Method of Improved Fuzzy Contrast Combined Adaptive...

Research ArticleMethod of Improved Fuzzy Contrast Combined AdaptiveThreshold in NSCT for Medical Image Enhancement

Fei Zhou1 ZhenHong Jia1 Jie Yang2 and Nikola Kasabov3

1College of Information Science and Engineering Xinjiang University Urumqi 830046 China2Institute of Image Processing and Pattern Recognition Shanghai Jiao Tong University Shanghai 200400 China3Knowledge Engineering and Discovery Research Institute Auckland University of Technology Auckland 1020 New Zealand

Correspondence should be addressed to ZhenHong Jia jzhh9009sohucom

Received 3 November 2016 Revised 6 April 2017 Accepted 14 May 2017 Published 28 June 2017

Academic Editor Ayache Bouakaz

Copyright copy 2017 Fei Zhou et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Noises and artifacts are introduced to medical images due to acquisition techniques and systems This interference leads to lowcontrast and distortion in images which not only impacts the effectiveness of the medical image but also seriously affects theclinical diagnoses This paper proposes an algorithm for medical image enhancement based on the nonsubsampled contourlettransform (NSCT) which combines adaptive threshold and an improved fuzzy set First the original image is decomposed into theNSCT domain with a low-frequency subband and several high-frequency subbands Then a linear transformation is adopted forthe coefficients of the low-frequency component An adaptive threshold method is used for the removal of high-frequency imagenoise Finally the improved fuzzy set is used to enhance the global contrast and the Laplace operator is used to enhance the detailsof themedical images Experiments and simulation results show that the proposedmethod is superior to existingmethods of imagenoise removal improves the contrast of the image significantly and obtains a better visual effect

1 Introduction

Computed tomography (CT) images and Magnetic Reso-nance Imaging (MRI) images are extensively used in thedetection of Cerebrovascular Accidents [1] The quality ofMRI imagery has made it an indispensable part of modernmedicine the quality of MRI imagery also directly influencesthe accuracy of doctorsrsquo diagnoses and treatments Medicalimages often experience interference from factors such asnoises and artifacts that may degrade the quality of theobtained image Additionally noise and artifacts introduceuncertainties to the medical image in the form of vaguenessin the homogeneity of image segments or vague contrastbetween the object and background This makes it diffi-cult to segment or detect the contours and textures of animage Image enhancement is one of the main concernsof image processing At the present time there are manymethods of image enhancement which can be classifiedinto two principal groups spatial domain-based methods

and transformation domain-basedmethodsThe widely usedhistogram equalization- (HE-) based methods are a form ofspatial domain-based methods [2] The resulting image has auniform distribution of intensity after equalization but thesemethods tend to overenhance the contrast if there are highpeaks in the histogram which can result in a harsh and noisyappearance of the resulting image Numerous approachesfor modifying histogram based contrast enhancement havebeen proposed in order to limit the level of enhancementThese modifications include automatic image equalizationusing Gaussian mixture modeling [3] power-constrainedcontrast enhancement based on histogram equalization [4]and entropy maximization histogrammodification for imageenhancement [5]The retinex theory was originally proposedby Land and is based on the human visual system [6]The retinex can provide color constancy and dynamic rangecompression [7] however the multiscale retinex algorithmcreates a halo phenomenon in high contrast areas With thedevelopment of multiresolution analysis many methods for

HindawiBioMed Research InternationalVolume 2017 Article ID 3969152 10 pageshttpsdoiorg10115520173969152

