Research Article Fusion Method for Remote Sensing Image ...downloads.hindawi.com/journals/jece/2014/437939.pdf · tiveness of remote sensing image fusion method based on fuzzy integral,

Research ArticleFusion Method for Remote Sensing ImageBased on Fuzzy Integral

Hui Zhou12 and Hongmin Gao1

1 College of Computer and Information Engineering Hohai University Nanjing 211100 China2 College of Computer and Software Nanjing Institute of Industry Technology Nanjing 210046 China

Correspondence should be addressed to Hui Zhou huizhouhhueducn

Received 11 April 2014 Accepted 9 August 2014 Published 3 September 2014

Academic Editor Jan Van der Spiegel

Copyright copy 2014 H Zhou and H GaoThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a kind of image fusion method based on fuzzy integral integrated spectral information and 2 single factorindexes of spatial resolution in order to greatly retain spectral information and spatial resolution information in fusion ofmultispectral and high-resolution remote sensing images Firstly wavelet decomposition is carried out to two images respectivelyto obtain wavelet decomposition coefficients of the two image and keep coefficient of low frequency of multispectral image andthen optimized fusion is carried out to high frequency part of the two images based on weighting coefficient to generate new fusionimage Finally evaluation is carried out to the image after fusion with introduction of evaluation indexes of correlation coefficientmean value of image standard deviation distortion degree information entropy and so forthThe test results show that thismethodintegrated multispectral information and space high-resolution information in a better way and it is an effective fusion method ofremote sensing image

1 Introduction

The starting points for researching remote sensing imagefusion at present can be divided into two categories onecategory is specific to the detailed application purpose andthe other category is aimed at the integrated quality for opti-mizing image The former is based on statistical theory andassorted with the understanding of ground object features onground sample area as well as the a priori knowledge likecognition so as to generate fusion model with the criterionof specific application purpose and reach the purpose ofdistinctly identifying some ground object features The lattermainly extract obvious feature information in image with themathematical tools like spectral analysis wavelet transformand so forth according to image imaging mechanism andits feature analysis and set up the relationship among imagedata feature information in different scale space so as toform the fusion model with the purpose of optimizingimage information content and comprehensive distinguish-ing feature However regardless of the remote sensing imagecarried out with any kind of purposes currently adopted

main method is greatly based on the fusion on pixel layerTherefore the process of remote sensing image fusion shouldbe firstly realized with high accuracy geometric registrationamong different image pixels and then with pixel spectruminformation fusion [1 2]

Different types of remote sensing images have differentspatial resolution spectral resolution and time phase reso-lution Fusion of remote sensing information is to combinetheir respective resolution advantages to compensate for thedeficiency of some resolution on single image At present theinformation fusion methods of remote sensing image mainlyare principal component analysis mineral or vegetationindex or ratio Tasseled Cap Multiplication Transform RatioTransform IHS based Transform and so forth All the abovemethods have the problem of partial loss of image spectralinformation with original resolution due to its limitationwhile wavelet transform can carry out image informationfusion to multiple wave bands which not only can utilizethe image spatial information of high resolution but alsocan keep the maximum integrality of the image spectralinformation with low resolution It is also the main purpose

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2014 Article ID 437939 9 pageshttpdxdoiorg1011552014437939

2 Journal of Electrical and Computer Engineering

for studying fusion technique of current remote sensingimage

Wavelet transformhas sound frequency division propertyin transform domain and statistical characteristics of waveletsparse reflected the obvious features of remote sensing imagelike edge line and domain and so forth Coefficient oflow frequency of multispectral image is kept to carry outoptimized fusion to the high frequency part of two imagesin accordance with weighting coefficient so as to create newfusion image The test carried out with remote sensing imagedata proved the effectiveness of this algorithm The methodfor integrating the two single factors of spectral informationand spatial resolution and the determination of the optimalpoint during the course of iterative optimization are still theproblems demanding prompt solution

This paper presented an image fusion method based onfuzzy integral specific to multispectral and high-resolutionimage fusion problem This method effectively integratedtwo single factor indexes of spectral information and spatialresolution and carried out pixel-level optimal fusion andintroduced fuzzy integral method which can convenientlyand efficiently determine the optimal weight number

2 Fusion Method and Fusion Rules of RemoteSensing Image

21 Fusion Method The detailed steps of image fusionmethod based on fuzzy integral are as follows [3ndash9]

(1) respectively register high resolution image spot intothree wave bands of multispectral image dmtm

(2) extract the three wave bands of multispectral imagedmtm respectively carry out 3 layers of wavelettransform to extract its coefficient of low frequency

(3) carry out 3 layers of wavelet transform to highresolution image spot so as to extract its coefficientsof high and low frequency

(4) carry out infusion to images in various wave bands inaccordance with fusion and image after fusion can beobtained after wavelet transform

(5) rectify weighting coefficients 1198961 and 1198962 of data fusionin fusion rules in accordance with optimizing evalua-tion index of fusion image and repeat Steps (4) sim (5)

(6) efficiently determine the optimal value of 119896 withutilization of fuzzy integral to end the optimizingprocess

(7) fusion image can be obtained after integrating thefusion image of the three wave bands

22 Fusion Rules The fusion rules of multispectral imagedmtm and high resolution image spot after 3 layers of waveletdecomposition are as follows

(1) extract the 3rd layer of coefficient of low frequency ofmultispectral image

(2) determine the fusion value of high frequency coef-ficient according to the following equation so as tocarry out pixel-level fusion

119860 = 11989611198601 + 11989621198602 (1)

wherein 1198601 and 1198602 are high frequency coefficients of dmtmand spot respectively 1198961 and 1198962 are required optimal weightcoefficients 1198961 and 1198962 meet 1198961 + 1198962 = 1 that is thedetermination of optimal weight coefficients can come downto 119896 = 1198961 = 1 minus 1198962 which meets the objective function

(3) carry out the 3rd layer of wavelet inverse transformaccording to the 3rd coefficient of low frequency ofmultispectral image and the high frequency coeffi-cient after being processed

