i

MEDICAL IMAGE CLASSIFICATION

USING

SUPPORT VECTOR MACHINE

A PROJECT REPORT

Submitted by

N.N.ABIMANYU

S.GUGAPRIYA

D.LALITHA

In partial fulfillment for the award of the degree

of

BACHELOR OF ENGINEERING

in

ELECTRONICS & COMMUNICATION ENGINEERING

SCHOOL OF COMMUNICATION & COMPUTER SCIENCES

KONGU ENGINEERING COLLEGE, PERUNDURAI

ANNA UNIVERSITY::CHENNAI 600 025

APRIL 2010

ii

ANNA UNIVERSITY::CHENNAI 600 025

BONAFIDE CERTIFICATE

Certified that this project report “MEDICAL IMAGE

CLASSIFICATION USING SUPPORT VECTOR MACHINE” is the

bonafide work of N.N.Abimanyu (71106106001), S.Gugapriya

(71106106029), and D.Lalitha (71106106047), who carried out the project

work under my supervision.

SIGNATURE

Dr. G. Murugesan, B.E., M.S., M.E., Ph.D.,

HEAD OF THE DEPARTMENT

Professor,

Department of Electronics &

Communication Engineering,

School of Communication &

Computer Sciences,

Kongu Engineering College,

Perundurai, Erode – 638 052.

SIGNATURE

Mr. K. Venkateswaran, M.E.,

SUPERVISOR

Lecturer,

Department of Electronics &

Communication Engineering,

School of Communication &

Computer Sciences,

Kongu Engineering College,

Perundurai, Erode – 638 052.

iii

CERTIFICATE OF EVALUATION

College Name : Kongu Engineering College

Branch : Electronics & Communication Engineering

Semester : VIII

S.No. Name of the

student Title of the project

Name of the supervisor with

designation

1. N.N. Abimanyu

(71106106001) MEDICAL IMAGE

CLASSIFICATION

USING SUPPORT

VECTOR

MACHINE

Mr. K. Venkateswaran, M.E.

Lecturer

ECE Department

2. S. Gugapriya

(71106106029)

3. D. Lalitha

(71106106047)

The report of the project work submitted by the above students in

partial fulfillment for the award of Bachelor of Engineering degree in

Electronics & Communication Engineering, Anna University was evaluated

and confirmed to be the report of the work done by the above students.

Submitted for the University examination held on …………………..

Internal Examiner External Examiner

iv

ACKNOWLEDGEMENT

We express our sincere thanks to our beloved Correspondent Thiru. V.

R. Sivasubramanian, B.Com., B.L., and all the members of Kongu Vellalar

Institute of Technology Trust at this high time for providing all the necessary

facilities to complete the course successfully.

We wish to express our profuse thanks and gratitude to our beloved

Principal Prof. S. Kuppusami, B.E., M.Sc (Engg), Dr.Ing (France) for his

constant encouragement in the successful completion of this project work.

We wish to thank our Dean Prof.S.Balamurugan B.E., M.Sc (Engg),

School of Communication And Computer Sciences for his timely advice and

help in the completion of the project.

We express our gratitude to Dr. G. Murugesan, B.E., M.S., M.E.,

Ph.D., Head of the Department, Electronics and Communication Engineering,

who has been the major source of inspiration to us throughout the duration of

our work.

We are thankful to our project co-ordinator Ms. D. Malathi, M.E. for

her valuable suggestions.

We intend to thank our guides Mr. K. Venkateswaran, M.E. and Mr.

S. Raja, M.E. for their valuable suggestions in the improvement of the

project.

We wish to express our sincere thanks to all the faculties of Electronics

and Communication Department and our friends for their constant support

towards the successful completion of this project.

v

ABSTRACT

The project presented in this report is aimed at developing an

automated machine learning algorithm for the classification of medical

images obtained from Magnetic Resonance Imaging (MRI) scans. This also

implies the necessity for applying transforms on images. The algorithm

consists of two steps: automatic extraction of features from the MRI images

through two different image transforms namely-Discrete Wavelet

Transform (DWT) and Gabor transform and their classification by creating

a classifier trained on the extracted results. The classifier used is the Support

Vector Machine (SVM) with linear kernel function. Further classification

and comparison of obtained results showed that the features extracted by

applying Gabor transform on MR images provide an accuracy of 100% by

using SVM with linear kernel function.

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TABLE OF CONTENTS

CHAPTER NO. TITLE PAGE NO.

ABSTRACT v

LIST OF TABLES viii

LIST OF FIGURES ix

LIST OF ABBREVIATIONS x

1. INTRODUCTION 1

2. LITERATURE REVIEW 2

3. MEDICAL IMAGE CLASSIFICATION 5

3.1 Medical Images 5

3.2 Applying Image Transforms 7

3.2.1 Image Transformations 7

3.2.2 Discrete Wavelet Transform 7

3.2.3 Gabor Transform 11

3.3 Feature Extraction 14

3.3.1 Gray Scale Feature 14

3.3.2 Shape Features 16

3.3.3 Texture Features 16

3.4 Data Set Formation 18

vii

3.5 Classification by SVM 19

3.5.1 Statistical Learning Theory 19

3.5.2 Support Vector Machine 20

3.5.3 Kernel Classifiers 23

3.5.4 Linear SVM 24

3.6 Performance of SVM 25

4. RESULTS 27

4.1 Results for transforms 27

4.1.1 Discrete Wavelet Transform 27

4.1.2 Gabor Transform 29

4.2 Results for Feature Extraction 32

4.3 Results for SVM Performance Measurement 37

4.3.1 Wavelet Performance measures 37

4.3.2 Gabor Performance measures 38

5. COMPARISON OF RESULTS AND ANALYSIS 40

6. CONCLUSION 42

REFERENCES 43

viii

LIST OF TABLES

TABLE NO. TITLE PAGE NO.

4.1 Normal Images – Mean 32

4.2 Normal Images – Variance 33

4.3 Normal Images – Entropy 33

4.4 Abnormal Images – Mean 34

4.5 Abnormal Images – Variance 35

4.6 Abnormal Images – Entropy 36

4.7 Performance Measures without 37

applying transforms

4.8 Performance Measures of DWT 37

based SVM

4.9 Performance Measures of Gabor 38

based SVM

5.1 Performance Measures – Comparison 40

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LIST OF FIGURES

FIGURE NO. TITLE PAGE NO.

