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Khushboo Singh, Satya Verma / International Journal of Engineering Research and Applications
                         (IJERA)           ISSN: 2248-9622       www.ijera.com
                               Vol. 2, Issue 4, June-July 2012, pp.724-726
           Detecting Brain Mri Anomalies By Using Svm Classification
                                       Khushboo Singh*, Satya Verma**
                                     *(Department of Computer Science, CSVTU, BHLAI
                                    ** (Department of Computer Science, CSVTU, BHLAI



 ABSTRACT                                                         these defective image are further investigated for the
          This research paper proposes an intelligent             detection of anomalies. This is for separating abnormal
classification technique to identify anomalies present in         image from the data collection containing both normal and
brain MRI. The manual interpretation of anomalies                 abnormal image. This results in significant cost and time
based on visual examination by radiologist/physician              saving. The motivation behind this paper is to develop a
may lead to missing diagnosis when a large number of              machine classification process for evaluating the
MRIs are analyzed. To avoid the human error, an                   classification performance of different classifiers to this
automated intelligent classification system is proposed           problem in terms of statistical performance measure.
which caters the need for classification of image slices
after identifying abnormal MRI volume, for anomalies
                                                                  II. OVERVIEW OF SVM LEARNING FOR
identification. In this research work, advanced
classification techniques based on Support Vector                 CLASSIFICATION
Machines (svm) are proposed and applied to brain                            The Support Vector Machine algorithm was first
image classification using features derived. SVM is a             developed in 1963 by Vapnik and Lerner [3] and Vapnik
artificial neural network technique used for supervised           and Chervonenkis [4] as an extension of the Generalized
learning of classification. This classifier is compared           Portrait algorithm. This algorithm is firmly grounded in the
with other pre store images for detecting the anomalies.          framework of statistical learning theory – Vapnik
From this analysis, The performance of svm classifier             Chervonenkis (VC) theory, which improves the
was evaluated in terms of classification accuracies and           generalization ability of learning machines to unseen data
the result confirmed that the proposed method has                 [5] [6]. In the last few years Support Vector Machines have
potential in detecting the anomalies.                             shown excellent performance in many real-world
                                                                  applications including hand written digit recognition [7],
                                                                  object recognition [8], speaker identification [9], face
Keywords – anomalies ,classification, detecting, MRI,
                                                                  detection in images [10] and text categorization [11]. SVM
SVM
                                                                  is a classification algorithm based on kernel methods [12],
                                                                  [13] and [14]. SVM very attractive is that classes which are
I. INTRODUCTION
                                                                  nonlinearly separable in the original space can be linearly
          The field of medical imaging gains its importance
                                                                  separated in the higher dimensional feature space. Thus
with increase in the need of automated and efficient
                                                                  SVM is capable of solving complex nonlinear
diagnosis in a short period of time .Computer and
                                                                  classification problems. Important characteristics of SVM
Information Technology are very much useful in medical
                                                                  are its ability to solve classification problems by means of
image processing, medical analysis and classification.
                                                                  convex quadratic programming (QP) and also the
Medical images are usually obtained by X-rays and recent
                                                                  sparseness resulting from this QP problem. The learning is
years by Magnetic Resonance (MR) imaging. Magnetic
                                                                  based on the principle of structural risk maximization.
Resonance Imaging (MRI) is used as a valuable tool in the
                                                                  Instead of minimizing an objective function based on the
clinical and surgical environment because of its
                                                                  training samples (such as mean square error), the SVM
characteristics like superior soft tissue differentiation, high
                                                                  attempts to minimize the bound on the generalization error
spatial resolution and contrast. It does not use harmful
                                                                  (i.e., the error made by the learning machine on the test
ionizing radiation to patients [1, 2].Magnetic Resonance
                                                                  data not used during training). As a result, an SVM tends
Images are examined by radiologists based on visual
                                                                  to perform well when applied to data outside the training
interpretation of the films to identify the presence of
                                                                  set. SVM achieves this advantage by focusing on the
anomalies . The shortage of radiologists and the large
                                                                  training examples that are most difficult to classify. These
volume of MRI to be analyzed make such readings labor
                                                                  “borderline” training examples are called support vectors.
intensive, cost expensive and often inaccurate. The
                                                                  In this paper, we treat image classification as a two class
sensitivity of the human eye in interpreting large numbers
                                                                  pattern classification problem. We apply all the MRI image
of images decreases with increasing number of cases,
                                                                  to classifier to determine whether the anomalie is present
particularly when only a small number of image are
                                                                  or not. We refer to these two classes throughout as “white”
affected. Hence there is a need for automated systems for
                                                                  and “non-white” image. The problem is how to construct a
analysis and classification of such medical images .
