Multiscale Medical Image Fusion in Wavelet Domain

Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 521034 10 pageshttpdxdoiorg1011552013521034

Research ArticleMultiscale Medical Image Fusion in Wavelet Domain

Rajiv Singh and Ashish Khare

Department of Electronics and Communication University of Allahabad Allahabad 211002 India

Correspondence should be addressed to Rajiv Singh jkrajivsinghgmailcom

Received 30 August 2013 Accepted 30 September 2013

Academic Editors A Takano and R Yan

Copyright copy 2013 R Singh and A Khare This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Wavelet transforms have emerged as a powerful tool in image fusion However the study and analysis of medical image fusionis still a challenging area of research Therefore in this paper we propose a multiscale fusion of multimodal medical images inwavelet domain Fusion of medical images has been performed at multiple scales varying from minimum to maximum level usingmaximum selection rule which provides more flexibility and choice to select the relevant fused images The experimental analysisof the proposed method has been performed with several sets of medical images Fusion results have been evaluated subjectivelyand objectively with existing state-of-the-art fusion methods which include several pyramid- and wavelet-transform-based fusionmethods andprincipal component analysis (PCA) fusionmethodThe comparative analysis of the fusion results has been performedwith edge strength (119876) mutual information (MI) entropy (E) standard deviation (SD) blind structural similarity index metric(BSSIM) spatial frequency (SF) and average gradient (AG) metrics The combined subjective and objective evaluations of theproposed fusion method at multiple scales showed the effectiveness and goodness of the proposed approach

1 Introduction

The development of multimodality medical imaging sen-sors for extracting clinical information has influenced toexplore the possibility of data reduction and having bettervisual representation X-ray ultrasound magnetic resonanceimaging (MRI) and computed tomography (CT) are a fewexamples of biomedical sensors These sensors are used forextracting clinical information which is generally comple-mentary in nature For example X-ray is widely used indetecting fractures and abnormalities in bone position CTis used in tumor and anatomical detection and MRI is usedto obtain information about tissues Thus none of thesemodalities is able to carry all complementary and relevantinformation in a single image Medical image fusion [1 2] isthe only possible way to combine and merge all relevant andcomplementary information from multiple source imagesinto single composite image which facilitates more precisediagnosis and better treatment

The basic requirements for image fusion [3] are asfollows first fused image should possess all possible relevantinformation contained in the source images second fusionprocess should not introduce any artifact or unexpectedfeature in the fused image

Image fusion can be classified into three categories pixellevel fusion feature level fusion and decision or symbollevel fusion [4] Pixel level fusion [5] deals with informationassociated with each pixel and fused image can be obtainedfrom the corresponding pixel values of source images Infeature level fusion [6] source images are segmented intoregions and features like pixel intensities edges and texturesare used for fusion Decision or symbol level fusion [7] is ahigh-level fusion which is based on statistics voting fuzzylogic prediction and heuristics and so forth For presentwork we have considered pixel level image fusion due to itssimple computation and understanding

Spatial and transformdomains [8] are the two fundamen-tal approaches for image fusion In spatial domain fusionthe fusion rule is directly applied to the intensity values ofthe source images Averaging weighted averaging principalcomponent analysis (PCA) [9] linear fusion [10] and sharpfusion [11] are a few examples of spatial domain fusionscheme One of the major disadvantages of spatial domainfusion method is that it introduces spatial distortions inthe resultant fused image and does not provide any spectralinformation These spatial distortions have been observed insharp fusion [11] method for medical images and reported

2 The Scientific World Journal

in [12] Since medical images are generally of poor contrastthe spatial information should be preserved in the medicalimages without introducing any distortion or noise Theserequirements of medical images are better preserved intransform domain fusion

Therefore transform domain fusion techniques havebeen used for fusion to overcome the limitations of spatialdomain fusion methods Pyramid and wavelet transforms[13] have been used for multiscale fusion under categoryof transform domain methods Transform domain fusion isperformed by decomposing source images into transformedrepresentations followed by application of fusion rules to thetransformed representation Finally fused image is obtainedby inverse transformation Pyramid and wavelet transformsare the mostly used transforms for image fusion Severalpyramid transforms like Laplacian pyramid [14] gradientpyramid [15] contrast pyramid [16] ratio of low pass pyramid[17] morphological pyramid [18] and FSD pyramid [19] havebeen used for image fusion However pyramid transformbased fusion methods suffered from blocking effect [20] inthe regions where the input images are significantly differentFurther pyramid-transform-based fusion methods do notprovide any directional information and have poor signal-to-noise ratio In contrast to pyramid transforms wavelettransforms have better representation of detailed features ofimage hence wavelet domain fusion methods provide betterresults than pyramid-based fusion methods

The discrete wavelet transform (DWT) is the most com-monly used wavelet transform for medical image fusionA simple DWT-based medical image fusion which followsweighted fusion rule has been introduced by Cheng et al[21] Another pixel- and region-based multiresolution imagefusion for MRI and CT image is discussed in [22] Severalliteratures on medical image fusion using DWT can be easilyfound in [23ndash30] which use different fusion rules for merg-ing multimodality medical images Some advanced waveletfamilies such as contourlet transform curvelet transformand nonsubsampled contourlet transform [31] have beenused for medical image fusion and it has been stated thatthese advanced wavelet families have better performancethan wavelet transforms However these are computationallycostly and require huge memory Further the study andanalysis of DWT for medical image fusion has not beenstudied well and it still needs attention of researchers