3.1 Normal Image 6

3.2 Abnormal Image 6

3.3 Three level wavelet decomposition

Tree 10

3.4 Wavelet Families 11

3.5 SVM principles 22

3.6 Linear SVM 25

4.1 Wavelet transform of abnormal image 27

4.2 Wavelet transform of normal image 28

4.3 Gabor sub-bands 29

4.4 Gabor Transform of normal image 30

4.5 Gabor Transform of abnormal image 31

x

LIST OF ABBREVIATIONS

MRI Magnetic Resonance Imaging

CADe Computer Aide Detection

CADx Computer Aided Diagnosis

t2fs T2 weighted FLAIR image

FLAIR Fluid Attenuated Inversion Recovery

ANN Artificial Neural Network

WT Wavelet Transform

CWT Continuous Wavelet Transform

DWT Discrete Wavelet Transform

GT Gabor Transform

COM Co-Occurrence Matrix

IDM Inverse Difference Moment

SVM Support Vector Machine

RBF Radial Basis Function

SLT Statistical Learning Theory

SRM Structural Risk Minimization

1

CHAPTER 1

INTRODUCTION

There are many factors in the process of the physicians’ diagnosis.

Firstly, the physicians’ diagnosis is subjective, because the diagnosis’ result is

affected by the doctors’ experience and ability; Secondly, the physicians’

diagnosis tends to omit some tiny changes that the human eyes can’t find;

thirdly, different physicians would get the different diagnosis’ conclusions for

the same medical image. Comparing to the physicians, the computer has

tremendous predominance in the aspect of avoiding the incorrect results.

Image Classification plays an important role in the fields of Medical

diagnosis, Remote Sensing, Image analysis and Pattern Recognition. Digital

image classification is the process of sorting of images into a finite number of

individual classes. In the case of main fields like medical diagnosis, images

have to be classified with maximum accuracy, or else it will lead to

incomplete treatment of the corresponding disease.

The main advantage of applying transform to a medical image before

extracting its features is to reduce redundant data present in the image.

Applying transforms can improve the accuracy and accordance of the

diagnosis’ result. First and second order statistics of the wavelet detail

coefficients provide descriptors that can discriminate intensity properties

spatially distributed throughout the image, according to various levels of

resolution. Then, using SVM classifier, these features are classified and

performance measures of SVM classifier such as accuracy, precision,

sensitivity, specificity are evaluated and compared with those from the non-

transformed images.

2

CHAPTER 2

LITERATURE REVIEW

Image Classification plays an important role in the fields of Medical

diagnosis, Remote sensing, Image analysis and Pattern Recognition.. In case

of main fields like medical diagnosis, images have to be classified with

maximum accuracy, or else it will lead to incomplete treatment to the

corresponding disease.

In order to achieve high classification accuracy in image classification,

numerous methods for feature extraction and image classification were

introduced. For feature extraction, different transforms like Wavelet,

Ridgelet, Curvelet, Contourlet transforms were used. For classification

different statistical classifiers like Feed forward Neural Networks(FNN)

,Feedback Neural Networks, Back propagation Neural

Networks(BPNN),Multi-Layer Perceptron(MLP),Hybrid Hopfield Neural

Networks(HHNN),Radial Basis Function Neural Network(RBF-NN)[1],Self-

Organizing Map(SOM) and kernel classifiers like Support Vector

Machine(SVM) are used.

One method is by using Ridgelet transform for feature extraction and

classification as explained in the paper “Ridgelet based Texture Classification

of Tissues in Computed tomography” [3] by Lindsay Semlera, Lucia Dettoria

and Brandon Kerrb of DePaul University, Chicago. This article focuses on

using Ridgelet-based multi-resolution texture analysis and also on

investigating the discriminating power of several Ridgelet based texture

descriptors. Even though Ridgelet transform provided good performance, but

3

it gives good results only in case of texture descriptors, which are somewhat

difficult to calculate.

A paper titled “A Comparison of Daubechies and Gabor Wavelets for

Classification of MR Images” [2] by Ulas Bagci, Li Bai of CMAIG proposes

a machine learning algorithm for classifying MR image using wavelet

transform and Gabor transform using SVM.But,results of 100% classification

accuracy in case of classifying normal and abnormal images were obtained

using SVM classifier of Sigmoid and RBF kernels only,which are more time

consuming and less effective than SVM classifier of linear kernel.

An article named “A Comparison of Wavelet-based and Ridgelet based

texture Classification of tissues in Computed Tomography”[3] by Lindsay

Semler, Lucia Dettori of DePaul University, Chicago presents a comparison

of wavelet-based and Ridgelet-based algorithms for medical image

classification. Tests on a large set of chest and abdomen CT images indicate

that, the one using texture features derived from the Haar wavelet transform

clearly outperforms the one based on Daubechies and Coiflet transform. The

tests also show that the Ridgelet-based algorithm is significantly more

effective, but it fails to recognize point coordinates in image which represents

the tumour effectively and does not provide 100% accuracy.

Another problem lies in the case of classification. Before SVM,

Artificial Neural Networks (ANN) were widely used for classification of

images and other applications. Many types of Artificial Neural

Networks(ANN) namely Feed forward Neural Networks(FNN) ,Feedback

Neural Networks, Back propagation Neural Networks(BPNN) ,Multi-Layer

Perceptron(MLP), etc were developed. But all of them have their own

4

advantages and disadvantages and no one of them provided 100%

classification accuracy.

With the introduction of kernel classifiers, SVM classifier becomes

more common. But, kernel classifiers called Support Vector Machine (SVM)

with linear kernel provided 100% classification accuracy. A comparison on

SVM and FNN was provided in the paper titled “Research on Comparison

and Application of SVM and FNN Algorithm” [5] written by Shaomei Yang

and Qian Zhu. This paper concluded that high recognition accuracy and high

speed convergence are achieved by using SVM rather than FNN.

