Edge Detection Techniques for Image Segmentation

CHAPTER 1

INTRODUCTION

The influence and impact of digital images on modem society is tremendous,

and image processing is now a critical component in science and technology. The rapid

progress in computerized medical image reconstruction, and the associated

developments in analysis methods and computer-aided diagnosis, has propelled medical

imaging into one of the most important sub-fields in scientific imaging. Imaging is an

essential aspect of medical science to visualize the anatomical structures of the human

body. Several new complex medical imaging modalities, such as X-ray, magnetic

resonance imaging (MRl), and ultrasound, strongly depend on computer technology to

generate or display digital images. With computer techniques, multidimensional digital

images of physiological structures can be processed and manipulated to help visualize

hidden diagnostic features that are otherwise difficult or impossible to identify using

planar imaging methods.

Image Segmentation is the process of partitioning a digital image into multiple

regions or sets of pixels which are similar with respect to some characteristic such as

color, texture or intensity. Adjacent regions are significantly different with respect to

the same characteristics. Segmentation produces a set of non-overlapping regions whose

union is the entire image. Segmentation algorithms for images generally based on the

discontinuity and similarity of image intensity values. Discontinuity approach is to

partition an image based on abrupt changes in intensity and similarity is based on

partitioning an image into regions that are similar according to a set of predefined

criteria. Therefore the choice of image segmentation technique is problem dependent

that has been considered. In this paper an attempt is made to segment an image based on

edge detection and further smoothening the image using various types of low pass filters

and analyse their effectiveness.

ECE DEPT. OF MGUCE Page 1

CHAPTER 2

LITERATURE REVIEW

2.1. EDGE DETECTION TECHNIQUES FOR IMAGE SEGMENTATION

Image segmentation is an essential step in image analysis. Segmentation

separates an image into its component parts or objects. The level to which the separation

is carried depends on the problem being solved. When the objects of interest in an

application have been inaccessible the segmentation must stop. Segmentation

algorithms for images generally based on the discontinuity and similarity of image

intensity values. Discontinuity approach is to partition an image based on abrupt

changes in intensity and similarity is based on partitioning an image into regions that

are similar according to a set of predefined criteria. Thus the choice of image

segmentation technique is depends on the problem being considered. Edge detection is a

part of image segmentation. The effectiveness of many image processing also computer

vision tasks depends on the perfection of detecting meaningful edges. It is one of the

techniques for detecting intensity discontinuities in a digital image.

The process of classifying and placing sharp discontinuities in an image is called

the edge detection. The discontinuities are immediate changes in pixel concentration

which distinguish boundaries of objects in a scene. Classical methods of edge detection

engage convolving the image through an operator, which is constructed to be perceptive

to large gradients in the image although returning values of zero in uniform regions.

There is a very large amount of edge detection techniques available, each technique

designed to be perceptive to certain types of edges. Variables concerned in the selection

of an edge detection operator consist of Edge orientation, Edge structure and Noise

environment.

2.1.1 General Steps In Edge Detection

Generally, Edge detection contains three steps namely Filtering, Enhancement

and Detection.

i. Filtering: Some major classical edge detectors work fine with high quality pictures,

but often are not good enough for noisy pictures because they cannot distinguish edges

of different significance. Noise is unpredictable contamination on the original image.

There are various kinds of noise, but the most widely studied two kinds are white noise

and “salt and pepper” noise. In salt and pepper noise, pixels in the image are very


different in color or intensity from their surrounding pixels; the defining characteristic is

that the value of a noisy pixel bears no relation to the color of surrounding pixels.

Generally this type of noise will only affect a small number of image pixels. When

viewed, the image contains dark and white dots, hence the term salt and pepper noise. In

Gaussian noise, each pixel in the image will be changed from its original value by a

small amount. Random noise to describe an unknown contamination added to an image.

To reduce the influence of noise, Marr suggested filtering the images with the Gaussian

before edge detection.

ii. Enhancement: Digital image enhancement techniques are concerned with improving

the quality of the digital image. The principal objective of enhancement techniques is to

produce an image which is better and more suitable than the original image for a

specific application. Linear filters have been used to solve many image enhancement

problems. Throughout the history of image processing, linear operators have been the

dominating filter class. Not all image sharpening problems can be satisfactorily

addressed through the use of linear filters. There is a need for nonlinear geometric

approaches, and selectively in image sharpening is the key to its success. A powerful

nonlinear methodology that can successfully address the image sharpening problem is

mathematical morphology.

iii. Detection: Some methods should be used to determine which points are edge points

or not.

