Research Article MRI and PET Image Fusion Using Fuzzy...

Research ArticleMRI and PET Image Fusion Using Fuzzy Logic andImage Local Features

Umer Javed12 Muhammad Mohsin Riaz3 Abdul Ghafoor3

Syed Sohaib Ali3 and Tanveer Ahmed Cheema2

1 Faculty of Engineering and Technology International Islamic University Islamabad 44000 Pakistan2 School of Engineering and Applied Sciences Isra University Islamabad 44000 Pakistan3 College of Signals National University of Sciences and Technology Islamabad 44000 Pakistan

Correspondence should be addressed to Abdul Ghafoor abdulghafoor-mcsnustedupk

Received 7 August 2013 Accepted 29 October 2013 Published 19 January 2014

Academic Editors S Bourennane and J Marot

Copyright copy 2014 Umer Javed et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An image fusion technique for magnetic resonance imaging (MRI) and positron emission tomography (PET) using local featuresand fuzzy logic is presented The aim of proposed technique is to maximally combine useful information present in MRI and PETimages Image local features are extracted and combined with fuzzy logic to compute weights for each pixel Simulation resultsshow that the proposed scheme produces significantly better results compared to state-of-art schemes

1 Introduction

Fusion of images obtained from different imaging systemslike computed tomography (CT) MRI and PET plays animportant role in medical diagnosis and other clinical appli-cations Each imaging technique provides a different level ofinformation For instance CT (based on X-ray principle) iscommonly used for visualizing dense structures and is notsuitable for soft tissues and physiological analysis MRI onthe other hand provides better visualization of soft tissuesand is commonly used for detection of tumors and othertissue abnormalities Likewise information of blood flow inthe body is provided by PET (a nuclear imaging technique)but it suffers from low resolution as compared toCTandMRIHence fusion of images obtained from different modalitiesis desirable to extract sufficient information for clinicaldiagnosis and treatment

Image fusion integrates (complementary as well as redun-dant) information from multimodality images to create afused image [1ndash6] It not only provides accurate description ofthe same object but also helps in required memory reductionby storing fused images instead of multiple source imagesDifferent techniques are developed for medical image fusionwhich can be generally grouped into pixel feature and

decision level fusion [7] Compared to feature and decisionpixel level methods [1 2] are more suited for medical imagingas they can preserve spatial details in fused images [1 8]

Conventional pixel level methods (including additionsubtraction multiplication and weighted average) are sim-pler but are less accurate Intensity Hue saturation (IHS)-based methods fuse the images by replacing the intensitycomponent [1 5 9] These methods generally produce high-resolution fused images but cause spectral distortion (due toinaccurate estimation of spectral information) [10] Similarlyprincipal components analysis basedmethods fuse images byreplacing certain principle components [11]

Multiresolution techniques including pyramids discretewavelet transform (DWT) contourlet curvelet shearlet andframelet transform image into different bands for fusion(a comprehensive comparison is presented in [12]) DWT-based schemes decompose the input images into horizontalvertical and diagonal subbands which are then fused usingadditive or substitutive methods Earlier DWT-based fusionschemes cannot preserve the salient features of the sourceimages efficiently hence producing block artifacts and incon-sistency in the fused results [2 3] Human visual system iscombined with DWT to fuse the low frequency bands usingvisibility and variance features respectively Local window

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 708075 8 pageshttpdxdoiorg1011552014708075

2 The Scientific World Journal

approach is used (to adjust coefficients adaptively) for noisereduction and maintaining homogeneity in fused image [4]However the method often produces block artifacts andreduced contrast [3 5] Consistency verification and activitymeasures combined with DWT can only capture limiteddirectional information and hence are not suitable for sharpimage transitions [13]

Texture features and visibility measure are used withframelet transform [5] to fuse high and low frequency com-ponents respectively Contourlet transform based methodsuse different and flexible directions to detect the intrinsicgeometrical structures [13] The common methods are vari-able weight using nonsubsampled contourlet transform [14]and bio-inspired activity measurer using pulse-coded neuralnetworks [15] However the down- and up-sampling incontourlet transform lack shift invariance and cause ringingartifacts [14] Curvelet transform uses various directions andpositions at length scales [16] however it does not providea multiresolution representation of geometry [17] Shear-let transform carries different features (like directionalitylocalization and multiscale framework) and can decomposethe image into any scale and direction to fuse the requiredinformation [17]

