise it is impossible to know the
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borders clearly. NAFCM algorithm is able to find almost accurate border even under high
noise as shown in Fig. 6.39(h). Table 6.5 shows that NAFCM algorithm gives good
clustering results (high Vpc and low Vpe) for high noise condition in melanoma image
segmentation
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(a)
(b)
(c)
(d)
Figure 6.1 (a) Original infrared image of an aluminium metal casting with porosity
(b) Histogram of figure 2.1(a). (c) Seed points. (d) Result of region growing
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(b)
(a)
(c)
Figure 6.2 (a) Original scenery image (b) Array of seed points (c) Result of region growing
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(a)
(b)
Figure 6.3 (a) Image of crack in a weld (b) Result of region split and merge with a
standard deviation >10 and mean intensity >15.
(a)
(b)
Figure 6.4 (a) Image of planet Saturn with a small isolated white star on the bottom right
side. (b) Result of point detection
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(a)
(b)
(c)
Figure 6.5. (a) Image of pill set (b) Result of running a horizontal line detection mask through the image (c)
Result of thresholding fig. (b) with mean of maximum and minimum value of pixels
Figure 6.6
(a)
(b)
(d)
(e)
(c)
(f)
(a) Original lena image (b) Output of Roberts edge detector (c) Output of Prewitt edge detector
(d) Output of Sobel detector (e) Output of Log detector (f) Output of Canny edge detector
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(a)
(b)
(c)
(d)
Figure 6.7: (a) A wooden block’s image. (b) Edges detected by the Sobel operator.
(c) Edges detected by the Canny edge detector (d) Edges detected by the studied
FIS system.
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(a)
(b)
(c)
Figure 6.8: (a) A digital cameras calibration pattern’s
image. (b) Edges detected by the Sobel operator . (c)
Edges detected by Canny edge detector. (d) Edges
detected by the studied FIS system.
(e)
(a)
(b)
(c)
Figure 6.9 (a) A digital cameras calibration pattern’s
image. (b) Edges detected by the Sobel operator. (c)
Edges detected by the Laplacian of Gaussian
operator. (d) Edges detected by the studied FIS
(d)
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(a)
(b)
(c)
Figure 6.10. Bird image and result of three edge
detection algorithms. (a)Bird image. (b) Sobel operator.
(c) Canny operator. (d) FMFED algorithm.
(d)
(a)
(b)
(c)
Figure 6.11. Tire image and result of three edge
detection algorithms. (a) Tire image. (b) Sobel operator.
(c) Canny operator. (d) FMFED algorithm.
(d)
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a b
c d
Figure 6.12. MRI brain image and results of three edge detection algorithms. (a) MRI
brain image. (b) Sobel operator . (c) Canny operator. (d) Proposed algorithm
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a b
c d
Figure 6.13. X-ray image of brain and results of three edge
detection algorithms. (a) X-ray image of brain. (b) Sobel
operator. (c) Canny operator. (d) FMFED algorithm.
a b
b d
Figure 6.14. Dental X-ray image and results of three edge
detection algorithms. (a) Dental X-ray image with abscess.
(b) Sobel operator. (c) Canny operator. (d) FMFED
algorithm.
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(a)
(d)
(b)
(e)
(c)
(f)
Figure 6.15 (a)-(c) Edges detected by FMFED algorithm (d)-(f) result of
applying morphological operators for segmentation
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(a)
(b)
(c )
(d)
(e)
(f)
(g)
(h)
(i)
Figure 6.16 (a) Original image. (b)-(d) The three clusters for c=3 in case of RGB color space. (e)
Segmented image in RGB color space. (f)-(h) The three clusters for c=3 in case of L*a*b* color
space. (i) Segmented image in L*a*b* color space.
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
Figure 6.17 (a) Original image.
(b)-(e) The four clusters for c=4 in case of RGB color space. (f)
Segmented image in RGB color space. (g)-(j) The four clusters for c=4 in case of L*a*b* color space.
(k) Segmented image in L*a*b* color space.