(4) take the image value of the 3rd layer of wavelet afterinverse transform as the coefficient of low frequencyof the 2nd layer of wavelet transform and the highfrequency coefficient is calculated according to (1)

(5) carry out the 1st layer of wavelet inverse transformaccording to Steps (3) and (4) to obtain the fusionimage

23 Optimizing Evaluation Index of Fusion Image andOptimalObjective Function

231 Evaluation Index of Spectral Information Correlationdegree of fusion image and multispectral image is used toidentify the evaluation index of spectral information Set 119891be image after fusion and119891

0bemultispectral image Different

Gaussian templates are selected in accordance with spatialresolution of multispectral image to carry out passivatingtreatment The lower the resolution ratio of 119891

0is the larger

the passivating template will be The evaluation index foridentifying spectral information is

119864sp = Corr (119891 1198910) =

sum119899

119895=1(119891119895minus 119891) (119891

0119895minus 1198910)2

radicsum119899

119895=1(119891119895minus 119891)2

sum119899

119895=1(1198910119895minus 1198910)2

(2)

wherein 119899 is the number of pixel points in image 119891 and 1198910

are gray average of image degree of correlation Corr(119891 1198910)

reflects similarity level of image 119891 1198910

232 Evaluation Index of Spatial Resolution Correspondingcorrelation degree of fusion image between high-frequencycomponent of gray scale and high-frequency component ofhigh-resolution image is used to identify index under spatialresolution [10ndash13] Set 119891

119867be high-resolution panchromatic

image Firstly the fusion image is transformed to grey levelimage and then to carry out wavelet decomposition so as toobtain 4 components119891

119886119891ℎ119891V119891119889 of the fusion image which

respectively present low-frequency component of fusionimage high-frequency component in horizontal directionhigh-frequency component in vertical direction and high-frequency component in diagonal direction In the same way

Journal of Electrical and Computer Engineering 3

it also can obtain 4 components 119891119867119886 119891119867ℎ

119891119867V and 119891

119867119889

of wavelet decomposition of high-resolution image Defineevaluation index of spatial resolution

119864119867119865

=[Corr (119891

ℎ 119891119867ℎ) + Corr (119891V 119891119867V) + Corr (119891

119889 119891119867119889)]

3

(3)

3 Proposed Method

31 Fuzzy Integral Based Fusion The key point of compre-hensive evaluation with the utilization of fuzzy integral isthe definition of fuzzy measure 119892(119909) and 119892

120582measure can

be adopted Under limited conditions of domain of discourse119883 = 119909

11199092 119909119899 (factor set) when 120582 = 0 if the fuzzy mea-

sure119892120582(119909119894) of single point set (single factor set) is determined

any 119860 sub 119883 measure can be obtained As for the problem ofmultispectral and high-resolution image fusion domain ofdiscourse is simplified to be 119883 = 119909

1 1199092 and the evaluation

factors are spectral information 1199091and spatial resolution 119909

2

The fuzzy measure is 119892120582(1199091) and 119892

120582(1199092) which can be simply

expressed as 1198921and 119892

2 then 119892(119909

1) = 119892

1 119892(119909

2) = 119892

2

119892(1199091 1199092) = 119892(119909

1) + 119892(119909

2) = 1 119890(119909) is evaluation

index of spectral information and evaluation index of spatialresolution then the corresponding evaluation indexes ofdomain of discourse 119883 are 119890(119909

1) = 119864sp and 119890(119909

2) = 119864

119867119865

which can be simply expressed as 1198901and 1198902 According to the

definition of fuzzy integral it can obtain

int119909

119890 (119909) ∘ 119892 (119909) = sup120597isin[01]

min [120597 119892 (119883 cap 119864120597)]

= max120597isin[01]

[min (120597 119892 (119864120597))]

(4)

Sequencing is carried out to 1199091and 119909

2according to the

values of 1198901and 1198902 which should be recorded as 120583

1and 120583

2

based on the sequencing order from small to large Under thiscondition there are two conditions for 120597 values when 120597 =

119890(1205831) 119864120597= 1198641= 1205831 1205832 then 119892(119864

1) = 1 when 120597 = 119890(120583

2)

119864120576= 1198642= 1205832 then 119892(119864

2) = 119892(120583

2)

According to the definition of fuzzy integral it can obtain

119865 = sup min [119890 (1205831) 119892 (119864

1)] min [119890 (120583

2) 119892 (119864

2)] (5)

There are the following values

(1) When 1198901gt 1198902 the sequencing order of 119909

1and 1199092from

small to large is 1205831= 1199092 1205832= 1199091 correspondingly

119890(1205831) = 1198902 119892(1198641) = 1 119890(120583

2) = 1198901 119892(1198642) = 119892(120583

2) =

119892(1199091) = 119892

1 then the fuzzy integral is 119865 = max(119890

1sdot

1198921 1198902)

(2) When 1198901lt 1198902 the sequencing order of 119909

1and 1199092from


119890(1205831) = 1198901 119892(1198641) = 1 119890(120583

2) = 1198902 119892(1198642) = 119892(120583

2) =

119892(1199092) = 119892

2 then the fuzzy integral is119865 = max(119890

1 1198902sdot

1198922)

(3) When 1198901= 1198902 119865 can be either of the above values in

(1) and (2)

During above inferring process the operation with theutilization of ldquosdotrdquo and ldquomax()rdquo function is derived fromldquomin()rdquo and ldquosup()rdquo and fuzzy integral value 119865 serves asintegrated evaluation results Utilization of fuzzy integralcan effectively integrate spectral information index and 2single factor indexes of spatial resolution so as to efficientlydetermine the optimal weight

32 Experimental Steps MATLAB software is selected asa test tool in this test Dmtm image and spot image areselected for the test to satisfy that the weighting coefficientof the optimal objective function is the intersection pointof 119864sp and 119864

