CHAPTER-3 IMAGE SEGMENTATION...

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CHAPTER-3

IMAGE SEGMENTATION TECHNIQUES

3.1 Introduction to Digital Image Processing

Digital image processing involves processing and manipulation of image

for better understanding and enhanced visual perception. There are two primary

motivations behind the emergence of image processing: enhancement of pictorial

information for better human interpretation and processing of scene data for

autonomous machine perception. The term “digital image processing” refers to

processing of digital images by means of digital computers [36]. The term ‘digital

computers’ in this definition not only denotes general purpose digital computers

such as a desktop Personal Computer(PC) or a workstation but also systems that

ranges from simple digital circuits to advanced parallel computers.

The history of image processing dates back to 1920 when Harry G.

Bartholomew and Maynard D. McFarlane invented the Bartlane Cable Picture

Transmission system which transmits images over cable lines across the Atlantic.

Initially only 5 gray levels were used to code the images which increased to 15 in

1929. The Bartlane Cable system cannot be considered as a pure digital image

processing system because analog instruments were used and absence of the

primary concepts used in digital computers. The digital computers began its

journey in the 1940s when John von Neumann put forward the principal concepts

of digital computers. A series of activities mostly comprising of development of

high-level language and invention of integrated circuits(IC) led to the formation of

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true digital computers. It was only in the early 1960s that the digital computers

became powerful enough to handle the

example of digital image processing is the processing of pictures of the moon

transmitted by the Ranger 7 s

place in the field of medical science, remote sen

physical sciences, archeology, military defen

The first step in digital image processing system is to acquire the images

and store them in storage device. The acquisition of image is done

various types of light sensors.

Metal Oxide Semiconductor

acquisition. Now a day, very high resolution cameras are available. The images

created are the result of illumination and reflection

function of light can be presented by a continuous

two-dimensional light intensity function

coordinates and the value of

the gray level of the image at that point. The function

approximated by equally spaced samples arranged in the form of an

as shown below [36]

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became powerful enough to handle the intricacies of digital image. The earliest


transmitted by the Ranger 7 spacecraft. Gradually digital image processing finds its

place in the field of medical science, remote sensing, biological application,

physical sciences, archeology, military defense and numerous other fields.

first step in digital image processing system is to acquire the images

and store them in storage device. The acquisition of image is done with the help of

various types of light sensors. Charged-coupled device (CCD) and Complementary

Metal Oxide Semiconductor (CMOS) sensor devices are mostly used in image


of illumination and reflection of the source light. The

function of light can be presented by a continuous function�� . An image is a

dimensional light intensity function �� where x and y are spatial

coordinates and the value of f at any point (x, y) is proportional to the brightness or

the gray level of the image at that point. The function �� approximated by equally spaced samples arranged in the form of an �

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The earliest


pacecraft. Gradually digital image processing finds its

sing, biological application,

se and numerous other fields.

first step in digital image processing system is to acquire the images

with the help of

and Complementary

sensor devices are mostly used in image


of the source light. The

An image is a

where x and y are spatial

at any point (x, y) is proportional to the brightness or

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The right side of the above equation is by definition a digital image [36].

The transformation of the continuous analog light function into the discrete matrix

representation is called sampling or quantization.

Figure 3.1: Digitization of continuous image.

The size of an image in computer memory is given by the function

� ��where N and M are the row and column and L is discrete gray levels

allowed for each pixel. L is typically an integer power of 2. The images are store in

computer in different formats each having some distinct characteristics. Some of

the popular and most commonly used formats are TIFF, JPEG, BMP, GIF, PNG

etc. Other image file formats are used to a lesser extent; these formats are often

proprietary, such as Adobe Photoshop .psd files. It is also helpful to understand the

common image file formats of digital images, how these file formats differ, and

what their recommended use is [37].