2.1.2 Image Segmentation

Image Segmentation is the process of partitioning a digital image into multiple

regions or sets of pixels. Essentially, in image partitions are different objects which

have the same texture or color. The image segmentation results are a set of regions that

cover the entire image together and a set of contours extracted from the image. All of

the pixels in a region are similar with respect to some characteristics such as color,

intensity, or texture. Adjacent regions are considerably different with respect to the

same individuality. The different approaches are (i) by finding boundaries between

regions based on discontinuities in intensity levels, (ii) thresholds based on the

distribution of pixel properties, such as intensity values, and (iii) based on finding the

regions directly. Thus the choice of image segmentation technique is depends on the

problem being considered.

Region based methods are based on continuity. These techniques divide the

entire image into sub regions depending on some rules like all the pixels in one region


must have the same gray level. Region-based techniques rely on common patterns in

intensity values within a cluster of neighboring pixels. The cluster is referred to as the

region in addition to group the regions according to their anatomical or functional roles

are the goal of the image segmentation. Threshold is the simplest way of segmentation.

Using thresholding technique regions can be classified on the basis range values, which

is applied to the intensity values of the image pixels. Thresholding is the transformation

of an input image to an output that is segmented binary image. Segmentation Methods

based on finding the regions directly find for abrupt changes in the intensity value.

These methods are called as Edge or Boundary based methods. Edge detection is the

problem of fundamental importance in image analysis. Edge detection techniques are

generally used for finding discontinuities in gray level images. To detect consequential

discontinuities in the gray level image is the important common approach in edge

detection. Image segmentation methods for detecting discontinuities are boundary based

methods.

2.1.3 Edge Detection Techniques

The edge representation of an image significantly reduces the quantity of data to

be processed, yet it retains essential information regarding the shapes of objects in the

scene. This explanation of an image is easy to incorporate into a large amount of object

recognition algorithms used in computer vision along with other image processing

applications. The major property of the edge detection technique is its ability to extract

the exact edge line with good orientation as well as more literature about edge detection

has been available in the past three decades. On the other hand, there is not yet any

common performance directory to judge the performance of the edge detection

techniques. The performance of an edge detection techniques are always judged

personally and separately dependent to its application.

Edge detection is a fundamental tool for image segmentation. Edge detection

methods transform original images into edge images benefits from the changes of grey

tones in the image. In image processing especially in computer vision, the edge

detection treats the localization of important variations of a gray level image and the

detection of the physical and geometrical properties of objects of the scene. It is a

fundamental process detects and outlines of an object and boundaries among objects

and the background in the image. Edge detection is the most familiar approach for

detecting significant discontinuities in intensity values.


There are many edge detection techniques in the literature for image

segmentation. The most commonly used discontinuity based edge detection techniques

are reviewed in this section. Those techniques are Roberts edge detection, Sobel Edge

Detection, Prewitt edge detection.

2.1.3.1 Roberts edge detection

The Roberts edge detection is introduced by Lawrence Roberts (1965). It

performs a simple, quick to compute, 2-D spatial gradient measurement on an image.

This method emphasizes regions of high spatial frequency which often correspond to

edges. The input to the operator is a grayscale image the same as to the output is the

most common usage for this technique. Pixel values in every point in the output

represent the estimated complete magnitude of the spatial gradient of the input image at

that point.

+1 0

0 -1

Gx Gy

Table 2.1. Roberts Edge Detection

2.1.3.2. Sobel edge detection

The Sobel edge detection method is introduced by Sobel in 1970 (Rafael

C.Gonzalez (2004)). The Sobel method of edge detection for image segmentation finds

edges using the Sobel approximation to the derivative. It precedes the edges at those

points where the gradient is highest. The Sobel technique performs a 2-D spatial

gradient quantity on an image and so highlights regions of high spatial frequency that

correspond to edges. In general it is used to find the estimated absolute gradient

magnitude at each point in n input grayscale image. In conjecture at least the operator

consists of a pair of 3x3 complication kernels as given away in under table. One kernel

is simply the other rotated by 90o. This is very alike to the Roberts Cross operator.

