Application of Image Fusion Techniques on Medical Images

Transcription

1 Internationa Journa of Current Engineering and Technoogy E-ISS , P-ISS IPRESSCO, A Rights Reserved Avaiabe at Research Artice Appication of Image usion Techniques on Medica Images Richa Gautam * and Shipa Datar Department of Eectronics and Communication Engg. Samrat Asho Technoogica Institute, Vidisha, RGPV, Madhya Pradesh, India Accepted 0 eb 07, Avaiabe onine eb 07, Vo.7, o. (eb 07) Abstract Image fusion finds numerous appications in remote sensing, sateite imaging, medica imaging etc. In medica science, in order to diagnose a disease, it is required that the image obtained from a particuar modaity shoud be highy informative and shoud have high accuracy and aso it shoud have high spatia as we as high spectra resoution. However, most of the avaiabe modaities aone are not capabe of doing it convincingy. To sove this probem, a technique caed image fusion has been evoved, in which two or more images are fused together to mae a new image. In medica image fusion two or more images obtained from different modaities are fused together to give us a desired image. Seection of fusion rue shoud be such that it must provide us a the reevant information and at the same time does not introduce any undesired features to the resuting image. In this paper we have proposed a method for fusing CT (Computed Tomography) and MRI (Medica Resonance Imaging) images based on second generation curveet transform. Proposed method is compared with the resuts obtained after appying the other methods based on Discrete Waveet Transform (DWT), Principa Component Anaysis (PCA), and Discrete Cosine Transform (DCT). Entropy, Standard Deviation, Pea Signa to oise Ratio (PSR), Percentage it Error (PE) and Spatia requency (S) are used as performance metric evauators. Keywords: Image fusion, CT, MRI, Second Generation Curveet Transform, DWT, PCA, Entropy, SD, PSR, PE, S.. Introduction Basic meaning of the image fusion is to fuse two or more images obtained from different modaities to produce a new image that is more informative than the source images. An image consists of different features. We can broady categorize them into textures and edges. Image obtained from one modaity is good at providing some specific information. or exampe CT image provides information about dense hard tissues whereas MRI provides information about soft tissues. So, in order to get mutipe information in a singe image, image fusion is done. A good image fusion technique shoud be capabe of providing compementary information and discarding the redundant one. Broady there are two cassifications of image fusion agorithms. irst one is spatia domain methods ie IHS (Intensity Hue Saturation) [Hongbo Wu, Yanqiu Xing, et a, 00], Brovey transform, PCA(Principa Component Anaysis )[ V.P.S. aidu and J.R. Rao, et a, 008] etc. In these methods image fusion is performed by directy manipuating the pixes of the respective images. Second one is transform domain methods, in which image is first transformed into frequency domain and then further processing is done. DWT (Discrete Waveet Transform) [Angoth, CY Dwith, Amarot Singh, et a, 03; Hongbo Wu, Yanqiu *Corresponding author: Richa Gautam Xing, et a, 00; Deepia.L, Mary Sindhua..M. Deepia.L, et a, 04], Curveet transform [Sweta Mehta, et a, 00; Kiran Parmar, Rahu Kher, et a, 0 ], pyramid transform [V.P.S. aidu, et a, 03] are exampes of transform domain methods. In order to obtain better resuts, hybrid methods have been evoved to expoit the benefits of different methods [Guruprasad S, M Z Kurian, H Suma et a, 05]. In this paper we have appied different fusion methods on the test given in [V.P.S. aidu, et a, 03]. Test data is a mutifocus image containing two aircrafts. Different fusion methods have been appied and then resuts are compared with that of the proposed method, which provides us better resuts. After this the same methods have been appied on two sets of medica images. In this paper two sets of CT and MRI images of brain are taen and then different fusion methods have been appied on them to have more informative fused image.. usion Methods In this section we have described image fusion methods based on DWT, PCA, DWT-PCA, DCT and Curveet transform.. Discrete Waveet Transform (DWT) Waveet is a waveform of imited duration having zero average vaue and nonzero norm. Waveet transform 6 Internationa Journa of Current Engineering and Technoogy, Vo.7, o. (eb 07)