2 BioMed Research International

image enhancement in the transform domain are appliedincluding the wavelet curvelet and contourlet methodsCurvelet transformations are able to best represent salientimage features like edges and details [8] The construction ofthe curvelet is not directly built into the discrete domain socurvelet transformations fail to achieve an optimal nonlinearapproximation for a higher order canonical singular edgeScratches appear at the edges of the image after imageprocessing A 2-dimensional discrete wavelet transformationis extended from the one-dimensional function thereforeit can only capture limited directions and it is not ableto effectively represent the directional information of theimage Contourlet transform is proposed in order to over-come this shortcoming of wavelet transform [9] Howevercontourlet transform is limited in shift-invariance becauseof the downsampling process in the Laplacian pyramid anddirectional filter bank and this drawback may cause pseudo-Gibbs phenomena around singularities which reduces thelocal information and weakens the features of the directionalselection da Cunha et al [10] proposed the nonsubsampledcontourlet transform (NSCT) which has the characteristic ofshift-invariance so that each pixel of the transform subbandscorresponds to that of the initial image in same spatiallocation It can isolate the noise from texture effectivelywhile refraining from the interference of new noise Sajjadiet al [11] put forward a set of simpler and more efficientfilters for nonsubsampled pyramid inNSCT and introduce animproved method for modification of directional subbandsrsquocoefficient which remove the noise while retaining a largeamount of detail information However the textures andedges of the processed image will be blurred Liu et al [12]proposed a method in NSCT domain combining unsharpmasking which can highlight the local region of textureinformation but the overall contrast has not been improvedPal andKing first employed fuzzy sets for image enhancementin 1981 and they received satisfactory results [13] Wang andYan [14] have designed an image enhancement algorithmbased on improved fuzzy domain in which an improvedfuzzy shrink function was used to conduct denoising butthe process of this algorithm is complex so that it will bringdifficulty to its application Hasikin and Isa [15] proposeda fuzzy technique to enhance low contrast images where Smembership function was used and the parameters in themembership function were computed using entropy and theindex of fuzziness Liu et al [16] presented a method basedon intuitionistic fuzzy sets theory in which the restrictedequivalence function is used to find themembership functionto avoid the defect of Pal-Kingrsquos algorithm and the newfuzzification hyperbolisation and defuzzification functionare used to deal with the object and background areasof the image in parallel but the problem of averting theamplification of noise and highlighting the textures anddetails at the same time has not been solved Wang et al[17] designed a medical image enhancement method basedon improved fuzzy contrast and adaptive threshold but themean membership function is included in the fuzzy contrastwhich makes the algorithm more complex and the fuzzycontrast value would be not accurate A constant is usedto replace the mean function which makes the calculation

simpler and the traditional threshold function has betterdenoising effect in this paper

The Laplacian filter is an isotropic filter which has beencommonly used as an enhancement operator to enhanceimage details Adaptive threshold function is adopted todistinguish image details and noises in high-frequency sub-bands of the NSCT domain which is used to remove noisesThis paper proposes an algorithm based on the aboveanalysis that combines the adaptive threshold function basedon NSCT and the improved fuzzy contrast enhancementThe adaptive threshold is implemented on high-frequencysubbands to eliminate the noise in order to avoid the ampli-fication of the noise when enhancing the edges and detailsThe core contribution lies in the improved fuzzy contrastenhancement which can dispel the quantization error insmall neighborhood and reduce the loss of the details inlarge neighborhood The combination of these methods canreserve more details of the initial image and thus increase thequality of the enhanced image Experiments demonstrate thatimages produced by the proposed enhancement method areobserved to be superior to the images obtained from othercomparative enhancement algorithms

2 Material and Methods

21 Figures Consent and Permissions The figures used inthis study were taken from several medical image resourcesmentioned in the acknowledgement sectionThe experimen-tal protocol of this study was reviewed and approved by theCollege of Information Science and Engineering XinjiangUniversity After fully carrying out the procedure of themethod proposed in this study all study subjects signedan informed consent form All methods in this study werestrictly executed in accordance with the approval guidelinesand regulations

22 Theoretical Analysis

221 The Theory of NSCT NSCT is an overcomplete trans-formation which has shift-invariant multiscale and multidi-rection features [18] The NSCT is built upon a 2D nonsub-sampled pyramid and nonsubsampled directional filter bank(NSDFB) The nonsubsampled pyramid can be obtained byremoving the downsamplers and upsamplers in the Laplacianpyramid which decides the multiscale decomposition ofthe NSCT The NSDFB is constructed by eliminating thedownsamplers and upsamplers in the directional filter bankwhich decides the directional decomposition of the NSCTThe NSCT can suppress the pseudo-Gibbs phenomena effec-tively capture the intrinsic geometrical structures accuratelyand separate the noise from the weak edge The overallstructure of the NSCT is shown in Figure 1(a) Figure 1(b)illustrates an example of the idealized frequency decomposi-tion