119867119865 therefore the optimal weighting coefficient

(convergence precision 120575 le 0001) can enable the fusionimage to reach the maximum spatial resolution meanwhilefurthest reduced color distortion while the utilization offuzzy integral can effectively integrate these 2 single factorindexes and efficiently determine the optimal weight

According to the two items of feature evaluation indexesdefined in (2) and (3) it should be substituted into (4) tocalculate the value of fuzzy integral 119865 Draw 119865 into thecoordinate system fuzzy integral value 119865 shows a nonlinearchanging process it has a peak point and this peak pointis the curve intersection point of the two feature indexesmdashoptimal weighting coefficient Therefore during the testprocess the maximum value of 119865 should be successivelysought and its corresponding value 119896 is the optimal weightIt is not necessary to substitute each value 119896 to calculate theweight therefore the test can be finished in a convenient andefficient way

The detailed test process is as follows

(1) respectively register high-resolution image in thethree wave bands of multispectral image dmtm

(2) respectively carry out wavelet decomposition to thethree wave bands of dmtm so as to extract itscoefficient of high and low frequency

(3) carry out wavelet decomposition to the registeredspot image so as to extract its coefficient of high andlow frequency

(4) determine the optimal high-frequency coefficientwith fuzzy integral

(5) carry out wavelet reverse transform layer by layer

(6) integrate the fusion images of the three wave bands

The determination process of the maximum value of thefuzzy integral is as follows firstly calculate value 119865 with thestep length of 01 during 119896 isin [0 1] further calculate value 119865with the step length of 001 near themaximum value of119865 andso on obtain value 119896 when degree of convergence 120575 le 0001so as to enable its corresponding fuzzy integral value 119865 tobe maximum at that time the two single factor evaluationindexes values 119864sp and 119864

119867119865are same on the whole which

satisfy the requirements of optimal objective function


Figure 1 Original TM (multispectral) image

4 Experiments and Analysis

41 Images for Experiments In order to prove the effec-tiveness of remote sensing image fusion method based onfuzzy integral this paper selects fusion test with a 1024 times

1024 TM multispectral image and a 1024 times 1024 SPOT high-resolution panchromatic image Figures 1 and 2 respectivelypresented the two remote sensing images for fusion afterspatial registration that is the TM multispectral image andSPOT high-resolution panchromatic image Figures 3 4 56 and 7 are relevant test result images It can be seen fromFigure 7 that the image after IHS based transform fusion hashigh definition but also has serious color distortion

42 Determination of Fuzzy Measure Value During the pro-cess of determining fuzzy measure value the values of fuzzymeasure 119892

1and 119892

2 respectively represent the emphasis to

multispectral image information and high-resolution imageinformation Therefore different 119892

1and 119892

2values will influ-

ence the image fusion effect in certain degree Three groupsof 1198921and 119892

2data are selected in this test for comparison the

optimal weighting coefficients 119896 obtained from it are shownin Table 1

It can be seen from above tables that the optimal weight-ing coefficients determined in the 2nd and 3rd wave bandsdetermined by different 119892

1and 119892

2values are consistent and

119864ℎ119891

and 119864sp are same on the whole while the weightingcoefficient in the 1st wave band is also very close to itAccording to the balance requirements of the evaluationindex of multispectral information and evaluation index ofhigh-resolution information 119896 = 0457 is selected for the 1stwave band then 119864sp = 09519 119864ℎ119891 = 09520

43 Evaluation of Image Fusion Effect

431 Categories of Performance Parameters The perform-ance parameters mainly can be divided into three categories

Figure 2 Original SPOT (high resolution) image

Figure 3 Fusion image based on fussy integral

Figure 4 Image after fusion of combinatorial algorithm based onenergy selection and wavelet transform


Figure 5 Image after fusion of combinatorial algorithm

Figure 6 Image after fusion based on PCA

Figure 7 Image after fusion based on IHS transform

Table 1

(a)

1198921= 07 119892

2= 03 119896 119865 119864sp 119864

ℎ119891

The 1st wave band 0457 09519 09519 09520The 2nd wave band 0459 09511 09511 09514The 3rd wave band 0487 09379 09380 09379

(b)

1198921= 03 119892

2= 07 119896 119865 119864sp 119864

ℎ119891


(c)

1198921= 02 119892

2= 08 119896 119865 119864sp 119864

ℎ119891


Category I means spectral preservation degree such as dis-tortion degree deviation index and correlation coefficientCategory II reflects expressive ability of spatial detail infor-mation such as variance information entropy cross entropyand definition Category III reflects image brightness infor-mation such as mean value [14ndash18]

432 Evaluation Statistical Parameter of Fusion Effect

(1) Mean Value and Standard Deviation In statistical theorystatistical mean value 120583 and standard deviation are definedas

120583 =1

119899

119899

sum

119894=1

119909119894

2=

1

119899 minus 1

119899

sum

119894=1

(119909119894minus 120583)2 (6)

wherein 119899 is total sample number 119909119894is the 119894th sample value

As for some image 119899 is the total pixels and 119909119894is the

grey level of the 119894th pixel then the mean value is the greylevel mean value of the pixel which is reflected to be meanbrightness to human eyes If themean value ismoderate thenthe visual effect will be good Standard deviation reflects thediscrete conditions of grey level compared with grey levelmean value The larger the standard deviation is the morediscrete the distribution of grey level will be At that time theprobabilities of occurrence of all the gray levels in images willbe closer and closer with each other so as to result in that thecontained information volumewill bemore andmore close tothe maximum value The mean value and standard deviationof image after multispectral image and fusion in this test areshown as in Tables 2 and 3

It can be seen from the table that the standard deviationof fusion image is higher than that of multispectral imagewhich shows that its contained information volume is morethan that of multispectral image

Comparing this test method with the combined methodof maximum and consistency detection of absolute value


Table 2 Mean value of multispectral image and fusion image

Mean value Multispectral image Fusion imageThe 1st wave band 480060 538250The 2nd wave band 624486 671111The 3rd wave band 837475 1020046