Another study titled “Improved Classification of Pollen texture Images

using SVM and MLP ”[4] by M. Fernandez-Delgado, P. Carrion, E.

Cernadas, J.F. Galvez, Pilar Sa-Otero, explored the use of more sophisticated

classifiers to improve the classification stage. It explains that SVM achieved

high accuracy when compared to k-Nearest Neighbours (KNN) and Multi-

Layer Perceptron (MLP). Also KNN requires storing of whole training set

and hence it is time consuming.

5

CHAPTER 3

MEDICAL IMAGE CLASSIFICATION

3.1 MEDICAL IMAGES

As the project’s main objective is to classify medical images, the first

and foremost need is the input to the algorithm, i.e., medical images. Here,

classification is done on medical images obtained from Magnetic Resonance

imaging (MRI) scans. Among different types of MRI scans like Diffusion

MRI, Functional MRI, FLAIR (Fluid Attenuated Inversion Recovery) MRI,

Interventional MRI, images taken here are FLAIR images of t2fs type. Fluid

attenuated inversion recovery (FLAIR) is a pulse sequence used in

magnetic resonance imaging which was invented by Dr. Graeme Bydder.

FLAIR can be used with both three dimensional imaging (3D FLAIR) or two

dimensional imaging (2D FLAIR).

The pulse sequence is an inversion recovery technique that nulls fluids.

For example, it can be used in brain imaging to suppress cerebrospinal fluid

(CSF) effects on the image, so as to bring out the periventricular hyperintense

lesions, such as multiple sclerosis (MS) plaques. By carefully choosing the

TI, the signal from any particular tissue can be nullified. The appropriate TI

depends on the tissue via the formula:

TI = ln2 * T1

One should typically yield a TI of 70% of T1. In the case of CSF

suppression, one aims for T2 weighted images.

T2-weighted scans use a spin echo (SE) sequence, with long TE and

long TR. They have long been the clinical workhorse as the spin echo

6

sequence is less susceptible to inhomogeneities in the magnetic field. They

are particularly well suited to edema as they are sensitive to water content

(edema is characterized by increased water content).

Also, this project mainly focuses on creating an algorithm for

classifying brain images especially and detecting any abnormalities in brain

like tumor. Therefore, the images which are given as input to the algorithm

are of two types –

1. Normal brain images (without tumor) (eg. Fig. 3.1) and

2. Abnormal brain images (with tumor) (eg. Fig. 3.2)

Fig. 3.1 Fig.3.2

Normal Image Abnormal Image

7

3.2 APPLYING IMAGE TRANSFORMS

3.2.1 IMAGE TRANSFORMATIONS

In different image processing applications, the main step considered is

applying transforms on images. This step is usually carried out for the

following reasons:

1. To reduce the redundant data in image

2. To reduce the actual size of image content.

3. Easy analysis.

The transform of a signal is a way to represent the signal. It does not

alter the information content present in the signal. There are different image

transformations available such as:

1. Cosine Transform 2.Sine Transform

3. Fourier Transform 4.Wavelet Transform

5. Ridgelet Transform 6. Curvelet Transform

7. Contourlet Transform 8.Riplet Transform

9. Gabor Transform, etc.

Among these most promising are - 1.Wavelet Transform and 2.Gabor

transform.

3.2.2 DISCRETE WAVELET TRANSFORM

The Wavelet Transform provides a time-frequency representation of

the signal. It was developed by Morlet to overcome the short comings of the

Short Time Fourier Transform (STFT) and Fourier Transform (FT), which

8

can also be used to analyze non-stationary signals where all frequencies have

an infinite coherence time. While FT and STFT give a constant resolution at

all frequencies, the Wavelet Transform uses multi-resolution technique by

which different frequencies are analyzed with different resolutions and a

coherence time proportional to the period of the signal.

Also, Fourier transform (FT) does not provide any information to show

where within single certain frequencies occur, i.e., information about the time

domain is lost. Since, most of the signals in the real-world change with time,

it is especially useful to characterize signals in both time and frequency

domain simultaneously. Wavelet transform is used for this reason.

The Wavelet Transform (WT) decomposes a signal into a linear sum of

basis-functions which are dilated and translated wavelets. A wavelet is a

function L2 () with zero average, normalized to one and centered in the

neighbourhood of t=0. A family of time-frequency components is obtained by

translating it by u and scaling it by .

Convolution of this wavelet function with the image will give us the

Wavelet transform of the image f(x,y). The wavelet transform of the image

can be analysed with respect to both time and frequency domains. Hence,

wavelet transform provides information about both time and frequency

domains at various resolutions.

Discrete Wavelet transform converts a discrete time signal into

wavelets. Discrete Wavelet transform is expressed as:

9

where dm(n) = <x, mn> and

are basis for L2() satisfying the biorthogonality condition ,which is defined

as(mn ,lk)=ml nk. In orthogonal case, mn can be used for both synthesis

and analysis of wavelets.

The two-dimensional Wavelet transform is carried out by applying

one-dimensional wavelet transform to the rows and columns of the two-

dimensional data consecutively. It is computed by successive lowpass and

highpass filtering of the discrete time-domain signal .This is called the Mallat

algorithm or Mallat-tree decomposition. In the figure 3.3, the signal is

denoted by the sequence x[n], where n is an integer. The low pass filter is

denoted by G0 while the high pass filter is denoted by H0. At each level, the

high pass filter produces detailed information; d[n], while the low pass filter

associated with scaling function produces coarse approximations,a[n].

Generally, there are three detailed components in images namely:

1.Horizontal, 2.Vertical and 3.Diagonal components. These three components

contain all the detailed information about high frequency contents present in

the image and hence they are used to extract image features rather than from

approximation components.

