DCT and Nural Netwrk

2013 International Conference on Signal Processing, Image Processing and Pattern Recognition [ICSIPRj

Brain Tumor Classification U sing Discrete Cosine Transform and Probabilistic Neural Networl<

D. SRIDHAR, Associate Professor Balaji Institute of Technology and Science, Warangal

Andhra pradesh, India. [email protected]

Abstract - In this paper, a new method for Brain Tumor Classification using Probabilistic Neural Network with Discrete Cosine Transformation is proposed. The conventional method for computerized tomography and magnetic resonance brain images cIassification and tumor detection is by human inspection. Operator assisted cIassification methods are impractical for large amounts of data and are also non reproducible. Computerized Tomography and Magnetic Resonance images contain a noise caused by operator performance which can lead to serious inaccuracies in cIassification. The use of Neural Network techniques shows great potential in the field of medical diagnosis. Hence, in this paper the Probabilistic Neural Network with Discrete Cosine Transform was applied for Brain Tumor Classification. Decision making was performed in two steps, i) Dimensionality reduction and Feature extraction using the Discrete Cosine Transform and ii) cIassification using Probabilistic Neural Network (PNN). Evaluation was performed on image data base of 20 Brain Tumor images. The proposed method gives fast and better recognition rate when compared to previous cIassifiers. The main advantage of this method is its high speed processing capability and low computational requirements.

Keywords - Brain tumor image cIassification, Probabilistic Neural Networks, Discrete Cosine Transform, Dimensionality Reduction, Feature Extraction.

I. INTRODUCTION

A brain tumor is an intracranial solid neoplasm or abnormal growth of cells within the brain or the central spinal canal. Brain tumor is one of the most COlnmon and deadly diseases in the world . Detection of the brain tumor in its early stage is the key of its cure. There are many different types of brain tumors that make the decision very complicated [1]. So classification of brain tumor is very important, in order to classify which type of brain tumor really suffered by patient. A good classification process leads to the right decision and provide good and right treatment. Treatments of various types of brain tumor are mostly depending on types of brain tumor. Treatment may different for each type, and usually determined by:

o Age, overall health, and medical his tory o Type, location, and size of the tumor o Extent of the condition oTolerance for specific medications, procedures, or therapies o Expectations for the course of the condition

978-1-4673-4862-1/13/$31.00 2013 IEEE

N. MURALI KRISHNA, Chief Consultant Offshore Programs in Asia,Jackson State University, USA

Hyderabad, India. [email protected]

o Opinion and preferences Classification of tumor is to identify what type of tumor it

iso The conventional methods, which are present in diagnosis, are Biopsy, Human inspection, Expert opinion and etc. The biopsy method takes around ten to fifteen days of time to give a result about tumor. The human prediction is not always correct, sometimes it becomes wrong but a computer cannot. The expert, hirnself cannot take the decision rather he refers to another expert to give his opinion, this process continues for long time [1] - [4].

In general, early stage brain tumor diagnose mainly includes Computed Tomography (CT) scan, Magnetic Resonance Imaging (MRl) scan, Nerve test, Biopsy etc [3]. At present with the rapid growth of the Artificial Intelligence (AI) development in Biomedicine, computer-aided diagnosis attracts more and more attention. In this paper, based on the power of Probabilistic Neural Network (PNN) , a computeraided brain tumor classification method is proposed. It utilized the feed-forward neural network to identify which type of brain tumor suffered by patient regarding to the image of brain tumor from the Magnetic Resonance Imaging (MRl) and Computed Tomography (CT) scan as inputs for the network.

In detecting the brain tumor type of each patient, doctor usually refer MRl image and make the report about the MRl analysis of the patient. This method will help doctor in diagnosing brain tumor patients. With the existence of proposed system, doctor can train the system with some known data and then, use this system to generate the MRl report of the patient after testing the data. The Flow chart of the proposed method is shown in figure 1.

In any classification system Dimensionality Reduction and Feature Extraction are very important aspects [7]. Images though small in size are having large dimensionality this leads to very large computational time, complexity and memory occupation. The performance of any classifier mainly depends on high discriminatory features of the images [8]. In the proposed method we used Discrete Cosine Transform for both dimensionality reduction and feature extraction.