Since estimation of decomposition levels for a wavelettransform [32] has always been challenging and literatureson multilevel medical image fusion [33] have been a moti-vation for us to explore DWT for multiscale image fusiontherefore in this work we have used DWT formultimodalitymedical image fusion and presented a new multiscale fusionapproach using maximum selection rule The multiscalefusion approach provides us flexibility to select appropriatefused medical image The experiments have been performedover several multimodality medical images at multiple scalesThe fusion results have been compared with other state-of-the-art fusion methods which include several pyramid- andwavelet-transform-based fusion methods and PCA fusionmethod The quantitative analysis of the fusion results hasbeen performed with edge strength (Q) mutual information

(MI) entropy (E) standard deviation (SD) blind structuralsimilarity index metric (BSSIM) spatial frequency (SF) andaverage gradient (AG) metrics

The rest of the paper is organized as follows Section 2explains the basics of DWT and its usefulness in imagefusionTheproposed fusionmethod is explained in Section 3Fusion results and evaluations are given in Section 4 Finallyconclusions of the work are given in Section 5

2 Wavelet Transform and Image Fusion

Recently wavelet transforms have emerged as a powerfulsignal and image processing tool which provides an efficientway of fusion usingmultiresolution analysis [34]This sectionexplains the basics ofDWTand its usefulness in image fusion

The DWT of a given signal 119865(119909) is performed byanalysis and synthesis of signal using scaling function 120601(119909)and wavelet function 120595(119909) [35 36] The basic equation ofmultiresolution theory is the scaling equation

120601 (119909) = radic2sum

119896

119897 (119896) 120601 (2119909 minus 119896) (1)

where 119897(119896)rsquos are the approximation or low-pass coefficientsand radic2 maintains the norm of the scaling factor by a factorof two

The wavelet function 120595(119909) which is responsible forcomputing high-frequency or detailed coefficients is given by

120595 (119909) = radic2sum

119896

ℎ (119896) 120601 (2119909 minus 119896) (2)

where ℎ(119896)rsquos are the high frequency or detailed waveletcoefficients

Signal decomposition is performed using the scalingcoefficients 119897(119896) and the wavelet coefficients ℎ(119896) Forwardwavelet analysis of signal 119865(119909) at any scale 119869 is denoted by

119865 (119909) = sum

119896

119862 (119895 119896) 120601119895119896 (119909) +sum

119895

sum119863(119895 119896) 120595119895119896 (119909) (3)

where 119862(119895 119896) and119863(119895 119896) are scaling and wavelet coefficientsat scale 119869 and can be computed by following relation

119862 (119895 119896) = sum

119896

119897 (119896 minus 2119898)119862 (119895 + 1 119896)

119863 (119895 119896) = sum

119896

ℎ (119896 minus 2119898)119862 (119895 + 1 119896)

(4)

Reconstruction of signal can be made by combining scal-ing and wavelet coefficients and mathematically it is repre-sented by

119862 (119895 + 1 119896) = sum

119896

119862 (119895 119896) 119897 (119898 minus 2119896) +sum

119896

119863(119895 119896) ℎ (119898 minus 2119896)

(5)

The forward and backward analysis of signals providesus the facility to have multiscale signal representations atvarying scales Further DWT analysis is capable of providingthree spatial orientations namely horizontal diagonaland

The Scientific World Journal 3

LH1

LL3 LH3

HL3 HH3 LH2

HL2 HH2

HL1 HH1

(a) (b)

Figure 1 2Ddecomposition process in discretewavelet transform (DWT) (a)DWTdecomposition up to level 3 (b) Two-level decompositionof Lena image

Image A

Image B

Fusionrule

Fused image

Wavelettransform

Inversewavelet

transform

Figure 2 A general image fusion scheme in wavelet domain

vertical This can be denoted by the following combinationof scaling and wavelet functions

120601LL (119909 119910) = 120601 (119909) 120601 (119910)

120595LH (119909 119910) = 120601 (119909) 120595 (119910)

120595HL (119909 119910) = 120595 (119909) 120601 (119910)

120595HH (119909 119910) = 120595 (119909) 120595 (119910)

(6)

The two-dimensional decomposition process usingDWTis shown in Figure 1 This can be easily seen that a 2D-DWT provides multiscale representation at different levelsFigure 1(a) shows the DWTdecompositions up to level 3 andFigure 1(b) shows the two level decomposition of Lena image

This wavelet decomposition is exploited for image fusionand could be easily understood from Figure 2 The DWTprovides an efficient way for performing image fusion atmultiple scales with several advantages These are as follows

LocalityThe information of an image is represented bywavel-et coefficients which is local in space and frequencyThus forfusion we can apply fusion rule locally and that would notaffect the other portions of the image

Multiresolution Analysis The image can be represented atdifferent scales and this allows producing fused images atmultiple levels [33]

EdgeDetectionWavelet transform can act as local edge detec-tors The edges in the image are represented by large waveletcoefficients at the corresponding locations while noise isgenerally represented by smaller values Wavelet transformrepresents three directional edges vertical horizontal anddiagonal This property helps in preserving the edges andimplementation of edge-sensitive fusion methods