2 Richa Gautam et a appied on a signa decomposes the signa into scaed (diated or expanded) and shifted (transated) versions of the chosen mother waveet. The term mother waveet impies that the other window functions are derived from this function. Waveet transform is appied in two domains viz continuous and discrete. CWT (Continuous Waveet Transform) is the correation between the waveet at different scaes (inverse of frequency) and the signa and is computed by changing the scae of the anaysis window each time, shifting it, mutipying it by the signa. Mathematica equation is given by x s s, s Xt t dt () In the above equation τ(transation) and s(scae) are variabes required for transforming the signa x(t). Psi (Ψ) is the transforming function nown as mother waveet. In DWT (Discrete Waveet Transform) a D signa (image) I(x, y) is first fitered through ow pass and high pass finite impuse response fiters (IR), having impuse response h[n] in horizonta direction and then decimated by factor of. This gives first eve decomposition. urther the ow pass fitered image is again fitered through ow pass and high pass IR fiters in vertica direction and then again decimated by to obtain second eve decomposition. itering operation is given by the convoution of the signa and impuse response of signa. x n hn x h n () Distortions in the fused image increase with the increase in the number of decomposition eves. So they shoud not be increased after desired eves. ow to perform inverse waveet transform, first upsampe the subband images by factor of coumn wise and then fiter them through ow pass and high pass IR fiters. Repeat the same process in next step row wise. ow add a the images to get the origina image. usion agorithm is as foows: We have two source images I (x, y) and I (x, y) obtained from CT and MRI scan of brain respectivey. Appication of Image usion Techniques on Medica Images b. Mean : By taing the average of the coefficients of both the images. c. Mix : By taing the average of the approximate coefficients of both the images and seecting the maximum pixes from detai coefficients of both the images. 6) ow appy IDWT to obtain the fused image.. Principa Component Anaysis (PCA) Principa Component Anaysis (PCA) is one of the famous techniques used for dimension reduction, feature extraction, and data visuaization. In genera, PCA is defined by the transformation of a high dimensiona vector space into a ow dimensiona space. This property of PCA is hepfu in reducing the size of medica image data which is of arge size without osing important information. In this method a number of correated variabes are transformed into uncorreated variabes caed principa components. Each principa component is taen in the direction of maximum variance and ie in the subspace perpendicuar to one another. usion agorithm is as foows: ) Convert the two source images into coumn vectors and mae a matrix M using these two coumn vectors. ) Cacuate the empirica mean vector aong each coumn and substract it from each of the coumns of the matrix. 3) Compute the covariance matrix C of the resuting matrix. 4) Compute the eigen vaues D and eigen vectors V of the covariance matrix. 5) Seect the eigenvector corresponding to arger eigenvaue and divide its each eement by mean of that eigenvector. This wi give us first principa component P. Repeat the same procedure with eigenvector corresponding to smaer eigenvaue to get second principa component P. V P V V() P V 6) used image is obtained by ) Tae two source images. ) Resize both of them to 56 x 56. 3) Convert both the images into grayscae if required. 4) Appy D- DWT on both the images and obtain its four components viz: one approximation and three detai ones. 5) ow appy the fusion rue as per the requirement. Here we have experimented with different fusion rues viz: a. Maximum pixe seection rue (a max): By seecting a maximum coefficients of both the images and fusing them. x y P I x, y P I x y I f,,.3 Hybrid agorithm (DWT-PCA) 6 Internationa Journa of Current Engineering and Technoogy, Vo.7, o. (eb 07) (3) This method is hybrid of both DWT and PCA appied on the source images. ) Obtain the waveet coefficients of the two source images. ) Convert the waveet coefficient matrices into coumn vectors.

