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Optik 125 (2014) 146– 153

Contents lists available at ScienceDirect

Optik

j o ur nal hom epage: www.elsev ier .de / i j leo

medical image fusion method based on energy classification ofEMD components

aohua Zhang ∗, Chuanting Zhang, Jianshuai Wu, He Liuchool of Information Engineering, Inner Mongolia University of Science and Technology, Baotou, Inner Mongolia 014010, PR China

r t i c l e i n f o

rticle history:eceived 29 January 2013ccepted 5 June 2013

eywords:edical image fusion

i-dimensional empirical mode

a b s t r a c t

A medical image fusion method based on bi-dimensional empirical mode decomposition (BEMD) anddual-channel PCNN is proposed in this paper. The multi-modality medical images are decomposed intointrinsic mode function (IMF) components and a residue component. IMF components are divided intohigh-frequency and low-frequency components based on the component energy. Fusion coefficients areachieved by the following fusion rule: high frequency components and the residue component are super-imposed to get more textures; low frequency components contain more details of the source image whichare input into dual-channel PCNN to select fusion coefficients, the fused medical image is achieved by

ecompositionual-channel PCNNnergy classificationntrinsic mode function

inverse transformation of BEMD. BEMD is a self-adaptive tool for analyzing nonlinear and non-stationarydata; it doesn’t need to predefine filter or basis function. Dual-channel PCNN reduces the computationalcomplexity and has a good ability in selecting fusion coefficients. A combined application of BEMD anddual-channel PCNN can extract the details of the image information more effectively. The experimentalresult shows the proposed algorithm gets better fusion result and has more advantages comparing withtraditional fusion algorithms.

. Introduction

Medical image fusion is a hot spot in medical image processingomain. At present, medical imaging mode is divided into twoategories: anatomical imaging modality and functional imagingodality. All medical image information is combined to process

he fusion of the multi-modality image, it benefits for finding morealuable information.

Medical image fusion aims at SPECT and MRI, CT and MRI,PECT and CT etc., multimode medical images. Wavelet transform isidely used in medical image fusion. It has good frequency charac-

eristics, but the wavelet transform depends on the predefined filterr the wavelet basis function; on the other hand, different filter oravelet basis function has a great influence in fusion results.

In order to expand the multi-scale analysis method, Huangroposed intrinsic mode function (IMF) and empirical modeecomposition (EMD) in 1998 [1]. EMD is an adaptive and multi-cale signal processing tool. The method can analyze non-linearitynd non-stationary data well [2]. EMD is a novel data represen-

ation and it has better spatial and frequency characteristics thanavelet analysis. 1D EMD with better physical characteristics can

e expanded to analyze 2D signal. EMD has already been used in the

∗ Corresponding author.E-mail address: zbh wj2004@imust.cn (B. Zhang).

030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.ttp://dx.doi.org/10.1016/j.ijleo.2013.06.075

© 2013 Elsevier GmbH. All rights reserved.

field of physical geography, biomedicine, mechanical engineeringand other fields [3].

In the process of 1D EMD screening, cubic spline function thatconstructs enveloping surfaces will be divergent in both ends ofthe data series and the edges will have large errors. On the otherhand, the errors propagate inward in the process of screening anddata series are polluted. Data will have boundary effect after Hilberttransformation.

For high-frequency IMF components are influenced by theboundary effect of EMD less than low-frequency IMF components[4], in order to improve the result of medical image fusion, dual-channel PCNN is proposed to select low-frequency coefficients inthis paper. IMF components on each layer include different spa-tial scale information. Although textures in several spatial scalesare different obviously, the method is convenient to extract thesetextures.

The outline of the paper is as follows. We introduce the BEMDin Section 2 to state method of BEMD in images decomposition andBIMF component classifier. In Section 3, we introduce dual-channelPCNN which is good at selecting fusion coefficients. In Section 4, theproposed fusion method is used for selecting coefficients whichare from BEMD. Then, we introduce the fusion steps in details. In

Section 5, we detailed analyze the advantages of the algorithmproposed in the paper using several groups of experiments andcomparing with classical methods of medical image fusion. In Sec-tion 6, it is conclusions.