3.2 Components of Digital image processing systems

A digital image processing system consists of several components, both

hardware and software. A simple personal computer can be used to carry out the

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image processing operations, though there are dedicated systems for image

processing. The dedicated systems are mostly related to specific applications and

industrial process such as microscopic image analysis system or printed circuit

board (PCB) testing system. Although large-scale image processing systems are

still being sold for massive imaging applications, such as processing of satellite

images, the trend continues toward miniaturizing and blending of general-purpose

small computers with specialized image processing hardware. Figure 3.2 depicts

the principal components of a typical digital image processing system. Each of the

components is discussed below:

Light sensors: It is a physical device which is sensitive to the energy

radiated by the object, whose image we want to capture. The second, called a

digitizer, is a device for converting the output of the physical sensing device into

digital form.

Image processing hardware: It usually consists of the digitizer just

mentioned and hardware that performs other primitive operations, such as an

arithmetic logic unit (ALU), which performs arithmetic and logical operations in

parallel on entire images. An example of how an ALU is used is in averaging

images as quickly as they are digitized, is the noise reduction process.

The computer: The computer used in an image processing system ranges

from a PC to a supercomputer. In dedicated applications, sometimes specially

designed computers are used to achieve a required level of performance. For a

general-purpose image processing systems almost any well-equipped PC-type

machine is suitable for offline image processing tasks.

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Software: Software for image processing consists of specialized modules

that perform specific tasks. A well-designed package also includes the capability

for the user to write code that, as a minimum, utilizes the specialized modules.

More sophisticated software packages allow the integration of those modules and

general-purpose software commands from at least one computer language. e.g.

Champ Software, MATLAB Image Processing Tool etc.

Mass storage: Storage capability is a must in any image processing

applications. An image of size 1024*1024 pixels, in which the intensity of each

pixel is an 8-bit quantity, requires one megabyte of storage space if the image is

not compressed. Thus dealing with thousands, or even millions of images,

providing adequate storage in an image processing system can be a challenging in

real time operation.

Image displays: The image displays in use today are mainly colour

monitors. Monitors are driven by the outputs of image and graphics display cards

that are an integral part of the computer system. Seldom are there requirements for

image display applications that cannot be met by display cards available

commercially as part of the computer system

Hardcopy devices: They include laser printers, film cameras, heat-

sensitive devices, inkjet units, and digital units, such as optical and CD-ROM

disks. Film provides the highest possible resolution, but paper is the obvious

medium of choice for written material. For presentations, images are displayed on

film transparencies or in a digital medium if image projection equipment is used.

The latter approach is gaining acceptance as the standard for image presentations.

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Networking: It is almost a default function in any computer system in use

today. Because of the large amount of data inherent in image processing

applications, the key consideration in image transmission is the required

bandwidth. In dedicated networks, this is not a problem, but communications with

remote sites via the Internet are of much concern. Fortunately, this situation is

improving quickly as a result of optical fiber and other broadband technologies 3G

network.

Figure 3.2: Components of Digital image processing system

3.3 Basic Steps in Digital Image Processing

An image processing system processes the image through several stages to

achieve the appropriate output. The efficiency of the result depends on every stage

of processing. The basic steps in digital image processing are described below.

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Image acquisition: Image acquisition is the first step of digital image

processing. It is the process of capturing the images of some objects and

transforming them into suitable digital formats for storing in the computer. Light

sensors are used to capture the image. Typically charged coupled device (CCD)

and complementary metal oxide semiconductor devices (CMOS) are used as light

sensors. The CCD or CMOS sensors captures analog signal of lights which are not

appropriate for computer processing. Another device, called Digitizer, transforms

the analog signal to digital form. The transformation process is called sampling and

quantization [38] [39].

Enhancement and Restoration: Various factors such as visibility,

brightness and contrast of grey level of pixels, amount of noise present are

responsible for the quality of an image. Before any actual processing, images need

to be in a state which is favourable for processing. There are two tasks:

enhancement and restoration. The idea behind enhancement techniques is to bring

out detail that is obscured, or simply to highlight certain features of interest in an

image. A familiar example of enhancement is when we increase the contrast of an

image because it looks better. Enhancement is a very subjective area of image

processing. Image restoration is an area that deals with improving the appearance

of an image. However, unlike enhancement, which is subjective, image restoration

is objective. The restoration techniques used must be based on mathematical or

probabilistic models of image degradation [40].

