Performance Analysis Of Multi Source Fused Medical Images Using Multiresolution Transforms

Image fusion combines information from multiple images of the same scene to get a composite image that is more suitable for human visual perception or further image-processing tasks. In this paper the multi source medical images like MRI (Magnetic Resonance Imaging), CT (computed tomography) & PET (positron emission tomography) are fused using different multi scale transforms. We compare various multi resolution transform algorithms, especially the latest developed methods, such as; Non Subsampled Contourlet Transform, Fast Discrete Curvelet, Contourlet, Discrete Wavelet transform and Hybrid Method (combination of DWT & Contourlet) for image fusion. The fusion operations are performed with all Multi resolution transforms. The fusion rules like local maxima and spatial frequency techniques are used for selection in the low frequency and high frequency subband coefficients, which can preserve more information and quality in the fused image. The fused output obtained after the inverse transform of fused sub band coefficients. The experimental results show that the effectiveness of fusion approaches in fusing multi source images. f n m n m n m


INTRODUCTION
The Image fusion is the process of combining information from two or more images of a scene into a single composite image which is more informative and is more suitable for visual perception or computer processing.The objective in the image fusion is to reduce uncertainty and minimize redundancy in the output, while maximizing relevant information particular to an application or task as well.Given the same set of input images, different fused images may be created depending on the specific application and what is considered as relevant information.There are several benefits in using image fusion: wider spatial and temporal coverage with decreased uncertainty, improved reliability and increased robustness of system performance [Ref.3].
The medical images like MRI and CT provides highresolution images with structural and anatomical information.PET images provide functional information with low spatial resolution.In the recent years, the success of MRI-CT, PET The rest of the paper is organized as follows: Section 2 explains Multiscale transforms.Section 3 presents generic fusion model.Section 4 explains the proposed method.Section 5 the discussion on the experimental results.In the laconic section, the paper is concluded.

A. Discrete Wavelet Transform
Discrete Wavelet transform (DWT) provides a framework in which a signal is decomposed, with each level corresponding to lower frequency sub band, and higher frequency sub bands.There are two main groups of transforms: continuous and discrete.In one dimension the idea of the wavelet transform is to present the signal as a superposition of wavelets.If a signal is represented by f (t), the wavelet decomposition is

Where
, m and n are integers.There exist very special choices of such that constitutes an ortho normal basis, so that the wavelet transform coefficient can be obtained by an inner calculation: (2.2) In order to develop a multiresolution analysis, a scaling function is needed, together with the dilated and translated parameters of .The signal can be decomposed in its coarse part and details of various sizes by projecting it onto the corresponding spaces.
Therefore, the approximation coefficients of the a n m, www.ijacsa.thesai.orgfunction at resolution and wavelet coefficients can be obtained: Where is a low pass FIR filter and is a high pass FIR filter.To reconstruct the original signal, the analysis filter can be selected from a biorthogonal set which have a related set of synthesis filters.These synthesis filters and can be used to perfectly reconstruct the signal using the reconstruction formula (2.5) Equations (2.3) and (2.4) are implemented by filtering and down sampling.Conversely equation (2.5) is implemented by an initial up sampling and a subsequent filtering.In the filter theory, these four sub images correspond to the outputs of low-low (LL), low-high (LH), high-low (HL), and high-high (HH) bands.By recursively applying the same scheme to the LL sub band multi resolution decomposition with a desire level can then be achieved.There, a DWT with K decomposition levels will have M=3*K+1 such frequency bands.

B. Contourlet Transform
The contourlet transform is first developed in continuous domain and then is discretized for sampled data; contoured transform starts with a discrete domain construction.The contourlet is also deemed as a "true" two dimensional transform that can capture the intrinsic geometrical structure of an image.Two filter banks are employed to implement the contoured transform as shown in Fig. 2.
The Laplacian pyramid is first used to capture the point discontinuities, and then a directional filter bank is used to link point discontinuities into linear structures.As the DWT, the contoured transform also has no shift invariant property because of the down-sampling operation.Do and Vetterli found that to obtain a sparser representation for 2-D piecewise smooth functions in R2, an effective method is to utilize a double filter bank scheme, that is, first apply a multiscale decomposition to capture point discontinuities and then perform a local directional decomposition to synthesize the nearby edge points into independent contour segments.
With a rich set of basis oriented at various directions and scales, contourlet can effectively capture the intrinsic contours and edges in natural images that set radiational multiresolution analysis methods are difficult to handle.Contourlet offer s a much richer sub band set of different directions and shapes, which helps to capture geometric structures in images much more efficiently [Ref.7].