Decorrelation Most of the wavelet coefficients of an imagetend to be approximately decorrelated that is dependenciesbetween wavelet coefficients are predominantly local Thusduring the fusion process if there is some change in waveletcoefficients then generally this would not affect the otherportions of image This allows applying fusion rule onselected wavelet coefficients without affecting other parts ofthe image

Energy Compaction In wavelet domain the most essentialinformation of the image is compressed into relatively fewlarge coefficients which coincides with the area of major


(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)

Figure 3 Fusion results for the first set of medical images (a) CT image (b) MRI image (c)ndash(i) fused images with proposed method fromlevel 2 to level 8 (j) GP method (k) CP method (l) RP method (m) PCA method (n) DWT with DBSS method and (o) SIDWT with Haarmethod

spatial activity (edges corners etc) This property facilitatesthe implementation of energy-based fusion rules whichpreserve the salient features of images

3 The Proposed Fusion Approach

The usefulness of DWT made it suitable for medical imagefusion where one wishes to capture all relevant informationfrom a single fused image with reduced cost and storage over-head The proposed fusion approach follows the framework

shown in Figure 2 decomposition was followed by applica-tion of fusion rule and reconstruction We have exploitedthe concept ofmultiresolution analysis withmultiscale fusionapproach The higher the scale is the more the detailedinformation is captured from source images to fused imageSince medical images are of poor contrast more detailed andrelevant information should be preserved Thus by varyingscale we have flexibility to select appropriate fused imagefor further operations For the proposed fusion scheme wevary the scale from minimum to maximum levels One of


(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)

Figure 4 Fusion results for the second set of medical images (a) MRA image (b) T1-MR image (c)ndash(i) fused images with proposed methodfrom level 2 to level 8 (j) GP method (k) CP method (l) RP method (m) PCA method (n) DWT with DBSS method and (o) SIDWT withHaar method

the important issues is the selection of wavelet for decompo-sition Regularity number of vanishing moment and finitesupport are the few important criteria for selecting motherwavelet [37] However it was shown in [31] that short filterbanks for wavelet decomposition are useful and works wellfor fusion Also [38] shows the effectiveness of selecting shortlength wavelet with a fixed criterion In both cases ldquodb3rdquowavelet has been found suitable for decomposition thereforewe used ldquodb3rdquo wavelet for the proposed fusion scheme

The proposed fusion approach is based on the maximumselection scheme as high-valued wavelet coefficients carrysalient information such as edges boundaries and contours

Therefore the absolute values of wavelet coefficients havebeen used for deciding fused wavelet coefficients For two-source medical images 1198681(119909 119910) and 1198682(119909 119910) the steps of theproposed fusion scheme are as follows

(i) Decompose source images using DWT

119882119897

1(119909 119910) = DWT [1198681 (119909 119910)]

119882119897

2(119909 119910) = DWT [1198682 (119909 119910)]

(7)

where 1198821198971(119909 119910) and 119882119897

2(119909 119910) are the wavelet coefficients of

source images 1198681(119909 119910) and 1198682(119909 119910) at scale 119897


(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)

Figure 5 Fusion results for the third set of medical images (a) MRI image (b) CT image (c)ndash(i) fused images with proposed method fromlevel 2 to level 8 (j) GP method (k) CP method (l) RP method (m) PCA method (n) DWT with DBSS method and (o) SIDWT with Haarmethod

(ii) Calculate fused wavelet coefficients119882119897119865(119909 119910) at scale

119897 by following the expression

119882119897

119865(119909 119910) =

119882119897

1(119909 119910) if 10038161003816100381610038161003816119882

119897

1(119909 119910)10038161003816100381610038161003816ge10038161003816100381610038161003816119882119897

2(119909 119910)10038161003816100381610038161003816

119882119897

2(119909 119910) if 10038161003816100381610038161003816119882

119897

2(119909 119910)10038161003816100381610038161003816gt10038161003816100381610038161003816119882119897

1(119909 119910)10038161003816100381610038161003816

(8)

(iii) Reconstruct fused image 119865119897(119909 119910) at scale 119897 usinginverse DWT

119865119897(119909 119910) = IDWT [119882119897

119865(119909 119910)] (9)

4 Fusion Results and Discussions

In this section we have shown fusion results for the proposedmethod The fusion results have been shown for threesets of medical image pairs of size 256 times 256 shown inFigures 3(a) 3(b) 4(a) 4(b) 5(a) and 5(b) respectively Theproposed method has been experimented at multiple scalesvarying from level 2 to level 8 (maximum level of scale) forthese medical images We have performed subjective andobjective comparisons to evaluate fusion results obtained bythe proposed method To perform subjective comparison


Table 1 Quantitative evaluation of fusion results for the first set of medical images

Fusion method Q MI E SD BSSIM SF AGProposed methodmdashlevel 2 07286 21396 59335 329163 05251 99138 37456Level 3 06675 16705 60177 329062 05121 103127 39258Level 4 06097 13475 61343 329446 04931 104907 40249Level 5 05844 13666 61673 337868 04856 105698 40154Level 6 05871 13352 62107 337941 04815 105912 40377Level 7 05862 13137 62215 337733 04805 105952 40422Level 8 05863 13204 62225 337558 04799 105947 40434GP 05784 10243 54698 197350 04793 66479 23911CP 02542 09452 19243 333962 05000 145826 27348RP 02658 09901 35655 331739 04794 146512 29503PCA 06395 26305 56220 283806 05371 69945 26799DWT with DBSS 04269 10342 55227 228441 04429 87605 31299SIDWT with Haar 07014 11510 53313 256650 04816 94682 33500

we have selected gradient pyramid (GP) contrast pyramid(CP) ratio pyramid (RP) PCA DWT with DBSS andSIDWT with Haar fusion methods which are available onhttpwwwmetapixde and provided by Rockinger [39]