-1 -2 -1

0 0 0

+1 +2 +1

Gx Gy

Table 2.2 Sobel Edge Detection


0 +1

-1 0

-1 0 -1

-2 0 +2

-1 0 +1

2.1.3.3. Prewitt edge detection

The Prewitt edge detection is proposed by Prewitt in 1970 (Rafael C.Gonzalez . To

estimate the magnitude and orientation of an edge Prewitt is a correct way. Even though

different gradient edge detection wants a quiet time consuming calculation to estimate the

direction from the magnitudes in the x and y-directions, the compass edge detection obtains the

direction directly from the kernel with the highest response. It is limited to 8 possible directions;

however knowledge shows that most direct direction estimates are not much more perfect. This

gradient based edge detector is estimated in the 3x3 neighborhood for eight directions. All the

eight convolution masks are calculated. One complication mask is then selected, namely with

the purpose of the largest module.

-1 -1 -1

0 0 0

+1 +1 +1

Gx Gy

Table 2.3 Prewitt Edge Detection

Prewitt detection is slightly simpler to implement computationally than the

Sobel detection, but it tends to produce somewhat noisier results.

2.1.4 Different Approaches

2.1.4.1 Genetic algorithm approach

Genetic algorithms (GA) are random search algorithms based on the theory of

biological evolution. These algorithms require an initial population of individuals,

which are representatives of possible solutions of the problem being solved. The

population evolves by transformations applied to its individuals while a fitness function

is used to determine the strength of the elements in the population. The elements of the

population are known as chromosomes and are represented by strings of bits. The

fitness function is usually computed with basis on the values of those bits. An iteration

of the algorithm is basically equivalent to a generation in the evolutionary process.

Mainly, a genetic algorithm consists of three most important operations. They are

Selection, Crossover and Mutation.

Selection: Fitness-proportional selection-The chromosome with minimum fitness value

and another randomly chosen chromosome are selected from the parent pool to process

crossover and mutation.


-1 0 +1

-1 0 +1

-1 0 +1

Crossover: The crossover recombines two individuals to have new ones which might

be better.

Mutation: The mutation procedure introduces random changes in the population in

order to steer the algorithm from local minimums that could prevent the discovery of

the global solutions to the problem.

The GA is started with a set of abstract candidate solutions population. These

solutions are represented by chromosomes (genotypes or genomes). The Solutions from

one population are taken and used to form a new population. This last process is

motivated by the hope that the new population will be better than the old one. In each

generation, the fitness of each candidate solution is evaluated, multiple candidate

solutions are stochastically selected from the current solutions (based on their fitness),

and modified (recombined and/or mutated and/or others “genetic” operations) to form a

new population of candidate solutions. The new population is then used in the next

iteration of the algorithm.

2.1.4.2 Neural network

Neural networks are nothing but the computer algorithms contend with how the

way the information is processed in nervous system. Neural network diversifies from

other artificial intelligence technique by means of the learning capacity. Digital images

are segmented by using neural networks in two step process. First step is pixel

classification that depends on the value of the pixel which is part of a segment or not.

Second step is edge detection that is the detection of all pixels on the borders between

different homogeneous areas which is part of the edge or not . Several neural networks

are available in the literature for edge detection. The potential base function for digital

image processing can be created using differential operators.

Generally, the neural network consists of three layers such as input layer, hidden

layer and output layer as in the fig. Each layer consists of fixed number of neurons

equal to the number of pixels in the image. The activation function of neuron is a multi-

sigmoid. The major advantage of this technique is that, it does not require a priori

information of the image. The number of objects in the image is found out

automatically.

Wavelet neural network (WNN) based on the wavelet transform theory, is a

novel, multiresolution, hierarchical artificial neural network, which originally combines

the good localization characteristics of the wavelet transform theory and the adaptive


learning virtue of neural networks..The first module extracts the feature and the second

one is WNN classifier which is used to locate the position of the edges.

Figure 2.1. Different Layers Of Neural Network

2.1.4.3 Morphology

We can organize images into two sets.(i) Binary images (ii)grey level and color

images. The binary images are two valued one that may be 0 or 1.The grey level

images, the pixel value may be any integer between 0 and some value. Color image is

an extension of grey level image where the values at each pixel represented by a vector

of three elements with respect to red, green and blue components of color information.

The most basic operations are dilation and erosion which may be defined by

using union and intersection. Dilation increases the object and erosion shrinks the

object. Using the basic operators’ dilation and erosion, two more operators are defined.

They are Opening and Closing. Opening retains only those parts of the objects that can

fit in the structuring element. Closing fills up small holes and gulfs. Thus they both can

extract fine shape features that are narrower than the structuring element.