The rest of this paper is organized as follows: Section 11 discusses computation of Discrete Cosine Transform for Brain Tumor images. Section III describes the PNN classifier. Section IV shows experimental results, and discusses possible

2013 International Conference on Signal Processing, Image Processing and Pattern Recognition [ICSIPRj 2

modifications and improvements to the system. Section V presents concluding remarks.

Train Data

DimensioDality ReductioD

u.singDCT

Testing usiog PNN

C IassificatioD

TestD:da

DimensionaJity ReductioD usiog

DCT

Figurei, Flow chart for the proposed method

11. DISCRETE COSINE TRANSFORM

Discrete Cosine Transform is a discrete sinusoidal unitary trans form consists of a set of basis vectors that are sampled eosine functions. Images have high correlation and redundant information which causes computational burden in terms of processing speed and memory utilization. The DCT has the property that, for a typical image, most of the visually significant information is concentrated in just a few coefficients. These coefficients can be used as a type of signatures that are useful for face recognition tasks [5],[6].

The DCT of an M x N gray scale matrix of the face image f (x, y) is defined as follows:

M -I N -I T (u , v ) = L L f (x, y)x (u )a (v)x

x=O y=o [ (2 x + 1 )u 1< ] [ (2 y + l)v 1< ] COS cos 2M 2N

Where a (u ) =

for u = 0 for u = 1,2,o o .,M-l

(1)

(2)

The values T (u, v) are the DCT coefficients. This technique is efficient for small square inputs such as image blocks of 8 x 8 pixels.

III. PROBABILISTIC NEURAL NETWORK

Probabilistic Neural Network is a type of Radial Basis Function (RBF) network, which is suitable for pattern classification. The basic structure of a probabilistic neural network is shown in figures 2 and 3. The fundamental

architecture has three layers, an input layer, a pattern layer, and an output layer. The pattern layer constitutes a neural implementation of a Bayes classifier, where the class dependent Probability Oensity Functions (POF) are approximated using a Parzen estimator[9]-[ 15]. Parzen estimator determines the POF by minimizing the expected risk in classifying the training set incorrectly. Using the Parzen estimator, the classification gets closer to the true underlying class density functions as the number of training sampies increases,

The pattern layer consists of a processing element corresponding to each input vector in the training set. Each output class should consist of equal number of processing elements otherwise a few classes may be inclined falsely leading to poor classification results. Each processing element in the pattern layer is trained once. An element is trained to return a high output value when an input vector matches the training vector. In order to obtain more generalization a smoothing factor is included while training the network.

The pattern layer classifies the input vectors based on competition, where only the highest match to an input vector wins and generates an output. Hence only one classification category is generated for any given input vector. If there is no relation between input patterns and the patterns programmed into the pattern layer, then no output is generated.

Input

Figure 2, Probabilistic Neural Network.

Pattern Layer

Compared to the feed forward back propagation network, training of the probabilistic neural network is much simpler. Since the probabilistic networks classify on the basis of Bayesian theory, it is essential to classify the input vectors into one of the two classes in a Bayesian optimal manner. This theory provides a cost function to comprise the fact that it may be worse to misclassify a vector that is actually a member of class A than it is to misclassify a vector that belongs to class


B. The Bayes rule classifies an input vector belonging to class A as,

(3)

Where, PA - Priori probability of occurrence of patterns in class A CA - Cost associated with classifying vectors

JA(x) - Probability density function of class A

The PDF estimated using the Bayesian theory should be positive and integratable over all x and the result must be 1. The probabilistic neural net uses the following equation to estimate the probability density function given by,

fA (x ) = ( y, 1

2n 2([ " m n

I

exp l - 2 ( x - X A ' X - X A, ) J Where

XAi - ith training pattern from class A

n - Dimension of the input vectors

(4)

(J - Smoothing parameter (corresponds to standard deviations

of Guassian distribution)

The functionJA (x) acts as an estimator as long as the parent density is smooth and continuous. JA (x) approaches the parent density function as the number of data points used for the estimation increases. The functionJA(x) is a sum of Guassian distributions.

Summatilm Un

Figure 3, Architecture of Probabilistic Neural Network.

IV. NUMERICAL RESULTS

Pattern Unttl

The proposed new method was applied on Brain Tumor image database containing 5 classes and each class having 4 images of size 70 x 60 with different background conditions. For simulations and proposed method evaluation Matlab is

used on a PC with Intel(R) core (TM) 2 Duo CPU and 2 GB RAM. The obtained results for tow databases are given separately as folIows.