C. Non Subsampled Contourlet Transform (NSCT)
In the foremost contourlet transform down samplers and up samplers are presented in both the laplacian pyramid and the Directional Filter Bank (DFB).Thus, it is not shift-invariant, which causes pseudo-Gibbs phenomena around singularities.NSCT is an improved form of contourlet transform.It is motivated to be employed in some applications, in which redundancy is not a major issue, i.e. image fusion.In contrast with contourlet transform, non subsampled pyramid structure and non subsampled directional filter banks are employed in NSCT.The non subsampled pyramid structure is achieved by using two-channel non subsampled 2-D filter banks.The DFB is achieved by switching off the downsamplers/up samplers in each two-channel filter bank in the DFB tree structure and up sampling the filters accordingly.As a result, NSCT is shiftinvariant and leads to better frequency selectivity and regularity than contourlet transform.Fig. 3 shows the decomposition framework of contourlet transform and NSCT [Ref.11].The NSCT structure consists in a bank of filters that splits the 2-D frequency plane in the subband; these are a non subsampled pyramid structure that ensures the Multiscale property and a non subsampled directional filter bank structure that gives directionality [Ref.15].

A. Curvelet Transform
The DWT, SWT, and DTCWT cannot capture curves and edges of images.More reasonable bases should contain geometrical structure information when they are used to represent images.Candes and Donoho proposed the Curvelet transform (CVT) with the idea of representing a curve as a superposition of bases of various lengths of width obeying the scaling width ≈ length .The CVT is referred to as the ""true" 2D transform.The discrete version implemented in this is a ""wrapping" transform.The second generation of Curvelet transform is presented in Fig: 4. Firstly, the 2D FFT is applied to the source image to obtain Fourier samples.Next, a discrete localizing window smoothly localizes the Fourier transform near the sheared wedges obeying the parabolic scaling.Then, the wrapping transformation is applied to re-index the data.Finally, the inverse 2D FFT is used to obtain the discrete CVT coefficients [Ref.16].The key issue in spatial domain algorithms is identifying the most important information in source images and fusing the salient information into the fused image [Ref.8].This paper includes the average pixel method and PCA method.The fusion rules are explained in the following sections.

A. Fusion rule of lower sub band coefficients
The coefficients in the coarsest scale sub band represent the approximation component of the source image.It is a smooth and sub sampled version of the original image.Therefore, most of the source images information is kept in low frequency bands.The proposed selection principles for the sub band coefficients are finally defined as the maximum selection rule is:

B. Fusion rule of higher sub band coefficients
The highpass sub band coefficients represent the detailed components of the source image; according to characteristic of HVS.So, it is easy to find that for the high resolution region the human visual interest is concentrated on the detection of changes in between regional contrast.Then spatial frequency measures in the overall activity an image is present.Therefore, we propose a scheme by computing the spatial frequency method in a neighbourhood to select the high frequency coefficients.The spatial frequency (SF), is originated from the HVS, indicates the overall active level in an image and measure the variation of pixels [9].For an M x N image I, with gray value I (i, j) at position (i, j) the spatial frequency is defined as Where RF and CF are the row frequency and column frequency respectively: :  Compare the obtained fused image from various transforms with different evaluation parameters from equation (6.1-6.10).

VI. EXPERIMENTAL RESULTS AND ANALYSIS
To evaluate the performance of the multi scale transforms, several experimental results are presented in this section.Experiments are performed on three different multisource images MRI, CT & PET.The MRI and PET images are downloaded from the Harvard university site (http:// www.med.harvard.edu/AANLIB/ home.html).Similarly the CT and MRI images are downloaded from www.imagefusion.orgwebsite link.The proposed method is applied to these image sets.To show the effectiveness of the multi scale transform the comparisons start with simple basic average method, PCA (principal component analysis) method and Brovery method under spatial domain techniques and DWT [Ref.[13][14]    A. Peak Signal to Noise Ratio (PSNR) PSNR (Peak Signal to Noise Ratio) is a metric for the ratio between the maximum possible power of a signal and power of corrupting noise that affects the fidelity of its representation.It is used to measure the quality of reconstructed images.(6.1)Where and are the pixel values of the ideal reference and the obtained fused image, respectively.M and N are the dimensions of the images.

B. Mutual Information (MI)
Mutual information of two random variables is a quantity that measures the mutual dependence of the two variables.Here, MI RI F measures the information that reference and the fused image shares: Where is the normalized joint gray level histogram of images R and I F , and are the normalized marginal histograms of the two images.
The mutual information I AF between the sources images A and the fused image F is defined as follows: Where P AF is the jointly normalized histogram of A and F, P A and P F are the normalized histogram of A and F, and a f represent the pixel value of the image A and F, respectively.The mutual information I BF between the source image B and the fused image F are similar to I AF .The mutual information between the source images A, B, and the fused image F is the sum of I AF and I BF , i.e. (6.4)

C. Gradient and Wrap
The gradient value and wrap values are facilitate the correlation between the resultant F and reference R images.If gradient value is high and wrap value is low then the two images are more correlated.The gradient and warp are defined as follows: 2 Where M and N are size of the image.