Prespecified transform matrix and learning techniquesare used with kernel singular value decomposition to fuseimages in sparse domain [18] In [19] image fusion has beenperformed using redundancy DWT and contourlet trans-form A pixel level neuro-fuzzy logic based fusion adjuststhe membership functions (MFs) using backpropagation andleast mean square algorithms [20] A spiking cortical modelis proposed to fuse different types of medical images [21]However these schemes are complex or work under certainassumptionsconstraints

A fusion technique for MRI and PET images using localfeatures and fuzzy logic is presentedThe proposed techniquemaximally combines the useful information present in MRIand PET images Image local features are extracted andcombined with fuzzy logic to compute weights for each pixelSimulation results based on visual and quantitative analysisshow the significance of the proposed scheme

2

119860-Trous-Based Image Fusion An Overview

In contrast to conventional multiresolution schemes (wherethe output is downsampled after each level) a-trous orundecimated wavelet provides shift invariance hence bettersuited for image fusion

Let different approximations 119868MRI119896 of MRI image 119868MRI(having dimensions 119872 times 119873) be obtained by successiveconvolutions with a filter 119891 that is

119868MRI119896+1 = 119868MRI119896 lowast 119891 (1)

where 119868MRI0 = 119868MRI and 119891 is a bicubic B-spline filter The 119896thwavelet plane119882MRI119896 of 119868MRI is

119882MRI119896 = 119868MRI119896+1 minus 119868MRI119896 (2)

The image 119868MRI is decomposed into low 119868MRI119871 and high 119868MRI119867frequency components as

119868MRI = 119868MRI119871 + 119868MRI119867

= 119868MRI119871 +119870

sum

119896=0

119882MRI119896(3)

where 119870 is the total number of decomposition levels Simi-larly PET image 119868PET in terms of low 119868PET119871 and high 119868PET119867frequency components is

119868PET (120573) = 119868PET119871 (120573) +119870

sum

119896=0

119882PET119896 (120573) (4)

where 120573 isin 119877 119866 119861 as PET images are assumed to be inpseudocolor [9]

Differentmethods are present in literature to fuse low andhigh frequency components which are generally grouped intosubstitute wavelet (SW) and additive wavelet (AW)The fusedimage 119868SW using SW is

119868SW (120573) = 119868PET119871 (120573) +119870

sum

119896=0

119882MRI119896 (5)

Note that SW method fuses image by completely replacingthe high frequency components of PET by high frequencycomponents of MRI image which can cause geometric andspectral distortion SW and IHS (SWI) are combined toovercome the limitation in fused image 119868SWI that is

119868SWI (120573) = 119868PET119871 (120573) minus119870

sum

119896=0

119882INT119896 +119870

sum

119896=0

119882MRI119896 (6)

where the intensity image 119868INT is

119868INT =1

119861

sum

120573

1015840

119868PET (1205731015840

) (7)

The substitution process in SWImethod sometimes results inloss of information as the intensity component is obtained bysimple averagingweighting

In AW method the fused image 119868AW is obtained byinjecting high frequency components of 119868MRI into 119868PET

119868AW (120573) = 119868PET (120573) +119870

sum

119896=0

119882MRI119896 (8)

AW method adds the same amount of high frequencies intolow-resolution bands which causes redundancy of high fre-quency components (hence resulting in spectral distortion)

To cater the limitation AW luminance proportional(AWLP) method injects the high frequencies in proportionto the intensity values [22] Consider

119868AWLP (120573) = 119868PET (120573) +119868PET (120573)

(1119861)sum

120573

1015840 119868PET (1205731015840

)

119870

sum

119896=1

119882MRI119896 (9)

The Scientific World Journal 3

where 119861 are total number of bands The fused image 119868AWLPof AWLP preserves the relative spectral information amongstdifferent bands The fused image using improved additivewavelet proportional (IAWP) [23] method is

119868IAWP (120573) = 119868PET (120573) +119868PET (120573)

(1119861)sum

120573

1015840 119868PET (1205731015840

)

times [

119870

sum

119896=1

119882MRI119896 minus119870

sum

119896=1

119882MRIR119896]

(10)

where119882MRIR119896 are wavelet planes of a low-resolution (a spa-tially degraded version of 119868MRI) MRI image 119868MRIR The 119868MRIRis obtained by filtering the high frequencies (by applying asmoothing filter)Themajor limitations of the above schemesincludes induction of redundant highlow frequencies andconsequently spatial degradations

3 Proposed Technique

The proposed scheme first decomposes the MRI and PETimages into low and high frequencies using a-trous waveletHigh and low frequencies are then fused separately accordingto defined criterion The overall fused image 119868