2.2 OPTIMIZED CLUSTERING METHOD FOR CT BRAIN

IMAGE SEGMENTATION

Over last two decades bio-image analysis and processing occupied an important

position. Image segmentation is the process of distinguishing the objects and

background in an image. It is an essential preprocessing task for many applications that

depend on computer vision such as medical imaging, locating objects in satellite

images, machine vision, finger print and face recognition, agricultural imaging and

other many applications. The accuracy of image segmentation stage would have a great


impact on the effectiveness of subsequent stages of the image processing. Image

segmentation problem has been studied by many researchers for several years; however,

due to the characteristics of the images such as their different modal histograms, the

problem of image segmentation is still an open research issue and so further

investigation is needed. Image Segmentation is the process of partitioning a digital

image into multiple regions or sets of pixels. Partitions are different objects in image

which have the same texture or colour. All of the pixels in a region are similar with

respect to some characteristic or computed property, such as colour, intensity, or

texture. Adjacent regions are significantly different with respect to the same

characteristics. The critical step in image interpretation is separation of the image into

object and background.


CHAPTER 3

MORPHOLOGY

Morphological processing is constructed with operations on sets of pixels.

Binary morphology uses only set membership and is indifferent to the value, such as

gray level or color, of a pixel. Morphological image processing relies on the ordering of

pixels in an image and many times is applied to binary and gray scale images. Through

processes such as erosion, dilation, opening and closing, binary images can be modified

to the user's specifications. Binary images are images whose pixels have only two

possible intensity values. They are normally displayed as black and white. Numerically,

the two values are often 0 for black, and either 1 or 255 for white. Binary images are

often produced by thresholding a gray scale or color image, in order to separate an

object in the image from the background. The color of the object (usually white) is

referred to as the foreground color. The rest (usually black) is referred to as the

background color. However, depending on the image which is to be threshold, this

polarity might be inverted, and in which case the object is displayed with 0 and the

background is with a non-zero value. Some morphological operators assume a certain

polarity of the binary input image so that if we process an image with inverse polarity

the operator will have the opposite effect. For example, if we apply a closing operator to

a black text on white background, the text will be opened.

3.1. IMAGE PRE-PROCESSING

The procedure for image pre-processing includes the following Steps: acquiring

a necessary bio-medical image specifically a MRI image; converting it to gray for a

colour image followed by type-casting the image to uint8 to have a reference data-type.

ROI within the brain image is extracted as a patient case is considered here.

The use of color in image processing is motivated by two principal factors; First

color is a powerful descriptor that often simplifies object identification and extraction

from a scene. Second, human can discern thousands of color shades and intensities,

compared to about only two dozen shades of gray. In RGB model, each color appears in

its primary spectral components of red, green and blue. This model is based on

Cartesian coordinate system. Images represented in RGB color model consist of three

component images. One for each primary, when fed into an RGB monitor, these three


images combines on the phosphor screen to produce a composite color image. The

number of bits used to represent each pixel in RGB space is called the pixel depth.

Consider an RGB image in which each of the red, green and blue images is an 8-bit

image. Under these conditions each RGB color pixel is said to have a depth of 24 bit.

3.2. IMAGE SEGMENTATION

To identify individual objects in an image, a segmentation operation is

performed. Both thresholding technique and edge based segmentation methods like

sobel, prewitt edge detector operators is applied.

The threshold value is obtained using the concept of symmetrical structure of the

brain. It is a well-known fact that human brain is symmetrical about its central axis and

throughout this work it has been assumed that the tumor is either on the left or on the

right side of the brain.

If the histograms of the images corresponding to the two halves of the brain are

plotted, a symmetry between the two histograms should be observed due to symmetrical

nature of the brain along its central axis. On the other hand, if any asymmetry is

observed, the presence of the tumor is detected. The differences of the two histograms

are plotted and the peak of the difference is chosen as the threshold point.

The proposed method of segmentation is implemented in two phases as follows:

3.2.1 Algorithm for Segmenting Image

1. In this work, bio-medical image has been considered. Hence the brain image is

taken for the work as input image.

2. As it is a colour image, initially it has converted into gray scale imageThe

process of conversion to grayscale image is performed as:Grayscale image

matrix A (x, y)= (Red component*0.3)+ (Green component *0.59)+ (Blue

component *0.11)

3. The point of interest is a particular area within the brain image, as it is of the

patient case. For this reason, the ROI was extracted for analysis of the

image.The ROI is evaluated by statistical method from the pixel by considering

the boundary.

