Discrete Wavelet Transform Based Medical Image ...

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International Journal of Systems , Algorithms & Applications

Discrete Wavelet Transform Based Medical Image Fusion using Spatial frequency Technique Roopa Maddali, 2Dr.K.Satya Prasad, 3CH.Hima Bindu 1 PG Student, ECE Department, QIS College of Engineering & Technology, Ongole, India. 2 Assoc.Professor, ECE Department, QIS College of Engineering and Technology, Ongole,India. 3 Rector & Professor in ECE Department, JNTUK, Kakinada, Andhra Pradesh, India. e-mail: [email protected], [email protected], [email protected] 1

construction filter bank. The input discrete sequence x is convolved with high-pass and low-pass analysis filters aH and aL, and each result is down sampled by two, yielding the transformed signals xH and xL. The signal is reconstructed through up-sampling and convolution with high and low synthesis filters sH and sL. For properly designed filters, the signal x is reconstructed exactly (y=x).

Abstract - This paper proposed an efficient image fusion algorithm for fusing medical images with the help of DWT & Spatial frequency techniques. The basic DWT is initially applied to obtain fine &coarse details of an image. For fusing the individual image coefficients are undergo different fusion techniques. In the case of low frequency coefficients are obtained with maximal absolute value and then the high frequency coefficients are selected by spatial frequency technique. Then the resultant image is reconstructed by using the Inverse wavelet transform .The quality of the fused output is measured by using mutual information and peak signal to noise ratio. Keywords: Image fusion, Discrete Wavelet Transform, Spatial Frequency

I. INTRODUCTION Image fusion is the process of combining relevant information from two or more images into single image. The resulting image should be more informative than any one of input images[2]. Fusion process can be performed at different levels of information representation stored in ascending order of abstraction: Signal, pixel, feature and symbol levels. The simplest multifocal image fusion is to take the average of the gray level source images pixel by pixel .This technique would produce several undesired effects and reduce feature contrast. To overcome this problem mulitresolution techniques are used.

Fig 1. A two-channel perfect-reconstruction filter bank.

In a 2-D DWT, a 1-D DWT is first performed on the rows and then columns of the data by separately filtering and down sampling. This results in one set of approximation coefficients and three sets of detail coefficients, which represent the horizontal, vertical and diagonal directions of image. In the language of filter theory, these four sub images correspond to the outputs of low-low (LL), low-high (LH), highlow (HL), high-high (HH) bands. Fig (2) Shows one level decomposition of an image f(x,y) in to four subbands LL, LH, HL, HH. Therefore, a DWT with N decomposition levels will have M = 3 N +1 such frequency bands [1]. Fig.2 shows the 2-D structures of the wavelet transform with one decomposition level.

The multiresolution techniques involve two kinds, one is pyramid transform another is wavelet transform. The typical examples of pyramid method are laplacian pyramid and the gradient pyramid. However for the reason of the pyramid method fails to introduce any spatial orientation selectivity in the decomposition process, the above mentioned methods often cause blocking effects in the fusion results. Another family of the mulitresolution fusion techniques is the wavelet based method, which usually used the discrete wavelet transform (DWT) in the fusion [4].

LL L

LH

F(x,y) HL H

The organization of this paper is as follows ,the section II explains 2-D DWT.In section III Introduction and importance of image fusion in medical images is discussed .In section IV the methodology for proposed method and implementation is explained. Finally in section V experimental results are shown.

ICRAET12|April 29-30,2012|Hyderabad|India

2 HH

Fig 2. 2-D DWT multiresolution image decomposition.

The expression for 2D Discrete Wavelet transform of the image is given by F(x,y) 1

II. DISCRETE WAVELET TRANSFORM Wavelet transforms provide a framework in which a signal is decomposed, with each level corresponding to a coarser resolution or lower frequency band, and higher frequency bands. The original concept and theory of wavelet-based multiresolution analysis came form haar [1].Fig. 1 illustrates the elements of a one-dimensional, two-channel perfect re-

Volume 2, Issue ICRAET12, May 2012, ISSN Online: 2277-2677

2

a

 xm yn , dxdy b   a

  f ( x, y ) 

….. (1) Where m,n are shifting parameters and a is the scaling parameter ψ(m,n) is Haar wavelet function.

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Discrete Wavelet Transform Based Medical Image Fusion using Spatial frequency Technique

Spatial frequency measures the overall activity level in an image. for an M x N image block X,with gray value X(m, n) at position (m, n) the spatial frequency is defined as

Fig. 3 illustrates the elements of a two-dimensional, twochannel perfect reconstruction filter bank. LL1

LH1

HL1

HH1


2 2 ( RF )  ( CF )

SF 

……..