119865

in terms ofhigh 119868

119865119867

and low 119868

119865119871

(120573) frequencies is

119868

119865

(120573) = 119868

119865119871

(120573) + 119868

119865119867

(11)

31 Fusion of Low Frequencies Fusion of low frequencies119868MRI119871 and 119868PET119871 is critical and challenging task Variousschemes utilize different criterions for fusion of low frequen-cies For instance one choice is to totally discard the lowfrequencies of one image another choice is to take averageor weighted average of both and so forth However theschemes provide limited performance as they do not caterthe spatial properties of image We have proposed fusion oflow frequency using differentweighting average for each pixellocation The weights are computed based on the amount ofinformation contained in vicinity of each pixel

311 Local Features Local variance (LV) and local blur (LB)features are used with fuzzy inference engine to compute thedesired weights for fusing low frequencies

LV [24] is used to evaluate the regional characteristics of119868PET119871 image and is defined as 119868LV

119868LV (120573119898 119899) =1

(2119898

1

+ 1) (2119899

1

+ 1)

times

119898+1198981

sum

1198982=119898minus119898

1

119899+1198991

sum

1198992=119899minus1198991

(119868PET (1205731198982 1198992)minus119868PET (120573))2

(12)

where 119868PET(120573) is the mean value of1198981

times 119899

1

window centeredat (119898 119899) pixel Note that image containing sharp edges resultsin higher value (and vice versa)

LB 119868LB is computed using local Renyi entropy [25] of119868PET119871 image Let 119875

120573119898119899

(119896) be the probability (or normalized

histogram) having intensity values 119896 = 1 2 119870 within alocal window (of size119898

1

times 119899

1

) centered at (120573119898 119899) pixel 119868LBis defined as [25]

119868LB (120573119898 119899) = minus

1

2

ln(119870

sum

119896

119875

3

120573119898119899

(119896)) (13)

High values of 119868LV and 119868LB show that 119868PET119871 containmore information and need to be assigned more weight ascompared to 119868MRI119871 image

312 Fuzzy Inference Engine Let high 120577LV1(119906) and low120577LV2(119906) Gaussian Membership functions (MFs) havingmeans 119906(1) 119906(2) and variances 120590(1)

119906

120590(2)119906

for LV be [26]

120577LV1 (119906) = 119890

minus((119906minus119906

(1))120590

(1)

119906)

2

120577LV2 (119906) = 119890


(2))120590

(2)

119906)

2

(14)

Similarly let high 120577LB1(V) and low 120583LB2(V) Gaussian MFshaving means V(1) V(2) and variances 120590(1)V 120590(2)V for LB be

120577LB119871 (V) = 119890

minus((VminusV119871)120590119871V )2

120577LB119867 (V) = 119890

minus((VminusV119867)120590119867V )2

(15)

The inputs 119868LV(120573119898 119899) and 119868LV(120573119898 119899) are mapped intofuzzy set using Gaussian fuzzifier [27] as

120577LVLB (119906 V) = 119890

minus((119906minus119868LV(120573119898119899))1205891)2

times 119890

minus((Vminus119868LB(120573119898119899))1205892)2

(16)

where 1205891

and 1205892

are noise suppression parameters The inputsare then processed by fuzzy inference engine using predefined IF-THEN rules [26 27] as follows

119877119906

(1) IF 119868LV(120573119898 119899) is high and 119868LB(120573119898 119899) is highTHEN 119868WT(120573119898 119899) is high

119877119906

(2) IF 119868LV(120573119898 119899) is low and 119868LB(120573119898 119899) is highTHEN 119868WT(120573119898 119899) is medium

119877119906

(3) IF 119868LV(120573119898 119899) is high and 119868LB(120573119898 119899) islowTHEN 119868WT(120573119898 119899) is medium

119877119906

(4) IF 119868LV(120573119898 119899) is low and 119868LB(120573119898 119899) is lowTHEN 119868WT(120573119898 119899) is low

The output MFs for high (having mean 119910(1) and variance120590

(1)

119910

) medium (having mean 119910(2) and variance 120590(2)119910

) and low(having mean 119910(3) and variance 120590(3)

119910

) are defined as

120577

1198821

(119910) = 119890


(1))120590

(1)

119910)

2

120577

1198822

(119910) = 119890


(2))120590

(2)

119910)

2

120577

1198823

(119910) = 119890


(3))120590

(3)

119910)

2

(17)

