A PSO Based method for Detection of Brain Tumors from MRI

Satish Chandra Dept. of CSE & IT

Jaypee University of IT

Waknaghat, Solan, India

satish.chandra@juit.ac.in

Rajesh Bhat Dept. of Computer Science

Indian Institute of Technology

Delhi, India

bhat.cc@iitd.ac.in

Harinder Singh Dept. of Mathematics

Jaypee University of IT

Waknaghat, Solan, India

harinder.singh@juit.ac.in

Abstract—Detection of brain tumors from MRI is a time

consuming and error-prone task. This is due to the diversity in

shape, size and appearance of the tumors. In this paper, we

propose a clustering algorithm based on Particle Swarm

Optimization (PSO). The algorithm finds the centroids of

number of clusters, where each cluster groups together brain

tumor patterns, obtained from MR Images. The results

obtained for three performance measures are compared with

those obtained from Support Vector Machine (SVM) and Ada

Boost. The performance analysis shows that qualitative results

obtained from the proposed model are comparable with those

obtained by SVM. However, to obtain better results from the

proposed algorithm we need to carefully select the different

values of PSO control parameters.

Keywords- Partcle Swarm Optimization, Support Vector

Machine, AdaBoost, MRI, Clustering.

I. INTRODUCTION

A brain tumor is an abnormal mass of tissue in which cells grow and multiply uncontrollably, seemingly unchecked by the mechanisms that control normal cells. In recent years, there has been rapid increase in the number of patients suffering from brain tumor. In spite of aggressive conventional and advanced treatments, the prognosis remains uniformly fatal. The reason is not only the rapid tumor growth but especially the fact that, long before the neoplasm can be diagnosed; it has already grossly invaded the surrounding brain parenchyma, rendering surgical removal virtually ineffective [1].

The diagnosis of brain tumors is a matter of prime concern for the medical experts because a) it is difficult to interpret from the MRI whether an evident anomaly is a tumor or not b) shortage of radiologists c) labor and cost involved d) tumors have large diversities in shape and appearance with intensities overlapping the normal brain tissues[2]. The most widely used tool for the diagnosis of brain tumors is magnetic resonance imaging (MRI). MRI is a medical imaging technique most commonly used in radiology to visualize the internal structure and function of the body. It provides a view inside the human body. The level of detail we can see is extraordinary compared with any other imaging modality. Here we present a PSO based

clustering which can be used to detect the presence of tumor pattern in MRI.

Section 2 of this paper presents a brief survey of the existing techniques for brain tumor pattern recognition. Section 3 gives a brief overview of PSO algorithm. In section 4, we present a model based on PSO for the detection of presence of the tumors. This is followed by a brief description of classification techniques used for comparing the result of the proposed model. Section 6 consists of implementation of the proposed model. Finally, the performance of the proposed model is compared with the other models.

II. RELATED WORKS

Image segmentation is the task of dividing an image into homogeneous regions. An objective function is needed for defining the homogeneity. A large number of techniques have been developed for medical image analysis in the last decade. In this section we present some of the significant approaches proposed by the researchers. Two types of learning methods have been used in image segmentation, viz, unsupervised and supervised methods.

The difference between Supervised and Unsupervised

methods is that supervised methods make use of training data that has been manually labelled, while unsupervised methods do not. The advantage of supervised methods is that relevant patterns in the data are discovered automatically, rather than through manual experimentation and intuition.

An unsupervised approach was proposed by Gibbs et al.

[3] for the segmentation of enhancing tumor pixels from

MRI. This system first applied an intensity threshold to a

manually selected region of interest, then used a region

growing algorithm to expand the threshold regions up to the

edges defined by a Sobel edge detection filter. Similar

approaches were proposed by Zhu and Yan [4] and Ho et

al.[5]. Clarke et al [6] designed a system based on Fuzzy C-

Means (FCM) and a linear sequence of knowledge- based

rules. One limitation of this system is that it requires

considerable amount of manual intervention.

666978-1-4244-5612-3/09/$26.00 c©2009 IEEE

The classification involves assigning a class, from a

finite set of classes, to an entity based on a set of features.

Supervised classification approaches involve two stages. In

first stage, called the training phase, labeled data is used to

learn a model that maps from features to labels. In the

second stage, called the testing phase labels are assigned to

unlabeled data based on the measured features. The main

contributions in these methods are of Clark, M. et al [6] and

Mazzara et al.[7]. Garcia and Moreno [8] proposed yet

another approach for automatic brain tumor segmentation

with Support Vector Machines.