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(a)
(b)
(c)
(d)
Figure 6.18 (a) Original image. (b)-(c) The two clusters for c=2 (h) Segmented
image
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(a)
(b)
(d)
(e)
(c )
Figure 6.19 (a) Original image. (b)-(d) The three clusters for c=3 (e) Segmented image
(a)
(b)
(c)
Figure 6.20 (a) Original image.
(b)-(c) The two clusters for
c=2 (e) Segmented image
(d)
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(a)
(b)
(c)
(d)
Figure 6.21 (a) Original image. (b)-(c) The two clusters for c=2 (d) Segmented image
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(a)
(b)
(c )
(d)
Figure 6.22. (a) Original image (b) Enhanced image (c) Segmented image without enhancement
(d) Segmented image after enhancement
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(a)
(b)
Figure 6.23. (a) Original image (b) Enhanced image (c) Segmented image
without enhancement (d) Segmented image after enhancement
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(a)
(b)
(c )
(d)
Figure 6.24. (a) Original image (b) Enhanced image (c) Segmented image
without enhancement (d) Segmented image after enhancement
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(a)
(b)
(c)
(d)
Figure 6.25. (a) Original image (b) Enhanced image (c) Segmented image without enhancement
(d) Segmented image after enhancement
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(a)
(e)
(i)
(b)
(f)
(j)
(c )
(d)
(g)
(h)
(k )
(l)
Figure 6.26 (a) Synthetic image with (-60,60) noise (b) – (d) First,
second and third cluster using FCM (e) – (g) First, second and third
cluster using sFCM (h) – (j) First, second and third cluster using
MSFCM (k) – (m) First, second and third cluster using NAFCM
(m)
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(a)
(b)
(e)
(f)
(i)
(c )
(g )
(j)
(k )
(d)
(h)
(l)
Figure 6.27 (a) Synthetic image with (-70,70) noise (b) – (d) First,
second and third cluster using FCM (e) – (g) First, second and third
cluster using sFCM (h) – (j) First, second and third cluster using
MSFCM (k) – (m) First, second and third cluster using NAFCM
(m)
103
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(d)
(e)
(f)
(g )
(h)
(i)
(j)
(k )
(l)
Figure 6.28 (a) Synthetic image with (-90,90) noise (b) – (d) First,
second and third cluster using FCM (e) – (g) First, second and third
cluster using sFCM (h) – (j) First, second and third cluster using
MSFCM (k) – (m) First, second and third cluster using NAFCM
(m)
104
Chapter 6
Simulation results and discussion
(a)
(e)
(i)
(b)
(c )
(f)
(g)
(j)
(d)
(h)
(k)
Figure 6.29 (a) Image of a weld crack with noise of (-35,35) (b) Result of LOG operator (c) Result of Canny
edge detector (d) Result of FIS (e) Result of FMFED (f) Result of FCM (g) Result of sFCM (h) Result of
MSFCM (i) Result of NAFCM (b) Result of region growing (c) Result of region split and merge
105
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(e)
(f )
(h)
(i)
(a)
(d)
(a)
(g)
(a)
Fig. 6.30. Comparison of segmentation results on a human image corrupted with a noise varying
between (-35,35). (a) Image with (-35,35) noise (b)-(d) Clustered image using FCM, sFCM and
MSFCM resp. (e)-(g) Segmented image using FCM, sFCM and MSFCM respectively.
106
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(d)
(e)
(f )
(a)
(a)
(g )
(h)
(i)
(a)
Fig.6.31. Comparison of segmentation results on a crossroad image corrupted with a noise
varing between (-35,35). (a) Image with (-35,35) noise (b)-(e) Clustered image using FCM,
sFCM , MSFCM and NAFCM resp. (f)-(i) Segmented image using FCM, sFCM, MSFCM and
NAFCM respectively.
107
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(d)
(e)
(f)
(a)
(a)
(g )
(h)
(i)
(a)
Fig.6.32. Comparison of segmentation results on a hand image corrupted with noise varying between (-45,
45). (a) Image with (-45,45) noise (b)-(e) Clustered image using FCM, sFCM, MSFCM and NAFCM
resp. (f)-(i) Segmented image using FCM, sFCM, MSFCM and NAFCM respectively.