The output of fuzzy inference engine is

120577

1015840

119882119871

(119910) = max119888119889119890

[sup119906V

120577LVLB (119906 V) 120577LV119888 (119906) 120577LV119889 (V) 120577119882119890 (119910)]

(18)


Table 1 Quantitative measures for fused PET-MRI images

Scenario Techniques Entropy [29] MI [29] SSIM [30] Xydeas and Petrovic [31] Piella [32]

Normalbrain

DWT [12] 5403 16607 06083 04944 07558GIHS [6] 5381 17017 07095 05362 08014GFF [33] 5115 17479 06803 04825 06741IAWP [23] 5152 17753 06735 03233 03331Proposed 5738 17912 06788 05746 08469

Grade IIastrocytoma


Grade IVastrocytoma


where 119888 119889 isin 1 2 and 119890 isin 1 2 3Theweights 119868WT(120573119898 119899)are obtained by processing fuzzy outputs using center averagedefuzzifier [27]

The 119868119865119871

(120573) image is obtained by weighted sum of 119868PET119871and 119868MRI119871 as

119868

119865119871

(120573119898 119899) = 119868WT (120573119898 119899) 119868PET119871 (120573119898 119899)

+ (1 minus 119868WT (120573119898 119899)) 119868MRI119871 (119898 119899) (19)

32 Fusion of High Frequencies Let 119882MRI-MRIR119896 representa wavelet plane of the resultant image 119868MRI minus 119868MRIR Thisensures that only those high frequency components are usedfor image fusion which are not already present in 119868MRIBy the virtue of this the proposed scheme not only avoidsredundancy of information but also results in improvedfusion results as compared to early techniquesThe fused highfrequency image 119868

119865119867

is

119868

119865119867

=

119870

sum

119896=1

119882MRI-MRIR119896 (20)

Note that 119868119865119867

is not dependent on the bands 120573 because 119868MRIis gray-scale image

4 Results and Discussion

The simulations of proposed and existing schemes are per-formed on PET and MRI images obtained from Harvarddatabase [28] The fusion database for brain images is classi-fied into normal grade II astrocytoma and grade IV astro-cytoma images The MRI and PET images are coregisteredwith 256times256 spatial resolutionThe proposed fusion schemeis compared visually and quantitatively (using entropy [29]mutual information (MI) [29] structural similarity (SSIM)

[30] Xydeas and Petrovic [31] metric and Piella [32] metric)with DWT [12] GIHS [6] IAWP [23] and GFF [33] schemes

The original MRI images belonging to normal braingrade II astrocytoma and grade IV astrocytoma are shownin Figures 1(a)ndash1(c) respectively Fluorodeoxyglucose (FDG)is a radiopharmaceutical commonly used for PET scansThe PET-FDG images of normal grade II and grade IVastrocytoma are shown in Figures 1(d)ndash1(f) respectivelyIt can be seen that different imaging modalities providecomplementary information for the same region

Figure 2 shows fused images (of normal brain) obtainedby using different techniques It can be seen from Figure 2(e)that the proposed technique has preserved the complemen-tary information of both modalities and the fuzzy basedweight assessment has enabled offering less spectral informa-tion loss as compared to other state-of-art techniques

Figure 3 shows fused images (of grade II astrocy-toma class) obtained by using different techniques FromFigure 3(e) it can be observed that the proposed techniqueprovides complementary information contained in bothmodalities and the fuzzy basedweight assessment has enabledoffering less spectral information loss as compared to otherstate of art techniques The improvement in fused images ismore visible in the tumorous region (bottom right corner)

Figure 4 shows fused images (of Grade IV astrocytoma)obtained by using different techniques Similar improvement(as that of Figures 2(e) and 3(e)) can be observed inFigure 4(e) It is easy to conclude that the proposed schemeprovides better visual quality compared to the existingschemes

Table 1 shows the quantitative comparison of differentfusion techniques Note that a higher value of the metricrepresents better quality The fused images obtained usingproposed technique provide better quantitative results in


(a) (b) (c)

(d) (e) (f)Figure 1 Original MRI and PET images (a)ndash(c) MRI (d)ndash(f) PET

(a) (b) (c)

(d) (e)Figure 2 Image fusion results for normal images (a) DWT [12] (b) GIHS [6] (c) GFF [33] (d) IAWP [23] (e) proposed technique


(a) (b) (c)

(d) (e)Figure 3 Image fusion results for grade II astrocytoma images (a) DWT [12] (b) GIHS [6] (c) GFF [33] (d) IAWP [23] (e) proposedtechnique

(a) (b) (c)