10

Fig 3.3 Three level wavelet decomposition tree

The advantages of DWT are:

1. It is easy to implement

2. It reduces the computation time

3. Resources required for the computation of DWT co-efficients are less.

4. It needs only O(N) operations to get computed and hence, it is also referred

to as the fast wavelet transform

In Wavelet Families there are a number of basis functions that can be

used as the mother wavelet for Wavelet Transformation. Since the mother

wavelet produces all wavelet functions used in the transformation through

translation and scaling, it determines the characteristics of the resulting

Wavelet Transform. They include Haar wavelet, Daubechies wavelet, Symlet,

Coiflet, Biorthogonal wavelet, Morlet, Meyer wavelet and Mexican Hat

wavelet as given in fig 3.4

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Fig 3.4 Wavelet Families (a)Haar (b)Daubechies (c)Coiflet1 (d)Symlet

(e)Meyer (f)Morlet (g)Mexican Hat

Haar wavelet is the oldest and simplest wavelet available which is used

as mother wavelet for classifying medical images. Since Haar wavelet is

suitable for representing the image in time domain, it is used here.

3.2.3 GABOR TRANSFORM

Gabor transforms are widely used in image analysis and computer

vision. The Gabor transform provides an effective way to analyze images and

has been elaborated as a frame for understanding the orientation and spatial

frequency selective properties of signals. It seems to be a good approximation

to the sensitivity profiles. The important advantages are infinite smoothness

and exponential decay in frequency. Gabor transform represents an approach

to characterise a time function in terms of time and frequency simultaneously.

12

A joint space-frequency analysis of any signal cannot be performed by

the Fourier transform. This can be easily performed by Short time Fourier

Transform (STFT).The STFT of a signal s(t) can be given as-

STFT (τ,) = s(t) g(t-τ) exp (-jt) dt

Thus, STFT of a signal is defined as Fourier Transform of the signal

s(t) windowed by the function g(t-τ).The STFT with a Gaussian window is

called a Gabor transform.

The Gabor transform can be regarded as a signal being convoluted with

a filter bank, whose impulse response in the time domain is Gaussian signal

modulated by sine and cosine waves. The characteristics of the Gabor

wavelets, especially for frequency and orientation representations, are similar

to those of human visual system, and they have been found to be particularly

appropriate for texture representation and discrimination. In the spatial

domain, the 2D Gabor filter is a Gaussian kernel function modulated by a

sinusoidal plane wave.

where f is the central frequency of the sinusoidal plane wave, is the anti-

clockwise rotation of the Gaussian and the plane wave, is the sharpness of

the Gaussian along the major axis parallel to the wave, and β is the sharpness

13

of the Gaussian minor axis perpendicular to the wave. γ = f / and η = f / β

are defined to keep the ratio between frequency and sharpness constant.

The Gabor filters are self-similar; all filters can be generated from one

mother wavelet by dilation and rotation. Each filter is in the shape of plane

waves with frequency f, restricted by a Gaussian envelope function with

relative width and β. To extract useful features from an image, normally a

set of Gabor filters with different frequencies and orientations are required.

The Gabor representation of a MR brain image M(~x) can be obtained

by convolving the image with the family of Gabor filters is given by:

where LHS denotes resultant Gabor representation of image M at orientation

u and scale v. Thus, the resultant Gabor feature set consists of the convolution

results of an input image M(x) with all of the Gabor wavelets:

14

The number of Gabor wavelets used varies with different applications.

Better results can be obtained, if 5 scales and 8 orientations are used for

classification of MR brain images. Extracted feature vectors are then

concatenated together to construct a new feature vector to be used for

classification purposes. In Figure 4.3, a MR brain image is convolved with

40 Gabor filters (8 orientations, 5 scales) and each row and column shows a

different scale and orientation respectively.

3.3 FEATURE EXTRACTION

Feature Extraction is an important step in image classification. It refers

to extraction of various characteristics of the image, either transformed or

untransformed. There are numerous features available in the image to get

extracted.

The feature extraction includes the

1. Gray scale (intensity) Extraction

2. Shape extraction

3. Texture extraction

3.3.1 GRAY SCALE FEATURES

In digital picture process, the two-dimensional digitized gray scale image

(M×N) can be seen as M×N pixels in two-dimensional surface XOY, each

pixel f(x,y) can be expressed as its gray value.

Mean

Mean or average value represents the arithmetic mean or average of all

pixels in the image f(x,y).

15

Variance

Variance is the first moment about the mean. It reflects the separate

degree of gray scale value.

Skewness

Skewness is the second moment about the mean. It takes the mean

value as the central data distribution not as symmetrical degree.

Kurtosis

Kurtosis is the third moment about the mean. It reflects the normal

distribution sharpness or smoothness of compared the data.

Histogram

The gray histogram is the gray scale value function; it describes the

rate of the pixels that have the same gray scale value in the picture.

where nb is the number of the pixels that the gray scale value is b, n is the

total number of the picture’s pixels.

16

The features aiming at the gray scale histogram is mainly the gray scale

average value, gray scale variance, gray Skewness, gray Kurtosis, gray energy

and gray entropy.

3.3.2 SHAPE FEATURES

The shape features have the characters that are scaling invariability,

rotation invariability, translation invariability, so they can become the object

recognition features. The features include the Normalized Moment of Inertia

(NMI), moment invariants and sphericity.

The shape features can highly identify the figure. As the exterior shapes of

brain image are all nearly ellipse, it can’t distinguish the image by extracting

the features to the whole image. Considering the place and character of the

certain pathological changes we select the ROI and extract its features.

3.3.3 TEXTURE FEATURES

A co-occurrence matrix (COM) is a square matrix whose elements

correspond to the relative frequency of occurrence p(i,j,d,h) of two pixel

values (one with intensity i and the other with intensity j ), separated by a

certain distance d in a given direction h . A COM is therefore a square matrix

that has the size of the largest pixel value in the image. The COM is scale

invariant. The matrices present the relative frequency distributions of gray

levels and describe how often one gray level will appear in a specified spatial

relationship to another gray level within each image.

17

The matrix was normalized by the following function:

where, R is the normalized function, which is usually set as the sum of the

matrix.

Energy

Energy is also called Angular Second Moment. It is a measure of the

homogeneousness of the image and can be calculated from the normalized

COM. It is a suitable measure for detection of disorder in texture image.

Higher values for this feature mean that the amplitude or intensity changes

less in the image, resulting in a much sparser COM.

Contrast

Contrast is a measure of amount of the local variation in the image. It

presents the degree of the legibility of the image. A higher contrast value

indicates a high amount of local variation, so the higher contrast is, the clearer

the image is.