3 Richa Gautam et a Appication of Image usion Techniques on Medica Images 3) Compute the covariance matrix using these vectors such that each matrix has first coumn vector obtained through first image and second coumn vector obtained through second image.mit wi give us four sets of covariance matrices. 4) Compute the eigen vaues D and eigen vectors V of the covariance matrices. 5) Seect the eigen vector corresponding to arger eigen vaue and divide its each eement by mean of that eigen vector. This wi give us first principa component P. Repeat the same procedure with eigenvector corresponding to smaer eigenvaue to get second principa component P. Do this for a four sets of covariance matrices. 6) Mutipy the normaised eigen vector vaues with the suitabe waveet coefficient matrix (P with approximate coefficient matrix of first image and P with approximate coefficient matrix of second image) 7) Do this for both approximate and detai coefficients of both the images. 8) ow appy IDWT to these manipuated coefficient matrices..4 Discrete Cosine Transform (DCT-D) Discrete Cosine transform (DCT) as the name impies transforms finite set of data points into cosine functions. DCT is a ourier reated transform ie Discrete ourier Transform (DT) with the ony difference that the former uses ony cosine functions whie the atter uses both sine and cosine functions. DCT has one of the interesting property of energy compaction. DCT is appied on both D and D signas. D DCT of a vector S(x) of size is given by S u au sx x u cos x0 Inverse D DCT is given by S x x u aus ucos x0 Where a u, u 0 and, u, 0 u, 0 x (4) (5) u is a discrete frequency variabe and x is pixe index. DCT has various variants. Two among them are requency Partition DCT (PDCT) and Mutiresoution DCT (MDCT). Both are discussed in the further sections. usion agorithm: ) Tae the two source images of equa size say Mx. ) Divide the first D image into rows and in them together in a chain form to have a D row vector R of size M. 3) Divide the second D image into coumns and in them together in a chain form to have a D coumn vector C of size M. 4) Appy DCT on both R and C separatey and then appy averaging operation on the vectors. 5) Appy inverse DCT on the resuting vector. 6) Convert D vector into D image..5 requency Partition DCT (PDCT) ) Repeat the first three steps of agorithm described in section.4. ) or each vector divide the DCT coefficients into ow frequency and high frequency compoents using partition factor f. Low frequency coefficients ie in the range 0 L Mf- and high frequency components ie in the range Mf L M. 3) Average the pixes of ow frequency coefficients of both the vectors and form a ow frequency vector (L). 4) Appy maximum pixe seection rue for high frequency coefficients of both the vectors and form a high frequency vector (H) 5) ow form vector V of size x having L and H as two components. 6) Appy inverse DCT. 7) Convert the D vector into D image..6 Mutiresoution DCT (MDCT) MDCT is one of the variants of DCT which is very simiar to waveets. The ony difference is IR fiters are repaced by DCT. In this method at first D-DCT is appied on the source image and divide the points into two haves. In first haf and second haf appy IDCT to obtain ow pass image L and high pass image H. ow again appy D-DCT on H and L images and then divide their respective points into two haves. On each haf appy IDCT to obtain HH, HL, LH and LL images. The same process can be continued further to obtain other sub band images. usion agorithm: ) Tae the source images and appy the preprocessing steps as mentioned in above methods. ) ow appy MDCT to obtain sub band images of each source image. 3) ow fusion rue is such that it wi seect maximum vaue of the two detai set of coefficients (sharpening operation) and for approximate set of coefficients appy averaging (smoothing) operation. 4) To obtain the fused image inverse MDCT has to be appied which is the reverse of the process as that of MDCT..7 Curveet Transform Curveet Transform is basicay an extension of Waveet Transform and they are becoming popuar day 63 Internationa Journa of Current Engineering and Technoogy, Vo.7, o. (eb 07)