Morphological Processing: Morphological processing deals with tools for

extracting image components that are useful in the representation and description

of shape. At first, morphological operations were defined for only binary image

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that is an image pixel value either 0 or 1. Later, several morphological techniques

have evolved which can handle gray level image also [40]. Morphological

operations apply a structuring element to an input image, creating an output image

of the same size. In a morphological operation, the value of each pixel in the output

image is based on a comparison of the corresponding pixel in the input image with

its neighbors [41]. By choosing the size and shape of the neighborhood, one can

construct a morphological operation that is sensitive to any specific shapes in the

input image.

Segmentation: It is the process of dividing an image into its constituent

parts. The goal of segmentation is to partition the object of interest according to the

requirement of specific application. Image segmentation is discussed in details in

Section 3.4.

Representation and Description: Representation and description always

follow segmentation, which is usually raw pixel data [36]. There are mainly two

ways of representation: boundary representation, which is appropriate when the

focus is on external shape characteristics, such as corners and inflections, and

regional representation is appropriate when the focus is on internal properties, such

as texture or skeletal shape. Description, also called feature selection, deals with

extracting attributes that result in some quantitative information of interest. They

are basic for differentiating one class of objects from another.

Object Recognition: It is the process that assigns a label to an object based

on its descriptors. For any object in an image, there are many 'features' which are

interesting points on the object that can be extracted to provide a "feature"

description of the object. This description extracted from a training image can then

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be used to identify the object when attempting to locate the object in a test image

containing many other objects as well [42] [43].

Figure 3.3depicts the flow of these basic steps in digital image processing.

Figure 3.3: Steps in Digital Image Processing

3.4 Image Segmentation

Image segmentation is the most basic and important part of image

processing which segments an image into meaningful areas according to some

characteristics such as gray level, spectrum, texture, colour, and so on. The goal of

image segmentation is to partition an image into a set of disjoint regions with

uniform and homogeneous attributes such as intensity, color, tone or texture etc

[44]. More precisely, image segmentation is the process of assigning a label to

every pixel in an image such that pixels with the same label share certain visual

characteristics.

Segmentation of nontrivial images is one of the most difficult tasks in

image processing [36]. The success of the subsequent image processing tasks

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depends on the robustness of the segmentation process. So a considerable amount

of care should be taken to improve the probability of the rugged segmentation.

There is no generalized 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 have received some degree of popularity. Most of the image

segmentation algorithms are based on two basic properties of intensity values:

discontinuity and similarity. The ‘discontinuity’ approach is to segment the image

based on abrupt change in intensity, such as edged in the images. The second

approach is based on some pre defined criteria upon which images are partitioned.

Thresholding, Region growing are some methods which fall into this category.

When designing the segmentation algorithm, most of the image processing

designer follows some paradigms such as [36]:

i. Regions of the image segmentation should be uniform and homogeneous

with respect to some characteristic such as gray tone or texture.

ii. Region interiors should be simple and without many small holes.

iii. Adjacent regions of segmentation should have significantly different

values with respect to the characteristic on which they are uniform.

iv. Boundaries of each segment should be simple, not ragged, and must be

spatially accurate.

Mathematically, image segmentation can be defined as a spatial region R

divided into n subregions, R1, R2,….Rn such that

(a) � � � ��

(b) ��is a connected set, � � ��

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(c) � � �� for all i and j, � � � (d) �� !��"#��

(e) �� $ �)=%&�'!��"#�(��()�(*+�,�#+-�"�.� � and �

Here, �� is a logical predicate defined over the points in set � and � is

a null set. From the above equations, we can say that the segmentation is complete

and every pixel in a region is connected in some way. Also, they indicate that the

regions must be disjoint and satisfy some properties of the pixels. There are several

methods of image segmentation [36] some which are discussed in the next section.