108
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(d)
(e)
(f )
(h)
(i)
(a)
(g)
Fig.6.33. Comparison of segmentation results on a bacteria image
corrupted with uniform random noise varying between (-90,90) . (a)
Original bacteria image (b) Image with (-90,90) noise (c)-(f) Clustered
image using FCM, sFCM, MSFCM and NAFCM resp. (g)-(i)
Segmented image using FCM, sFCM, MSFCM and NAFCM
respectively.
(j)
109
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(d)
(e)
(f )
(g)
(h)
(i)
Fig.6.34. Comparison of segmentation results on a stork image corrupted
with uniform random noise varying between (-60,60) . (a) Original
bacteria image (b) Image with (-60,60) noise (c)-(f) Clustered image
using FCM, sFCM, MSFCM and NAFCM resp. (g)-(i) Segmented
(j)
image using FCM, sFCM, MSFCM and NAFCM respectively.
110
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(a)
(d)
(e)
(f )
(g)
(h)
(i)
(a)
Fig.6.35. Comparison of segmentation results on a human
image corrupted with uniform random noise varying
between (-90,90) . (a) Original bacteria image (b) Image
with (-90,90) noise (c)-(e) Clustered image using
FCM,sFCM,
MSFCM
and
NAFCM
resp.
(f)-(h)
Segmented image using FCM, sFCM, MSFCM and
(j)
NAFCM respectively.
111
Chapter 6
Table 6.1:
Simulation results and discussion
Comparision between various fcm based clustering methods with varying uniform
random noise in RGB color space for hand image.
Noise = (-35,35)
Noise= (-45,45)
Noise= (-60,60)
Noise = (-90,90)
Clustering methods
V pc
V pc
V pc
V pc
V pe
FCM
0.6190
0.6684
0.5732
0.7349
0.5253
0.4737
0.8898
sFCM
0.6203
0.6644
0.5632
0.7361
0.5246
0.8098
0.4761
0.8864
MSFCM
0.6206
0.6643
0.5644
0.7349
0.5266
0.8072
0.4768
0.8854
NAFCM
0.6294
0.6638
0.5790
0.7353
0.5249
0.8024
0.4783
0.8847
V pe
V pe
V pe
0.8090
Table 6.2: Comparision between various fcm based segmentation techniques with varying uniform
random noise in LAB color space for hand image
Noise = (-35,35)
Clustering
methods
V pc
V pe
Noise = (-45,45)
V pc
V pe
Noise = (-60,60)
V pc
V pe
Noise = (-90,90)
V pc
V pe
FCM
0.6256 0.6582
0.5444 0.7796
0.5561 0.7652
0.5372 0.7958
sFCM
0.8213 0.2644
0.8697 0.2876
0.7505 0.3361
0.7142 0.4906
MSFCM
0.8862 0.1682
0.8722 0.2682
0.7662 0.3282
0.7263 0.4782
NAFCM
0.8682 0.2543
0.8602 0.2704
0.7837 0.3107
0.7614 0.4122
112
Chapter 6
Simulation results and discussion
Table 6.3: Comparision between the fcm based segmentation techniques with varying uniform
random noise in LAB color space for various test images.