Table 3 Variance of multispectral image and fusion image

Variance The 1st waveband

The 2nd waveband

The 3rd waveband

Multispectral image 262903 297145 244353Image after fusion 275264 30 6260 244566Energy selectionmethod 245099 275120 224653

Combined method ofmaximum andconsistency detectionof absolute value

219932 240895 194255

Combined method ofPCA and wavelettransform

262368 313601 250627

Table 4 Correlation coefficient in this test

Correlationcoefficient

Multispectral imageand fusion image

High-resolutionimage and fusion

imageThe 1st wave band 09519 09125The 2nd wave band 09511 09089The 3rd wave band 09380 07421

the variances of all the wave bands are larger than those ofthis method while the larger standard deviation means thatthe probabilities of occurrence of all the grey levels in imagesmore and more tend to be same and the included infor-mation volume more and more tends to be the maximumtherefore the information contained in the image after fusionin this test is more than the information volume of the fusionmethod based on the maximum and consistency detectionof absolute value Similarly the variance data of this test isalso larger than that of the energy selection method and thecontained information volume is alsomore than thismethod

Comparing this test method with combined method ofPCA and wavelet transform the variance is slightly less thanthe value obtained in this method which shows that thecontained information volume is also slightly less than thatof the image obtained in this method

(2) Correlation Coefficient The correlation coefficient of theimage reflects the degree of correlation of the two images andthe transform degree of spectral information of multispectral

image can be seen through comparing the correlation coef-ficients of the images before and after fusion increase Thecorrelation coefficients of the two images are defined as

sum119894119895[(119891119894119895minus 119890119891) times (119892

119894119895minus 119890119892)]

radicsum119894119895[(119891119894119895minus 119890119891)2

] times sum119894119895[(119892119894119895minus 119890119892)2

]

(7)

wherein 119891119894119895

and 119892119894119895 respectively are the grey levels on

point (119894 119895) of the two images The correlation coefficient ofmultispectral image and image after fusion as well as thecorrelation coefficient of high-resolution image and imageafter fusion in this test are shown in Table 4

It can be seen from Table 4 that it balanced the informa-tion of multispectral image and high-resolution image in abetter way in this test Both the correlation coefficients inthe 1st and 2nd wave bands exceeded 09 and the correlationcoefficient of high-resolution image and fuse image in the 3rdwave band is slightly poor In general the correlation coeffi-cient of multispectral image and fuse image is better whichputs particular emphasis on the information of multispectralimage

Compared with the data in Tables 5 and 6 the correlationcoefficient of multispectral image and fusion image in thistest data is obviously higher than that of the other twomethods but the correlation coefficient of high-resolutionimage and fusion image is lower than that of those twomethods which show that this test put particular emphasison multispectral information But it can be seen from thedata in the 1st and 2nd wave bands that the correlationcoefficient of both categories reaches more than 09 whichshows that this test pays attention to the balance of thecorrelation coefficient of both categories The test resultsagree with the theory It can be seen from the table thatthe data in the 3rd wave band are generally low but thecorrelation coefficient of the multispectral image and thefusion image in this test still reaches more than 09 whichshows that the multispectral information is still kept wellwhile the correlation coefficient of the high-resolution imageand the fusion image is slightly lower than that of the othertwo methods but the difference is not large In general thistest balanced multispectral information and high-resolutioninformation As for the correlation coefficient it has bettereffect

(3) Distortion Degree The spectral distortion degree of imagedirectly reflects the spectral anamorphose of multispectralimage and the smaller distortion degree is betterThe spectraldistortion degree is defined as

119863 =1

119899sum

119894

sum

119895

100381610038161003816100381610038161198811015840

119894119895minus 119881119894119895

10038161003816100381610038161003816 (8)


Table 5 Combinedmethod ofmaximum and consistency detectionof absolute value





Table 6 Combined method based on energy selection and wavelettransform





Table 7 Spectral distortion degree

Spectral distortiondegree

The 1st waveband

The 2nd waveband

The 3rd waveband

Combination of fuzzyintegral and wavelettransform

77653 77870 186638

Combination ofmaximum absolutevalue and consistencydetection

133177 187888 189686

Combination of PCAand wavelet transform 287838 162149 81825

wherein 119863 is spectral distortion value 119899 is the size of imageand 1198811015840

119894119895and 119881

119894119895are respectively the grey levels at point (119894 119895)

on the fusion increased image and the original image Thespectral distortion degrees in this test are shown as in Table 7

It can be seen from Table 7 that comparing this testmethod with combined method of maximum and consis-tency detection of absolute value while all the distortiondegrees reflects the anamorphose of the multispectral imageand fusion result image The less distortion degree showsthe less anamorphose while this test put the emphasis onmultispectral information and the theory coincides with thepractice

Compared with the combined method of PCA andwavelet transform firstly the distortion of the 2nd wave bandis small which shows that the spectral information is keptwell while that of the 3rd wave band is obviously larger thanthat of this method which shows that the 3rd wave band isslightly distorted

(4) Information Entropy In 1948 the originator of moderninformation theory Claude Elwood Shannon worked out thatthe average information119867 and the entropy of statistical ther-modynamics have same probabilitymathematical expression

Table 8 Information entropy

Information entropy The 1st waveband

The 2nd waveband

The 3rd waveband

Based on fuzzyintegral and wavelettransform

45291 47003 45535

Combination ofenergy selection andwavelet transform

44169 46055 44781


43177 44789 43436


Therefore he defined the average information as entropy thatis

1199010= 1199011= sdot sdot sdot = 119901

119871minus1=1

119871 119867 = minus119888

119871minus1

sum

119894=0

119901119894ln119901119894 (9)

wherein 119888 is a constant relatedwith logarithmic systemWhenbinary system is selected 119888 = 1 andwhen e system is selected119888 = 1 ln 2 The grey levels of various elements of a singleimage can be deemed to be independent samples then thegrey level distribution of this image is 119875 = 119901