3.4.1 Thresholding

The simplest method of image segmentation is called the thresholding

method. This method is based on a clip-level (or a threshold value) to turn a gray-

scale image into a binary image. The key of this method is to select the threshold

value (or values when multiple-levels are selected). Several popular methods used

in industry are: the maximum entropy method, [36] Otsu's method (maximum

variance) [44]. k-means clustering [44] can also be used in this regard.

Thresholding is based on the fact that different objects in an image have different

level of luminance or colour value. Luminance thresholding is of two types: bilevel

luminance thresholding, that is, images having only luminance level such as a

printed page having black letters on white background; and multilevel luminance

thresholding that is an image with multiple value of luminance [45]. Colour

thresholding is based on a nonstandard colour component, loosely called intensity.

The basic principle of thresholding is to set a luminance or colour intensity

threshold, T and comparing each pixel (x, y) of an image f(x,y) with T. If at the

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point (x,y), f(x,y)>T, then the point is called an object point; otherwise called a

background point. The segmented image g(x,y) is defined as [36]

-�� /�� 0 �1�� 2 � 3

When T is constant over the entire image, the process is called global

thresholding. When T changes over an image it is called variable thresholding.

There is also a third kind called local or regional thresholding where the value of

T at any point (x,y) depends on the properties of its neighbourhood. If T depends on

spatial coordinates (x,y) themselves, then variable thresholding is called adaptive

thresholding.

The presence of noise effects the outcome thresholding segmentation.

Image smoothing and thresholding with edge detection are two common methods

to nullify the effect of noise on thresholding. In statistics and image processing, to

smooth a data set is to create an approximating function that attempts to capture

important patterns in the data, while leaving out noise or other fine-scale

structures/rapid phenomena. In smoothing, the data points of a signal are modified

so that number of individual points (presumably because of noise) is reduced, and

points that are lower than the adjacent points are increased leading to a smoother

signal [46]. Edge detection is a fundamental tool in image processing, machine

vision and computer vision, particularly in the areas of feature detection and

feature extraction [39].

N. Otsu [47] proposed a global thresholding method where the weighted

sum of within-class variances of the foreground and background pixels is

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minimized to establish an optimum threshold. A 2D gray-level intensity function

f(x, y) whose value is the gray-level can generally show the characteristics of an

image. If it ranges from 0 to L-1, where L is the number of distinct gray-levels, and

the number of pixels with gray-level � in �� be the total number of pixels in a given

image, the probability of occurrence of gray-level ��is defined as [47]

nnp ii /=

The average gray-level of the entire image is computed as [47]

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==

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L

iiT ipµ

For single thresholding, the pixels of an image will be divided into two

classes, C1= {0, 1,…, t} and C2 = {t+1, t+2,…, L-1}, where t is the threshold value.

C1 and C2 correspond to the objects of interest and the background. The

probabilities of the two classes are obtained as [47]

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==1

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tii

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ii ptpt ωω

The means of the two classes can be computed as [47]

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ii tipttipt ωµωµ

Using discriminant analysis, Otsu [47] showed that the optimal threshold t*

can be determined by maximizing the between-class variance; defined as [47]

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)}({ 2

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* tMaxArgt BLt

σ<≤

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Where the between-class variance, 45��6 �,��is defined as [47]

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2 ))()(())()(()( TTB ttttt µµωµµωσ −+−=

3.4.2 Region based methods

There are three primary methods for region based segmentation of image.