                                                                  classifier [i.e., a decision function f(x)] that can correctly
          The MRI may contain both normal image and               classify an input pattern x that is not necessarily from the
defective image. The defective or abnormal image are              training set.
identified and separated from the normal image and then               i.    Linear SVM classifier

                                                                                                                724 | P a g e
Khushboo Singh, Satya Verma / International Journal of Engineering Research and Applications
                         (IJERA)           ISSN: 2248-9622       www.ijera.com
                               Vol. 2, Issue 4, June-July 2012, pp.724-726
Let us begin with the simplest case, in which the training
patterns are linearly separable. That is, there exists a linear                          MR
function of the form                                                                     imag
f(x) = w T x + b (1)                                                                     e
such that for each training example xi, the function
yields ( ) ≥ 0 i f x for = +1, i y                                                    classification
           and f(xi)<0 for yi=-1.
In other words, training examples from the two different
classes are separated by the hyperplane
f(x) = w T x + b =0,                                                                   comparison
where w is the unit
vector and
 b is a constant.
For a given training set, while there may exist many                                    Pattern
hyperplanes that maximize the separating margin between                                 matching
the two classes, the SVM classifier is based on the
hyperplane that maximizes the separating margin between
the two classes (Figure 1). In other words, SVM finds the                                Detected
hyperplane that causes the largest separation between the                              slice/output
decision function values for the “borderline” examples
from the two classes. In Figure 1, SVM classification with        Figure 2. MR Image slices Classification
a hyperplane that minimizes the separating margin between
the two classes are indicated by data points marked by “X”        IV. PROPOSED METHODOLOGY
s and “O”s. Support vectors are elements of the training set                The proposed methodology of classifying MR
that lie on the boundary hyperplanes of the two classes.          image of human brain is shown in Figure 2.The method
                                   Optimal Hyperplane             uses the steps of classification Comparison and pattern
                                                                  matching. Significant difference observed in variety of
                                                                  textural measurements in MR image, is used for this
                   Hyperplane                                     classification. The various measurements based on
                       Maximum Margin                             statistical matrix textural features from the MR images are
                              Hyperplane                          given as input to the classifiers for training. If the features
                                                                  of new slices are given as input, the trained classifier can
                                                                  able to classify it.
                                                                  The classifiers such as Support Vector classifiers of neural
                                                                  network classifiers analyzed.
                              Class 1                                 i.    MR image data
                                   Class 2                                  Magnetic Resonance Imaging (MRI) uses
                                                                  magnetic energy and radio waves to create images
                                                                  (“slices”) of the human body. MR imaging measures the
                                                                  magnetic properties of nuclei within the body tissues. The
         Figure 1. SVM classification                             energy absorbed by the nuclei is then released, returning
                                                                  the nuclei to their initial state of equilibrium and this
III. PROBLEM IDENTIFICATION                                       transmission of energy by the nuclei is observed as the
         The conventional method in medicine for brain            MRI signal.MR images are generated by the resonating
MR images classification and anomalies detection is               nuclei for each spatial location. The image gray level in
human inspection. Operator-assisted classification methods        MRI mainly depends on three tissue parameters viz.,
are impractical for large amounts of data and are also non-       proton density (PD), spin-lattice (T1) and
reproducible. MR images also always contain a noise               spin-spin (T2) relaxation time [15]. Generally, for most of
caused by operator performance which can lead to serious          the soft tissues in the body, the proton density is very
inaccuracies classification. The MR images data is by             homogenous but may exhibit higher intensity for gray
nature, a huge, complex and cognitive process. Accurate           matter. T1 and T2 are sensitive to the local environment;
diagnosis of MR images data is not an easy task and is            they are used to characterize different tissue types. T1, T2
always time consuming. In some extreme scenario,                  and PD type images are mostly used by different
diagnosis with wrong result and delay in delivery of a            researchers [16, 17] for different MR applications.