222 The Traditional Fuzzy Enhancement Algorithm andAnalysis In light of conventional fuzzy enhancement theoryassume that 119868 is a fuzzymatrix the size of an image119883 is119898times 119899

BioMed Research International 3

Inputimage

Band-passDirectional subband


Low-pass subband

(a)

휔2

휔1

(minus휋 minus휋)

(휋 휋)

(b)

Figure 1 (a) NSCT structure and its decomposition process (b) Idealized schematic diagram of frequency resolution

and 119871 is the grey levels of the image then 119868 can be describedas follows

119868 =119872

⋃119898=1

119873

⋃119899=1

120583119898119899119909119898119899 (1)

where 119898 = 1 2 119872 119899 = 1 2 119873 119909119898119899 is the intensityof (119898 119899)th pixel 120583119898119899 denotes the membership value of119909119898119899 In Pal and Kingrsquos fuzzy enhancement algorithm themembership function is described as follows

120583119898119899 = 119866 (119909119898119899) = [1 + (119871 minus 1) minus 119909119898119899119865119889 ]minus119865119890 (2)

where 119871 is the maximum gray level of the image 119883 119865119889 and119865119890 are related to 120583119898119899 and denote the reciprocal factor andexponent factor respectively When 119865119890 = 2 120583119898119899 = 120583119888 =119866(119909119888) 119909119888 it is called the crossover point Another fuzzy setis produced by recursion calling as follows

1205831015840119898119899 = 119879119903 (120583119898119899) = 119879119903 (119879119903minus1 (120583119898119899)) 119903 = 1 2 (3)

where 119879119903(120583119898119899) is defined as successive applications and canbe expressed as follows

119879119903 (120583119898119899) = 2 (120583119898119899)2 0 le 120583119898119899 le 051 minus 2 (1 minus 120583119898119899)2 05 le 120583119898119899 le 1

(4)

Finally (119898 119899) pixel value in the enhanced image is obtainedby 1199091015840119898119899 = 119866minus1(1205831015840119898119899)

However there are two faults in Pal and Kingrsquos methodOne is the crossover point that is fixed at 05 making itdifficult to adapt to the various images The other is themembership function changes from [120583min 1] rather than[0 1] which will lose the image information of the low grayvalue area after the inverse transformation [17]

Local contrast is based on calculating gray level differencebetween a specified pixel and its neighboring pixel [19]According toThakur and Mishra [20] the fuzzy contrast canbe defined as follows

119865119888 (119898 119899) =100381610038161003816100381610038161003816100381610038161003816120583119898119899 minus 120583119898119899120583119898119899 + 120583119898119899

100381610038161003816100381610038161003816100381610038161003816 (5)

where 120583119898119899 is the average value of a neighboring windowwithout a center pixel

23 The Proposed Method

231 The Enhancement of Low-Frequency Subband The low-frequency subband of the original image decomposed byNSCT contains the basic information of the image andincludes less noise while the portion of the basic informationrelates to the overall contrast of the image In order toeffectively improve the contrast of the image it is necessaryto linearly stretch the low-frequency subbandThis is done byfirst computing the greyscale value of the minimum 119909min andthe maximum 119909max and then modifying the grayscale rangefrom (119909min 119909max) to (0 255) by a linear mapping functionThe mapping function is as follows

119910 = 119891 (119909) = 255 times (119909 minus 119909min)(119909max minus 119909min) (6)

232 Denoising in High-Frequency Subband Part of thehigh-frequency subband contains the edge details and noisesof the original image it can be divided into three categoriesstrong edge weak edge and noise Modifying the coefficientsof the high-frequency subband retains the strong edgehighlights the weak edge and suppresses noise effectivelyIn order to remove noise and retain more details of high-frequency subbands an adaptive threshold based on BayesShrink is used for image denoising [21] The Bayes Shrinkthreshold is computed as follows

119879119861 = 1198881205902

1205902119909 (7)

where 119888 is a constant between 0 and 1 In this paper 119888 istaken as 08 1205902 and 1205902119909 are the noise variance and the signalvariance respectively Here a robust median operator is usedfor calculating the noise variance 120590

120590 = median 10038161003816100381610038161003816119889119894119895 (119897 119896)1003816100381610038161003816100381606745