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. BEMD and BIMF component classifier

.1. Method of BEMD

For 2D signal, such as image, source image can be decomposednto several 2D IMF components and a residue component by BEMD5,6], whose frequencies are from high to low. BIMF meets twoonstraints: the local mean of the original 2D signals should beymmetric and its own mean is zero; its maximum is positive,inimum is negative. IMF components have the following char-

cteristics: (1) In data set, the number of maximum points set andinimum points is equal to the number of zero crossing points,

r their difference is less than 1; (2) At any point, the mean ofnvelope constituted by minimum and maximum is close to zero.MF components are near orthogonal, they represent every fre-uency of local data and they correspond to high-frequency and

ow frequency data, the residue component represents develop-ent tendency of the original image. BEMD is a kind of completely

elf-adaptive decomposition, a large extent image decomposi-ion depends on the characteristics of data itself. It means that ifcreening stop condition is consistent, the number of BIMF dependsn the data characteristics [7]. So, the number of BIMF may beifferent in different images. The steps of BEMD algorithm are asollows:

) Initialization, the residue component R = I, I is the source image.) If the residue R is monotone or it reaches decomposition number

of an image, the algorithm stops; Otherwise, make H = R and thescreening process starts.

) The extrema in image P are achieved, maximum points set andminimum points set in the region are searched.

) The maximum points set and the minimum points set are planeinterpolated, and upper enveloping surfaces U(m, n) and lowerenveloping surfaces L(m, n) of the image are achieved, the meanvalue M of the image H is also solved by enveloping surfaces.

M(m, n) = (U(m, n) + L(m, n))/2

) Hk(m, n) = Hk−1(m, n) − M(m, n), screening process is used forjudging the stop condition which is shown in formula (6), if thestop condition is not satisfied, turns to step 3.

) If the BIMF D(m, n) = H(m, n), an IMF component is achieved.) Function R(m, n) can be expressed by R(m, n) = R(m, n) − D(m, n),

and turns to step 2.

In the above method, the cores of the method are plane inter-olation, how to get extrema and screening stop condition. After J

ayers BEMD, the final decomposition process can be expressed as:

(m, n) =J∑

j=1

Dj(m, n) + RJ(m, n), J ∈ N (1)

where Dj is the jth 2D BIMF, RJ is the residue component after Jayers decomposition.

.2. Time-frequency characteristics of BEMD

1D IMF is a kind of simple-component, at any time, there is onlyn instantaneous frequency, and its instantaneous frequency cane solved by HHT [8,9]. For BIMF, it is a kind of multi-component,

t needs to be transformed by Hilbert transform to get the ampli-

ude and phase of the image. For the ith BIMF component, it will beepresented as a complex value simple-component:

i(t) = Di(t) + j · H(Di(t)) = ai(t)ej�i(t) (2)

5 (2014) 146– 153 147

where t = [m, n]T, Di (t) is the ith BIMF, H(Di (t)) is the 2D Hilberttransformation, ai(t) is the amplitude modulation function of BIMF,�i(t) is the phase modulation function of BIMF.

Local instantaneous frequency can be computed using phasemodulation function. Because phase modulation function is 2D, soinstantaneous frequency is directional, local horizontal instanta-neous frequency and local vertical instantaneous frequency can beachieved taking the derivative of horizontal and vertical instanta-neous frequency:

fm = ∂

∂m�i(t), fn = ∂

∂n�i(t) (3)

The instantaneous frequency of BIMF component makes useof the solved local horizontal instantaneous frequency and localvertical instantaneous frequency. The root-mean-square of localhorizontal instantaneous frequency and local vertical instan-taneous frequency of BIMF are selected as the instantaneousfrequency features. It is available to show local point information;its definition is shown as follows:

E(m, n) =

√(∂

∂m�i(t)

)2 +(

∂∂n

�i(t))2

2(4)

2.3. Key issues of BEMD

2.3.1. Plane interpolation methodIn BEMD, discrete points are processed by interpolation to get

fitting surface. Its main methods include triangulation combinedlinear interpolation and radial basis function interpolation. In 2Dspace, triangulation interpolation is that the interpolation regionis segmented into simple small triangle regions, interpolation sur-face is constructed in small triangles, and small triangles are splicedto get a big interpolation surface. The extrema in the image areregarded as discrete points to rebuild surfaces in radial basis func-tion interpolation.