correct diagnosis decision could occur due to the
complexity and cognitive process of which it is involved.            ii.    Classifier used for comparison
                                                                  Support Vector Machine: Support Vector Machine offers
                                                                  an extremely powerful method of obtaining models for
                                                                  classification [18]. They provide a mechanism for
                                                                  choosing the model structure in a manner which gives low

                                                                                                                 725 | P a g e
Khushboo Singh, Satya Verma / International Journal of Engineering Research and Applications
                              (IJERA)           ISSN: 2248-9622       www.ijera.com
                                    Vol. 2, Issue 4, June-July 2012, pp.724-726
generalization risk and empirical risk. The idea behind the     [6]    V. Vapnik, “The Nature of Statistical Learning
support vector machines is to look at the RBF network as a             Theory”, Springer, New York 1995.
mapping machine, through the kernels, into a high               [7]    B. Scholkopf, S. Kah-Kay, C. J. Burges, F. Girosi,
dimensional feature space. The output of an SVM is a                   P. Niyogi, T. Poggio, and V.Vapnik, “Comparing
linear combination of the training examples projected onto             support vector machines with Gaussian kernels to
a high-dimensional feature space through the use of kernel             radial basis function classifiers,” IEEE trans
functions.                                                             Signal Processing, vol. 45, pp. 2758-2765, 1997.
                                                                [8]    M. Pontil and A. Verri, “Support vector machines
V. IMPLENTATION OF PROPOSED                                            for 3-D object recognition,” IEEE Trans. pattern
METHODOLOGY                                                            anal. Machine Intel., vol. 20,pp. 637-646, 1998.
      i.  MR image data                                         [9]    V. Wan and W.M Campbell, “Support vector
          The image used in this work, were taken from                 machines      for    speaker     verification  and
internet. This are 2 dimension image with black and white              identification,” in Proc. IEEE Workshop Neural
colour. Any random images of brain were considered in                  Networks for Signal Processing, Sydney,
this work.                                                             Australia, pp. 775-784, 2000.
   ii.    Training & Testing Data                               [10]   E. Osuna, R. Freund, and F. Girosi, “Training
          The MRI image slices were grouped into two                   support vector machines: Application to face
classes, namely normal and abnormal depending on the                   detection,” in Proc. Computer Vision and Pattern
anomalies present in the image. The MRI data set contains              Recognition,Puerto Rico, pp. 130-136, 1997.
150 image (120 abnormal slices and 20 normal slices) and        [11]   T. Joachims, “Transductive inference for text
from which two different sets are grouped to have biased               classification using support vector machines,”
and unbiased                                                           published at the Int. Conf.Machine Learning,
training of classifier and other are used for testing.                 Slovenia, 1999.
  iii.    Classifier                                            [12]   B. Schölkopf and A. J. Smola, “Learning with
          The MRI were classified using KULeuven’s                     Kernels”, MIT Press, 2002.
MATLAB SVM matlab toolbox used for classification.              [13]   T. Hastie, R. Tibshirani, J. Friedman, “The
Various parameters of the classifiers are selected. In our             Elements of Statistical Learning”, New York,
study, the SVM – classifier, the value of the standard                 Springer Verlag, 2003.
deviation (σ ) is used.                                         [14]   N. Cristianini and J. Shawe-Taylor, “An
  iv.     Performance measures                                         Introduction to Support Vector
          Result of classification could have an error rate            Machines”,Cambridge, U.K, Cambridge Univ.
and on occasion will either fail to identify an abnormality,           Press,2000.
or identify an abnormality which is not present.                [15]   S.C. Bushong, “Magnetic Resonance Images
                                                                       physical and biological principles”.Mosby Year
VI. CONCLUSION AND FUTURE WORK                                         Book, New York, NY, 1996.
This experiment can detect the first object of class which is   [16]   N. B. Karayiannis and Pin-I Pai, “Segmentation
fail to identify the other abnormalities present in the                of Magnetic Resonance Images Using Fuzzy
image.Focusing on the various features of the object or                Algorithms for Learning Vector Quantization”,
anomalies. Different parameter should help to find out                 IEEE Transactions On Medical Imaging, Vol.
anomalies. More than one object should be detected.                    18,No. 2, pp. 172-180, 1999.
                                                                [17]   C. A. Cocosco, A P. Zijdenbos, A. C. Evan,“A
           REFERENCES                                                  Fully Automatic and Robust Brain MRI Tissue
                                                                       Classification Method”, Medical Image Analysis.
[1]           J. G. Webster, Ed., Medical Instrumentation:             Vol.7. No. 4, pp. 513 –527, 2003.