IDM

The Inverse Difference Moment (IDM) reflects the local texture

changes. It is another feature of image contrast.

18

Entropy

Entropy is a statistical measure of randomness that can be used to

characterize the texture of the input image. The entropy of the image reflects

the gray asymmetrical extent and complicated extent.

We have considered three important features-two gray scale features

namely mean and variance and one texture feature namely entropy are

calculated and used to create datasets for SVM classification.

3.4 DATASET FORMATION

As prior to classification by SVM the extracted features must be

arranged in dataset. All the images used for classification are got from

hospital. There are totally 38 images, of which 7 images are got from healthy

persons and the remaining 31 images are got from persons who are suffering

from brain tumour.

As classification by SVM consists of two phases namely: training and

testing phases, all images are used for these two phases in the following

manner:

For training phase: 11 abnormal images and 3 normal images are used.

For testing phase: 20 abnormal images and 4 normal images are used.

19

3.5 CLASSIFICATION BY SVM

3.5.1 STATISTICAL LEARNING THEORY

Learning can be thought of as inferring regularities from a set of

training examples. Various learning algorithms allow the extraction of

regularities. If the learning has been successful, these intrinsic regularities

will be captured in the values of some parameters of a learning machine.

Geometry provides a very intuitive background for the understanding and the

solution of many problems in Machine Learning.

Statistical learning theory addresses a key question that arises when

constructing predictive models from data-how to decide whether a particular

model is adequate or whether a different model would produce better

predictions. Whereas classical statistics typically assumes that the form of the

correct model is known and the objective is to estimate the model parameters,

statistical learning theory presumes that the correct form is completely

unknown and the goal is to identify mathematical form and none of them need

be correct. The theory provides a sound statistical basis for assessing model

adequacy under these circumstances, which are precisely the circumstances

encountered in machine learning, pattern recognition, and exploratory data

analysis.

Estimating the performance of competing models is the central issue in

statistical learning theory. Performance is measured through the use of loss

functions. The loss Q(z,) between a data vector z and a specific model

(one with values assigned to all parameters) is a score that indicates how well

performs on z, with lower scores indicating better performance. Statistical

Learning Theory forms the basis of classification by Support Vector Machine

(SVM).

20

3.5.2 SUPPORT VECTOR MACHINE

Support Vector Machines (SVMs) are a new supervised classification

technique that has its basis in Statistical Learning Theory .Based on machine

vision fields such as character, handwriting digit and text recognition there

has been increased interest in their application to image classification. SVMs

are non-parametric hence they boost the robustness associated with Artificial

Neural Networks and other nonparametric classifiers. The purpose of using

SVM is to obtain the acceptable results fast and easily.

The Support Vector Machine is a theoretically superior machine

learning methodology with great results in classification of high dimensional

datasets .A classification task usually involves with training and testing data

which consist of some data instances. Each instance in the training set

contains one “target value” (class labels) and several “attributes” (features).

The goal of SVM is to produce a model which predicts target value of data

instances in the testing set which are given only the attributes.

SVM functions by nonlinear projection of the training data in the input

space to a feature space of higher (infinite) dimension by use of a kernel

function φ. Then SVM identifies a linear separating hyperplane with the

maximal margin in this higher dimensional space. This process enables the

classification of remote sensing datasets which are usually nonlinearly

separable in the input space. In many instances, classification in high

dimension feature spaces results in overfitting of the input space. However, in

SVMs, overfitting is controlled through the principle of structural risk

minimization. The empirical risk of misclassification is minimised by

maximizing the margin between the data points and the decision boundary. In

21

practice this criterion is softened to the minimisation of a cost factor

involving both the complexity of the classifier and the degree to which

marginal points are misclassified. The tradeoff between these factors is

managed through a margin of error parameter which is tuned through cross-

validation procedures.

The SVM paradigm in Machine Learning presents a lot of advantages

over other approaches such as:

1) Uniqueness of the solution (as it is guaranteed to be the global minimum of

the corresponding optimization problem),

2) Good generalization properties of the solution,

3) Rigid theoretical foundation based on SLT and optimization theory,

4) Common formulation for the class separable and the class non-separable

problems as well as for linear and non-linear problems (through kernel trick).

5) Clear geometric intuition of the classification problem.

Due to these very attractive properties, SVM have been successfully

used in a number of applications.

SVM allows the construction of various learning machines by choice

of different dot products. Thus the influence of the set of function that can be

implemented by a specific learning machine can be studied in a unified frame

work.

SVM builds support vectors on results of statistical learning theory,

namely on the Structural Risk Minimisation principle guaranteeing high

generalization ability. There is reason to believe that decision rules

constructed by the support vector algorithm do not reflect incapabilities of

learning machine but rather the regularities of data.

22

Fig 3.5 SVM principle

A SVM finds the best separating (maximal margin) hyperplane

between two classes of training samples in the feature space, which is in line

with optimizing bounds concerning the generalization error. The playground

for SVM is the feature space H, which is a Reproducing Kernel Hilbert Space

(RKHS), where the mapped patterns reside (Ф: X->H). It is not necessary to

know the mapping Ф itself analytically, but only its kernel, i.e., the value of

the inner products of the mappings of all the samples (K (x1, x2) =

<Ф(x1),(x2)> for all x1, x2 є X) .Through the “kernel trick”, it is possible to

transform a nonlinear classification problem to a linear one, but in a higher

(maybe infinite) dimensional space H2. Once the patterns are mapped in the

feature space, provided that the problem for the given model (kernel) is

separable, the target of the classification task is to find the maximal margin

hyperplane.

23

Principle of Structural Risk Minimisation Technique (SRM) is an

inductive principle of use in machine learning. Commonly in machine

learning a generalized model must be selected from a finite data set, with the

consequent problem of overfitting the model becoming too strongly tailored

to the particularities of the training set and generalizing poorly to new data.

The SRM principle addresses this problem by balancing the Modd’s

complexity against its success at fitting the training data.

The functions used to project the data from input space to feature space

are called kernels.

K (xi, xj) ≡φ(xi)Tφ(xj) is called the kernel function.