Its general solution is:

s(t) = p(t) +N∑

i=1

�i�(||t − ti||) (5)

where p(t) is the first order polynomial, by solving first N + 3 orderlinear system of equations, combination coefficient �i and multino-mial coefficient ci of radial basis function can be achieved. The entireinterpolation surface is achieved substituting all points coordinatevalues. Triangulation interpolation is fast, but has large errors inthe low-frequency image. It is fit for decomposing high-frequencyparts in high-frequency image. Radial basis function interpolationis fit for low-frequency image with less extrema.

In plane interpolation, the extrema are processed by Delaunaytriangulation. Cubic interpolation is introduced in the divided tri-angles. The advantages of the method based on triangulation andcubic interpolation are as follows: firstly, extrema (the maximumor the minimum) used for interpolation are not must square meshand the extrema in an image are normally discrete, irregular; On theother hand, the interpolation plane from the method is not smooth,in fact, it is 2D plane interpolation.

The extrema symmetric extension is proposed in this paper toprevent end effect of BEMD. Edge of the image is regarded as sym-metry axis, and extrema around edges are expended. Extension isto make the decomposed data completely and the errors aroundfour edges are reduced to propagate inwardly.

2.3.2. The stop condition of screening process of BEMDThe number of zero crossing points in BIMF is not easy to statis-

tics, so the constraint condition of BIMF can be regarded as the stop

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48 B. Zhang et al. / Op

ondition of screening process of BEMD. Cauchy-type convergenceonditions and energy difference trace can also be used as the stopondition. In this paper, Cauchy-type convergence conditions areelected, and SD is 0.3.

The stop condition of screening process is: SD is used for repre-enting the standard deviation. For 2D BEMD, SD is shown as theollowing formula (6). If SD is less than the threshold, the screeningrocess stops.

D =X∑x

Y∑y

(hk−1(x, y) − hk(x, y))2

h2k−1(x, y)

(6)

here x, y are the width and height of the image. Standard devi-tion is based on the convergence of BEMD. In screening process,k(x, y) is more and more close to IMF components steadily. So, theumerator in formula (6) is more and more close to zero, it meanshat SD is close to zero finally.

.4. BIMF component classifier

Fig. 1 is an example of BEMD, Fig. 1(a) is decomposed into 9

ayers, Fig. 1(b–j) are BIMF components from the first layer to theth layer and Fig. 1(k) is the residue component. BEMD has theollowing advantages:

Fig. 1. Example of BEMD.

5 (2014) 146– 153

(1) The decomposed images achieved by BEMD are from fine tocoarse and undistorted, its results are ideal and it is good fortexture extraction.

(2) The image is divided into small parts and large coefficientmatrix is changed into small matrix during every screeningprocess. It can save memory space of matrix efficiently.

(3) The computing speed is improved by the way of dividing imageinto small parts.

For BIMF components are extracted layer-by-layer, it is localfrequency is from high to low values. Local frequency of BIMF com-ponents includes some strong contrast physical information, suchas highlight edges of source images, line and zone boundary, etc.In this paper, image features are extracted from 2D BIMF compo-nents based on dual-channel PCNN. The features are used for fusingimage and improving fusion results.

Each BIMF component contains different frequency coefficients,the lower the order of the BIMF, the more high-frequencycoefficients contains. Coefficients magnitude of different BIMFcomponents varies greatly. So BIMF’s energy can be adopted as afeature to classify the components. Parseval’s theorem is used toobtain the energy of the original image (E) and the energy of eachIMF component (Ei); Ri can be selected as the classification criteria.

Ri = Ei

E(7)

Ei = 1S

S−1∑i=0

Li2 (8)

where Li is the amplitude of the amplitude spectrum, S is the num-ber of coefficients which the component contains, i is the layersnumber of BIMF components.

The number of image decomposition layers decides the amountof images information of the BIMF and residue components contain,Fig. 1(a) is decomposed into 1–4 layers respectively, Fig. 2(a–h) arethe BIMF and residue components. Fig. 2(e–h) shows that the morelayers, the less information the residue component contains. Forfurther analysis, Fig. 1(a) is decomposed into 9 layers in this paper;Fig. 3 shows the energy distribution corresponding to the respec-tive layers component. The energy contains in the components ofthe different layers are different, the former three and the residuecomponent contain larger energy than others.

The relationship between the energy and the image informationcan be shown in Fig. 4(a–f), are the different layers of BIMF compo-nents superimposed the residue component. Fig. 4(c–e) is almostno difference which proves that less energy the component has lessinformation the component contains.