0 1199011 119901

119871minus1

119901119894is the ratio between pixel number in which the grey level

equals 119894 and the total pixel number of the image and 119871 is thetotal grey level As for the image histogramwith the grey levelrange of 0 1 119871 minus 1 the information entropy is definedas

119867 = minus

119871minus1

sum

119894=0

119901119894ln119901119894 (10)

It is easy to know 0 le 119867 le ln 119871 When some 119901119894= 1

119867 = 0 when 1199010= 1199011= sdot sdot sdot = 119901

119871minus1= 1119871 119867 = ln 119871

Image information entropy is an important index formeasur-ing image information richness and the detailed expressiveability of image can be compared through the comparisonto image information entropy The entropy size reflects theinformation volume carried by image The larger the entropyof fusion image is the more the information volume con-tained in fusion image will be In addition if the probabilitiesof occurrence of all the grey levels in images tend to be samethen the contained information volume will tend to be themaximum The values of information entropy in the test areshown as Table 8

It can be seen from Table 8 that the information entropydata obtained with this test method are larger than thedata obtained with other test methods while the volume ofinformation entropy reflects the information volume carriedby image The larger the entropy of fusion image is the morethe information volume carried by fusion image will be Theinformation entropy values obtained with this test methodare larger than the values obtained with other test methodswhich shows that the information volume contained in


the fusion image of this test is larger with better fusion effectand the effectiveness of this method

5 Conclusions

The following conclusions can be obtained through researchand test in this paper

(1) The optimal image fusion method based on fuzzyintegral presented in this paper combined the featuresof fuzzy integral and wavelet transform to carry outpixel-level optimal fusion to high-frequency coeffi-cient introduced fuzzy integral method to effectivelyintegrate the spectral information and the 2 singlefactor indexes of spatial resolution conveniently andefficiently determined the optimal weight so as toenable the image after fusion to reach the maximumspatial resolution reduced color distortion in maxi-mum degree which balanced the two feature indexesof spatial detail information and spectral informationin fusion effect and effectively improved the spectralinformation index of fusion image

(2) When the optimal fusion of multi-index is consid-ered the utilization of fuzzy integral can effectivelyintegrate themulti-index factorsThe feature for fuzzyintegral of integrated multifactor can be used infusion problem of multispectral and high-resolutionimages and the results will be more suitable forsubjective feeling of people to fusion image

(3) It is presented in this paper that the utilization of fuzzyintegral can efficiently determine the optimal weightwhich enables calculated amount of the algorithm tobe less and the fusion effect can satisfy the require-ments in most occasions with certain use value

In addition in the methods presented in this paperhigh-frequency coefficient is determined by optimal weightwhich is based on pixel-level fusion method The optimalfusion method for remote sensing image based on waveletstatistical property can be considered in IHS space waveletfusion method is used for the high-frequency part withintensity component I to carry out high-frequency detailedfeature fusion of high-frequency subband Fuzzy integral isused for the low-frequency part to carry out fusion Suchkind of detailed processing to high-frequency part shouldreceive better effectWavelet transformmethod is an effectivealgorithm in current fusion field There are questions ofhow to determine the order of wavelet transform and carryout fusion of coefficients within wavelet domain in a mosteffective way These contents are crucial to image fusionwhich should be further researched

Conflict of Interests

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

References

[1] JWang K Song andXHe ldquoMulti-spectral image fusion basedon the characteristic of imaging systemrdquo in IEEE InternationalConference on Information and Automation (ICIA rsquo13) pp 643ndash647 Yinchuan China August 2013

[2] Z Fang C Cao W Jiang W Ji M Xu and S Lu ldquoMulti-spectral image inter-band registration technology researchrdquoin Proceedings of the 32nd IEEE International Conference onGeoscience and Remote Sensing Symposium (IGARSS 12) pp4287ndash4290 Munich Germany July 2012

[3] H Feng X Li and J Chen ldquoA comparative study of four FuzzyIntegrals for classifier fusionrdquo in Proceedings of the InternationalConference on Machine Learning and Cybernetics (ICMLC rsquo10)pp 332ndash338 July 2010

[4] M Guijarro R Fuentes-Fernandez P J Herrera A Ribeiroand G Pajares ldquoNew unsupervised hybrid classifier based onthe fuzzy integral applied to natural textured imagesrdquo IETComputer Vision vol 7 no 4 pp 272ndash278 2013

[5] A C B Abdallah H Frigui and P Gader ldquoAdaptive local fusionwith fuzzy integralsrdquo IEEE Transactions on Fuzzy Systems vol20 no 5 pp 849ndash864 2012

[6] W Li D Wang and T Chai ldquoFlame image-based burningstate recognition for sintering process of rotary kiln usingheterogeneous features and fuzzy integralrdquo IEEE Transactionson Industrial Informatics vol 8 no 4 pp 780ndash790 2012

[7] 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

[8] G Xiao Z Jing J Li L Liu and SWang ldquoOptimal image fusionmethod based on fuzzy integralrdquo Journal of Shanghai JiaotongUniversity vol 39 no 8 pp 1312ndash1316 2005

[9] X Yang J Pei and W-H Yang ldquoFusion evaluation usingSugenos integralrdquo Chinese Journal of Computers vol 24 no 8pp 815ndash818 2001

[10] B Tao JWang andQ Zhang ldquoImage fusion based on relativityof wavelet coefficientsrdquo Laser amp Infrared vol 36 no 3 pp 227ndash230 2006

[11] G Xiao Z Jing L J X Li and H Leung ldquoAnalysis ofcolor distortion and improvement for IHS image fusionrdquo inProceedings of the IEEE International Conference on IntelligentTransportation Systems pp 80ndash85 Shanghai China October2003

[12] N Guoqiang ldquoStudy on multi-band image fusion algorithmsand its progressingrdquo Photoelectron Technique and Informationvol 14 no 5 pp 11ndash17 2001