(35,-35)
Techniques
Hand
image
in figure
V pc
(45,-45)
V pe
V pc
( 60,-60)
V pe
V pc
(90,-90)
V pe
V pc
V pe
FCM
0.6256 0.6582
0.5914 0.7116
0.5561 0.7652
0.5372 0.7958
sFCM
0.8213 0.2644
0.8697 0.2876
0.7505 0.3361
0.7142 0.4906
MSFCM
0.8862 0.1682
0.8722 0.2682
0.7662 0.3282
0.7263 0.4782
NAFCM
0.8682 0.2543
0.8602 0.2704
0.7837 0.3107
0.7614 0.4122
FCM
0.5627 0.6508
0.5444 0.6796
0.5365 0.6922
0.5112 0.7836
sFCM
0.7807 0.2268
0.7727 0.2298
0.6711 0.4889
0.5256 0.5213
MSFCM
0.7931 0.2129
0.7784 0.2188
0.6720 0.4847
0.5388 0.5208
NAFCM
0.7623 0.3315
0.7332 0.3781
0.6965 0.4406
0.6918
FCM
0.8772 0.2258
0.8316 0.2919
0.7500 0.4018
0.7468 0.4069
sFCM
0.9870 0.0563
0.9754 0.1101
0.9012 0.1617
0.8016 0.3378
MSFCM
0.9896 0.0421
0.9782 0.1121
0.9041 0.1576
0.8123 0.3268
NAFCM
0.9621 0.1162
0.9299 0.1217
0.9139 0.3143
0.8721
0.2193
FCM
0.9186 0.1104
0.9273 0.1483
0.8872
0.2122
0.7274
0.4317
sFCM
0.9882 0.0129
0.9773 0.0364
0.9378
0.1542
0.8538
0.3413
MSFCM
0.9986 0.0131
0.9784 0.0482
0.9390 0.1531
0.8674 0.3265
NAFCM
0.9699 0.0528
0.9693 0.0538
0.9685 0.0856
0.9364 0.1201
FCM
0.7766 0.4236
0.7158 0.5159
0.6455 0.6173
0.6220 0.6635
sFCM
0.9846 0.0573
0.9011 0.1891
0.8618 0.2261
0.7981 0.4509
MSFCM
0.9924 0.0121
0.9268 0.1383
0.8735 0.2213
0.8184 0.3870
NAFCM
0.9778 0.0892
0.9149 0.1191
0.8868 0.1208
0.8691
6.31(a)
Crossroad
image
in figure
6.32(a)
Bacteria
image
in figure
0.4509
6.33(a)
Bird
image
in figure
6.34(a)
Woman
image
in
figure
6.35(a)
113
0.2498
Chapter 6
Simulation results and discussion
Table : 6.4 : Number of misclassified pixels with FCM,sFCM,MSFCM and NAFCM for synthetic
image shown in figure 6.2(a) with different noise values
Noise
C
L
A
S
S
Clustering methods
FCM
sFCM
MSFCM
NAFCM
Percentage of misclassified pixels in cluster 1, 2 and 3
1
0.1058
0
0
0.0677
2
0.0088
0
0
0.0147
3
0.0665
0.0055
0
0.0665
1
16.9915
0.0055
0.0021
0
3.7992
0.0021
0
0
0.7594
0.0055
0.0055
0.0055
1
58.8833
32.5532
29.769
0.0973
2
30.8202
13.0897
11.9596
0.2619
3
17.8271
0.6763
0.5876
1.2417
1
67.339
65.7837
63.2854
2.7843
2
37.2591
27.0710
25.8174
1.2007
3
21.4911
2.4224
2.0067
1.5854
1
712.7775
76.7477
77.1239
5.0418
2
99.9117
33.4922
32.0679
1.2919
3
23.2761
6.5466
3.5477
1.5355
(-40,40)
(-60,60)
2
3
(-70,70)
(-80,80)
(-90,90)
114
Chapter 6
Simulation results and discussion
(a)
(b)
(c )
(d)
(e)
(f )
(g)
(h)
(i )
Figure 6.36. (a) Original image (b) Image with (-60,60) noise (c)-(e)
Object in 1st , 2nd
& 3rd cluster
respectively using FCM
st
rd
(f)
Segmented image using FCM (g)-(i) Object in 1 ,2nd & 3 cluster
using proposed NAFCM (j) Segmented image using NAFCM.
(j)
115
Chapter 6
Simulation results and discussion
(a)
(b)
(d)
(e)
(g)
(h)
(c )
(f )
Figure 6.37. (a) Original image (b) Image with (-60,60) noise (b)-(c) Object in 1st , 2nd & 3rd cluster
respectively using FCM (d) Segmented image using FCM (e)-(f) Object in 1st & 3rd cluster using
NAFCM (f) Segmented image using NAFCM.
116
Chapter 6
Simulation results and discussion
(a)
(d)
(b)
(c )
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
Figure 6.38. (a)Original image (b) Image with (-90,90) noise (c)-(f) Object in 1st , 2nd , 3rd & 4th cluster
respectively using FCM (g) Segmented image using FCM (h)-(k) Object in 1st ,2nd , 3rd & 4th cluster using
NAFCM (l) Segmented image using NAFCM.