Out of these, region growing is the simplest one. Region growing methods involve

grouping of neighboring pixels of similar amplitude together to form a segmented

region. However, some constraints must be placed on the growth pattern to achieve

acceptable results [39]. Brice et al. [48] proposed a region-growing method based

on a set of simple growth rules. In the first stage of the process, pairs of quantized

pixels are combined together in groups called atomic regions if they are of the

same amplitude. Two heuristic rules are invoked to dissolve weak boundaries

between atomic boundaries. Referring to Figure 3.4, let R1 and R2 be two adjacent

regions with perimeters P1 and P2, respectively, which have previously been

merged. After the initial stages of region growing, a region may contain previously

merged subregions of different amplitude values. Also, let C denote the length of

the common boundary and let D represent the length of that portion of C for which

the amplitude difference Y across the boundary is smaller than a significance

factor. The regions R1 and R2 are then merged if

7��89�� 9�: 0 ;6

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Figure 3

;6 is a constant typically set to

method provides reasonably accurate segmentation of simple scenes with few

objects and little texture

Yakimovsky [49] has attempted to improve the region

establishing merging constraints based on estimated Bayesian probability densities

of feature measurements of each region.

The second method based on region is

merge image segmentation techniques are based on a quad tree data representation

whereby a square image segment is broken (split) into four quadrants if the original

image segment is non-uniform 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 [50]. Splitting and merging attempts to divide an image into

uniform regions. The basic representational structure is pyramidal, i.e. a square

region of size < =< at one le

below it. Usually the algorithm starts from the initial assumption that the entire

image is a single region, and then computes the homogeneity criterion to see if it is

TRUE. If FALSE, then the square regi

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Figure 3.4: Region growing geometry

is a constant typically set to � �> . The Brice et al. [48] region growing


objects and little texture. But it did not perform well on more complex scenes.

Yakimovsky [49] has attempted to improve the region-growing concept by

erging constraints based on estimated Bayesian probability densities

of feature measurements of each region.

The second method based on region is split and merge method

image segmentation techniques are based on a quad tree data representation


uniform in attribute. If four neighboring squares are found to

they are replaced (merge) by a single square composed of the four

Splitting and merging attempts to divide an image into


at one level of a pyramid having 4 sub-regions of



TRUE. If FALSE, then the square region is split into the four smaller regions. This

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region growing


perform well on more complex scenes.

growing concept by

erging constraints based on estimated Bayesian probability densities

split and merge method. Split and

image segmentation techniques are based on a quad tree data representation


uniform in attribute. If four neighboring squares are found to

they are replaced (merge) by a single square composed of the four

Splitting and merging attempts to divide an image into


regions of same size



into the four smaller regions. This

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process is then repeated on each of the sub-regions until no further splitting is

necessary. The process terminates when no further merges are possible. These

small square regions are then merged if they are similar to give larger irregular

regions. However, the problem with this method is that any two regions may be

merged if adjacent and if the larger region satisfies the homogeneity criteria, but

regions which are adjacent in image space may have different parents or be at

different levels in the pyramidal structure.

Figure 3.5: Partitioned image and corresponding quad tree

The third method based on region is watershed method. The basic concept

of watershed method is to visualize the image in three dimensions: two spatial

coordinates versus intensity. In such topographic and hydrologic interpretation,

three types of points are considered: points belonging to a regional minimum,

points where a drop of water, if placed on any of these points would fall certainly

to a local minimum, and points where water equally likely to fall to more than one

such minimum. The accumulation of water in the vicinity of a local minimum is

called a catchment basin. All points that drain into a common catchment basin are

part of the same watershed. Hence a region surrounded by ridge is called a valley

[51]. A ridge is the loci of maximum gradient of the altitude surface. There are two

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basic algorithmic approaches to the computation of the watershed of an image:

rainfall and flooding. In the rainfall approach, local minima are found throughout

the image. Each local minimum is given a unique tag. Adjacent local minima are

combined with a unique tag. Next, a conceptual water drop is placed at each

untagged pixel. The drop moves to its lower-amplitude neighbor until it reaches a

tagged pixel, where it assumes the tag value. Figure 3.6(a) illustrates a section of a

digital image encompassing a watershed in which the local minimum pixel is

represented as black square and the dashed line represents the path of a water drop

to the local minimum [51].

In the flooding approach, conceptual single pixels are placed at each local

minimum. A sea of pixel proceeds to fill up the neighbouring are of the pixel

located at the local minima. If there is over flow of pixels, the extra pixels are

discarded. Figure 3.6(b) shows a profile of the filling process of a catchment basin

[51].