             Application and Design New York: John Wiley &      [18]   C. J. C. Burges, “A tutorial on support vector
             Sons, Inc., pp. 551-555,1998.                             machines for pattern recognition”,Data Mining
[2]          E. Haack, et al., Magnetic Resonance Imaging,             and Knowledge Discovery,2(2):121–167, 1998.
             Physical Principles and Sequence Design.
             Wieley-Liss, New York, 1999.
[3]          V. Vapnik and A. Lerner, “Pattern recognition
             using generalized portrait method”, Automation
             and Remote Control,24, 1963.
[4]          V. Vapnik and A. Chervonenkis, “A note on class
             of perceptron”, Automation and Remote Control,
             24 1964.
[5]          A. J. Smola and B. Schoelkopf, “A tutorial on
             support      vector     regression”,NeuroCOLT2
             Technical Report Series NC2-TR-1998-030,
             ESPRIT working group on Neural and
             Computational Learning Theory, NeuroCOLT2,
             1998.
                                                                                                          726 | P a g e

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Detecting Brain MRI Anomalies Using SVM Classification

  • 1. Khushboo Singh, Satya Verma / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, June-July 2012, pp.724-726 Detecting Brain Mri Anomalies By Using Svm Classification Khushboo Singh*, Satya Verma** *(Department of Computer Science, CSVTU, BHLAI ** (Department of Computer Science, CSVTU, BHLAI ABSTRACT these defective image are further investigated for the This research paper proposes an intelligent detection of anomalies. This is for separating abnormal classification technique to identify anomalies present in image from the data collection containing both normal and brain MRI. The manual interpretation of anomalies abnormal image. This results in significant cost and time based on visual examination by radiologist/physician saving. The motivation behind this paper is to develop a may lead to missing diagnosis when a large number of machine classification process for evaluating the MRIs are analyzed. To avoid the human error, an classification performance of different classifiers to this automated intelligent classification system is proposed problem in terms of statistical performance measure. which caters the need for classification of image slices after identifying abnormal MRI volume, for anomalies II. OVERVIEW OF SVM LEARNING FOR identification. In this research work, advanced classification techniques based on Support Vector CLASSIFICATION Machines (svm) are proposed and applied to brain The Support Vector Machine algorithm was first image classification using features derived. SVM is a developed in 1963 by Vapnik and Lerner [3] and Vapnik artificial neural network technique used for supervised and Chervonenkis [4] as an extension of the Generalized learning of classification. This classifier is compared Portrait algorithm. This algorithm is firmly grounded in the with other pre store images for detecting the anomalies. framework of statistical learning theory – Vapnik From this analysis, The performance of svm classifier Chervonenkis (VC) theory, which improves the was evaluated in terms of classification accuracies and generalization ability of learning machines to unseen data the result confirmed that the proposed method has [5] [6]. In the last few years Support Vector Machines have potential in detecting the anomalies. shown excellent performance in many real-world applications including hand written digit recognition [7], object recognition [8], speaker identification [9], face Keywords – anomalies ,classification, detecting, MRI, detection in images [10] and text categorization [11]. SVM SVM is a classification algorithm based on kernel methods [12], [13] and [14]. SVM very attractive is that classes which are I. INTRODUCTION nonlinearly separable in the original space can be linearly The field of medical imaging gains its importance separated in the higher dimensional feature space. Thus with increase in the need of automated and efficient SVM is capable of solving complex nonlinear diagnosis in a short period of time .Computer and classification problems. Important characteristics of SVM Information Technology are very much useful in medical are its ability to solve classification problems by means of image processing, medical analysis and classification. convex quadratic programming (QP) and also the Medical images are usually obtained by X-rays and recent sparseness resulting from this QP problem. The learning is years by Magnetic Resonance (MR) imaging. Magnetic based on the principle of structural risk maximization. Resonance Imaging (MRI) is used as a valuable tool in the Instead of minimizing an objective function based on the clinical and surgical environment because of its training samples (such as mean square error), the SVM characteristics like superior soft tissue differentiation, high attempts to minimize the bound on the generalization