117
Chapter 6
Simulation results and discussion
(a)
(b)
(d)
(e)
(g)
(c )
(f )
(h)
Figure 6.39. (a)Original image (b) Image with (-90,90) noise (c)-(d) Object in 1st & 2nd cluster
respectively using FCM (e) Segmented image using FCM (f)-(g) Object in 1st & 2nd cluster
using NAFCM (h) Segmented image using NAFCM.
118
Chapter 6
Simulation results and discussion
(a )
(b)
(c)
(d)
Figure 6.40. (a) Original image (b) Image with (-60,60) noise (c) Skin lesion segmented with FCM
technique after addition of noise (d) Skin lesion segmented using NAFCM after addition of noise.
(a)
(b)
(c)
(d)
Figure 6.41. (a) Original image (b) Image with (-60,60) noise (c) Skin lesion segmented
with FCM technique after addition of noise (d) Skin lesion segmented using NAFCM
after addition of noise.
119
Chapter 6
Simulation results and discussion
Table 6.5 Effect of increasing noise on the various tumor test images
(35,-35)
Tumor
image
in
figure
6.36(a)
figure
6.37(a)
figure
6.38(a)
figure
6.39(a)
(45,-45)
( 60,-60)
(90,-90)
Techniques
V pc
FCM
0.6520 0.6089
0.6056 0.6783
0.5599 0.7487
0.4963 0.8515
NAFCM
0.8424 0.2067
0.8206 0.2403
0.8162 0.2448
0.8081 0.3204
FCM
0.6237 0.6450
0.5847 0.7073
0.5384 0.7818
0.4816 0.8752
NAFCM
0.8171 0.3407
0.8028 0.3605
0.7932 0.3725
0.7623 0.4255
FCM
0.7729 0.4203
0.7397 0.4779
0.6838 0.5682
0.5844 0.7159
NAFCM
0.8907 0.2126
0.8858 02216
0.8745 0.2329
0.8568 0 .2399
FCM
0.6880 0.5557
0.6496 0.6155
0.5992 0.6927
0.5296 0.7998
NAFCM
0.8541 0.2858
0.8389 0.3109
0.8202 0.3416
0.7831 0.3967
V pe
V pc
120
V pe
V pc
V pe
V pc
V pe
Chapter 6
Simulation results and discussion
6.3 Conclusion
In chapter 2, various basic methods of image segmentation have been studied. It is
observed from Fig. 6.1- Fig 6.6 that edge detectors are quite simple to execute and they
are able to find the edges of objects present in all kind of images. Whereas, the region
based methods are application dependent and the condition for region growing or region
splitting and merging may change from one image to another. Hence the fuzzy edge
detection based segmentation algorithms are explored in the next chapter.
In chapter 3 two fuzzy methods for edge detection based segmentation are studied, the
conclusion regarding the two methods is as follows:
FIS for edge detection based segmentation:
From the simulation results in Fig. 6.7-Fig 6.9 it can be very easily concluded that the
FIS system developed better than the popular Sobel but its results are not as good as
Canny operator. But one of the main problems with implementing such a FIS system is
the amount of time required during processing. One of the main problems in
implementing a FIS system is the amount of time required during processing. In addition
to that, despite being used in a wide range of applications, both the structure of
membership functions and derivation of their relevant parameters were still very much
application domain and image dependent.
Multilevel fuzzy edge detector for segmentation:
This method has clear advantage over the rule based method as it does not involve
changing the structure of membership function according to a particular application. This
method gives better edges as compared to Sobel and Canny edge detector as seen in
Fig.6.10- Fig.6.14 and it is also much faster as compared to the FIS algorithm for edge
detection.