[13] H-T Huo and Y Xian-xiang ldquoThe application of wavelettransform in the fusion of remotely sensed imagesrdquo Journal ofImage and Graphics vol 8 no 5 pp 513ndash515 2003

[14] YMCui GQNi Y L Zhong YWang andY SNiu ldquoAnalysisand evaluation of the effect of image fusion using statisticsparametersrdquo Journal of Beijing Institute of Technology vol 20no 1 pp 102ndash106 2000

[15] W Xiuqing and Z Rong ldquoA method and application in datafusion of multiresolution imagesrdquo Computer Engineering vol26 no 3 pp 31ndash32 2000

[16] J Li G Chen Z Chi and C Lu ldquoImage coding qualityassessment using fuzzy integrals with a three-component imagemodelrdquo IEEE Transactions on Fuzzy Systems vol 12 no 1 pp99ndash106 2004


[17] L ShuTao andW Yaonan ldquoSelection of optimal decompositionlevel of wavelet for multi focus image fusionrdquo Systems Engineer-ing and Electronics vol 24 no 6 pp 45ndash48 2002

[18] T Tu S Su H Shyu and P S Huang ldquoA new look at IHS-likeimage fusion methodsrdquo Information Fusion vol 2 no 3 pp177ndash186 2001

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



for studying fusion technique of current remote sensingimage

Wavelet transformhas sound frequency division propertyin transform domain and statistical characteristics of waveletsparse reflected the obvious features of remote sensing imagelike edge line and domain and so forth Coefficient oflow frequency of multispectral image is kept to carry outoptimized fusion to the high frequency part of two imagesin accordance with weighting coefficient so as to create newfusion image The test carried out with remote sensing imagedata proved the effectiveness of this algorithm The methodfor integrating the two single factors of spectral informationand spatial resolution and the determination of the optimalpoint during the course of iterative optimization are still theproblems demanding prompt solution

This paper presented an image fusion method based onfuzzy integral specific to multispectral and high-resolutionimage fusion problem This method effectively integratedtwo single factor indexes of spectral information and spatialresolution and carried out pixel-level optimal fusion andintroduced fuzzy integral method which can convenientlyand efficiently determine the optimal weight number

2 Fusion Method and Fusion Rules of RemoteSensing Image

21 Fusion Method The detailed steps of image fusionmethod based on fuzzy integral are as follows [3ndash9]

(1) respectively register high resolution image spot intothree wave bands of multispectral image dmtm

(2) extract the three wave bands of multispectral imagedmtm respectively carry out 3 layers of wavelettransform to extract its coefficient of low frequency

(3) carry out 3 layers of wavelet transform to highresolution image spot so as to extract its coefficientsof high and low frequency

(4) carry out infusion to images in various wave bands inaccordance with fusion and image after fusion can beobtained after wavelet transform

(5) rectify weighting coefficients 1198961 and 1198962 of data fusionin fusion rules in accordance with optimizing evalua-tion index of fusion image and repeat Steps (4) sim (5)

(6) efficiently determine the optimal value of 119896 withutilization of fuzzy integral to end the optimizingprocess

(7) fusion image can be obtained after integrating thefusion image of the three wave bands

22 Fusion Rules The fusion rules of multispectral imagedmtm and high resolution image spot after 3 layers of waveletdecomposition are as follows

(1) extract the 3rd layer of coefficient of low frequency ofmultispectral image

(2) determine the fusion value of high frequency coef-ficient according to the following equation so as tocarry out pixel-level fusion

119860 = 11989611198601 + 11989621198602 (1)

wherein 1198601 and 1198602 are high frequency coefficients of dmtmand spot respectively 1198961 and 1198962 are required optimal weightcoefficients 1198961 and 1198962 meet 1198961 + 1198962 = 1 that is thedetermination of optimal weight coefficients can come downto 119896 = 1198961 = 1 minus 1198962 which meets the objective function

(3) carry out the 3rd layer of wavelet inverse transformaccording to the 3rd coefficient of low frequency ofmultispectral image and the high frequency coeffi-cient after being processed

(4) take the image value of the 3rd layer of wavelet afterinverse transform as the coefficient of low frequencyof the 2nd layer of wavelet transform and the highfrequency coefficient is calculated according to (1)

(5) carry out the 1st layer of wavelet inverse transformaccording to Steps (3) and (4) to obtain the fusionimage

23 Optimizing Evaluation Index of Fusion Image andOptimalObjective Function

231 Evaluation Index of Spectral Information Correlationdegree of fusion image and multispectral image is used toidentify the evaluation index of spectral information Set 119891be image after fusion and119891

0bemultispectral image Different

Gaussian templates are selected in accordance with spatialresolution of multispectral image to carry out passivatingtreatment The lower the resolution ratio of 119891

0is the larger

the passivating template will be The evaluation index foridentifying spectral information is

119864sp = Corr (119891 1198910) =

sum119899

119895=1(119891119895minus 119891) (119891

0119895minus 1198910)2

radicsum119899

119895=1(119891119895minus 119891)2

sum119899

119895=1(1198910119895minus 1198910)2

(2)

wherein 119899 is the number of pixel points in image 119891 and 1198910

are gray average of image degree of correlation Corr(119891 1198910)

reflects similarity level of image 119891 1198910

232 Evaluation Index of Spatial Resolution Correspondingcorrelation degree of fusion image between high-frequencycomponent of gray scale and high-frequency component ofhigh-resolution image is used to identify index under spatialresolution [10ndash13] Set 119891

119867be high-resolution panchromatic

image Firstly the fusion image is transformed to grey levelimage and then to carry out wavelet decomposition so as toobtain 4 components119891

119886119891ℎ119891V119891119889 of the fusion image which

respectively present low-frequency component of fusionimage high-frequency component in horizontal directionhigh-frequency component in vertical direction and high-frequency component in diagonal direction In the same way



119891119867V and 119891

119867119889


119864119867119865

=[Corr (119891

ℎ 119891119867ℎ) + Corr (119891V 119891119867V) + Corr (119891

119889 119891119867119889)]