3.5.3 KERNEL CLASSIFIERS

Depending on the kernel function used, SVM classifier is classified into

different types namely:

1. Linear SVM

2. Polynomial SVM

3. Radial Basis Function (RBF) SVM

4. Sigmoid SVM

Four basic kernels functions used are:

• Linear:

K(xi, xj) = xTixj.

• Polynomial:

K(xi, xj) = (γxiTxj+r)

d, γ > 0.

• Radial basis function (RBF):

K(xi, xj) = exp(−γkxi− xjk2), γ > 0.

24

• Sigmoid:

K(xi, xj) = tanh(γxiTxj+ r)

Here, γ, r, and d are kernel parameters.

In this project linear SVM classifier is used for the classification of MR

brain images.

3.5.4 LINEAR SUPPORT VECTOR MACHINE

The task of image classification is similar to the following problem:

Consider the problem of classifying m points in the n-dimensional real space

R n, represented by the m*n matrix A, according to membership of each point

Ai in the class A+ or A- as specified by a given m*m diagonal matrix D with

plus ones or minus ones along its diagonal. For this problem the standard

support vector machine with a linear kernel is given by the following

quadratic program with parameter υ>0

Here ω is the normal to the bounding planes and γ determines their

location relative to the origin. The plane ω*x+b>1 bounds the class A+

points, possibly with some error, and the plane ω*x+b>1 bounds the class A-

points, also possibly with some error. The linear separating surface is the

plane ω*x+b=0 which is the midway between the bounding planes.

25

Fig.3.6 Linear SVM

3.6 PERFORMANCE OF SVM

The performance of Linear Support Vector Machine (SVM) classifier is

to be measured to find the extent of classification of MR images. It is done by

calculating the performance measures of the classifier. The performance

measures of SVM classifier are:

1. Accuracy/Classification rate/Efficiency

2. Precision

3. Sensitivity/Recall

4. Specificity

26

Accuracy

Accuracy is the probability that a diagnostic test is correctly performed.

Accuracy = (TP + TN)/(TP + TN + FP + FN)

Precision

Precision is the probability that a diagnostic test is correctly performed,

when certain classes of images come consecutively. It is the degree of

accuracy.

Precision=TP/(TP+FP)

Sensitivity

Sensitivity (true positive fraction) is the probability that a diagnostic

test is positive, given that the person has the disease.

Sensitivity = TP/(TP + FN)

Specificity

Specificity (true negative fraction) is the probability that a diagnostic

test is negative, given that the person does not have the disease.

Specificity = TN/(TN + FP)

Where:

TP (True Positives) : Correctly classified positive cases,

TN (True Negative) : Correctly classified negative cases,

FP (False Positives) : Incorrectly classified negative cases, and

FN (False Negative) : Incorrectly classified positive cases

27

CHAPTER 4

RESULTS

4.1 RESULTS FOR TRANSFORMS

The Discrete Wavelet transform with Haar function and Gabor

transform were applied to the MR images, both normal and abnormal. The

following results were obtained.