The edge detection algorithms are normally followed by edge linking procedures to
bridge gaps in region boundary. We apply simple morphological tools for the edge
linking problem. The results of applying edge linking by morphological operators on the
edge detected image, is shown in Fig 6.15. The edge detection method considered for all
these images is FMFED algorithm. The reason for not applying FIS based edge detector
is its poor quality of edge detection compared to some older techniques like canny edge
121
Chapter 6
Simulation results and discussion
detector. The algorithm is also much faster as compared to the FIS algorithm for edge
detection
In chapter 4, algorithms for segmentation of color images using fuzzy clustering have
been developed
The segmentation method described in section 4.4 uses Fuzzy c-means as a tool for
segmentation. The simulation results in Fig. 6.16-Fig. 6.21, show how the FCM is
applied for segmentation. By observing the results it can be said that FCM can be
successfully applied for clustering based segmentation of different types of images.
The algorithm described in section 4.5 applies, enhancement algorithm (CLAHE) to
FCM. The enhancement is applied only to the Luminosity layer (L) as it is the layer
containing information about brightness of the image. By first enhancing the image and
then performing clustering we are able to extract quite good segmentation results. The
CLAHE algorithm spreads the brightness uniformly among all the pixels hence too bright
pixels does not remain too bright and pixels having low brightness value are made to
have more high brightness information.
From the simulation results in chapter 6 (Fig. 6.22-Fig 6.25) it can be said that:
CLAHEFCM improves the clustering and hence segmentation results of images which
are not evenly illuminated.
In chapter 5, algorithms for segmentation by incorporating spatial property of pixels in
fuzzy clustering have been developed. The algorithm described in section 5.2 presents a
modified spatial FCM algorithm (MSFCM) and observes its effect on color images
degraded by random noise. The algorithm was realized by modifying the spatial function
as described above. Qualitative (Fig.6.26-Fig. 6.35 ) and quantitative experimental results
(Table 6.3) show that the proposed MSFCM (highest Vpc and lowest Vpe) algorithm is
superior to standard FCM, sFCM and NAFCM when the clustering is done under low
noise condition.
The proposed method (NAFCM) is an extension of FCM algorithm which takes into
account the neighbourhood attraction of the pixels and observes its effect on
segmentation of color images degraded by random noise. The algorithm is tested on a
122
Chapter 6
Simulation results and discussion
synthetic image ( Fig. 6.26- Fig. 6.28), greyscale image (Fig. 6.29) and various other
images (Fig. 6.30-Fig 6.35), having a noise of (-60,60) and higher . The results obtained
by using proposed method have been compared with the results of other FCM based
segmentation techniques. By observing the results (Fig. 2.26-Fig.6.35 and Table 6.3) it
can be said that NAFCM (highest Vpc and lowest Vpe) gives the best clustering and hence
segmentation result under high noise condition.
Since the objective function of standard FCM was not modified in both the proposed
methods, as in case of most techniques applying FCM for segmentation, the inbuilt FCM
function present in recent MATLAB versions can be very easily applied for problem
related to clustering and segmentation while applying these two algorithms.
By observing Table 6.1 and Table 6.2 it can be said that clustering based segmentation
performed in LAB color space gives higher values of V pc and lower values for V pe
(condition for good clustering and segmentation) under increasing noise increasing from
(-35,35) to (-90,90), as compared to clustering based segmentation in RGB color space.
From Table 6.4 it is observed that as noise increases the percentage of misclassified
pixels for every class also increases. MSFCM based segmentation gives the least
percentage of misclassified pixels under low noise condition. NAFCM based
segmentation gives the least percentage of misclassified pixels for every class under high
noise condition.
From Table 6.5 it can be concluded that NAFCM can be used for segmentation of
melanoma images.
123
CHAPTER 7
Conclusion
124
Chapter 7
Conclusion
7
Preview
In this research work various popular fuzzy techniques used for image segmentation
available in the literature are studied. These fuzzy techniques can be combined with any
other method to enhance the ability of the algorithm in good segmentation. However, due
to the limitation of other fuzzy techniques, fuzzy clustering based segmentation has been
considered in this thesis. One major limitation with FCM based segmentation is that it
does not take into consideration the spatial context of the image pixels, due to this FCM
clustering based segmentation is sensitive to noise and imaging artefacts.
Hence to compensate for this drawback of FCM clustering based segmentation, efforts
have been made to develop algorithms, which are an extension to the standard FCM and
take into account the spatial context of pixels. These algorithms are observed to perform
well on noisy images. An FCM clustering algorithm for segmentation of images under
uneven illumination has also been developed.