Figure 1. Sample MRI images of brain. The arrows show the presence of tumors.

Ming-Ni Wu et al.[9] used a Color-Based K-Means Clustering Segmentation for the brain tumor detection. The key concept in this segmentation algorithm with K-means is to convert a given gray-level MR image into a color space image and then separate the position of tumor objects from other items of an MR image by using K-means clustering and histogram-clustering. Experiments demonstrate this method can successfully achieve segmentation for MR brain images to help pathologists distinguish exactly lesion size and region .

With the evolution and exploitation of biologically

inspired computing, a number of image clustering methods have been developed based genetic algorithms (GA) and PSO etc. Pantelis Georgiadis et al.[10] proposed a model based on Least Squares Features Transformed-Probabilistic Neural Network (LSFT-PNN) to classify between the primary and secondary brain tumors. This pattern recognition system investigates whether the use of volumetric textural features might improve brain tumor classification accuracy when analysing routinely taken MRI images. Omran et al [11] have used PSO for image clustering for the first time. In this paper we have modified the algorithm proposed by Omran et al. ANN have also been applied successfully to Image Clustering problem.

III. PARTICLE SWARM OPTIMIZATION

Particle swarm optimization is a swarm intelligence optimization technique that was inspired by the behaviour of flocks of birds [12]. It is a kind of intelligence that is based on social-psychological principles and provides insights into social behavior, as well as contributing to engineering applications. The recent years have seen tremendous growth in the use of PSO in various areas of computing ranging from networking, classification, scheduling, training of artificial neural network to feature extraction and image processing.

The advantage of PSO over many of the other optimization algorithms is its relative simplicity and ease of use. PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. The potential solutions, called particles, fly through the problem space by following the current optimum particles.

In the basic PSO a problem is given, and some way to

evaluate a proposed solution to it exists in the form of a

fitness function. A communication structure or social

network is also defined, assigning neighbors for each

individual to interact with. Then a population of individuals

defined as random guesses at the problem solutions is

initialized. These individuals are called the candidate

solutions. They are also known as the particles, hence the

name particle swarm. An iterative process to improve these

candidate solutions is set in motion. The particles iteratively

evaluate the fitness of the candidate solutions and remember

the location where they had their best success. The

individual's best solution is called the particle best or the

local best (denoted here by lbest).

A particle is attracted toward the best position it has

visited (with respect to an objective function) and towards

the best position found by the particles in its neighborhood

(this strategy is reffered to as best-of-neighborhood)[13].

Populations are organized according to some sort of

communication structure or topology, often thought of as a

social network. The topology typically consists of

bidirectional edges connecting pairs of particles, so that if j

is in i’s neighborhood, i is also in j ’s. Each particle

communicates with some other particles and is affected by

the best point found by any member of its topological

neighborhood.

Suppose that the population size is N. The position

vector and the velocity vector of particle in the -dimensional

search space can be represented as

1 2( , .... )i i i iDx x x x= and 1 2( , .... )i i i iDv v v v= respectively.

The best previous position of particle i is recorded and

represented as 1 2( , .... )i i i iDp p p p= . The best position

2009 World Congress on Nature & Biologically Inspired Computing (NaBIC 2009) 667

reached by all the particles in the population so far is

represented as 1 2( , .... )g g g gDp p p p= .

The velocity and position of the particle are changed

according to the following equation:

1 1 2 2( ) ( )id id id id gd idv wv c r p x c r p x= + − + − (1)

id id idx x v= + (2)

IV. PSO BASED MRI CLASSIFICATION MODEL

The basis of the classification of MRI images in the proposed model is that different feature types manifest different pixel values based on spectral reflectance and emittance properties. This type of classification, which is based on pixel-by-pixel spectral information (i.e. the set of radiance measures obtained in the various wavelength bands for each pixel) is referred to as spectral pattern recognition [14]. Other types of classifications are spatial and temporal pattern recognition.

A single particle represents the Nc cluster means. Each

particle xi is constructed as xi=(mi1, mi2,…, miNc). The fitness function used is given by

1 max 2 max min( , ) ( , ) ( ( ))i i i i if x Z w d Z x w z d x= + − (3)

Where, max ( , )i id Z x is the maximum average Euclidean

distance of particles to their associated classes and

min ( )id x is the minimum distance between any pair of

clusters. We propose the following image classification algorithm

which is a modified version of PSO based algorithm proposed by Omran et al.