4 Richa Gautam et a by day in the fied of image processing because of their abiity to provide good representation of edges in an image. In irst generation curveet transform image is first spitted into sma overapping ties foowed by Ridgeet transform on each tie. To understand digita curveet transform we have to start with continuous curveet transform. Consider two windows V(t) and W(r) nown as corner window and radius window respectivey which are supported in t [-,] and r [/,]. Permitting condition for them is W V t r, t, r 3 4,3 ; t, ; or scaes 0, ourier domain window is given by U 3 4 r, W r V (6),, Appication of Image usion Techniques on Medica Images (, ) x R x x (7) R θ denotes the rotation matrix with ange θ. Curveet coefficients can be obtained by the inner product of f L (R ) and Ψ,,. x C,, f,,, f R,, xdx (8) Since Second generation curveet transform (DCT) does not uses Ridgeet Transform hence faster than the irst generation curveet transform. In this transform basis functions used are ong ridges and their shape at scae is of - by -/. Curveets has one of the unique property as they provide optimay sparse representation of obects with edges. DCT has two methods of impementation. irst is based on Unequay Spaced ast ourier Transform (UST) and the second one based on wrapping agorithm. In this paper wrapping agorithm is used. The oca window used is given by impies rounding operations. U represents wedge window in poar coordinates shown in the fig. ig. Continuous tiing of frequency domain into wedges U w W wv w Where W V w w w w V w w 0 Where w, w w w Discrete Curveet is given by 3 4 T T x s x S b,, Where S θ is the shear matrix (9) (0) S tan 0 and b quantizes, Discrete Curveet Transform is given by ig. Discrete tiing of frequency domain wu S w T exp i S b w dw C,, f, Since T S () is not a perfect rectange therefore fast fourier transform agorithm cannot be used. Rewrite the above equation as In order to define Curveets at scae -, 0, orientation at θ,, and position at (, ) / x R (, ) we wi use the foowing equation C,, f f wu S w T exp i b, S w dw wu S wexp i b, w dw 64 Internationa Journa of Current Engineering and Technoogy, Vo.7, o. (eb 07) ()

5 Richa Gautam et a DCT using wrapping agorithm. ) Tae n x n image f[i, i ]. ) Choose the coarsest decomposition scae, using curveets or waveets. 3) ppy - and obtain fourier sampes f i, i ]. 4) or each scae ange found the product f i, i ]V [i, i ]. 5) Wrap this product around the origin. 6) Appy the inverse D-T to the wrapped data to obtain DCT coefficients. Proposed fusion agorithm is as foows ) Appy DCT wrapping on the source images and obtain the C{,i}{,} and C{,i}{,} curveet coefficients. ) Choose any one of the methods for seecting the coefficients. Maximum pixe seection (a max), Minimum pixe seection (a min) or mean of the coefficients obtained from the two images. 3) In our proposed fusion method maximum rue has been used since it improves the sharpness of the fused image due to which saient features become more visibe and hence image quaity improves. 4) Appy inverse DCT wrapping agorithm to the coefficients to get the fused image CT image Resize 56x56 MRI image Appication of Image usion Techniques on Medica Images 3. Performance Evauation Metrics 3. With reference image ) Percentage it Error (PE) norm( IR I ) 00 PE norm( IR ) Its vaue is high if the difference between the reference image and fused image is more. It shoud be as ow as possibe. ) Pea signa to noise ratio (PSR) L PSR 0og0 High vaue of M IR i, I i, M i this impies more simiarity between the fused image and reference image. 3. Without reference image ) Standard Deviation (SD) L i0 i i h ( i), I i ih I h i L i0 I is the normaized histogram of the fused image and L denotes the number of frequency bins in the histogram. SD indicates the contrast of the image and its vaue increases with contrast in the image. ) Spatia requency (S) S R C RGB Gray DCT to Row requency R M M i0 Coumn requency I i, i, Curveet Coefficients usion by maximum pixe seection of rest of the coefficients C M M 0 i I i, I ( i, ) It tes about the activity eve in the image 3) Entropy IDCT ( ) ( ) Where ( ) is the normaized histogram of the fused ig.3 ow chart of proposed agorithm image and is the number of frequency bins in the 65 Internationa Journa of Current Engineering and Technoogy, Vo.7, o. (eb 07)