4. The desired threshold value was obtained using the following method:


a. The image pixels were stored as a variable (say I) where I showed the

values of the pixels in a 2D matrix (row - column) form.

b. Number of rows and columns were assigned some other variables (say

Rand CL).

c. Floor division by 2 was performed on the column value and assigned

another variable name (say C).

d. For the left-half of the image, new matrix was formed using for loop by

rows from 1: R as outer loop and columns from 1: C as inner loop.

e. For the other half of the image, the column value from C+ 1: CL is

considered as the inner loop.

f. The histogram of the resulting left half and right half image was

calculated.

g. The difference of the two histograms was then calculated and the

resultant difference is plotted using bar graph to select the threshold

point.

5. The image was then binarized using this threshold value by the following

method:

a. A zero matrix of same size of original image matrix (say F) was

considered.

b. Each pixel value of the image matrix was compared with the threshold

point.

c. If the value of pixel is greater than threshold, that pixel value in 'f matrix

was assigneda value 255, otherwise 0 was assigned to that.

d. This process was repeated till all the pixel values were compared to

threshold point

6. The unwanted boundary is removed.

7. The edge detection was performed initially using Sobel operator, but the final

smoothed method is with the following morphological operations:

a. Suitable structuring elements (SE) was created. The shape of all

structuring elements may be line based flat, linear or both. Different

structuring elements were selected for the erosion and dilation

operations. In order to have a basic link between both the operations a

difference angle= 90° between the dilation angle and the erosion angle is

considered.


b. Dilate the image. Dilation of a gray-scale image A (x, y) by a gray-scale

structuring element B(s, t) can be performed by:

A⊕B=max (i , j )∀ B ¿ …3.1

c. Start from forming an array XO of zeros which is same size as the array

containing A, except at the locations in XO corresponding to the given

point in each hole, which is set to one. Then, the following procedure

fills all the holes with ones: Xk=(Xk−1⊕B)⋂Aⁿ . The algorithm

terminates at the iteration step k if Xk=Xk−1

d. Erode the image. Erosion of image A (x, y) by a gray-scale structuring

element B (s, t) can be performed by:

A⊖B=min (i , j )∀ B {a [ m− j ,m−k ]+b [ j , k ]} …3.2

e. Find the edges using morphological operator for different

structuringelements

Edge( A)=( A⊕B)−( A⊖B) …3.3

Where' A' represents the input image

f. Closing of gray-scale image A (x, y) by gray-scale structuring element B

(s, t) is denoted by as follows:

A· B=(( A⊕B)⊖B) …3.4

3.2.2 Algorithm for Smoothening

1. The image of size M*N was acquired.

2. The padding parameters P and Q were obtained, where P=2*M and Q=2*N.

3. The padded image size P*Q was formed by appending necessary number of

zeros to input image.

4. The DFT of the padded image was computed.

5. The filter with the size P*Q was generated using the mathematical formula/filter

function.

6. The filter was multiplied with the image in the frequency domain.

7. The Inverse FFT of the resulting image was performed.

8. Final smoothed image was obtained by extracting the M*N region.


CHAPTER 4

FILTER

The found result requires to be smoothen. In smoothing, the data points of a

signal are modified so individual points (presumably because of noise) are reduced, and

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

Smoothing may be used in two important ways that can aid in data analysis by being

able to extract more information from the data as long as the assumption of smoothing

is reasonable and by being able to provide analyses that are both flexible and

robust.Noise in an image tends to produce some peak values in the image which can be

reduced by using low-pass filter.Different types of low pass filters are used to verify the

experimental result.

1. Butterworth filter

2. Bessel filter

3. Chebyshev filter

4. Gaussian filter

The basic steps for filtering in frequency domain is shown as:

Figure 4.1 Frequency Domain Filtering Operation


Input image

(f(x,y))

Fourier transfor

m

Filter function (H(u,v))

Inverse Fourier transfor

m

post processi

ng

Enhanced image(g(x,y))

The DO value is fixed initially, by taking 25% the width of Fourier transform.