The performance of the proposed algorithms for segmentation has been compared with
existing algorithms. The objective evaluation metric used for clustering based
125
Chapter 7
Conclusion
segmentation are partition coefficient and partition entropy. All algorithms have been
compared with respect to their execution time.
7.1 Comparative Analysis
The execution time of various segmentation methods such as region based segmentation
method, edge detection based segmentation method and clustering based segmentation
method is compared in Table 7.1. The hardware platform used is a Pentium IV core 2 duo
processor, 2.4GHz (clock), 2GB (RAM) with windows vista 64 bit operating system.
A qualitative comparison between various existing algorithms and FCM is done on a
weld crack image. The results are shown in Fig. 7.1.
The existing and the proposed segmentation algorithms are simulated on a different color
test image. The test image is corrupted with a noise varying between (-35, 35), (-45, 45),
(-60, 60) and (-90, 90). The performance of various clustering methods is compared in
terms of V pc and V pe in LAB color space (used in our algorithm) is shown in Table 7.2.
126
Chapter 7
Conclusion
Table 7.1: Segmentation performance of various segmentation methods in terms of Execution time
Region based segmentation
method
Edge
detection
segmentation method
Clustering
segmentation method
based
based
Segmentation methods
Execution time (sec)
Region growing
5.78
Region split and merge
5.906
LOG
0.985
Canny
1.781
FIS
13.328
Multi-level fuzzy edge detector
1.593
FCM
1.469
CLAHEFCM
1.625
sFCM
2.141
MSFCM
2.266
NAFCM
2.922
127
Chapter 7
Conclusion
(a)
(e)
(b)
(f)
(c )
(d)
(g )
(h)
Figure. 7.1 (a) Image of a weld crack (b) result of region growing (c) Result of region split and
merge (d) Result of LOG operator (e) Result of Canny edge detector (f) Result of FIS (g) Result of
FMFED (h) result of FCM
128
Chapter 7
Conclusion
Table 7.2: Comparision between the fcm based segmentation techniques with varying uniform
random noise in LAB color space for various test images.
(35,-35)
Techniques
Hand
image
in figure
V pc
(45,-45)
V pe
V pc
( 60,-60)
V pe
V pc
(90,-90)
V pe
V pc
V pe
FCM
0.6256 0.6582
0.5914 0.7116
0.5561 0.7652
0.5372 0.7958
sFCM
0.8213 0.2644
0.8697 0.2876
0.7505 0.3361
0.7142 0.4906
MSFCM
0.8862 0.1682
0.8722 0.2682
0.7662 0.3282
0.7263 0.4782
NAFCM
0.8682 0.2543
0.8602 0.2704
0.7837 0.3107
0.7614 0.4122
FCM
0.5627 0.6508
0.5444 0.6796
0.5365 0.6922
0.5112 0.7836
sFCM
0.7807 0.2268
0.7727 0.2298
0.6711 0.4889
0.5256 0.5213
MSFCM
0.7931 0.2129
0.7784 0.2188
0.6720 0.4847
0.5388 0.5208
NAFCM
0.7623 0.3315
0.7332 0.3781
0.6965 0.4406
0.6919
FCM
0.8772 0.2258
0.8316 0.2919
0.7500 0.4018
0.7468 0.4069
sFCM
0.9870 0.0563
0.9754 0.1101
0.9012 0.1617
0.8016 0.3378
MSFCM
0.9896 0.0421
0.9782 0.1121
0.9041 0.1576
0.8123 0.3268
NAFCM
0.9621 0.1162
0.9299 0.1217
0.9139 0.3143
0.8722
0.2193
FCM
0.9186 0.1104
0.9273 0.1483
0.8872
0.2122
0.7274
0.4317
sFCM
0.9882 0.0129
0.9773 0.0364
0.9378
0.1542
0.8538
0.3413
MSFCM
0.9986 0.0131
0.9784 0.0482
0.9390 0.1531
0.8674 0.3265
NAFCM
0.9699 0.0528
0.9693 0.0538
0.9685 0.0856
0.9364 0.1201
FCM
0.7766 0.4236
0.7158 0.5159
0.6455 0.6173
0.6220 0.6635
sFCM
0.9846 0.0573
0.9011 0.1891
0.8618 0.2261
0.7981 0.4509
MSFCM
0.9924 0.0121
0.9268 0.1383
0.8735 0.2213
0.8184 0.3870
NAFCM
0.9778 0.0892
0.9149 0.1191
0.8868 0.1208
0.8692
6.31(a)
Crossroad
image
in figure
6.32(a)
Bacteria
image
in figure
0.4509
6.33(a)
Bird
image
in figure
6.34(a)
Woman
image
in
figure
6.35(a)
129
0.2498
Chapter 7
Conclusion
7.2 Conclusion
In Table 7.1 it is observed that LoG has the least execution time among all segmentation
methods considered as it is the simplest method. Among the clustering based
segmentation method, the standard FCM based segmentation takes the least execution
time.