(d) (e)Figure 4 Image fusion results for grade IV astrocytoma images (a) DWT [12] (b) GIHS [6] (c) GFF [33] (d) IAWP [23] (e) proposedtechnique


terms of entropy [29] MI [29] SSIM [30] Xydeas andPetrovic [31] and Piella [32] metrics

5 Conclusion

An image fusion technique for MRI and PET using localfeatures and fuzzy logic is presented The proposed schememaximally combines the useful information present in MRIand PET images using image local features and fuzzy logicWeights are assigned to different pixels for fusing low fre-quencies Simulation results based on visual and quantitativeanalysis show that the proposed scheme produces signifi-cantly better results compared to state of art schemes

6 Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] G Bhatnagar Q M J Wu and Z Liu ldquoHuman visual systeminspiredmulti-modal medical image fusion frameworkrdquo ExpertSystems with Applications vol 40 no 5 pp 1708ndash1720 2013

[2] L Yang B L Guo and W Ni ldquoMultimodality medical imagefusion based on multiscale geometric analysis of contourlettransformrdquo Neurocomputing vol 72 no 1ndash3 pp 203ndash211 2008

[3] K Amolins Y Zhang and P Dare ldquoWavelet based image fusiontechniquesmdashan introduction review and comparisonrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 62 no 4pp 249ndash263 2007

[4] 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 579341 13pages 2010

[5] G Bhatnagar and Q M J Wu ldquoAn image fusion frameworkbased on human visual system in framelet domainrdquo Inter-national Journal of Wavelets Multiresolution and InformationProcessing vol 10 no 1 Article ID 1250002 2012

[6] T Li and YWang ldquoBiological image fusion using aNSCT basedvariable-weight methodrdquo Information Fusion vol 12 no 2 pp85ndash92 2011

[7] S T Shivappa B D Rao and M M Trivedi ldquoAn iterativedecoding algorithm for fusion of multimodal informationrdquoEurasip Journal on Advances in Signal Processing vol 2008Article ID 478396 10 pages 2008

[8] B Yang and S Li ldquoPixel-level image fusion with simultaneousorthogonal matching pursuitrdquo Information Fusion vol 13 no 1pp 10ndash19 2012

[9] S Daneshvar and H Ghassemian ldquoMRI and PET image fusionby combining IHS and retina-inspired modelsrdquo InformationFusion vol 11 no 2 pp 114ndash123 2010

[10] Z Wang D Ziou C Armenakis D Li and Q Li ldquoA compar-ative analysis of image fusion methodsrdquo IEEE Transactions onGeoscience and Remote Sensing vol 43 no 6 pp 1391ndash14022005

[11] 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

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

[13] M N Do and M Vetterli ldquoThe contourlet transform an effi-cient directional multiresolution image representationrdquo IEEETransactions on Image Processing vol 14 no 12 pp 2091ndash21062005

[14] D Li and H Chongzhao ldquoFusion for CT image and MR imagebased on nonsubsampled transformationrdquo in Proceedings of theIEEE International Conference on Advanced Computer Control(ICACC rsquo10) vol 5 pp 372ndash374 March 2010

[15] X-B Qu J-W Yan H-Z Xiao and Z-Q Zhu ldquoImage fusionalgorithm based on spatial frequency-motivated pulse cou-pled neural networks in nonsubsampled contourlet transformdomainrdquo Acta Automatica Sinica vol 34 no 12 pp 1508ndash15142008

[16] E Candes L Demanet D Donoho and L X Ying ldquoFast dis-crete curvelet transformsrdquoMultiscale Modeling and Simulationvol 5 no 3 pp 861ndash899 2006

[17] Q-G Miao C Shi P-F Xu M Yang and Y-B Shi ldquoA novelalgorithm of image fusion using shearletsrdquo Optics Communica-tions vol 284 no 6 pp 1540ndash1547 2011

[18] N N Yu T S Qiu andW H Liu ldquoMedical image fusion basedon sparse representation with KSVDrdquo in Proceedings of theWorld Congress on Medical Physics and Biomedical Engineeringvol 39 pp 550ndash553 2013

[19] S Rajkumar and S Kavitha ldquoRedundancy Discrete WaveletTransform and Contourlet Transform for multimodality medi-cal image fusionwith quantitative analysisrdquo inProceedings of the3rd International Conference on Emerging Trends in Engineeringand Technology (ICETET rsquo10) pp 134ndash139 November 2010