For objective evaluation of proposed fusion approachwith other state-of-the-art fusion methods nonreferencemetrics are required as no ground truth image is available forcomparison Therefore we have used nonreference metricsnamely edge strength (Q) mutual information (MI) entropy(E) standard deviation (SD) blind structural similarity indexmetric (BSSIM) spatial frequency (SF) and average gradient(AG) for objective evaluation of our work

The illustration of fusion results is separately given inSections 41 and 42 for subjective and objective evaluationsrespectively

41 Subjective Evaluation The first set of medical images isbrain CT and MRI shown in Figures 3(a) and 3(b) It can beeasily seen that the CT image shows the edgy structure whileMRI provides information about soft tissues The resultsfor proposed multiscale fusion method have been shown inFigures 3(c)ndash3(i) from level 2 to level 8 These results showthe variations in contrast of fused image as level progressesOn comparing the obtained fused images from level 2 to level8 (shown in Figures 3(c)ndash3(i)) with GP CP RP and PCAfused images which are shown in Figures 3(j)ndash3(m) it canbe easily concluded that the proposed method outperformsthese fusion methods and has good visual representation offused image The fused images with GP CP RP and PCAmethods are not able to capture the information from CTand MRI pairs Further the proposed method has the betterquality than DWT with DBSS and nearly same with SIDWTwith Haar fusion methods

The second set of medical images is magnetic resonanceangiogram (MRA) and T1-MR image which is shown inFigures 4(a) and 4(b) The comparison of proposed fusionresults with GP CP RP PCA DWT with DBSS and SIDWTwith Haar fusion methods shown in Figures 4(c)ndash4(o)clearly implies that the fused images with proposed method

have better quality and contrast in comparison to other fusionmethods

Similarly on observing the third set of medical images(CT and MRI) and fusion results for these images which areshown in Figures 5(a)ndash5(o) one can easily verify the fact thatagain the proposedmethod has been found superior in termsof visual representation over GP CP RP PCA DWT withDBSS and SIDWT with Haar fusion methods

42 Objective Evaluation For objective evaluation of thefusion results shown from Figures 3ndash5 we have used sevennonreference fusion metrics edge strength (Q) [40] mutualinformation (MI) [41] entropy (E) [9 12 27] standarddeviation (SD) [12 27] blind structural similarity indexmetric (BSSIM) [33] spatial frequency (SF) [9 33] andaverage gradient (AG) [27] These metrics are well defined inthe literature and are used excessively for objective evaluationof fusion results Higher values of these metrics imply betterfused result We have computed the values of fusion resultsand tabulated them in Tables 1ndash3 for fusion results shown inFigures 3ndash5 respectively

On observing Table 1 one can easily observe that thefusionmeasures for proposedmultiscale fusionmethod fromlevel 2 to level 8 have higher values of fusion measures thanany of the GP CP RP PCA DWT with DBSS and SIDWTwith Haar fusion methods However the proposed fusionmethod from level 2 to level 8 has lesser values of SF thanCP and RP fusion methods Also the proposed method haslesser values of BSSIM than PCA fused image For these caseswe have performed an overall comparison in Table 1 and itsimply states that the proposed multiscale fusion method hasbetter performance for the first set of medical images

Similarly observation of Table 2 yields that the proposedfusion method form level 2 to level 8 has higher values offusionmeasures than other fusionmethods except values ofQfor PCA and SIDWT with Haar fusion methods and value ofBSSIM for PCA fusion method However an overall compar-ison again shows the superiority of the proposed multiscalefusion scheme for the second set of medical images


Table 2 Quantitative evaluation of fusion results for the second set of medical images


Table 3 Quantitative evaluation of fusion results for the third set of medical images


Moreover Table 3 shows the goodness of the proposedfusion method for the third set of medical images except Qand BSSIM fusion measures But again by the same criteriachosen forTables 1 and 2 the proposedmultiscale fusion fromlevel 2 to level 8 has better performance thanGP CP RP PCADWT with DBSS and SIDWT with Haar fusion methods

43 Combined Evaluation Since the subjective and objectiveevaluations separately are not able to examine fusion resultswe have combined both subjective and objective evaluationsThe values of fusion measures for fusion results of the firstset of medical images (Figure 3) are shown in Table 1 Theobservations from Table 1 show the variations in the values ofSF for CP and RP fusion methods and BSSIM for PCA fusionmethod The proposed method from level 2 to level 8 haslesser value of thesemeasures however qualitative evaluationof the proposed fusion method from Figure 3 clearly provesthe superiority of the proposedmethod over CP RP and PCAfusionmethods as these are not able to merge edge and tissueinformation from source CT and MRI images

Again Table 2 shows the higher values of Q for PCA andSIDWT with Haar fusion method and value of BSSIM for