It is observed from Fig. 7.1 that FCM based segmentation gives the best segmentation
result without noise. The segmentation by FCM clustering gives a smooth contour of the
weld crack as compared to other methods.
By observing Table 6.1 and Table 6.2 it can be said that clustering based segmentation
performed in LAB color space gives higher values of V pc and lower values for V pe
(condition for good clustering and segmentation) under increasing noise increasing from
(-35,35) to (-90,90), as compared to clustering based segmentation in RGB color space.
Hence it can be concluded that for real life images, FCM based segmentation in
LAB color space gives better results as compared to RGB color space.
By observing Fig. 6.26 - Fig 6.35 and Table 7.2, it can be said that the proposed
MSFCM gives the best clustering(highest Vpc and lowest Vpe) result under low noise
condition as compared to FCM, sFCM or NAFCM. It is also observed that NAFCM gives
the best clustering (highest Vpc and lowest Vpe) and hence segmentation result under high
noise condition.
Hence it is concluded that MSFCM gives the best clustering and hence segmentation
result under low noise condition and NAFCM gives the best clustering and
segmentation result under high noise condition.
From Table 6.4 it is observed that as noise increases the percentage of misclassified
pixels for every class also increases. MSFCM based segmentation gives the least
percentage of misclassified pixels under low noise condition. NAFCM based
segmentation gives the least percentage of misclassified pixels for every class under
high noise condition.
130
Chapter 7
Conclusion
7.3 Scope of Future work
1.
The execution time of the proposed method is an area of concern. Hence clustering
methods which are less time consuming can be developed for segmentation.
2.
The fuzzy clustering based method can be combined with other methods like
Genetic algorithm and Level set methods to give better segmentation results.
3.
The number of cluster has to be fixed initially in FCM based segmentation methods.
Some method which doesn’t require fixing of number of clusters before clustering can
also be used for segmentation.
131
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Contributions by Candidate
1. K. Nirulata, S.Meher, “An Efficient Edge Detector for Digital Images”,
Proceedings of national conference on devices, intelligent systems and
communications, MITDISC-2007,MIT-Manipal,7th-8th dec-2007.
2. K. Nirulata, S.Meher, “Color Image segmentation using Fuzzy Clustering”,
Proceedings of International Conference on Emerging Technologies and
Applications in Engg., Tech. and Sciences ,ICETAETS-2008,Saurastra
University,Rajkot,13th-14th Jan-2008.pg.no.-1105-1109.
3. K. Nirulata, S.Meher, “Segmentation Of Unevenly Illuminated Color Images”,
Proceedings of IEEE sponsored conference on Computational Intelligence,
Control and Computer vision in Robotics and Automation, CICCRA-2008,NITRourkela,pg.no.23-27.
4. K. Nirulata, S.Meher, “Segmentation of Noisy Color Images”, Accepted for
publication in International Journal of Applied Artificial Intelligence in
Engineering System.
5. K. Nirulata, S.Meher, “Segmentation of Noisy Color Images using
Neighborhood property of Digital Image”, Accepted for publication in
International Journal of Computer Science and Management System.
6. K. Nirulata, S.Meher, “Skin Tumor Segmentation using Fuzzy c-means
Clustering with Neighbourhood Attraction”, Communicated to International
Journal of Computers and Electrical Engineering.
139
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