[20] J Teng S Wang J Zhang and X Wang ldquoNeuro-fuzzy logicbased fusion algorithm of medical imagesrdquo in Proceedings of the3rd International Congress on Image and Signal Processing (CISPrsquo10) vol 4 pp 1552ndash1556 October 2010

[21] RWang YWuM Ding and X Zhang ldquoMedical image fusionbased on spiking cortical modelrdquo in Medical Imaging 2013Digital Pathology vol 8676 of Proceedings of SPIE 2013

[22] L Alparone LWald J Chanussot CThomas P Gamba and LM Bruce ldquoComparison of pansharpening algorithms outcomeof the 2006 GRS-S data-fusion contestrdquo IEEE Transactions onGeoscience and Remote Sensing vol 45 no 10 pp 3012ndash30212007

[23] Y Kim C Lee D Han Y Kim and Y Kim ldquoImproved additive-wavelet image fusionrdquo IEEE Geoscience and Remote SensingLetters vol 8 no 2 pp 263ndash267 2011

[24] D-C Chang and W-R Wu ldquoImage contrast enhancementbased on a histogram transformation of local standard devia-tionrdquo IEEE Transactions on Medical Imaging vol 17 no 4 pp518ndash531 1998

[25] S Gabarda and G Cristobal ldquoBlind image quality assessmentthrough anisotropyrdquo Journal of the Optical Society of America Avol 24 no 12 pp B42ndashB51 2007

[26] M M Riaz and A Ghafoor ldquoFuzzy logic and singular valuedecomposition based throughwall image enhancementrdquoRadio-engineering Journal vol 22 no 1 p 580 2012

[27] L X Wang A Course in Fuzzy Systems and Control PrenticeHall New York NY USA 1997

[28] Harvard Medical Atlas Database httpwwwmedharvardeduAANLIBhomehtml

[29] G Qu D Zhang and P Yan ldquoInformation measure forperformance of image fusionrdquo Electronics Letters vol 38 no 7pp 313ndash315 2002


[30] ZWang A C Bovik H R Sheikh and E P Simoncelli ldquoImagequality assessment from error visibility to structural similarityrdquoIEEE Transactions on Image Processing vol 13 no 4 pp 600ndash612 2004

[31] C S Xydeas and V Petrovic ldquoObjective image fusion perfor-mance measurerdquo Electronics Letters vol 36 no 4 pp 308ndash3092000

[32] G Piella ldquoImage fusion for enhanced visualization a variationalapproachrdquo International Journal of Computer Vision vol 83 no1 pp 1ndash11 2009

[33] S Li X Kang and J Hu ldquoImage fusion with guided filteringrdquoIEEE Transactions on Medical Imaging vol 22 no 7 pp 2864ndash2875 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



approach is used (to adjust coefficients adaptively) for noisereduction and maintaining homogeneity in fused image [4]However the method often produces block artifacts andreduced contrast [3 5] Consistency verification and activitymeasures combined with DWT can only capture limiteddirectional information and hence are not suitable for sharpimage transitions [13]

Texture features and visibility measure are used withframelet transform [5] to fuse high and low frequency com-ponents respectively Contourlet transform based methodsuse different and flexible directions to detect the intrinsicgeometrical structures [13] The common methods are vari-able weight using nonsubsampled contourlet transform [14]and bio-inspired activity measurer using pulse-coded neuralnetworks [15] However the down- and up-sampling incontourlet transform lack shift invariance and cause ringingartifacts [14] Curvelet transform uses various directions andpositions at length scales [16] however it does not providea multiresolution representation of geometry [17] Shear-let transform carries different features (like directionalitylocalization and multiscale framework) and can decomposethe image into any scale and direction to fuse the requiredinformation [17]

Prespecified transform matrix and learning techniquesare used with kernel singular value decomposition to fuseimages in sparse domain [18] In [19] image fusion has beenperformed using redundancy DWT and contourlet trans-form A pixel level neuro-fuzzy logic based fusion adjuststhe membership functions (MFs) using backpropagation andleast mean square algorithms [20] A spiking cortical modelis proposed to fuse different types of medical images [21]However these schemes are complex or work under certainassumptionsconstraints

A fusion technique for MRI and PET images using localfeatures and fuzzy logic is presentedThe proposed techniquemaximally combines the useful information present in MRIand PET images Image local features are extracted andcombined with fuzzy logic to compute weights for each pixelSimulation results based on visual and quantitative analysisshow the significance of the proposed scheme

2

119860-Trous-Based Image Fusion An Overview

In contrast to conventional multiresolution schemes (wherethe output is downsampled after each level) a-trous orundecimated wavelet provides shift invariance hence bettersuited for image fusion