In this paper BIMF components are divided into two categories:high-frequency and low-frequency components accordance withtheir energies, if the formula (9) is satisfied, the components willbe selected as the high-frequency components, the remaining BIMFcomponents are selected as the low-frequency components.⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

Tj =

j∑i=1

Ej

E> 90%

Ei

Ei+1< 5, i = 1, 2, ...n − 1

(9)

where Tj represents the proportion of the first j layers BIMF compo-nents and the total energy, j represents the layer number of satisfythe conditions of the high-frequency components, n representsBIMF layer number component.

B. Zhang et al. / Optik 125 (2014) 146– 153 149

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neuron, its value is 0 or 1, Tij is the dynamic threshold, ˛L, ˛Tisthe constant, Uij is the firing mapping image, and it is the inter-nal activity of neuron. The final image can be achieved using Uij. IfUij[n] > Tij[n], the neuron generates a pulse, called a firing. In fact,

Fig. 2. BIMF component

. Dual-channel PCNN

PCNN has complex structure and needs to set many parame-ers [10], even the improved simplified model has shortcomingsf uneven brightness zone resolution, and it’s not conducive toim image information extracting [11,12]. In contrast, dual-channelCNN has an advantage in this regard [13]. The low-frequency com-onents are significantly dim compare with other components.

The dual-channel PCNN is different from PCNN in compositionf neurons, as shown in Fig. 5:

The dual-channel PCNN neurons include: the receptive field,odulation domain and pulse generating domain. The dual-

hannel PCNN can be expressed as follows:The receptive field:

Aij [n] = SA

ij [n] (10)

Bij [n] = SB

ij[n] (11)

ij[n] = e−˛L Lij[n − 1] + VL

∑kl

WijklYkl[n − 1] (12)

odulation domain:

ij[n] = max(FAij [n](1 + ˇA

ij[n]Lij[n]), FBij [n](1 + ˇB

ij[n]Lij[n])) (13)

Fig. 3. Energy comparison of BEMD components.

the residue component.

pulse generating domain:

Yij[n] ={

1, Uij[n] > Tij[n]

0, otherwise(14)

Tij[n] = e−˛T Tij[n − 1] + VT Yij[n] (15)

where FAij

and FBij

are external outputs, SAij

[n], SBij[n] represent the

input stimulus, n represents the number of iterations, Lij is the link-ing input. ̌ is the linking weight. wijkl is the synaptic connections,VL, VT are normalization constants, Yij is the pulse output of the

Fig. 4. Components selectively superposition (a) the first layer superposed theresidue, (b) the first two layers superposed the residue, (c) the first 3 layers super-posed the residue, (d) the first 4 layers superposed the residue, (e) the first 5 layerssuperposed the residue, (f) the first 3 layers superposed.

150 B. Zhang et al. / Optik 125 (2014) 146– 153

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(

CoefFd =CoefAd, if(Ud[n] = FA,d[n](1 + ˇA,dLd[n])

CoefBd, if(Ud[n] = FB,d[n](1 + ˇB,dLd[n])(16)

Fig. 5. The model of Dual-channel PCNN.

fter n iterations, the number of firings of the neuron is used toepresent the information of the image at the corresponding point.iring map is constructed by the number of firings and is regardeds output of dual-channel PCNN.

Aim to shortcomings of PCNN model in image fusion domain,ombines with the characteristics of multi-focus image, this paperroposes the dual-channel PCNN which are motivated by low-requency components of BIMF. The low-frequency componentseflect the image details; details of the original images can be bettereflected in the fused image.

. Medical image fusion based on BEMD and dual-channelCNN

Medical image is severely affected by the noise, the contrast ofhe image is low and it is difficult to distinguish the details by theuman eye. So the fusion method needs to consider the particular-

ties of the medical image. In BEMD, medical image is decomposednto BIMF components and a residue component. They representifferent physical meanings: the residue component is the approxi-ate representation of the medical image gray value and it contains

he texture information, BIMF components represent the edge andtructural information of the medical image, there are significantifferences among BIMF components. To compare the medical

mage with the other images, CT and MR images are decomposednto 9 layers in this paper, Fig. 6 shows the energy distribution ofach layer, and it is significantly different to Fig. 4, the residue com-onent contains less image information and there are significantifferences among BIMF components, Fig. 7 shows the superimpos-