error spatial resolution and contrast. It does not use harmful (i.e., the error made by the learning machine on the test ionizing radiation to patients [1, 2].Magnetic Resonance data not used during training). As a result, an SVM tends Images are examined by radiologists based on visual to perform well when applied to data outside the training interpretation of the films to identify the presence of set. SVM achieves this advantage by focusing on the anomalies . The shortage of radiologists and the large training examples that are most difficult to classify. These volume of MRI to be analyzed make such readings labor “borderline” training examples are called support vectors. intensive, cost expensive and often inaccurate. The In this paper, we treat image classification as a two class sensitivity of the human eye in interpreting large numbers pattern classification problem. We apply all the MRI image of images decreases with increasing number of cases, to classifier to determine whether the anomalie is present particularly when only a small number of image are or not. We refer to these two classes throughout as “white” affected. Hence there is a need for automated systems for and “non-white” image. The problem is how to construct a analysis and classification of such medical images . classifier [i.e., a decision function f(x)] that can correctly The MRI may contain both normal image and classify an input pattern x that is not necessarily from the defective image. The defective or abnormal image are training set. identified and separated from the normal image and then i. Linear SVM classifier 724 | P a g e
  • 2. Khushboo Singh, Satya Verma / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, June-July 2012, pp.724-726 Let us begin with the simplest case, in which the training patterns are linearly separable. That is, there exists a linear MR function of the form imag f(x) = w T x + b (1) e such that for each training example xi, the function yields ( ) ≥ 0 i f x for = +1, i y classification and f(xi)<0 for yi=-1. In other words, training examples from the two different classes are separated by the hyperplane f(x) = w T x + b =0, comparison where w is the unit vector and b is a constant. For a given training set, while there may exist many Pattern hyperplanes that maximize the separating margin between matching the two classes, the SVM classifier is based on the hyperplane that maximizes the separating margin between the two classes (Figure 1). In other words, SVM finds the Detected hyperplane that causes the largest separation between the slice/output decision function values for the “borderline” examples from the two classes. In Figure 1, SVM classification with Figure 2. MR Image slices Classification a hyperplane that minimizes the separating margin between the two classes are indicated by data points marked by “X” IV. PROPOSED METHODOLOGY s and “O”s. Support vectors are elements of the training set The proposed methodology of classifying MR that lie on the boundary hyperplanes of the two classes. image of human brain is shown in Figure 2.The method Optimal Hyperplane uses the steps of classification Comparison and pattern matching. Significant difference observed in variety of textural measurements in MR image, is used for this Hyperplane classification. The various measurements based on Maximum Margin statistical matrix textural features from the MR images are Hyperplane given as input to the classifiers for training. If the features of new slices are given as input, the trained classifier can able to classify it. The classifiers such as Support Vector classifiers of neural network classifiers analyzed. Class 1 i. MR image data Class 2 Magnetic Resonance Imaging (MRI) uses magnetic energy and radio waves to create images (“slices”) of the human body. MR imaging measures the magnetic properties of nuclei within the body tissues. The Figure 1. SVM classification energy absorbed by the nuclei is then released, returning the nuclei to their initial state of equilibrium and this III. PROBLEM IDENTIFICATION transmission of energy by the nuclei is observed as the The conventional method in medicine for brain MRI signal.MR images are generated by the resonating MR images classification and anomalies detection is nuclei for each spatial location. The image gray level in human inspection. Operator-assisted classification methods MRI mainly depends on three tissue parameters viz., are impractical for large amounts of data and are also non- proton density (PD), spin-lattice (T1) and reproducible. MR images also always contain a noise spin-spin (T2) relaxation time [15]. Generally, for most of caused by operator performance which can lead to serious the soft tissues in the body, the proton density is very inaccuracies classification. The MR images data is by homogenous but may exhibit higher intensity for gray nature, a huge, complex and cognitive process. Accurate matter. T1 and T2 are sensitive to the local environment; diagnosis of MR images data is not an easy task and is they are used to characterize different tissue types. T1, T2 always time consuming. In some extreme scenario, and PD type images are mostly used by different diagnosis with wrong result and delay in delivery of a researchers [16, 17] for different MR applications. correct diagnosis decision could occur due to the complexity and cognitive process of which it is involved. ii. Classifier used for comparison Support Vector Machine: Support Vector Machine offers an extremely powerful method of obtaining models for classification [18]. They provide a mechanism for choosing the model structure in a manner which gives low 725 | P a g e