Brain tumor image database is shown in figure 4 and its normalized version is shown in figure 5. Before doing simulation size of the brain tumor images are reduced to 4 x 4. These reduced size images are used as inputs to the Discrete Cosine Transform and it gives 16 features per image as output. For this database the graph drawn between Image size vs recognition rate is shown in figure 7 and the graph drawn between number of features per sampie (Sampie dimension) vs recognition rate is shown in figure 8. From these figures it is clear that Image size of 4x4 with sampie dimension 6 is giving maximum recognition rate of 100%.

Training set

Figure 4, Brain Tumor Image Databse

N onnalized Training Set

Figure 5, Normalized Brain Tumor Image Databse


Test Image E quivalentImage

Figure 6(a), Class I

Test Image Equ ivaJentImage

Figure 6(b), Class 2

Test Image E quivalentImage

Figure 6( c), Class 3

Test Image Equivalent Image

Figure 6(d), Class 4

Test Image E quivaJentImage

Figure 6( e), Class 5

Plot of % Recognition verses Image size 101,-----,------,-----,------,-----,-----,

1 00_81------+-------+---.... --- .... --.... .. 1 .. --.... - .. --...... .......... f .. - .......... -.......... + .......... .......... ....

100_ 6 1------+-------+--------------------+.-----------... --...... ---.... ;- --- .. ---.... --.... ---.... --+--- ... -..... --..... -..... -

100.4 1------+---- :.:::: 100_2 1------+-------- ------------------- ---------... --c: 100 1------+---------_+------1__----+_-u 0) 99_81------+----

99_61------+------ ------------------

99.4 1------+---- -- _ ... _ ... _ .. _ ... _ ..

99_2 1-----+--------- ---------------------

994-------- 8---- 10--12----14-- 16

I m ag e size Figure 7, Plot of Recognition Rate verses image size

The feature vectors of the brain tumor images obtained at the output of the Discrete eosine Transform are given to the Probabilistic Neural Network for classification. Probabilistic Neural network (PNN) gives fast and accurate classification of Brain tumor images. The test sampies from 5 classes and there equivalent images obtained from the classifier are shown in figure 6(a) to 6(e). In simulation three different combinations of training and test image sampies are used as

i) 15 training images and 5 test images ii) 10 training images and lOtest images iii) 5 training images and 15 test images

Simulation was done with the above three sets of data and the obtained results are summarized in the tabular form as shown in table 1.


No of No of Training Sampies per class No of Test Sampies Recognition Rate classes Sampies Sampies per class (Max)

5 15 3 5 1 100 5 10 2 10 2 100 5 5 1 15 3 100

Table - I Recognition Rate for different Training and Test sampies for AT &T (ORL) database

Plot of % Recognition verses SampIe dimension 100

90 / 1/

80

70 0

1----+-.----+--.. -.. -... -- .---... -.. -.. -.. -.. ---... -.....

I u Q) '#. 60

50

I 1----.---++---+-_ .. _ .. _ .. _- .---.. -.. -.. -.. -.. ---... -..... \ I 1----1-++---+-.. -.. -.. - .. . -.. -.-.. -.. -. .-.-.. -..... \ I 40 0 2 4 6 10 12 14 16

Sample dimen s ion

Figure 8, Plot of Recognition Rate versed Sampie dimension

No of features per image used in Discrete Cosine Transform as input = 16 No of features per image used for classification = 6

For 15 training sampies, the average training time taken is 3.2760 sec. For 5 test sampies the average testing time taken is 1.076 sec that means 0.2152 sec time is taken for the testing of one sampie. This is very small classification time when compare to any other Neural Network classification time.

VI. CONCLUSION

In this paper, a new method for Brain Tumor Classification is presented. This new method is a combination of Discrete Cosine Transform and Probabilistic Neural Network. By using these algorithms an efficient Brain Tumor Classification method was constructed with maximum recognition rate of 100%. Simulation results using Brain Tumor database demonstrated the ability of the proposed method for optimal feature extraction and efficient Brain Tumor classification.

The ability of our proposed Brain Tumor Classification method is demonstrated on the basis of obtained results on

Brain Tumor image database. For generalization, the proposed method should achieve 100% Recognition rate on other Brain Tumor image databases and also on other combinations of training and test sampies. In the proposed method only 5 classes of Brain tumors are considered, but this method can be extended to more classes of Brain tumors.

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