3

(3)

3 Proposed Method


120582measure can







2




2 then 119892(119909

1) = 119892

1 119892(119909

2) = 119892

2

119892(1199091 1199092) = 119892(119909

1) + 119892(119909

2) = 1 119890(119909) is evaluation


1) = 119864sp and 119890(119909

2) = 119864

119867119865



int119909

119890 (119909) ∘ 119892 (119909) = sup120597isin[01]

min [120597 119892 (119883 cap 119864120597)]

= max120597isin[01]

[min (120597 119892 (119864120597))]

(4)


2according to the


1and 120583

2


119890(1205831) 119864120597= 1198641= 1205831 1205832 then 119892(119864

1) = 1 when 120597 = 119890(120583

2)

119864120576= 1198642= 1205832 then 119892(119864

2) = 119892(120583

2)


119865 = sup min [119890 (1205831) 119892 (119864

1)] min [119890 (120583

2) 119892 (119864

2)] (5)



1and 1199092from


119890(1205831) = 1198902 119892(1198641) = 1 119890(120583

2) = 1198901 119892(1198642) = 119892(120583

2) =

119892(1199091) = 119892


1sdot

1198921 1198902)


1and 1199092from


119890(1205831) = 1198901 119892(1198641) = 1 119890(120583

2) = 1198902 119892(1198642) = 119892(120583

2) =

119892(1199092) = 119892


1 1198902sdot

1198922)


(1) and (2)






















1and 119892



1and 119892

2values will influ-





1and 119892


119864ℎ119891











Table 1

(a)

1198921= 07 119892

2= 03 119896 119865 119864sp 119864

ℎ119891


(b)

1198921= 03 119892

2= 07 119896 119865 119864sp 119864

ℎ119891


(c)

1198921= 02 119892

2= 08 119896 119865 119864sp 119864

ℎ119891





120583 =1

119899

119899

sum

119894=1

119909119894

2=

1

119899 minus 1

119899

sum

119894=1

(119909119894minus 120583)2 (6)











The 2nd waveband

The 3rd waveband



219932 240895 194255


262368 313601 250627










sum119894119895[(119891119894119895minus 119890119891) times (119892

119894119895minus 119890119892)]

radicsum119894119895[(119891119894119895minus 119890119891)2

] times sum119894119895[(119892119894119895minus 119890119892)2

]

(7)

wherein 119891119894119895






119863 =1

119899sum

119894

sum

119895

100381610038161003816100381610038161198811015840

119894119895minus 119881119894119895

10038161003816100381610038161003816 (8)














The 1st waveband

The 2nd waveband

The 3rd waveband


77653 77870 186638


133177 187888 189686



119894119895and 119881








The 2nd waveband

The 3rd waveband


45291 47003 45535


44169 46055 44781


43177 44789 43436



1199010= 1199011= sdot sdot sdot = 119901

119871minus1=1

119871 119867 = minus119888

119871minus1

sum

119894=0

119901119894ln119901119894 (9)


0 1199011 119901

119871minus1



119867 = minus

119871minus1

sum

119894=0

119901119894ln119901119894 (10)



119871minus1= 1119871 119867 = ln 119871





5 Conclusions








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119891119867V and 119891

119867119889


119864119867119865

=[Corr (119891

ℎ 119891119867ℎ) + Corr (119891V 119891119867V) + Corr (119891

119889 119891119867119889)]

3

(3)

3 Proposed Method


120582measure can







2




2 then 119892(119909

1) = 119892

1 119892(119909

2) = 119892

2

119892(1199091 1199092) = 119892(119909

1) + 119892(119909

2) = 1 119890(119909) is evaluation


1) = 119864sp and 119890(119909

2) = 119864

119867119865



int119909

119890 (119909) ∘ 119892 (119909) = sup120597isin[01]

min [120597 119892 (119883 cap 119864120597)]

= max120597isin[01]

[min (120597 119892 (119864120597))]

(4)


2according to the


1and 120583

2


119890(1205831) 119864120597= 1198641= 1205831 1205832 then 119892(119864

1) = 1 when 120597 = 119890(120583

2)

119864120576= 1198642= 1205832 then 119892(119864

2) = 119892(120583

2)


119865 = sup min [119890 (1205831) 119892 (119864

1)] min [119890 (120583

2) 119892 (119864

2)] (5)



1and 1199092from


119890(1205831) = 1198902 119892(1198641) = 1 119890(120583

2) = 1198901 119892(1198642) = 119892(120583

2) =

119892(1199091) = 119892


1sdot

1198921 1198902)


1and 1199092from


119890(1205831) = 1198901 119892(1198641) = 1 119890(120583

2) = 1198902 119892(1198642) = 119892(120583

2) =

119892(1199092) = 119892


1 1198902sdot

1198922)


(1) and (2)






















1and 119892



1and 119892

2values will influ-





1and 119892


119864ℎ119891











Table 1

(a)

1198921= 07 119892

2= 03 119896 119865 119864sp 119864

ℎ119891


(b)

1198921= 03 119892

2= 07 119896 119865 119864sp 119864

ℎ119891


(c)

1198921= 02 119892

2= 08 119896 119865 119864sp 119864

ℎ119891





120583 =1

119899

119899

sum

119894=1

119909119894

2=

1

119899 minus 1

119899

sum

119894=1

(119909119894minus 120583)2 (6)











The 2nd waveband

The 3rd waveband



219932 240895 194255


262368 313601 250627










sum119894119895[(119891119894119895minus 119890119891) times (119892

119894119895minus 119890119892)]

radicsum119894119895[(119891119894119895minus 119890119891)2

] times sum119894119895[(119892119894119895minus 119890119892)2

]

(7)

wherein 119891119894119895






119863 =1

119899sum

119894

sum

119895

100381610038161003816100381610038161198811015840

119894119895minus 119881119894119895

10038161003816100381610038161003816 (8)