(a) (b)

Figure 3.6: (a) Rainfall watershed and (b) Flooding watershed

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3.5 Image segmentation based on fuzzy clustering techniques

Fuzzy clustering is known for its ability to handle uncertainties artificial

intelligence. While the application of fuzzy sets in cluster analysis and classifier

design was in progress, application of fuzzy clustering in image processing was

evolving in parallel to the aforesaid development [52]. This development was

based on the realization that many of the basic image processing concepts, such as

edge or region boundary do not lend themselves well to precise definition. A gray

tone image possesses ambiguity within pixels due to multi level brightness in the

image. Conventional image segmentation methods divide an image into

meaningful parts based on some criteria. The partition involves only two-valued

logic. A pixel can be in one of the segmented portions or it cannot. Higher level of

processing yields a great amount of erroneous results due to this rigidity. A

classical example of this drawback is the skeleton extraction of a region through

medial axis transformation. The medial axis transformation of a region in a gray

tone image is defined based on its boundary. The boundary of gray tone is well

defined and therefore the medial axis transformation is likely to give erroneous

result if we compute it from crisp segmented image. So, it is convenient to avoid

fixed decisions regarding the segmentation criteria by incorporating flexibility of

fuzzy clustering.

There are several fuzzy clustering algorithms which are used in image

segmentation; Fuzzy c-Means (FCM) algorithm is the most widely used one. The

FCM algorithm is based on an objective function described in Section 2.5.2 in the

second chapter. The objective function is very suitable to define the relationship

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among the pixels in an image. The pixels are considered as data points and the

fuzzy classification matrix denotes the memberships of pixels in clusters. FCM

algorithm can be used to segment both gray level and colour images. Also, another

facility is that we can set the number of clusters that is the number of segmented

parts in advance. A deviation from the expected value might help us to find any

fault in the segmentation process. The objective function of FCM algorithm can be

modified and extended as the requirements change. The adaptability of the

objective function makes FCM suitable for different kind of images. Segmentation

of any image needs to be validated after completion. A typical and well practiced

mean is visual observation of the images by the experts of the concerned field.

Mathematical heuristics are available for validating the segmentation some of

which are complex and computationally expensive. FCM has some validity

measures which can be incorporated within the algorithm and thus it minimizes the

computational effort as well as yields satisfactory results. In literature, we can find

a numerous application FCM algorithm in image segmentation.

Trivedi et al. [53] proposed a fuzzy set theoretic image segmentation

algorithm for aerial image segmentation. The method is based on region growing

principal using a pyramid data structure. The algorithm is hierarchical in nature.

Segmentation of the images at a particular level of processing is done by FCM

algorithm. In multi level segmentation, level � regions are considered

homogeneous when image elements have largest cluster membership values of

greater than a prescribed threshold. If homogeneity test fails, regions are split to

form next level of regions which are again subjected to FCM algorithm. Hall et al.

[54] applied FCM with neural network to segment MRI images. Huntsberger et al.

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[55] applied FCM in image segmentation with refined iterative manner. Keller et

al. [56] used a modified version of FCM in image segmentation. The cluster

centers are updated using the FCM formula, but the new membership values for

each point are calculated using an S-type function based feature value of each point

and the fuzzy means. Backer et al. [57] developed a general strategy of clustering

based fuzzy approach. The set of samples is at first divided into * disjoint sets. The

membership of each point in the initialized clusters is based on some affinity

measures such as distance concept, neighbourhood concept. Three criterion

functions are used based on fuzzy concept. This strategy is very favourable for

image segmentation. Multispectral images are also processed with FCM algorithm

[56] [58] [59].