Figure 4.2 Frequency Rectangle

Then the distance from point (u, v) to the centre of the frequency rectangle D (u,

v) is calculated from the mesh grid frequency using the following formula:

D (u , v )=¿¿ …4.1

Where m,n are the no of rows and columns of the image

4.1 BUTTERWORTH FILTER

The Butterworth filter is a type of signal processing filter designed to have a flat

frequency response as possible in the pass band. It is also referred to as a maximally flat

magnitude filter. The transfer function is,

H (u , v )= 1

1+[D (u , v )

D0

]2 n …4.2

Figure 4.3 Output Using Butterworth Filter


4.2. BESSEL FILTER

Bessel's Differential Equation is defined as:

x2 y″+x y '+( x2−n2) y=0 …4.3

Where 'n' is a non-negative real number. The solutions of this equation are called

Bessel Functions of order n. Bessel function, for integer values of n, in integral

representation:

Jn ( X )= 12 π

∫−π

π

ei ¿¿¿ …4.4

Figure 4.4 Output Using Bessel Filter

4.3. CHEBYSHEV FILTER

Chebyshev filters are filters having a steeper roll-off and more pass band ripple

(type I) or stop band ripple (type II) than Butterworth filters. Chebyshev filters have the

property that they minimize the error between the idealized and the actual filter

characteristic over the range of the filter, but with ripples in the pass band. Its transfer

function is:

Gn (ω)=|H n ( jω )|= 1

√1+ϵ 2Tn2( ωω0

) …4.5

Where:£ is ripple factor. 000 is cut-off frequency


Tn is the nth order Chebyshev polynomial , Tn(x )=cos¿ …4.6

Figure 4.5 Output Using Chebyshev Filter

4.4. GAUSSIAN FILTER

Gaussian filters have the properties of having no overshoot to a step function

input while minimizing the rise and fall time. This behaviour is closely connected to the

fact that the Gaussian filter has the minimum possible group delay.Thetransfer function

of the Gaussian filter is:

H (u , v )=e−D2 (u , v)/2 D02

…4.7

Figure 4.6 Output Using Gaussian Filter


CHAPTER 5

QUALITY MEASUREMENT

5.1. MSE and PSNR

During the process of smoothing, the reconstructed image is subject to a wide

variety of distortion. Subjective evaluations emphasizes on the visual image quality,

which is too inconvenient, time consuming, and complex. The objective image quality

metrics like Peak Signal to Noise Ratio (PSNR), or Mean Squared Error (MSE) is

thought to be the best for the image processing application. The MSE metric is most

widely used for it is simple to calculate, having clear physical interpretation and

mathematically convenient. MSE is computed by averaging the squared intensity

difference of reconstructed image 12, and the original image, 11. Then from it the

PSNR is calculated. Mathematically,

MSE=∑M , N

[ I1¿ (m ,n )−I 2(m , n)]2

M∗N¿ …5.1

Where, M X N is the size of the image and assuming the gray scale image of 8

bits per pixel (bpp).

PSNR is defined as,

PSNR=10 log10(R2

MSE) …5.2

Where, R is the maximum pixel value of image.


Figure 5.1 Mean Squared Error

Figure 5.2 Peak Signal to Noise Ratio

5.2. SSIM

But, they are not very well matched to human visual perception. It has been seen

that even for the same PSNR values, the visual quality for two reconstructed images is

different at different bit rate. It is because the pixels of the natural images are highly

structured and exhibit strong dependencies. The SSIM system separates the task of

similarity measurement in to three comparisons: luminance, contrast and structure. The

overall similarity measure is defined as:

S ( x , x ' )=f (l ( x , x ' ) ,c ( x , x ' ) , s ( x , x ' )) …5.3

Where, x is the original assuming to be completely perfect and x' is the

reconstructed image such that both are non-negative images.

I(x, x') = luminance comparison function, which in tum the function of the mean

values of x and x'.

c (x, x') = contrast comparison function and they are function of the standard

deviation of x and x'

s (x, x' ) = structure comparison function


SL.No. SMOOTHING FILTERS SSIM

1 Chebyshev filter 0.9995

2 Butterworth filter 0.9996

3 Bessel filter 0.9991

4 Gaussian filter 0.9997

Table 5.1 Structural Similarity Index Measurement


CHAPTER 6

CONCLUSION

The proposed method can be applied to detect the region of the tumor and for

further analysis. This technique can be proved to be handy tool for the practitioners

especially the physicians engaged in this field. Though the number of steps is more, but

it is simple to apply and the result should be accurate. It has been established in the

environment of MATLAB 8.2 platform. The alternative methods may be applied for

accuracy level such as thresholding and smoothing method. Also optimization can be

performed and kept for future work.


Documents

Edge Detection Techniques for Image Segmentation