  • 3. Khushboo Singh, Satya Verma / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, June-July 2012, pp.724-726 generalization risk and empirical risk. The idea behind the [6] V. Vapnik, “The Nature of Statistical Learning support vector machines is to look at the RBF network as a Theory”, Springer, New York 1995. mapping machine, through the kernels, into a high [7] B. Scholkopf, S. Kah-Kay, C. J. Burges, F. Girosi, dimensional feature space. The output of an SVM is a P. Niyogi, T. Poggio, and V.Vapnik, “Comparing linear combination of the training examples projected onto support vector machines with Gaussian kernels to a high-dimensional feature space through the use of kernel radial basis function classifiers,” IEEE trans functions. Signal Processing, vol. 45, pp. 2758-2765, 1997. [8] M. Pontil and A. Verri, “Support vector machines V. IMPLENTATION OF PROPOSED for 3-D object recognition,” IEEE Trans. pattern METHODOLOGY anal. Machine Intel., vol. 20,pp. 637-646, 1998. i. MR image data [9] V. Wan and W.M Campbell, “Support vector The image used in this work, were taken from machines for speaker verification and internet. This are 2 dimension image with black and white identification,” in Proc. IEEE Workshop Neural colour. Any random images of brain were considered in Networks for Signal Processing, Sydney, this work. Australia, pp. 775-784, 2000. ii. Training & Testing Data [10] E. Osuna, R. Freund, and F. Girosi, “Training The MRI image slices were grouped into two support vector machines: Application to face classes, namely normal and abnormal depending on the detection,” in Proc. Computer Vision and Pattern anomalies present in the image. The MRI data set contains Recognition,Puerto Rico, pp. 130-136, 1997. 150 image (120 abnormal slices and 20 normal slices) and [11] T. Joachims, “Transductive inference for text from which two different sets are grouped to have biased classification using support vector machines,” and unbiased published at the Int. Conf.Machine Learning, training of classifier and other are used for testing. Slovenia, 1999. iii. Classifier [12] B. Schölkopf and A. J. Smola, “Learning with The MRI were classified using KULeuven’s Kernels”, MIT Press, 2002. MATLAB SVM matlab toolbox used for classification. [13] T. Hastie, R. Tibshirani, J. Friedman, “The Various parameters of the classifiers are selected. In our Elements of Statistical Learning”, New York, study, the SVM – classifier, the value of the standard Springer Verlag, 2003. deviation (σ ) is used. [14] N. Cristianini and J. Shawe-Taylor, “An iv. Performance measures Introduction to Support Vector Result of classification could have an error rate Machines”,Cambridge, U.K, Cambridge Univ. and on occasion will either fail to identify an abnormality, Press,2000. or identify an abnormality which is not present. [15] S.C. Bushong, “Magnetic Resonance Images physical and biological principles”.Mosby Year VI. CONCLUSION AND FUTURE WORK Book, New York, NY, 1996. This experiment can detect the first object of class which is [16] N. B. Karayiannis and Pin-I Pai, “Segmentation fail to identify the other abnormalities present in the of Magnetic Resonance Images Using Fuzzy image.Focusing on the various features of the object or Algorithms for Learning Vector Quantization”, anomalies. Different parameter should help to find out IEEE Transactions On Medical Imaging, Vol. anomalies. More than one object should be detected. 18,No. 2, pp. 172-180, 1999. [17] C. A. Cocosco, A P. Zijdenbos, A. C. Evan,“A REFERENCES Fully Automatic and Robust Brain MRI Tissue Classification Method”, Medical Image Analysis. [1] J. G. Webster, Ed., Medical Instrumentation: Vol.7. No. 4, pp. 513 –527, 2003. Application and Design New York: John Wiley & [18] C. J. C. Burges, “A tutorial on support vector Sons, Inc., pp. 551-555,1998. machines for pattern recognition”,Data Mining [2] E. Haack, et al., Magnetic Resonance Imaging, and Knowledge Discovery,2(2):121–167, 1998. Physical Principles and Sequence Design. Wieley-Liss, New York, 1999. [3] V. Vapnik and A. Lerner, “Pattern recognition using generalized portrait method”, Automation and Remote Control,24, 1963. [4] V. Vapnik and A. Chervonenkis, “A note on class of perceptron”, Automation and Remote Control, 24 1964. [5] A. J. Smola and B. Schoelkopf, “A tutorial on support vector regression”,NeuroCOLT2 Technical Report Series NC2-TR-1998-030, ESPRIT working group on Neural and Computational Learning Theory, NeuroCOLT2, 1998. 726 | P a g e