4.1.1 DISCRETE WAVELET TRANSFORM

Fig.4.1

Wavelet transform of abnormal image

28

Fig.4.2

Wavelet transform of normal image

29

4.1.2 GABOR TRANSFORM

Fig.4.3

Gabor sub-bands

30

Fig.4.4

Gabor Transform of normal image

31

Fig.4.5

Gabor Transform of abnormal image

32

4.2 RESULTS FOR FEATURE EXTRACTION

In this the feature extraction results such as mean, variance and entropy

values for both normal and abnormal images, without and with applying

wavelet and Gabor transformations are given as follows,

Image

Mean

Without Transform Wavelet Gabor

(Sub-band 1) Horizontal Vertical Diagonal

Image 1 60.74703 0.037695 0.093213 0.000317 0.251645

Image 2 56.40564 0.046558 0.091089 0.001172 0.235427

Image 3 56.32641 0.051931 0.059011 0.005503 0.286015

Image 4 58.95343 0.049337 0.066793 0.001343 0.287435

Image 5 68.64449 0.056753 0.104955 0.00174 0.339758

Image 6 70.68972 0.062788 0.102326 0.000313 0.323999

Image 7 56.61366 0.046875 0.094604 0.000342 0.271618

Table 4.1 Normal Images – Mean

33

Table 4.2 Normal Images – Variance

Table 4.3 Normal Images – Entropy

Image

Variance

Without Transform Wavelet Gabor

(Sub-band 1) Horizontal Vertical Diagonal

Image 1 2891.725 62.92573 50.4192 2.032886 0.044661

Image 2 2369.369 57.73664 45.22733 1.953733 0.040062

Image 3 2861.059 69.58309 67.54331 3.643807 0.068496

Image 4 3059.756 69.86778 71.42149 3.549834 0.061923

Image 5 4193.412 81.61674 73.89571 3.67788 0.087613

Image 6 4173.711 80.50006 73.31604 3.333723 0.074757

Image 7 2005.429 54.35772 40.09178 2.547767 0.049764

Image

Entropy

Without Transform

Wavelet Gabor

(Sub-band 1) Horizontal Vertical Diagonal

Image 1 0.04601 1.22917 1.348253 1.525145 7.067558

Image 2 0.046103 1.243307 1.3554 1.528097 6.928274

Image 3 0.042084 1.235241 1.299876 1.497687 7.117588

Image 4 0.042005 1.224813 1.29799 1.492563 7.132964

Image 5 0.046667 1.190325 1.259527 1.465836 7.210374

Image 6 0.046762 1.191948 1.25965 1.474173 7.186631

Image 7 0.04601 1.216871 1.287355 1.49454 7.067558

34

Image

Mean

Without Transform Wavelet Gabor

(Sub-band 1) Horizontal Vertical Diagonal

Image 1 44.6699 0.043616 0.071741 0.000916 0.275158

Image 2 36.6242 0.053906 0.077075 7.32E-05 0.28023

Image 3 57.9026 0.045923 0.083789 0.002222 0.247304

Image 4 55.8079 0.038306 0.077734 0.001074 0.263427

Image 5 51.7139 0.044006 0.077087 0.000183 0.276598

Image 6 55.1247 0.046 0.067322 0.000346 0.267245

Image 7 54.1993 0.052643 0.061106 0.001516 0.28876

Image 8 53.3235 0.047933 0.073222 0.000732 0.312288

Image 9 49.8209 0.052948 0.073639 0.00294 0.332287

Image 10 56.3098 0.04066 0.058034 0.001801 0.285401

Image 11 57.4865 0.046356 0.065684 0.002879 0.27992

Image 12 76.994 0.057016 0.104016 0.002879 0.325076

Image 13 75.3437 0.052534 0.099584 0.000225 0.305669

Image 14 75.7451 0.042781 0.098295 0.001991 0.30544

Image 15 72.9491 0.048465 0.09534 0.000563 0.294071

Image 16 72.0666 0.045297 0.108248 0.001828 0.292423

Image 17 67.9041 0.050343 0.088654 0.000814 0.280234

Image 18 63.5098 0.0573 0.089111 0.000464 0.288493

Image 19 67.2230 0.047266 0.088062 0.000537 0.300335

Image 20 65.9541 0.045044 0.094971 0.004272 0.294079

Image 21 66.4657 0.054529 0.095325 8.54E-05 0.293742

Image 22 62.9119 0.055029 0.093604 0.001172 0.282132

Image 23 66.3750 0.05575 0.097644 0.001379 0.301768

Image 24 68.7174 0.057751 0.096448 0.004602 0.319182

Image 25 36.8495 0.001372 0.008499 0.001082 0.151476

Image 26 36.5772 0.002877 0.015546 0.002349 0.146255

Image 27 36.4418 0.003194 0.010505 0.002323 0.135219

Image 28 35.7769 0.005754 0.013725 0.001056 0.117068

Image 29 34.1989 0.00293 0.004408 0.001795 0.132999

Image 30 35.6062 0.006202 0.001874 0.00161 0.13789

Image 31 36.5106 0.003946 0.004025 0.000699 0.155908

Table 4.4 Abnormal Images – Mean

35

Image

Variance

Without Transform Wavelet Gabor

(Sub-band 1) Horizontal Vertical Diagonal

Image 1 3074.957 45.2334 23.89255 1.681724 0.226409

Image 2 2216.829 33.04906 16.64941 1.577053 0.22223

Image 3 2919.207 58.86982 44.82321 1.835159 0.203457

Image 4 3453.95 57.30016 37.80715 1.713261 0.216925

Image 5 3469.815 53.62047 27.9559 1.799635 0.228751

Image 6 3096.86 54.13341 41.61895 2.36158 0.221209

Image 7 3280.115 59.26085 40.41683 2.638464 0.24328

Image 8 3468.613 59.65723 39.96407 3.090099 0.267676

Image 9 3396.621 60.73324 39.6609 3.361088 0.301476

Image 10 3013.183 67.5673 68.50105 3.282204 0.249265

Image 11 3262.737 62.39801 56.1362 2.669302 0.244138

Image 12 4768.797 80.14766 70.45372 2.669302 0.275816

Image 13 4533.509 71.62744 60.21357 3.232478 0.262391

Image 14 4685.575 78.90971 63.72544 3.317919 0.268795

Image 15 4513.721 72.547 62.16007 3.181601 0.256495

Image 16 4579.436 69.05656 62.94815 3.01611 0.24539

Image 17 4306.119 60.29156 54.93299 2.56416 0.229173

Image 18 2904.708 70.198 55.69006 2.925376 0.242471

Image 19 3307.889 76.85706 64.99517 3.422935 0.250287

Image 20 3327.111 68.24504 65.98338 3.216113 0.239318

Image 21 3560.139 61.61814 62.5934 2.89766 0.235636

Image 22 3186.652 51.54247 46.8791 2.492735 0.222

Image 23 2802.463 66.34095 48.72643 2.943655 0.249485

Image 24 3172.501 79.34072 60.32123 3.514329 0.26923

Image 25 2641.164 75.10117 52.95186 3.766885 0.323131

Image 26 2780.292 72.00747 51.93181 3.444566 0.302872

Image 27 2851.483 63.2016 46.25931 2.906308 0.278063

Image 28 2927.764 45.76717 35.66286 2.058119 0.233298

Image 29 2283.569 57.25194 41.55681 2.828104 0.265601

Image 30 2417.582 66.79382 48.52081 3.271357 0.288454

Image 31 2511.656 83.11073 52.94149 3.973229 0.33414

Table 4.5 Abnormal Images – Variance

36

Image

Entropy

Without Transform Wavelet Gabor

(Sub-band 1) Horizontal Vertical Diagonal

Image 1 0.04601 1.22975 1.360388 1.518533 7.074133

Image 2 0.046057 1.229486 1.354789 1.522715 7.102217

Image 3 0.046057 1.234505 1.358728 1.52438 6.980089

Image 4 0.046057 1.231195 1.347056 1.531343 7.038835

Image 5 0.04601 1.222984 1.343129 1.525853 7.08164

Image 6 0.042044 1.237614 1.314423 1.506982 7.080376

Image 7 0.042044 1.224281 1.3119 1.49547 7.149141

Image 8 0.042163 1.220224 1.287376 1.482197 7.21587

Image 9 0.042084 1.217412 1.29642 1.48085 7.249478

Image 10 0.042044 1.233267 1.305855 1.500817 7.13097

Image 11 0.042005 1.233912 1.308709 1.509876 7.122963