PCA fusionmethod than the proposed fusion scheme for thesecond set of medical images However from Figure 4 it canbe easily seen that the proposedmethodprovides better visualrepresentation than any of these fusion methods Hencecombined evaluation shows the goodness of the proposedmultiscale fusion approach

The fusion measures of Figure 5 are given in Table 3 forthe third set of medical images The measures show thevariations in the value of Q and BSSIM for the proposedmethod and the proposed method has lesser values of Qthan GP CP RP and SIDWT with Haar fusion methodsand lesser values of BSSIM than RP PCA and SIDWT withHaar fusion methods However qualitative analysis of fusionresults shown in Figure 5 clearly shows that GP CP RP andSIDWT with Haar fusion methods have failed to incorporatethe features of the source CT andMRI images into one image

Thus this combined evaluation for fusion results shownin Figures 3ndash5 with fusion measures tabulated in Tables 1ndash3 clearly proves the superiority of the proposed multiscalefusion approach over GP CP RP PCA DWTwith DBSS andSIDWT with Haar fusion methods


5 Conclusions

In this work we have proposed a newmultiscale image fusionapproach for multimodal medical images in wavelet domainand usedDWT for proposed fusionmethodThemultimodalmedical images are fused at multiple scales from level 2(minimum) to level 8 (maximum) scales with maximumfusion rule The multiscale image fusion method enables theselection of appropriate fused image with better flexibilityTo show the effectiveness of the proposed work we haveperformed subjective evaluation and objective evaluation ofthe proposed fusion method with gradient pyramid (GP)contrast pyramid (CP) ratio pyramid (RP) PCA DWTwith DBSS and SIDWT with Haar fusion methods Thecomparative analysis of the fusion results has been performedwith edge strength (Q) mutual information (MI) entropy(E) standard deviation (SD) blind structural similarity indexmetric (BSSIM) spatial frequency (SF) and average gradient(AG) fusion metrics Since the subjective and objectiveevaluations are separately not sufficient for analysis of fusionresults we have performed combined evaluation whichproved the superiority of the proposed multiscale fusionapproach over GP CP RP PCA DWT with DBSS andSIDWT with Haar fusion methods

References

[1] V Barra and J-Y Boire ldquoA general framework for the fusion ofanatomical and functionalmedical imagesrdquoNeuroImage vol 13no 3 pp 410ndash424 2001

[2] B V Dasarathy ldquoInformation fusion in the realm of medicalapplicationsmdasha bibliographic glimpse at its growing appealrdquoInformation Fusion vol 13 no 1 pp 1ndash9 2012

[3] O Rockinger and T Fechner ldquoPixel-level image fusion the caseof image sequencesrdquo in Signal Processing Sensor Fusion andTarget Recognition VII vol 3374 of Proceedings of SPIE pp 378ndash388 April 1998

[4] C Pohl and J L Van Genderen ldquoMultisensor image fusion inremote sensing concepts methods and applicationsrdquo Interna-tional Journal of Remote Sensing vol 19 no 5 pp 823ndash854 1998

[5] V PetrovicMultisensor Pixel-level image fusion [PhD disserta-tion] University of Manchester 2001

[6] J J Lewis R J OrsquoCallaghan S G Nikolov D R Bull andC N Canagarajah ldquoRegion-based image fusion using complexwaveletsrdquo in Proceedings of the 7th International Conference onInformation Fusion (FUSION rsquo04) pp 555ndash562 InternationalSociety of Information Fusion (ISIF) Stockholm Sweden July2004

[7] Y Zhao Y Yin andD Fu ldquoDecision-level fusion of infrared andvisible images for face recognitionrdquo inProceedings of the ChineseControl andDecisionConference (CCDC rsquo08) pp 2411ndash2414 July2008

[8] T Stathaki Image Fusion Algorithms and Applications Aca-demic Press 2011

[9] V P S Naidu and J R Raol ldquoPixel-level image fusion usingwavelets and principal component analysisrdquo Defence ScienceJournal vol 58 no 3 pp 338ndash352 2008

[10] J G P W Clevers and R Zurita-Milla ldquoMultisensor and mul-tiresolution image fusion using the linear mixing modelrdquo inImage Fusion Algorithms and Applications T Stathaki Ed pp67ndash84 Academic Press Elsevier 2008

[11] J Tian L Chen L Ma and W Yu ldquoMulti-focus image fusionusing a bilateral gradient-based sharpness criterionrdquo OpticsCommunications vol 284 no 1 pp 80ndash87 2011

[12] R Singh and A Khare ldquoFusion of multimodal medical imagesusing Daubechies complex wavelet transformmdasha multiresolu-tion approachrdquo Information Fusion 2012

[13] A B Hamza Y He H Krim and A Willsky ldquoA multiscaleapproach to pixel-level image fusionrdquo Integrated Computer-Aided Engineering vol 12 no 2 pp 135ndash146 2005

[14] P J Burt and E H Adelson ldquoThe laplacian pyramid as acompact image coderdquo IEEE Transactions on Communicationsvol 31 no 4 pp 532ndash540 1983

[15] P J Burt ldquoA gradient pyramid basis for pattern selective imagefusionrdquo in Proceedings of the SID International Symposium pp467ndash470 1992

[16] A Toet L J van Ruyven and J M Valeton ldquoMerging thermaland visual images by a contrast pyramidrdquo Optical Engineeringvol 28 no 7 pp 789ndash792 1989