6 Richa Gautam et a histogram. Entropy as a parameter indicates the information content of the image. It is sensitive to noise and high vaue of entropy indicates high information content in the image. 4. Resut and Anaysis In this section we wi discuss the resuts obtained by appying above mentioned agorithms on test data. Appication of Image usion Techniques on Medica Images Tabe Resuts obtained for first set of data S. o Method PE PSR SD S DWT a max DWT mean DWT mix PCA Hybrid Curveet mean Curveet a max PDCT MRDCT ig. (a) Reference image This is the actua image which we want to recover using fusion of the two mutifocus images (fig. (b) and fig. (c)) obtained from the same image. rom the above tabe we can see that Curveet by a max method gives the best resuts. In [V.P.S. aidu, et a, 03] image fusion is done through six different methods and their resuts are compared using above mentioned parameters for same set of test data. They have obtained best resuts using the method dua tree muti-resoution DCT (DTMDCT) foowed by Lapacian pyramid (LPD) based method. Tabe beow shows the resuts they have obtained and compared with the resuts from our proposed method. Tabe Comparison with the proposed method S. o Method PE PSR SD S DTMDCT LPD Curveet a max We can see that proposed method improves PE and PSR and aso resuts of SD and S are very cose to their resuts. ig. (b) ig. (b) and fig. (c) are the images that are obtained by burring the two aircrafts shown in fig. (a) aternatey. ig (d) used image by curveet a max ig. (c) ow we have appied same methods on two sets of medica data. Medica data consists of CT and MRI images of brain. 66 Internationa Journa of Current Engineering and Technoogy, Vo.7, o. (eb 07)

7 Richa Gautam et a Appication of Image usion Techniques on Medica Images irst set of data ig 3(c) used image ig (a) CT image ig (b) MRI image Tabe 3 Resuts of fused image for data set S. o Method Entropy SD S DWT max DWT Avg DWT mix PCA Hybrid Curveet mean Curveet a max PDCT MRDCT ig 3 (a) CT image ig (c) used image Second set of data ig 3 (b) MRI image Tabe 4 Resuts of fused image for data set S. o Method Entropy SD S DWT a max DWT Avg DWT mix PCA Hybrid Curveet mean Curveet a max PDCT MRDCT rom tabe 3 and tabe 4 we can see that Curveet with maximum seection rue provides best resuts. Concusion We have appied various fusion methods on three sets of data and it is observed that fusion by Curveet using maximum seection rue provides better resuts when compared with those of other methods. References Yong Yang (00) Medica image fusion via an effective waveet-based approach EURASIP Journa on Advances in Signa Processing. V.P.S aidu and J.R. Rao (008) Pixe eve image fusion using waveets and principa component anaysis Defence Science Journa, 58, Vive Angoth, CY Dwith, Amarot Singh (03) A nove waveet based image fusion for brain tumor detection Internationa Journa Of Computer Vision and Signa Processing, (), -7. Deepia.L, Mary Sindhua..M (04) Performance anaysis of image fusion agorithms using Haar waveet Internationa Journa Of Computer Science and Mobie Computing, 3, Sweta Mehta, Prof. Biith Maraarandy (03) CT and MRI image fusion using curveet transform Journa Of Information,Knowedge and research In Eectronics and Communication Engineering,, Kiran Parmar, Rahu Kher (0) A comparative anaysis of mutimodaity medica image fusion methods IEEE, V.P.S aidu (03) ove image fuson techniques using DCT Internationa ourna of computer science and business informatics,5, -8. V.P.S aidu (00) Discrete cosine transform based image fusion, Defence science ourna, 60, Guruprasad S, M Z Kurian, H Suma (05), usion of CT and PET medica images using hybrid agorithm DWT- DCT-PCA, IEEE, C.V.Rao, J.Maeswara Rao, A.Senthi Kumar, D.S.Jain, V.K.Dadhwa (04), Sateite image fusion using fast discrete curveet transform, Advance Computing Conference,04 IEEE Internationa, Internationa Journa of Current Engineering and Technoogy, Vo.7, o. (eb 07)