1. Initialize each particle to contain Nc randomly

selected cluster means.

2. While ( iS -1 >δ )

a) For each particle i

i. For each pixel zp

Calculate d(zp,mij) for all clusters Cij.

Assign zp to Cij. Where

d(zp,mij)= min (c=1,2,…Nc ) d(zp,mij)

ii. Calculate fitness, f(xi(t),Z)

b) Find the global best solution ( )y t∧

c) Update the cluster cetroids using equations (1) and

(2).

In the above algorithm, zp denotes the pixels and mj

denotes the mean of cluster j. Si [15] is the silhouette validity index given by,

( ) / max( , )i i i i iS b a a b= − (4)

where a(i) is the average dissimilarity of i-particles to all other particles in the same cluster; b(i) is the minimum of average dissimilarity of i-particles to all particles in other cluster (in the closest cluster). It is followed from the formula that . If silhouette value is close to 1, it means that sample is “well-clustered” and it was assigned to a very appropriate cluster. If silhouette value is about zero, it means that that sample could be assign to another closest cluster as well, and the sample lies equally far away from both clusters. If silhouette value is close to –1, it means that sample is “misclassified” and is merely somewhere in between the clusters. The overall average silhouette width for the entire plot is simply the average of the S(i) for all

objects in the whole dataset. δ is the permissible tolerance

defined by the user. .

V. CLASSIFIERS USED FOR COMPARISION

A. Support Vector Machine(SVM)

Support vector machines are a particular family of learning machines, first introduced by Vapnik[16] as an alternative to neural networks, and that have been successfully employed to solve clustering problems, specially in biological applications. SVM are classifiers with the distinct characteristic that they aim to find the optimal hyperplane such that the expected generalization error (i.e., error for the unseen test patterns) is minimized. Instead of directly minimizing the empirical risk calculated from the training data, SVMs perform structural risk minimization to achieve good generalization (i.e., minimize an upper bound on expected generalization error). The optimization criterion is the width of the margin between the classes (i.e., the empty area around the decision boundary defined by the distance to the nearest training patterns). The goal of training a SVM is to find the separating plane with the largest margin (i.e., find the support vectors). For example, optimization of the following quadratic programming problem to find the values

for the Lagrange multipliers i associated with the

classification constraintsan optimization problem, we minimize a regularization penalty

2 2

1

|| || / 2 / 2 / 2d

T

i

j

w w w w=

= =� (5)

subject to the classification constraints as follows:

0[ ] 1T

i iy w w x+ − >0, i=1,2,…,n (6)

The attained margin is now given by 1/ || ||w . To use

support vector machines we have to specify only the inner

products (or kernel) between the examples T

ix x .

Suppose some data points are given each belong to one of two classes, and the goal is to decide which class a new data point will be in. In the case of support vector machines, a data point is viewed as a p-dimensional vector (a list of p numbers), and we want to know whether we can separate

668 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC 2009)

such points with a p – 1 -dimensional hyperplane. This is called a linear classifier.

Fig.2 Linear SVM In 1992, Bernhard Boser, Isabelle Guyon and Vapnik suggested a way to create non-linear classifiers by applying the kernel trick to maximum - margin hyperplanes.We can easily obtain classifier by mapping our examples x =[x1, x2]

into longer feature vectors reprented by ( )x .

Fig. 3 Non Linear SVM

The model used for comparision makes use of a

polynomial kernel represented by,

( , ') (1 ( '))T pK x x x x= + (7)

where p = 2, 3, . . .. To get the feature vectors we

concatenate all pth order polynomial terms of the

components of x (weighted appropriately).

The rationale behind using the polynomial kernel of

degree 3 is that the previous experiments have shown that

SVM with a linear kernel obtained the best classification

score between 80-85%, whereas SVM with polynomial

kernel of degree 3 obtained the best classification score 88-

90%.[17].

B. AdaBoost Classifier

Boosting is a general method for improving the performance of any learning algorithm . AdaBoost, short for Adaptive Boosting, is a machine learning algorithm, formulated by Yoav Freund and Robert Schapire [18]. It is a meta-algorithm, and can be used in conjunction with many other learning algorithms to improve their performance. AdaBoost is adaptive in the sense that subsequent classifiers built are tweaked in favor of those instances misclassified by previous classifiers.It consists of generating an ensemble of weak classifiers (which need to perform only slightly better than random guessing) that are combined according to an arbitrarily strong learning algorithm [19]. It has been applied with great success to several benchmark machine-learning problems using rather simple learning algorithms such as decision trees or linear regression [20].