(3)

... ...

(4)

…...

(5)

Where RF and CF are the row frequency

RF 

Fig.3.DWT structure with labeled sub bands

1 M N 2   X (m, n)  X (m, n 1) MN m 1 n  2

And Column frequency

III. IMAGE FUSION Digital image technology has been widely used in medical fields. However these medical images can only show parts of human tissues clearly because of limitations of imaging principles. People hope to fuse images which contain complementary information into one image and make the fused image preserve all useful information and can provide clinical diagnosis and surgical design with references[5]. According to theoretical models of HVS, we know that the human eyes have different sensitivities, to the wavelet coefficients of low resolution bands and high frequency bands [3].

CF 

1 N M 2  X (m, n)  X (m 1, n) MN n1m2

respectively. Fusion of high frequency bands of X and Y images consist of following steps Step 1: Decompose LH, HL, HH bands of image x and y in to several 3x3, 8x8, 16x16 blocks. Step 2: Calculate spatial frequency of each block of every Image. Step 3: Compare spatial frequencies of two corresponding Blocks XLL and YLL and construct the ith block Z Of the fused image as

The general fusion process is accomplished by the following steps Step1: The images to be fused must be registered to assure the corresponding pixels are aligned. Step 2: These images are decomposed into wavelet transformed images respectively, based on the wavelet transformation. The transformed images include one low frequency portion (low-low band) and three high frequency portions (low-high bands, high-low bands, and high-high bands). Step 3: The transform Coefficients of two images are fused based on low and high subband fusion rules. Step 4: The fused image is constructed by performing an inverse wavelet transform based on resultant transform coefficients from step 3.

X  X LL ( m , n ) SF LL  SF YLL  TH  X Y Y LL ( m , n ) SF LL  SF LL  TH  Z LL ( m , n )   X LL ( m , n )  Y LL ( m , n )  Otherwise  2   

……. (6)

TH is user defined threshold value. Apply the same above rule for ZHL,ZHH also.

IV. THE PROPOSED FUSION METHOD In this paper, as our main objective is to fuse the CT and MR images, the characteristics of the images should be considered CT image supports clear bones information but no soft tissues information, while contrast to CT images the MR image provides clear soft tissues information but no bones information. Consider only two source images, X and Y, and the fused image Z. The fusion method is as follows. a) Low Frequency Band Fusion Since the low frequency band is the original image at coarser resolution level, it can be considered as a smoothed and sub sampled version of the original image. Based on the pervious analysis of the characteristics of the CT & MR images, here for the low frequency band, a maximum-selection (MS) fusion rule to produce a single set of coefficients is used firstly. The scheme selects the largest absolute wavelet coefficient at each location from the input images as the coefficient at that location in the fused image[1]:

Z LL = max X LL (m, n), YLL (m, n) 

…. (2) b) High frequency Band Fusion For the high frequency bands, since the purpose of the image fusion requires that the fused image must not discard any useful information contained in the source images and effectively preserve the details of input images such as edges and textures. Volume 2, Issue ICRAET12, May 2012, ISSN Online: 2277-2677 ICRAET12|April 29-30,2012|Hyderabad|India

Fig. 4. Schematic diagram of proposed method

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The larger the value of mutual information the better is the fusion result. b) PEAK SIGNAL TO NOISE RATIO The more subjective qualitative measurement of distortion is the Peak Signal –to-Noise Ratio (PSNR).It uses a constant value in which to compare the against instead of a fluctuating signal as in SNR. Fig.5. Fusion Process for LL band

PSNR  10 log

2

255

1 2   (G(m,n) Z (m,n)) MN

(10)

. TABLE1: EVALUATION OF FUSED IMAGE

Fusion Method

PSNR

MI

DWT with Pixel Averaging

15.3410

1.1183

DWT with Maximum Selec on (MS)Rule 20.6102 DWT with MS and Spa al Frequency Rule (Proposed Meth-

24.5996

1.2241 2.8180

The following figure shows two input images CT,MRI and their fused image by using mentioned techniques in table 1.