D. Effective Great Degrees
This is because that the metrics Q AB/F and Q 0 mainly measure the amount of salient information transferred from source images into the fused image [Ref.17].The metric Q AB/F is defined as follows: (6.7) The dynamic range of Q AB/F is [0 1], and it should be as close to 1 as possible.
Another metric Q O is as follows: (6.8)Where represents the coherence between A and F, denote the standard deviation of A and F: , represent the mean value of A and F respectively, similarly calculate Q o (B,F) using above equation then finally the Q 0 value is as follows: (6.9) The Q 0 range is -1≤ Q 0 ≤1 and it should be also as close to 1 as possible.

E. Correlation
It computes the correlation coefficient between fused image F and reference image R. to computes the correlation coefficient using following equation: (6.10)Where and are mean values of fused and reference images respectively.

VII. CONCLUSION
In this paper, performance analysis is compared with different multi scale transforms for the fusion of multi source images.The fusion procedure is discussed with different subband fusion rules to obtain fused image from different multi sources.The obtained fusion results are compared with different evaluation parameters.The comparison of transform methods are starts with those of the pixel averaging, PCA method and Brovery methods.Finally those compared with DWT, Contourlet, Hybrid Method (is combination of DWT & Contourlet), Fast Discrete Curvelet and NSCT fusion methods.We calculated and analyzed tools such as; PSNR, MI, Effective great degrees, gradient, wrap, standard deviation, mean and entropy values.
-MRI [Ref.1]& PET-CT [Ref.6]imaging in the clinical field triggered considerable interest in noninvasive functional and anatomical imaging.The limited spatial resolution in PET images is often resulted unsatisfactory in morphological analysis.Combining anatomical and functional tomography datasets provide much more qualitative detection and quantitative determination in this area [Ref .1,Ref .10].So far, several fusion algorithms based on multi source medical images have been proposed.The MRI-CT image fusion using edge preserved technique proposed by Xianghi et al, based on multi scale toggle contrast operator [Ref .4].The MRI-PET image fusion proposed by Sabalan Daneshvar et al based on combining HIS (Hue Intensity Saturation model) and retina models improve the functional and spatial information content [Ref .1].The CT-PET image fusion proposed by Yuhui Liu et al, based on multi wavelet transform adds more details and structure information [Ref .6].

Fig 1 :
Fig 1: Structure of 2-D DWT 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 result in one set of approximation coefficients and three set of detail coefficients, as shown in Fig 1, where , , represent the horizontal, vertical and diagonal directions of the image , respectively.

Fig 4 :
Fig 4: The second generation of Curvelet transforms III.HYBRID METHOD The hybrid method can be referred from [Ref.2, Ref.17] references.In this paper reference [Ref.17]method is considered as basic method to do further comparisons.IV.GENERIC MODEL OF MULTISCALE-BASED IMAGE FUSION In this paper, there are two different input medical source images A and B (like MRI & CT, MRI & PET, CT & PET).The image fusion algorithm should preserve all the salient features of source images.Fig 5 illustrates the generic image fusion frame work based on Multiscale image decomposition methods.The source images are firstly decomposed into lowfrequency sub bands and a sequence of high-frequency sub bands in different scales and orientations.Then the fusion coefficients are obtained from sub bands according to fusion rules.Finally, fused image is reconstructed by applying inverse transform on the fused sub bands.

Fig 5 :
Fig 5: Block diagram of generic model of multi scale image fusion


ijacsa.thesai.orgEach image is partitioned into BxB blocks.The said blocks value varies according to the interest of the user, we consider 8x8 as a block size to obtain more accurate values.Then, compare the spatial frequencies of two corresponding coefficient values in each blocks of and to construct the new block of fused image . of Multiscale transform method has accomplished the following Steps:  Decompose the source images A and B into low frequency subband and a series of high frequency sub bands at L levels by using various Multiscale transforms.Fuse the low frequency subband coefficients and high frequency subband coefficients according to lower subband fusion rule equation (4.1) and higher subband fusion rules equation (4.2-4.5). Reconstruct the original image based on the new fused coefficients of sub bands by taking respective inverse Multiscale Transform, thus fused image is obtained.
, Contourlet Transform[Ref.5],Hybrid Method is combination of DWT & Contourlet [Ref.2,Ref.12] and Non subsampled contourlet transform in transform domain techniques.The fused image output based on different methods is shown from Fig 6 -8.The performances of fused medical images are shown in Fig: 9 using Multiscale transform with different evaluation parameters.
Appendix A and The graphical representation of all performance evaluation parameters are hown below (Fig 9):

Fig: 9 :
Fig: 9: Performance of fused medical image using different Multiscale transforms with different evaluation parameters.