Let different approximations 119868MRI119896 of MRI image 119868MRI(having dimensions 119872 times 119873) be obtained by successiveconvolutions with a filter 119891 that is

119868MRI119896+1 = 119868MRI119896 lowast 119891 (1)

where 119868MRI0 = 119868MRI and 119891 is a bicubic B-spline filter The 119896thwavelet plane119882MRI119896 of 119868MRI is

119882MRI119896 = 119868MRI119896+1 minus 119868MRI119896 (2)

The image 119868MRI is decomposed into low 119868MRI119871 and high 119868MRI119867frequency components as

119868MRI = 119868MRI119871 + 119868MRI119867

= 119868MRI119871 +119870

sum

119896=0

119882MRI119896(3)

where 119870 is the total number of decomposition levels Simi-larly PET image 119868PET in terms of low 119868PET119871 and high 119868PET119867frequency components is

119868PET (120573) = 119868PET119871 (120573) +119870

sum

119896=0

119882PET119896 (120573) (4)

where 120573 isin 119877 119866 119861 as PET images are assumed to be inpseudocolor [9]

Differentmethods are present in literature to fuse low andhigh frequency components which are generally grouped intosubstitute wavelet (SW) and additive wavelet (AW)The fusedimage 119868SW using SW is

119868SW (120573) = 119868PET119871 (120573) +119870

sum

119896=0

119882MRI119896 (5)

Note that SW method fuses image by completely replacingthe high frequency components of PET by high frequencycomponents of MRI image which can cause geometric andspectral distortion SW and IHS (SWI) are combined toovercome the limitation in fused image 119868SWI that is

119868SWI (120573) = 119868PET119871 (120573) minus119870

sum

119896=0

119882INT119896 +119870

sum

119896=0

119882MRI119896 (6)

where the intensity image 119868INT is

119868INT =1

119861

sum

120573

1015840

119868PET (1205731015840

) (7)

The substitution process in SWImethod sometimes results inloss of information as the intensity component is obtained bysimple averagingweighting

In AW method the fused image 119868AW is obtained byinjecting high frequency components of 119868MRI into 119868PET

119868AW (120573) = 119868PET (120573) +119870

sum

119896=0

119882MRI119896 (8)

AW method adds the same amount of high frequencies intolow-resolution bands which causes redundancy of high fre-quency components (hence resulting in spectral distortion)

To cater the limitation AW luminance proportional(AWLP) method injects the high frequencies in proportionto the intensity values [22] Consider

119868AWLP (120573) = 119868PET (120573) +119868PET (120573)

(1119861)sum

120573

1015840 119868PET (1205731015840

)

119870

sum

119896=1

119882MRI119896 (9)



119868IAWP (120573) = 119868PET (120573) +119868PET (120573)

(1119861)sum

120573

1015840 119868PET (1205731015840

)

times [

119870

sum

119896=1

119882MRI119896 minus119870

sum

119896=1

119882MRIR119896]

(10)




119865


119865119867

and low 119868

119865119871


119868

119865

(120573) = 119868

119865119871

(120573) + 119868

119865119867

(11)




119868LV (120573119898 119899) =1

(2119898

1

+ 1) (2119899

1

+ 1)

times

119898+1198981

sum

1198982=119898minus119898

1

119899+1198991

sum

1198992=119899minus1198991

(119868PET (1205731198982 1198992)minus119868PET (120573))2

(12)


times 119899

1



120573119898119899



1

times 119899

1


119868LB (120573119898 119899) = minus

1

2

ln(119870

sum

119896

119875

3

120573119898119899

(119896)) (13)



119906

120590(2)119906

for LV be [26]

120577LV1 (119906) = 119890


(1))120590

(1)

119906)

2

120577LV2 (119906) = 119890


(2))120590

(2)

119906)

2

(14)


120577LB119871 (V) = 119890

minus((VminusV119871)120590119871V )2

120577LB119867 (V) = 119890

minus((VminusV119867)120590119867V )2

(15)


120577LVLB (119906 V) = 119890

minus((119906minus119868LV(120573119898119899))1205891)2

times 119890

minus((Vminus119868LB(120573119898119899))1205892)2

(16)

where 1205891

and 1205892


119877119906


119877119906


119877119906


119877119906



(1)

119910



119910

) are defined as

120577

1198821

(119910) = 119890


(1))120590

(1)

119910)

2

120577

1198822

(119910) = 119890


(2))120590

(2)

119910)

2

120577

1198823

(119910) = 119890


(3))120590

(3)