The 1st waveband

The 2nd waveband

The 3rd waveband


77653 77870 186638


133177 187888 189686



119894119895and 119881








The 2nd waveband

The 3rd waveband


45291 47003 45535


44169 46055 44781


43177 44789 43436



1199010= 1199011= sdot sdot sdot = 119901

119871minus1=1

119871 119867 = minus119888

119871minus1

sum

119894=0

119901119894ln119901119894 (9)


0 1199011 119901

119871minus1



119867 = minus

119871minus1

sum

119894=0

119901119894ln119901119894 (10)



119871minus1= 1119871 119867 = ln 119871





5 Conclusions








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















1and 119892



1and 119892

2values will influ-





1and 119892


119864ℎ119891











Table 1

(a)

1198921= 07 119892

2= 03 119896 119865 119864sp 119864

ℎ119891


(b)

1198921= 03 119892

2= 07 119896 119865 119864sp 119864

ℎ119891


(c)

1198921= 02 119892

2= 08 119896 119865 119864sp 119864

ℎ119891





120583 =1

119899

119899

sum

119894=1

119909119894

2=

1

119899 minus 1

119899

sum

119894=1

(119909119894minus 120583)2 (6)











The 2nd waveband

The 3rd waveband



219932 240895 194255


262368 313601 250627










sum119894119895[(119891119894119895minus 119890119891) times (119892

119894119895minus 119890119892)]

radicsum119894119895[(119891119894119895minus 119890119891)2

] times sum119894119895[(119892119894119895minus 119890119892)2

]

(7)

wherein 119891119894119895






119863 =1

119899sum

119894

sum

119895

100381610038161003816100381610038161198811015840

119894119895minus 119881119894119895

10038161003816100381610038161003816 (8)














The 1st waveband

The 2nd waveband

The 3rd waveband


77653 77870 186638


133177 187888 189686



119894119895and 119881








The 2nd waveband

The 3rd waveband


45291 47003 45535


44169 46055 44781


43177 44789 43436



1199010= 1199011= sdot sdot sdot = 119901

119871minus1=1

119871 119867 = minus119888

119871minus1

sum

119894=0

119901119894ln119901119894 (9)


0 1199011 119901

119871minus1



119867 = minus

119871minus1

sum

119894=0

119901119894ln119901119894 (10)



119871minus1= 1119871 119867 = ln 119871





5 Conclusions








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Table 1

(a)

1198921= 07 119892

2= 03 119896 119865 119864sp 119864

ℎ119891


(b)

1198921= 03 119892

2= 07 119896 119865 119864sp 119864

ℎ119891


(c)

1198921= 02 119892

2= 08 119896 119865 119864sp 119864

ℎ119891





120583 =1

119899

119899

sum

119894=1

119909119894

2=

1

119899 minus 1

119899

sum

119894=1

(119909119894minus 120583)2 (6)











The 2nd waveband

The 3rd waveband



219932 240895 194255


262368 313601 250627










sum119894119895[(119891119894119895minus 119890119891) times (119892

119894119895minus 119890119892)]

radicsum119894119895[(119891119894119895minus 119890119891)2

] times sum119894119895[(119892119894119895minus 119890119892)2

]

(7)

wherein 119891119894119895






119863 =1

119899sum

119894

sum

119895

100381610038161003816100381610038161198811015840

119894119895minus 119881119894119895

10038161003816100381610038161003816 (8)














The 1st waveband

The 2nd waveband

The 3rd waveband


77653 77870 186638


133177 187888 189686



119894119895and 119881








The 2nd waveband

The 3rd waveband


45291 47003 45535


44169 46055 44781


43177 44789 43436



1199010= 1199011= sdot sdot sdot = 119901

119871minus1=1

119871 119867 = minus119888

119871minus1

sum

119894=0

119901119894ln119901119894 (9)


0 1199011 119901

119871minus1



119867 = minus

119871minus1

sum

119894=0

119901119894ln119901119894 (10)



119871minus1= 1119871 119867 = ln 119871





5 Conclusions








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














The 2nd waveband

The 3rd waveband



219932 240895 194255


262368 313601 250627










sum119894119895[(119891119894119895minus 119890119891) times (119892

119894119895minus 119890119892)]

radicsum119894119895[(119891119894119895minus 119890119891)2

] times sum119894119895[(119892119894119895minus 119890119892)2

]

(7)

wherein 119891119894119895






119863 =1

119899sum

119894

sum

119895

100381610038161003816100381610038161198811015840

119894119895minus 119881119894119895

10038161003816100381610038161003816 (8)














The 1st waveband

The 2nd waveband

The 3rd waveband


77653 77870 186638


133177 187888 189686



119894119895and 119881








The 2nd waveband

The 3rd waveband


45291 47003 45535


44169 46055 44781


43177 44789 43436



1199010= 1199011= sdot sdot sdot = 119901

119871minus1=1

119871 119867 = minus119888

119871minus1

sum

119894=0

119901119894ln119901119894 (9)


0 1199011 119901

119871minus1



119867 = minus

119871minus1

sum

119894=0

119901119894ln119901119894 (10)



119871minus1= 1119871 119867 = ln 119871





5 Conclusions








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















The 1st waveband

The 2nd waveband

The 3rd waveband


77653 77870 186638


133177 187888 189686



119894119895and 119881








The 2nd waveband

The 3rd waveband


45291 47003 45535


44169 46055 44781


43177 44789 43436



1199010= 1199011= sdot sdot sdot = 119901

119871minus1=1

119871 119867 = minus119888

119871minus1

sum

119894=0

119901119894ln119901119894 (9)


0 1199011 119901

119871minus1



119867 = minus

119871minus1

sum

119894=0

119901119894ln119901119894 (10)



119871minus1= 1119871 119867 = ln 119871





5 Conclusions








References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5 Conclusions








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









Documents

Research Article Fusion Method for Remote Sensing Image ...downloads.hindawi.com/journals/jece/2014/437939.pdf · tiveness of remote sensing image fusion method based on fuzzy integral,