ng results of different decomposed layers of Fig. 6(b), Fig. 7(a–c)ave significant discrepancies in their respective energies, the dif-

erences of the image are obvious, Fig. 7(c–e) have approximatelyquivalent energies, they are difficult to distinguish, BIMF com-onents can be classified as high frequency and low frequencyomponents, the high frequency components contain more tex-ures, which have larger energy and have been affected by noiseeriously, low frequency components have less energy but containhe edge information. BIMF components can be divided into theow frequency and high frequency components based on energy ofhe components, and then fusion rules are built respectively, in thisay the contrast of the image will be enhanced and the edge and

tructure information of the medical image will be protected, theused image will contain rich image textures and details.

The fusion rules are built to fuse the BIMF components and theesidue component respectively, suppose N is the times of iterationf dual-channel PCNN and detailed fusion steps are as follows:

1) Registration medical image A and B are decomposed by BEMD

and getting a series of BIMF components and a residue compo-nent;

2) BIMF components are divided into two categories according toformula (9): low frequency and high frequency components;

Fig. 6. Energy distribution and energy ratio of different components.

(3) High frequency components and the residue component aresuperimposed;

(4) Low frequency components are input into dual-channel PCNNto select the low frequency fusion coefficients;(4.1) Initialization: Ld

ij[0] = 0, Ud

ij[0] = 0, �d

ij[0] =

0, Ydij

[0] = 0, � = 0.4, d is the dth layer.(4.2) According to formulas (10–15),

Ldij[n], Ud

ij[n], �d

ij[n], Yd

ij[n] are calculated.

(4.3) If n = N is satisfied, the iteration finishes. The selection ruleof fusion coefficients is as follows:{

Fig. 7. Components selectively superposition (a) the first layer, (b) the first twolayers, (c) the first 3 layers, (d) the first 9 layers, (e) the source image.

B. Zhang et al. / Optik 12

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Fig. 8. The algorithm structure diagram.

where CoefFd is the fusion coefficient. CoefAd and CoefBd

are respectively the corresponding BIMF coefficients inimage A and B; low frequency fusion coefficients areselected.

5) The entire coefficients are transformed into the fused imagebased on BEMD inverse transform. The algorithm structure dia-gram of the paper is shown in Fig. 8.

. Experimental results and analysis

Three groups’ experiments are done to verify the proposedlgorithm in the paper. Every group’s experimental images areegistrated [14]. Fig. 6(a and b) is the source image in the first group

xperiment. Fig. 6(a) is CT image, Fig. 6(b) is MR image; Fig. 9(a–d)s the source images of the second and the third group experi-

ents. Fig. 9(a and c) is CT images; Fig. 9(b and d) is MR images. Allhese images are considered as referenced images to compare with

Fig. 9. Source image.

5 (2014) 146– 153 151

fusion images attained from the proposed algorithm in the paperand other algorithms.

5.1. Objectivity evaluation index

5.1.1. Mutual informationMutual information expresses how much information of source

image is fused into the result image [15]. The larger the mutualinformation is, the better the fusion effect. Supposed that A and Bare source images and F is the fused image, then the calculationof mutual information between A and F, B and F are respectivelyshown as formulas (17) and (18):

IAF =∑a,f

pAF (a, f ) logpAF (a, f )

pA(a)pF (f )(17)

IBF =∑b,f

pBF (b, f ) logpBF (b, f )

pB(b)pF (f )(18)

where pAF and pBF are joint histogram of the source images and F, pA,pB, pF are respectively the histogram of A, B, C and a, b, f are the pixelvalues of respective image. The calculation of mutual informationis shown as formula (19):

MI = IAF + IBF (19)

5.1.2. QAB/F

QAB/F expresses how much edge information is fused from thesource image into the fusion image [16]. The larger the value of QAB/F

is, the more edge information will be fused into the fusion image.The better fusion result is achieved. QAB/F is shown as formula (20):

Q AB/F =

N∑n=1

M∑m=1

(Q AF (n, m)wA(n, m) + Q BF (n, m)wB(n, m))

N∑i=1

M∑j=1

(wA(i, j) + wB(i, j))

(20)

Q AF (n, m) = Q AFg (n, m)Q AF

a (n, m) with 0 ≤ QAF(n, m) ≤ 1, Q AFg (n, m)

and Q AFa (n, m) model perceptual loss of information in F, in terms of

how well the strength and directional values of a pixel (n, m) in A orB are represented in the fusion image. If A = 0, it corresponds to thecomplete loss of edge information at location (n, m) as transferredfrom A or B into F. If A = 1, it indicates “fusion” from A to F with noloss of information. wA(n, m) and wB(n, m) reflect the importanceof QAF(n, m) and QBF(n, m).