[17] A Toet ldquoImage fusion by a ration of low-pass pyramidrdquo PatternRecognition Letters vol 9 no 4 pp 245ndash253 1989

[18] A Toet ldquoA morphological pyramidal image decompositionrdquoPattern Recognition Letters vol 9 no 4 pp 255ndash261 1989

[19] C H Anderson ldquoFilter-subtract-decimate hierarchical pyra-mid signal analyzing and synthesizing techniquerdquo US Patent4718104 A 1998

[20] H Li B S Manjunath and S K Mitra ldquoMultisensor imagefusion using the wavelet transformrdquo Graphical Models andImage Processing vol 57 no 3 pp 235ndash245 1995

[21] S Cheng J He and Z Lv ldquoMedical image of PETCT weightedfusion based on wavelet transformrdquo in Proceedings of the2nd International Conference on Bioinformatics and BiomedicalEngineering (iCBBE rsquo08) pp 2523ndash2525 May 2008

[22] G Piella and H Heijmans ldquoMultiresolution image fusionguided by a multimodal segmentationrdquo in Proceedings ofAdvanced Concepts for Intelligent Vision Systems (ACIVS rsquo02)pp 175ndash182 Ghent Belgium 2002

[23] H Zhang L Liu and N Lin ldquoA novel wavelet medical imagefusion methodrdquo in Proceedings of the International ConferenceonMultimedia and Ubiquitous Engineering (MUE rsquo07) pp 548ndash553 April 2007

[24] S Vekkot and P Shukla ldquoA novel architecture for waveletbased image fusionrdquoWorld Academy of Science Engineering andTechnology vol 57 pp 372ndash377 2009

[25] Y Yang ldquoMultiresolution image fusion based on wavelet trans-form by using a novel technique for selection coefficientsrdquoJournal of Multimedia vol 6 no 1 pp 91ndash98 2011

[26] J Teng X Wang J Zhang S Wang and P Huo ldquoA multimo-dality medical image fusion algorithm based on wavelet trans-formrdquo in Advances in Swarm Intelligence vol 6146 of LectureNotes in Computer Science pp 627ndash633 Springer Berlin Ger-many 2010

[27] Y Yang D S Park S Huang and N Rao ldquoMedical imagefusion via an effective wavelet-based approachrdquo Eurasip Journalon Advances in Signal Processing vol 2010 Article ID 5793412010

[28] Y Yang ldquoMultimodal medical image fusion through a newDWT based techniquerdquo in Proceedings of the 4th Interna-tional Conference on Bioinformatics and Biomedical Engineering(iCBBE rsquo10) pp 1ndash4 June 2010

[29] B Alfano M Ciampi and G D Pietro ldquoA wavelet-basedalgorithm for multimodal medical image fusionrdquo in SemanticMultimedia pp 117ndash120 Springer Berlin Germany 2007


[30] G Qu D Zhang and P Yan ldquoMedical image fusion by wavelettransform modulus maximardquo Optics Express vol 9 no 4 pp184ndash190 2001

[31] S Li B Yang and J Hu ldquoPerformance comparison of differentmulti-resolution transforms for image fusionrdquo InformationFusion vol 12 no 2 pp 74ndash84 2011

[32] P S Pradhan R L King N H Younan and D W HolcombldquoEstimation of the number of decomposition levels for awavelet-based multiresolution multisensor image fusionrdquo IEEETransactions on Geoscience and Remote Sensing vol 44 no 12pp 3674ndash3686 2006

[33] Z Xu ldquoMedical image fusion using multi-level local extremardquoInformation Fusion 2013

[34] S Mallat A Wavelet Tour of Signal Processing Academic Press1999

[35] G Pajares and J M de la Cruz ldquoA wavelet-based image fusiontutorialrdquo Pattern Recognition vol 37 no 9 pp 1855ndash1872 2004

[36] C S Burrus R A Gopinath H Guo J E Odegard and I WSelesnick Introduction to Wavelets and Wavelet Transforms APrimer Prentice Hall Upper Saddle River NJ USA 1998

[37] M Unser and T Blu ldquoWavelet theory demystifiedrdquo IEEE Trans-actions on Signal Processing vol 51 no 2 pp 470ndash483 2003

[38] A Khare and U S Tiwary ldquoSoft-thresholding for denoisingof medical imagesmdasha multiresolution approachrdquo InternationalJournal onWaveletsMultiresoultion and Information Processingvol 3 no 4 pp 477ndash496 2005

[39] O Rockinger httpwwwmetapixde[40] C S Xydeas and V Petrovic ldquoObjective image fusion perfor-

mance measurerdquo Electronics Letters vol 36 no 4 pp 308ndash3092000

[41] G Qu D Zhang and P Yan ldquoInformation measure for per-formance of image fusionrdquo Electronics Letters vol 38 no 7 pp313ndash315 2002

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Navigation and Observation



in [12] Since medical images are generally of poor contrastthe spatial information should be preserved in the medicalimages without introducing any distortion or noise Theserequirements of medical images are better preserved intransform domain fusion