Fig. 6. Fusion Process for High frequency band

V. EXPERIMENTAL RESULTS The proposed method is implemented in latest version of MATLAB and it is simulated. The CT and MRI images are downloaded from www.metapix.com site. After Simulation the results along with figures are outlined as follows. The experiment is performed on different MRI &CT scan images of body. The same experiment also performed on nearly 10 different medical images. The following table provides the comparison between existed methods and proposed method. By observing this, the proposed method is giving better results than existed methods. Two criteria considered are:

(a)

(c)

a) MUTUAL INFORMATION It is a metric defined as the some of MI between each source image and fused image. Considering two source images X & Y and fused image Z .

I

Z,X

(Z , X ) 

P

Z,X

( Z , X ) log

P (Z , X ) P ( z ) P ( x)

….(7)

X

P Z ,Y ( Z , Y ) I Z ,Y ( Z , Y )   P Z ,Y ( Z , Y ) log P Z (z) PY ( y)

…….(8)

Where PX,PY and PZ are probability density function in the images X, Y and Z respectively .PZ,X and PZ,Y are joint probability functions. Thus the image fusion performance measure can be defined as

MI  I Z , X Z , X   I Z ,Y Z , Y 

……..

Volume 2, Issue ICRAET12, May 2012, ISSN Online: 2277-2677 ICRAET12|April 29-30,2012|Hyderabad|India

(d )

(e)

VI. CONCLUSION In this paper ,we proposed a new approach for medical image fusion by using the spatial frequency .The main importance of proposed scheme is to obtain more information in fused image. Extensive experiments on studying the fusion performance with different block sizes and thresholds have been made. The results shows that the proposed methods is superior both quantitatively and visually.

Z,X

Z

(b)

VII. ACKNOWLEDGMENT The first and second author would like to express their cordial thanks to QIS College of Engineering and Technology, Management for providing facilities to carry this work.

(9)

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M.Roopa is currently doing P.G. course in DECS branch in QIS College of Engineering & Technology, Ongole.

VIII. REFERENCES [1] Yong Yang , Dong Sun Park,Shuying Huang , Zhijun Fang, Zhengyou Wang.”Wavelet based Approach for fusing Computed Tomography and Magnetic Resonance Images.”, 2009 IEEE, pp.5770-5772. [2] Nemir Ahmed Al-Azzawi,Harsa Amylia Mat Sakim,Ahmed Kwan Abdullah “An efficient medical Image fusion Method Using Contourlet Transform Based on PCM”. Industrial Electronics & Applications, 2009. ISIEA 2009. IEEE Symposium,Kuala Lumpur.pp.11-14. [3] Ling Tao,Zhi-Yu Qian.”An Improved Medical Image Fusion Algorithm Based on Wavelet Transform.” Natural Computation (ICNC), 2011 Seventh International Conference . Shanghai. pp.76 – 78. [4] Yong Yang “ Multimodal Medical Image FusionThrough a New DWT Based Technique”. Bioinformatics and Biomedical Engineering (iCBBE), 2010 4th International Conference , Chengdu ,pp.1-4. [5] Xiaoli Zhang,Xiongfei Li,Zhaojun Liu . “An expert Knowledge weighted model for evaluating medical image fusion” .Computer Science and Service System (CSSS), 2011 International Conference anjing.pp.2035 – 2038. [6] V.P.S Naidu and J.R Raol . “Pixel- level Image Fusion Using Wavelets and Principals Component Analysis”. Int Defense science Journal, Vol 58, No-3, May 2008, pp , 384-352, DESIDOC. National Aerospace Laboraties, Bangalore-160017.

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Ch.Hima bindu is currently working as Associate Professor in ECE Department, QIS College of Engineering & Technology, ONGOLE, Andra Pradesh, India. She is working towards her Ph.D. at JNTUK, Kakinada, India. She received her M.Tech. from the same institute. She has ten years of experience of teaching undergraduate students and post graduate students. She has published 10 research papers in International journals and more than 8 research papers in National & International Conferences. Her research interests are in the areas of image Segmentation, image Feature Extraction and Signal Processing. Dr.K.Satya Prasad is currently Rector and Professor in ECE Department, JNTUK, Kakinada, India. He received his Ph.D. from IIT, Madras. He has more than 32 years of experience in teaching and 25 years of R & D. He is an expert in Digital Signal Processing. He guided 10 PhD’s and guiding 10 PhD scholars. He authored Electronic Devices and Circuits, Network Analysis and Signal & Systems text books. He held different positions in his carrier like Head of the Department, Vice Principal, Principal for JNTU Engg College and Director of Evaluation & presently the Rector of JNTUK.. He published more than 100 technical papers in national and International journals and conferences. The area of interest includes Digital Signal Processing, Image Processing, Communications etc.

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