5.2. Analysis of fusion results

The fusion results of the first group experiment are shown inFig. 10. Fig. 10(a) is the fusion result using the proposed method.Fig. 10(b–f) are the fusion images based on the Laplacian (Lap)method, discrete wavelet transform (DWT) method, shift invari-ant DWT (SIDWT) method, gradient pyramid and ratio pyramidmethod, respectively. In Fig. 10(a–f), it is evidently to find thatthe fusion image of the proposed method is clearer than othermethods. Moreover, the fusion result of DWT-based method, asshown in Fig. 10(c), introduces many ‘artifacts’ around edgesbecause DWT lacks shift-invariance. It is proven that the proposedmethod can decrease the pseudo-Gibbs phenomena successfully

and improve the quality of the fusion image. Fig. 10(b) indicatesthat the Laplacian-based method provides better performance infusion medical images compares with DWT-based. However, fromFig. 10(b) is not extracted all useful information of the source

152 B. Zhang et al. / Optik 125 (2014) 146– 153

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Fig. 12. Comparison of fusion results.

Table 1Objective evaluation of the first experiment.

Proposed Lap DWT SIDWT Gradientpyramid

RatioPyramid

MI 3.4596 2.5564 2.1149 2.6289 2.9546 3.2335QAB/F 0.7604 0.7293 0.6162 0.7269 0.6806 0.4640

Table 2Objective evaluation of the second experiment.

Proposed Lap DWT SIDWT Gradientpyramid

RatioPyramid

MI 2.5115 2.7081 2.4050 2.6206 2.5886 2.6202QAB/F 0.6097 0.64119 0.5635 0.6228 0.5994 0.5104

Table 3

Fig. 10. Comparison of fusion results.

mages perfectly. Above all, Fig. 10(a) has the best visual quality andontains most of the useful information of the source images, andeantime, fewer artifacts are introduced during the fusion process.The fusion results of the second and the third group experi-

ents are shown as Figs. 11 and 12. Fig. 11(a–f) and Fig. 12(a–f)re the fusion images based on the above methods, respectively.ig. 11(a) and Fig. 12(a) show the proposed method conveys moreseful information from the source images to the fusion imagehen compares with the other methods.

For further comparison, besides visual observation, two objec-ive evaluation indexes are used to compare the fusion results.he first evaluation index is the mutual information (MI). It is aetric defined as the sum of mutual information between each

nput image and the fused image. The second evaluation indexs QAB/F metric, which considers the amount of edge informationransferred from the input images to the fused image. This methodses a Sobel edge detector to calculate strength and orientation

nformation at each pixel in both source and the fusion images.

n comparison, Tables 1–3 show the objective criteria on mutualnformation (MI) and QAB/F of Figs. 10–12. The indexes show thathe proposed method has the best fusion results.

Fig. 11. Comparison of fusion results.

Objective evaluation of the third experiment.

Proposed Lap DWT SIDWT Gradientpyramid

RatioPyramid

MI 4.1541 3.0212 2.7221 3.0884 3.2534 3.883QAB/F 0.6339 0.6080 0.5351 0.6450 0.5785 0.3729

6. Conclusion

BEMD is a data-driven function, medical image features canbe extracted from decomposed components, and it is fit to pro-cess two-dimensional non-linear and non-steady-state data. Inthis paper, medical images are decomposed by BEMD, image fea-ture extraction is based on BIMF and the residue components,low-frequency fusion coefficients are selected based on the dual-channel PCNN. All of the comparisons indicate the proposedmethod contain more image features; more details are preservedin the fusion process. From analysis above, the conclusion is thatthe proposed algorithm also shows significant improvement overthe traditional fusion methods, whether in subjective evaluation orobjective evaluation criterion.

Acknowledgements

This work was supported by the National Natural Science Foun-dation of China (61261028, 61179019), Ministry of Education

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roject (Z2009-1-01033), Inner Mongolian Natural Science Foun-ation (2010MS0907), Inner Mongolian College research projectsNJ10097).

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