Therefore transform domain fusion techniques havebeen used for fusion to overcome the limitations of spatialdomain fusion methods Pyramid and wavelet transforms[13] have been used for multiscale fusion under categoryof transform domain methods Transform domain fusion isperformed by decomposing source images into transformedrepresentations followed by application of fusion rules to thetransformed representation Finally fused image is obtainedby inverse transformation Pyramid and wavelet transformsare the mostly used transforms for image fusion Severalpyramid transforms like Laplacian pyramid [14] gradientpyramid [15] contrast pyramid [16] ratio of low pass pyramid[17] morphological pyramid [18] and FSD pyramid [19] havebeen used for image fusion However pyramid transformbased fusion methods suffered from blocking effect [20] inthe regions where the input images are significantly differentFurther pyramid-transform-based fusion methods do notprovide any directional information and have poor signal-to-noise ratio In contrast to pyramid transforms wavelettransforms have better representation of detailed features ofimage hence wavelet domain fusion methods provide betterresults than pyramid-based fusion methods

The discrete wavelet transform (DWT) is the most com-monly used wavelet transform for medical image fusionA simple DWT-based medical image fusion which followsweighted fusion rule has been introduced by Cheng et al[21] Another pixel- and region-based multiresolution imagefusion for MRI and CT image is discussed in [22] Severalliteratures on medical image fusion using DWT can be easilyfound in [23ndash30] which use different fusion rules for merg-ing multimodality medical images Some advanced waveletfamilies such as contourlet transform curvelet transformand nonsubsampled contourlet transform [31] have beenused for medical image fusion and it has been stated thatthese advanced wavelet families have better performancethan wavelet transforms However these are computationallycostly and require huge memory Further the study andanalysis of DWT for medical image fusion has not beenstudied well and it still needs attention of researchers

Since estimation of decomposition levels for a wavelettransform [32] has always been challenging and literatureson multilevel medical image fusion [33] have been a moti-vation for us to explore DWT for multiscale image fusiontherefore in this work we have used DWT formultimodalitymedical image fusion and presented a new multiscale fusionapproach using maximum selection rule The multiscalefusion approach provides us flexibility to select appropriatefused medical image The experiments have been performedover several multimodality medical images at multiple scalesThe fusion results have been compared with other state-of-the-art fusion methods which include several pyramid- andwavelet-transform-based fusion methods and PCA fusionmethod The quantitative analysis of the fusion results hasbeen performed with edge strength (Q) mutual information

(MI) entropy (E) standard deviation (SD) blind structuralsimilarity index metric (BSSIM) spatial frequency (SF) andaverage gradient (AG) metrics

The rest of the paper is organized as follows Section 2explains the basics of DWT and its usefulness in imagefusionTheproposed fusionmethod is explained in Section 3Fusion results and evaluations are given in Section 4 Finallyconclusions of the work are given in Section 5

2 Wavelet Transform and Image Fusion

Recently wavelet transforms have emerged as a powerfulsignal and image processing tool which provides an efficientway of fusion usingmultiresolution analysis [34]This sectionexplains the basics ofDWTand its usefulness in image fusion

The DWT of a given signal 119865(119909) is performed byanalysis and synthesis of signal using scaling function 120601(119909)and wavelet function 120595(119909) [35 36] The basic equation ofmultiresolution theory is the scaling equation

120601 (119909) = radic2sum

119896

119897 (119896) 120601 (2119909 minus 119896) (1)

where 119897(119896)rsquos are the approximation or low-pass coefficientsand radic2 maintains the norm of the scaling factor by a factorof two

The wavelet function 120595(119909) which is responsible forcomputing high-frequency or detailed coefficients is given by

120595 (119909) = radic2sum

119896

ℎ (119896) 120601 (2119909 minus 119896) (2)

where ℎ(119896)rsquos are the high frequency or detailed waveletcoefficients

Signal decomposition is performed using the scalingcoefficients 119897(119896) and the wavelet coefficients ℎ(119896) Forwardwavelet analysis of signal 119865(119909) at any scale 119869 is denoted by

119865 (119909) = sum

119896

119862 (119895 119896) 120601119895119896 (119909) +sum

119895

sum119863(119895 119896) 120595119895119896 (119909) (3)

where 119862(119895 119896) and119863(119895 119896) are scaling and wavelet coefficientsat scale 119869 and can be computed by following relation

119862 (119895 119896) = sum

119896

119897 (119896 minus 2119898)119862 (119895 + 1 119896)

119863 (119895 119896) = sum

119896

ℎ (119896 minus 2119898)119862 (119895 + 1 119896)

(4)

Reconstruction of signal can be made by combining scal-ing and wavelet coefficients and mathematically it is repre-sented by

119862 (119895 + 1 119896) = sum

119896

119862 (119895 119896) 119897 (119898 minus 2119896) +sum

119896

119863(119895 119896) ℎ (119898 minus 2119896)

(5)

The forward and backward analysis of signals providesus the facility to have multiscale signal representations atvarying scales Further DWT analysis is capable of providingthree spatial orientations namely horizontal diagonaland


LH1

LL3 LH3

HL3 HH3 LH2

HL2 HH2

HL1 HH1

(a) (b)


Image A

Image B

Fusionrule

Fused image

Wavelettransform

Inversewavelet

transform



120601LL (119909 119910) = 120601 (119909) 120601 (119910)

120595LH (119909 119910) = 120601 (119909) 120595 (119910)

120595HL (119909 119910) = 120595 (119909) 120601 (119910)

120595HH (119909 119910) = 120595 (119909) 120595 (119910)