Image 12 0.046667 1.183855 1.259021 1.474565 7.178054

Image 13 0.04662 1.196428 1.283083 1.485851 7.143073

Image 14 0.04662 1.20201 1.280835 1.488458 7.133883

Image 15 0.046667 1.214072 1.288439 1.495205 7.099794

Image 16 0.046667 1.2072 1.29658 1.498235 7.120152

Image 17 0.046715 1.215082 1.306171 1.510551 7.086348

Image 18 0.04601 1.207481 1.274256 1.485508 7.113188

Image 19 0.046057 1.198508 1.272535 1.470825 7.146436

Image 20 0.04601 1.200482 1.270475 1.489269 7.136099

Image 21 0.04601 1.198974 1.27809 1.487759 7.142772

Image 22 0.04615 1.208821 1.28574 1.49064 7.142772

Image 23 0.046103 1.198707 1.271244 1.485709 7.148212

Image 24 0.04601 1.190959 1.257168 1.466409 7.185435

Image 25 0.969726 0.798299 0.804175 0.877173 3.950262

Image 26 0.962768 0.777796 0.791559 0.859575 3.90922

Image 27 0.958183 0.769407 0.783881 0.857869 3.824544

Image 28 0.947184 0.764631 0.771277 0.837862 3.692486

Image 29 0.972916 0.802867 0.822998 0.89641 3.939474

Image 30 0.971439 0.805303 0.81776 0.886377 3.95897

Image 31 0.973666 0.812416 0.813293 0.888803 3.988039

Table 4.6 Abnormal Images – Entropy

37

4.3 RESULTS FOR SVM PERFORMANCE MEASUREMENT

After the feature extraction of normal and abnormal images, the

extracted results are classified using the SVM classifier with linear kernel and

the performance of SVM classifier is measured.

The performance measured without applying transforms is shown

below,

Accuracy Precision Sensitivity Specificity

73.33 73.33 100 0

Table 4.7 Performance Measures without applying transforms

4.3.1 WAVELET PERFORMANCE MEASURES

Accuracy Precision Sensitivity Specificity

Horizontal 73.3 73.3 100 0

Vertical 73.3 76.9 90.9 25

Diagonal 73.3 73.3 100 0

Table 4.8 Performance Measures of DWT based SVM

38

4.3.2 GABOR PERFORMANCE MEASURES

Sub band Accuracy Precision Sensitivity Specificity

Sub band 1 100 100 100 100

Sub band 2 73.33 76.9 90.91 25

Sub band 3 73.33 78.57 100 25

Sub band 4 73.33 78.57 100 25

Sub band 5 80 78.57 100 25

Sub band 6 73.33 73.33 100 0

Sub band 7 73.33 73.33 100 0

Sub band 8 73.33 78.57 100 25

Sub band 9 80 78.57 100 25

Sub band 10 73.33 73.33 100 0

Sub band 11 73.33 73.33 100 0

Sub band 12 73.33 73.33 100 0

Sub band 13 80 78.57 100 25

Sub band 14 86.67 100 81.81 100

Sub band 15 80 78.57 100 25

Sub band 16 73.33 73.33 100 0

Sub band 17 73.33 73.33 100 0

Sub band 18 73.33 78.57 90.9 0

Sub band 19 80 78.57 90.9 0

Sub band 20 73.33 73.33 100 0

Sub band 21 73.33 73.33 100 0

Sub band 22 80 78.57 100 25

Sub band 23 80 78.57 100 25

Sub band 24 73.33 73.33 100 0

Sub band 25 73.33 73.33 100 0

Sub band 26 73.33 73.33 100 0

Sub band 27 80 78.57 100 25

Sub band 28 80 83.33 90.9 50

Sub band 29 80 78.57 100 25

39

Sub band 30 73.33 73.33 100 0

Sub band 31 73.33 73.33 100 0

Sub band 32 80 78.57 100 25

Sub band 33 80 78.57 100 25

Sub band 34 73.33 73.33 100 0

Sub band 35 73.33 73.33 100 0

Sub band 36 73.33 73.33 100 0

Sub band 37 73.33 73.33 100 0

Sub band 38 80 78.57 100 25

Sub band 39 73.33 73.33 100 0

Sub band 40 73.33 73.33 100 0

Table 4.9 Performance Measures of Gabor based SVM

40

CHAPTER 5

COMPARISON OF RESULTS AND ANALYSIS

Performance

measures Accuracy Precision Sensitivity Specificity

Without transform 73.33 73.33 100 0

With

DWT

Horizontal 80 100 100 100

Vertical 86.67 84.6 100 50

Diagonal 86.67 100 100 100

With Gabor

transform

(Sub-band -1)

100 100 100 100

Table 5.1 Performance Measures – Comparison

After obtaining the results, they are compared with one another to

determine which provide good results. From the obtained results, the

following things are inferred:

1. If images are classified directly without applying any transform, it provided

a classification accuracy of 73.33%, but specificity becomes 0.This means

that SVM classifier finds more difficulty in recognizing the abnormal images,

when it is fed with features from untransformed images as inputs.

2. If images are classified by extracting features through wavelet transform, it

provided a classification accuracy of 73.33%, precision of 76.8% and

specificity of 25%.This means that SVM classifier finds more difficulty in

recognizing about 3/4th of abnormal images available, when it is fed with

features from wavelet transformed images as inputs.

41

3. If images are classified by extracting features through Gabor transform

with 5 scales and 8 orientations, it provided a classification accuracy of

100%,precision of 100% and specificity of 100% even in the first sub

band itself(scale-1,orientation-1).This means that SVM classifier finds more

easiness when it is fed with simply first sub band of Gabor extracted features.

42

CHAPTER 6

CONCLUSION

The real world data is generally imperfect for two reasons: one is that

the data can be incomplete for the lack of the necessary information; the other

is that data may be inaccurate, because it includes the noise and even the

wrong information.

With this incomplete real world data, how to extract the specific image

feature is still a present major issue. Feature extraction and selection are

essential in case of image classification. Once we have extracted the features,

the feature selection aiming at improving classification accuracy and reducing

the restless feature plays an important role in classification because the SVM

has its influence on classification. In this project, the proposed approach

based on linear SVM has demonstrated great potential and usefulness in MRI

image classification.

From the above analysis ,it is clear that medical images are perfectly

classified with 100% classification accuracy when they are given to Gabor

transform based Support Vector Machine (SVM) with linear kernel. Also, in

addition to 100% classification accuracy, it provides high recognition

efficiency and high speed convergence when comparing to discrete wavelet

transform based Support Vector Machine (SVM) with linear kernel. Also,

results show that Gabor extracted features provide greater and absolute

resolution to images in their classification process. These entire factors make

Gabor Transform based Support Vector Machine (SVM) with linear kernel

more efficient than other classifiers in medical image classification process.

43

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