Lung et al. [60] have developed generalized Spatial Fuzzy C-Means

Clustering algorithm (GSFCM) for brain MRI segmentation. GSFCM utilizes

given pixel attributes and spatial local information weighted equally to neighbours

based on their distance attributes. Results have shown that GSFCM outperforms

conventional FCM. Zhou et al. [61] have presented a mean shift based FCM for

the extraction of skin lesions. They have proposed a mean shift based fuzzy c-

means objective function that is a mean field term is incorporated in the standard

FCM objective function. Experimental results have shown that their algorithm is

capable of extracting skin lesion borders proficiently. Du et al. [62] has proposed

an enhanced segmentation technique that applies sigma filter to every

neighbouring pixel of targets. Visual and quantitative assessment has revealed that

the proposed method works better than the original FCM. Sudhavani et al. [63]

presented modified fuzzy C-Means clustering algorithm for lip image

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segmentation. Kannan et al. [64] have developed an efficient fuzzy segmentation

algorithm for breast magnetic resonance imaging data. They have acquired an

objective function of FCM called Kernel Induced FCM which is based on hyper

tangent function which is in turn based on two functions namely kernel, hyper

tangent and Langrangian multipliers. Yang et al. [65] describes a modified FCM

objective function based on presence of noise. Guo et al. [66] proposed a

segmentation method where the data set is reduced by redefining the feature

vectors and initialize the FCM algorithm with an enhanced cluster center formula.

The method aims at reducing the computational time of FCM. Laszlo Szilagyi [67]

developed a hybrid c-means algorithm as generalization of fuzzy, possibilistic, and

hard c-means algorithm. The hybrid model is induced with some novel image

segmentation method to form a virtual endoscopic procedure using MRI images of

brain. Shasidhar et al. [68] developed a modified FCM algorithm in segmentation

of brain MRI where a comprehensive feature vector space is used for the

segmentation technique. Comparative analysis in terms of segmentation efficiency

and convergence rate is performed between the conventional FCM and the

modified FCM. Saha et al. [69] describes a support vector machine (SVM) based

fuzzy clustering techniques and segments satellite images using the proposed

method. Mohapatra et al. [70] proposes a judicious integration of rough sets and

fuzzy sets suitably employed towards leukocyte segmentation in a clustering

framework. In their study, the goodness of fuzzy sets and rough sets is suitably

integrated to achieve improved segmentation performance. The membership

concept of fuzzy sets is efficient in handling of overlapping partitions, and the

rough sets provide a reasonable solution to deal with uncertainty, vagueness, and

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incompleteness in data. Such synergistic combination gives the proposed scheme

an edge over standard cluster-based segmentation techniques, that is, K-means, K-

medoid, fuzzy c-means, and rough c-means. Wang et al. [71] put forwards a novel

two-dimensional fuzzy C-means (2DFCM) algorithm for the molecular image

segmentation. The 2DFCM algorithm is composed of three stages. The first stage

is the noise suppression by utilizing a method combining a Gaussian noise filter

and anisotropic diffusion techniques. The second stage is the texture energy

characterization using a Gabor wavelet method. The third stage is the feeding of

introduction of spatial constraints provided by the de-noised data and textural

information into the two-dimensional FCM clustering algorithm. The incorporation

of intensity and textural information allows the 2DFCM algorithm to produce

satisfactory segmentation results for images corrupted by noise and intensity

variations.

Beevi et al. [72] have developed a robust segmentation technique that

exploits histogram based FCM algorithm for the segmentation of medical images.

The algorithm first removes noise from the images and then segmentation is

performed. Sparse 3D transform-domain collaborative filtering is used to perform

denoising. Histogram is used to initialize the parameters of the FCM to avoid

convergence in local minima. Spatial probability is incorporated in the objective

function to boost the robustness of algorithm against noise. In the proposed

segmentation methodology, two types of spatial information are incorporated in the

membership function of FCM. First is Apriori probability and other is Fuzzy

Spatial Information. Apriori Probability is incorporated in the membership

function to assign a noisy pixel to a cluster that contains a large number of noisy

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pixels in its neighborhood. Fuzzy Spatial Probability is incorporated in the

membership function and a pixel gets a higher membership value to a cluster when

its neighborhood pixels have high membership value to that cluster [72]. This

approach converges more quickly than the conventional FCM and attains reliable

segmentation accuracy apart from noise levels.