(6)









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)






119882119897

1(119909 119910) = DWT [1198681 (119909 119910)]

119882119897

2(119909 119910) = DWT [1198682 (119909 119910)]

(7)

where 1198821198971(119909 119910) and 119882119897




(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)




119882119897

119865(119909 119910) =

119882119897

1(119909 119910) if 10038161003816100381610038161003816119882

119897

1(119909 119910)10038161003816100381610038161003816ge10038161003816100381610038161003816119882119897

2(119909 119910)10038161003816100381610038161003816

119882119897

2(119909 119910) if 10038161003816100381610038161003816119882

119897

2(119909 119910)10038161003816100381610038161003816gt10038161003816100381610038161003816119882119897

1(119909 119910)10038161003816100381610038161003816

(8)


119865119897(119909 119910) = IDWT [119882119897

119865(119909 119910)] (9)




























5 Conclusions


References












































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of







Sensors






Volume 2014

RoboticsJournal of





Journal of









LH1

LL3 LH3

HL3 HH3 LH2

HL2 HH2

HL1 HH1

(a) (b)


Image A

Image B

Fusionrule

Fused image

Wavelettransform

Inversewavelet

transform



120601LL (119909 119910) = 120601 (119909) 120601 (119910)

120595LH (119909 119910) = 120601 (119909) 120595 (119910)

120595HL (119909 119910) = 120595 (119909) 120601 (119910)

120595HH (119909 119910) = 120595 (119909) 120595 (119910)

(6)









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)






119882119897

1(119909 119910) = DWT [1198681 (119909 119910)]

119882119897

2(119909 119910) = DWT [1198682 (119909 119910)]

(7)

where 1198821198971(119909 119910) and 119882119897




(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)




119882119897

119865(119909 119910) =

119882119897

1(119909 119910) if 10038161003816100381610038161003816119882

119897

1(119909 119910)10038161003816100381610038161003816ge10038161003816100381610038161003816119882119897

2(119909 119910)10038161003816100381610038161003816

119882119897

2(119909 119910) if 10038161003816100381610038161003816119882

119897

2(119909 119910)10038161003816100381610038161003816gt10038161003816100381610038161003816119882119897

1(119909 119910)10038161003816100381610038161003816

(8)


119865119897(119909 119910) = IDWT [119882119897

119865(119909 119910)] (9)




























5 Conclusions


References












































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of







Sensors






Volume 2014

RoboticsJournal of





Journal of









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)






119882119897

1(119909 119910) = DWT [1198681 (119909 119910)]

119882119897

2(119909 119910) = DWT [1198682 (119909 119910)]

(7)

where 1198821198971(119909 119910) and 119882119897




(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)




119882119897

119865(119909 119910) =

119882119897

1(119909 119910) if 10038161003816100381610038161003816119882

119897

1(119909 119910)10038161003816100381610038161003816ge10038161003816100381610038161003816119882119897

2(119909 119910)10038161003816100381610038161003816

119882119897

2(119909 119910) if 10038161003816100381610038161003816119882

119897

2(119909 119910)10038161003816100381610038161003816gt10038161003816100381610038161003816119882119897

1(119909 119910)10038161003816100381610038161003816

(8)


119865119897(119909 119910) = IDWT [119882119897

119865(119909 119910)] (9)




























5 Conclusions


References












































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of







Sensors






Volume 2014

RoboticsJournal of





Journal of









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)






119882119897

1(119909 119910) = DWT [1198681 (119909 119910)]

119882119897

2(119909 119910) = DWT [1198682 (119909 119910)]

(7)

where 1198821198971(119909 119910) and 119882119897




(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)




119882119897

119865(119909 119910) =

119882119897

1(119909 119910) if 10038161003816100381610038161003816119882

119897

1(119909 119910)10038161003816100381610038161003816ge10038161003816100381610038161003816119882119897

2(119909 119910)10038161003816100381610038161003816

119882119897

2(119909 119910) if 10038161003816100381610038161003816119882

119897

2(119909 119910)10038161003816100381610038161003816gt10038161003816100381610038161003816119882119897

1(119909 119910)10038161003816100381610038161003816

(8)


119865119897(119909 119910) = IDWT [119882119897

119865(119909 119910)] (9)




























5 Conclusions


References












































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of







Sensors






Volume 2014

RoboticsJournal of





Journal of









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o)




119882119897

119865(119909 119910) =

119882119897

1(119909 119910) if 10038161003816100381610038161003816119882

119897

1(119909 119910)10038161003816100381610038161003816ge10038161003816100381610038161003816119882119897

2(119909 119910)10038161003816100381610038161003816

119882119897

2(119909 119910) if 10038161003816100381610038161003816119882

119897

2(119909 119910)10038161003816100381610038161003816gt10038161003816100381610038161003816119882119897

1(119909 119910)10038161003816100381610038161003816

(8)


119865119897(119909 119910) = IDWT [119882119897

119865(119909 119910)] (9)




























5 Conclusions


References












































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of







Sensors






Volume 2014

RoboticsJournal of





Journal of

































5 Conclusions


References












































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of







Sensors






Volume 2014

RoboticsJournal of





Journal of






















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of







Sensors






Volume 2014

RoboticsJournal of





Journal of








Multiscale Medical Image Fusion in Wavelet Domain

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