119910)

2

(17)


120577

1015840

119882119871

(119910) = max119888119889119890

[sup119906V

120577LVLB (119906 V) 120577LV119888 (119906) 120577LV119889 (V) 120577119882119890 (119910)]

(18)




Normalbrain


Grade IIastrocytoma


Grade IVastrocytoma



The 119868119865119871


119868

119865119871

(120573119898 119899) = 119868WT (120573119898 119899) 119868PET119871 (120573119898 119899)

+ (1 minus 119868WT (120573119898 119899)) 119868MRI119871 (119898 119899) (19)


119865119867

is

119868

119865119867

=

119870

sum

119896=1

119882MRI-MRIR119896 (20)

Note that 119868119865119867











(a) (b) (c)


(a) (b) (c)



(a) (b) (c)


(a) (b) (c)




5 Conclusion




References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119868IAWP (120573) = 119868PET (120573) +119868PET (120573)

(1119861)sum

120573

1015840 119868PET (1205731015840

)

times [

119870

sum

119896=1

119882MRI119896 minus119870

sum

119896=1

119882MRIR119896]

(10)




119865


119865119867

and low 119868

119865119871


119868

119865

(120573) = 119868

119865119871

(120573) + 119868

119865119867

(11)




119868LV (120573119898 119899) =1

(2119898

1

+ 1) (2119899

1

+ 1)

times

119898+1198981

sum

1198982=119898minus119898

1

119899+1198991

sum

1198992=119899minus1198991

(119868PET (1205731198982 1198992)minus119868PET (120573))2

(12)


times 119899

1



120573119898119899



1

times 119899

1


119868LB (120573119898 119899) = minus

1

2

ln(119870

sum

119896

119875

3

120573119898119899

(119896)) (13)



119906

120590(2)119906

for LV be [26]

120577LV1 (119906) = 119890


(1))120590

(1)

119906)

2

120577LV2 (119906) = 119890


(2))120590

(2)

119906)

2

(14)


120577LB119871 (V) = 119890

minus((VminusV119871)120590119871V )2

120577LB119867 (V) = 119890

minus((VminusV119867)120590119867V )2

(15)


120577LVLB (119906 V) = 119890

minus((119906minus119868LV(120573119898119899))1205891)2

times 119890

minus((Vminus119868LB(120573119898119899))1205892)2

(16)

where 1205891

and 1205892


119877119906


119877119906


119877119906


119877119906



(1)

119910



119910

) are defined as

120577

1198821

(119910) = 119890


(1))120590

(1)

119910)

2

120577

1198822

(119910) = 119890


(2))120590

(2)

119910)

2

120577

1198823

(119910) = 119890


(3))120590

(3)

119910)

2

(17)


120577

1015840

119882119871

(119910) = max119888119889119890

[sup119906V

120577LVLB (119906 V) 120577LV119888 (119906) 120577LV119889 (V) 120577119882119890 (119910)]

(18)




Normalbrain


Grade IIastrocytoma


Grade IVastrocytoma



The 119868119865119871


119868

119865119871

(120573119898 119899) = 119868WT (120573119898 119899) 119868PET119871 (120573119898 119899)

+ (1 minus 119868WT (120573119898 119899)) 119868MRI119871 (119898 119899) (19)


119865119867

is

119868

119865119867

=

119870

sum

119896=1

119882MRI-MRIR119896 (20)

Note that 119868119865119867











(a) (b) (c)


(a) (b) (c)



(a) (b) (c)


(a) (b) (c)




5 Conclusion




References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Normalbrain


Grade IIastrocytoma


Grade IVastrocytoma



The 119868119865119871


119868

119865119871

(120573119898 119899) = 119868WT (120573119898 119899) 119868PET119871 (120573119898 119899)

+ (1 minus 119868WT (120573119898 119899)) 119868MRI119871 (119898 119899) (19)


119865119867

is

119868

119865119867

=

119870

sum

119896=1

119882MRI-MRIR119896 (20)

Note that 119868119865119867











(a) (b) (c)


(a) (b) (c)



(a) (b) (c)


(a) (b) (c)




5 Conclusion




References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)


(a) (b) (c)



(a) (b) (c)


(a) (b) (c)




5 Conclusion




References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)


(a) (b) (c)




5 Conclusion




References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5 Conclusion




References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Date post:	19-Mar-2018
Category:	Documents
Upload:	vannguyet
View:	213 times
Download:	1 times

Research Article MRI and PET Image Fusion Using Fuzzy...

Documents