Krindis et al. [73] have developed Fuzzy Logic Information C-Means

Clustering (FLICM) algorithm. FLICM is introduced with a new factor in

objective function of FCM and the new factor ?@� has following characteristics

[73]:

• It incorporates local spatial and gray level information in a fuzzy way to

preserve robustness and noise insensitiveness.

• It controls the influence of the adjacent pixels depending on their distance

from middle pixel.

• It uses original image as input and avoids preprocessing steps to preserve

image details.

• It is free from any parameter selection.

This new novel fuzzy factor is defined mathematically as [73]

?@� � A �)�� B ��CD�

�E�

F� G H@�I6J�� G K@J6

Where ith pixel is the center of the local window e.g., 3*3, k is reference

cluster and jth pixel belongs to the set of neighbors that fall into a window around

ith pixel �� and )�� is Euclidean distance between pixels i and j . The factor ?L�

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is free from any control parameter for balancing image detail and noise. The

stability between noise and image details is automatically attained by the fuzziness

of every pixel of the image. The factor ?L� formulates the influence of the pixels

within the local window, to change flexibly according to their distance from the

middle pixel by using Euclidean distance that is�)��. It is important to note that the

factor ?L� reflects the damping extent of the neighbors with the spatial distances

from the central pixel. The modified objective function is defined as [73]

�M �AANO@�MP

@��Q�� G K@Q6 B ?@�

D

��

FLICM has some advantages over the FCM algorithm such as

insensitiveness towards noise and free from any parameter initialization.

Kannan et al. [74] have proposed a Novel Fuzzy Clustering C-Means

Algorithm (NFCM) for intensity inhomogeneities or weighted bias estimation and

segmentation of T1-T2 Brain MRI images of same patient. Authors also have

presented a center knowledge method to reduce the running time of the algorithm.

The Center Knowledge Algorithm rearranges the data matrix with respect to its

relabeling mean value and data is partitioned into c groups. A distance table is than

created to show the distance between the elements within each group. Maximum

distance between the groups is computed and a mean value is calculated. The

objective function has been modified for the said problem in [74] as follows

�M �AAH�@MNR)�@6 B S�)�@= �6T�

@��

P

��B �* N� GA)�@M

P

��T

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�

where��)�@= � Q�@ B ; G U@ G K�Q6, ;�V��1�� and R� S 0 1

Objective function is minimized by employing same approach as that of

conventional FCM. �M is differentiated with respect to H�@, K� and U@ and is than

set equal to zero in order to get estimators for U, V and b. These estimators are then

used to design an algorithm to calculate tissue class and bias class. Lagrange

multiplier is then used to perform the task of membership evaluation. The

advantage of NFCM is that it can be applied at an early phase of automated data

analysis. NFCM is found to deal effectively with image intensity inhomogeneities

and noise present in the image.

Fuzzy clustering, over the years, has proved to be a powerful tool for image

segmentation. Most of the imaging techniques used in practice such satellite

imaging or medical imaging contain fair amount of uncertainty or vagueness.

Segmentation methods driven by crisp decision cannot handle this uncertainty

prudently. The subtle variations present in complex images are not too well

adapted to hard decisions. Fuzzy clustering algorithms can be extended and

modified according to the needs of a particular application. In medical imaging

various kinds of images exist, from radiological images to microscopic cytological

images. The bones and the tissue in radiological images or the cell and nucleus in

cytological images are hard to distinguish through hard segmentation. The

variations in intensity or gray level are so subtle that hard segmentation tends to

produce faulty result. The criterion or objective function and the flexible

membership function of fuzzy clustering efficiently deal with the situation. The

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application of Fuzzy c-means (FCM) algorithm in cytological image segmentation

is studied and discussed in details in the coming chapters.

CHAPTER-3 IMAGE SEGMENTATION...

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