The AdaBoost algorithm takes as input a labeled training

set, 1 1 2 2( , ) {( , ), ( , ).......( , )}n nx y x y x y x y= where

Ny

nx R∈ and { 1, 1}ny ∈ − + and calls a weak or base

learning algorithm iteratively. At each iteration, a certain

confidence weight ( )t iD x is given (and updated) to each

training sample . The weights of incorrectly classified samples are increased so that the weak learner is forced to focus on the hard patterns in the training set. The task of the

base learner reduces to find a hypothesis :th x y→ for

the distribution tD . At each iteration, the goodness of a

weak hypothesis is measured by its error

[ ( ) ( )]t t i iP h x y Di= ≠ =� (8)

Once the weak hypothesis has been calculated, AdaBoost

chooses a parameter (1/ 2) ln((1 ) / ))t t t= − .The

distribution is next updated in order to increase the weight (or importance) of samples misclassified and to decrease the weight of correctly classified patterns.

VI. EXPERIMENTAL RESULTS

A. Experimental Details

A total 110 abnormal and 62 normal axial MRI images were acquired from various hospitals of North India. All the images under study were acquired using the Siemens 0.2 or 1.5-Tesla MR Systems. For all the MRI images the pixels were extracted and their spatial coordinates and intensities were used for constructing the Gray Level Co-Occurrence Matrixes (GCM). Haralick features [21] based on GCMs was used due to their proven applicability to analyze objects with irregular outlines. From the computation of GCM ,the texture measures computed are

a) Entropy: A measure of nonuniformity in the image based on the probability of co-occurrence values.

b) Energy: A measure of homogeneity . c) Difference moment: A measure of contrast.

2009 World Congress on Nature & Biologically Inspired Computing (NaBIC 2009) 669

d) Inverse Difference Moment: A measure of local homogeneity.

e) Correlation: A measure of linear dependency of brightness.

The three classifiers were applied on all the MRI

images and results of classification were recorded. The parameters of PSO were varied so as to give the best results. The effect of changing the parameters of PSO is given in Table 2. The result of classification may yield four types of classes namely, True Positive(TP), False Positive(FP), True Positive(TP) and True Negative(TN). The contingency table for classification is given in Table 1.

Table 1. Contingency table

Real Group Classificaion Result

Normal Abnormal

Normal TN FP

Abnormal FN TP

B. Performance Comparision

The most commonly used performance measures in classification are Precision and Recall. Precision can be seen as a measure of exactness or fidelity, whereas Recall is a measure of completeness. In a statistical classification task, the Precision for a class is the number of true positives (i.e. the number of items correctly labeled as belonging to the positive class) divided by the total number of elements labeled as belonging to the positive class (i.e. the sum of true positives and false positives, which are items incorrectly labeled as belonging to the class). Recall in this context is defined as the number of true positives divided by the total number of elements that actually belong to the positive class (i.e. the sum of true positives and false negatives, which are items which were not labeled as belonging to the positive class but should have been).

In a classification task, a Precision score of 1.0 for a class C means that every item labeled as belonging to class C does indeed belong to class C (but says nothing about the number of items from class C that were not labeled correctly) whereas a Recall of 1.0 means that every item from class C was labeled as belonging to class C (but says nothing about how many other items were incorrectly also labeled as belonging to class C) [22]. The formula for precision and recall are given by Precision= TP / (TP+FP) * 100 Recall= TP / (TP + FN) * 100 Also, Accuracy= (TP + TN) / (TP + TN + FP +FN) * 100 Error= 1- Precision

C. Comparision Results

As we are interested only in the detection of brain tumors present in MRI images, we do not present the values obtained for the fitness function, quantization error, dmax, ,

dmin etc. We report the statistics of correctly classified images only. The result of comparison for various classifiers is given in Table 2.

Table2. Classification Results for Various algorithms

Classifier Precision (%)

Recall( %)

Accuracy( %)

Proposed PSO Based algorithm 92.76 96.24 94.42

SVM (Polynomial kernel) 93.33 95.28 92.71

AdaBoost 90.25 91.66 89.31

VII. CONCLUSIONS

A modified version of PSO based algorithm is proposed

for the classification of MRI images. The performance analysis shows that qualitative results obtained from the proposed model are comparable with those obtained by SVM. However, in order to obtain better results from the proposed algorithm we need to carefully select the different values of PSO control parameters.

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