120590119909 = radicmax (1003816100381610038161003816119904119897119896 minus 12059021003816100381610038161003816 0)

119904119897119896 = 1119898119899119898

sum119894=1

119899

sum119895=1

1198892119897119896 (119894 119895)

(8)


where 119904119897119896 denotes the mean square value of the subbandcoefficient in 119897th level and 119896th direction 119898 and 119899 representthe size of the image and 119889119894119895(119897 119896) is the pixel value at (119894 119895) in119897th level and 119896th direction

The average 119904119897 of each level is introduced as follows

119904119897 = (sum119899119896=1 119904119897119896)2119897 (9)

The weighted factors in different directions are computed bythe following equation

120582 = 119904119897119904119897119896 (10)

Adaptive threshold in this study is calculated as follows

119879 = 120582119879119861 (11)

We adopt the priority threshold 119879 to suppress noise

1198891015840119894119895 = 119889119894119895 119889119894119895 gt 1198790 119889119894119895 lt 119879

(12)

where 1198891015840119894119895 is the coefficient after denoising

233 The Improved Fuzzy Contrast Function and FuzzyEnhancement Operator In this paper the reconstructedimage is mapped to the fuzzy domain using the followingequation

119906119894119895 = 119909119894119895 minus 119909min

119909max minus 119909min (13)

In (13) 119909119894119895 is the reconstructed image pixel value and 119909minand 119909max are the maximum and minimum value of thereconstruct image

The improved fuzzy contrast can be defined as follows

119865 =10038161003816100381610038161003816119906119894119895 minus 1199031003816100381610038161003816100381610038161003816100381610038161003816119906119894119895 + 11990310038161003816100381610038161003816

(14)

Then a nonlinear transformation can be applied to 119865 1198651015840 =120595(119865)Ψ(119865) is a convex transformation that results in 120595(0) = 0

120595(1) = 1 The nonlinear enhancement function used in thispaper is given below

120595 (119909) = 1 minus 119890minus1198961199091 minus 119890minus119896 (15)

where 119896 is an adjustment factor of the nonlinear enhance-ment which takes the value of 1

The adjusted membership function is

1199061015840119894119895 = 119906119894119895 (1 minus 1198651015840) 119906119894119895 le 1199031 minus (1 minus 119906119894119895) (1 minus 1198651015840) 119906119894119895 ge 119903

(16)

r = 02

r = 05

r = 08

02 04 06 08 10Membership

0

01

02

03

04

05

06

07

08

09

1

Enha

ncem

ent o

pera

tor

Figure 2The curve shape of the fuzzy contrast enhancement when119903 takes values as 02 05 and 08

Finally transfer 1199061015840119894119895 in the fuzzy domain to the spatial domainusing the following formula

1199091015840119894119895 = 1199061015840119894119895 (119909max minus 119909min) + 119909min (17)

In (14) and (16) 119903 is an adapted operator from 0 to 1The different values of 119903 represent different fuzzy contrastenhancement curves adapted to different images [22] Fig-ure 2 shows the shape of the curve when 119903 take values of 0205 and 08

In general the detail area is dominated by high grayscale and the background field is dominated by low grayscale Experiments have found that when r is too small thebackground area is overenhancedwhich results in a reductionof the definition and the overall contrast of the image when119903 is too big the detail area is overenhanced which influencesthe visual effects Therefore in this paper we take 119903 withinthe range of 04 to 06 Figure 3 shows the processing resultsof the same image when 119903 takes values of 02 05 and 08

234 Description of the Proposed Algorithm

(1) Process the input image based onNSCT obtaining thelow-frequency subband and several high-frequencysubbands

(2) Use (6) to obtain linear enhancement The adaptivethreshold process is used for high-frequency sub-bands to suppress image noise through (7)ndash(12)

(3) Reconstruct the enhanced image from the modi-fied coefficient of low-frequency subband and high-frequency subband by inverse transformation ofNSCT

(4) Adopt the improved fuzzy contrast enhancementmethod to enhance the overall contrast of the image


(a) Original image (b) 119903 = 02 (c) 119903 = 05 (d) 119903 = 08

Figure 3 The processing results of a same image when r respectively take values of 02 05 and 08

(a) (b) (c)

(d) (e) (f)

Figure 4 Five methods of enhancing medical images (a) Original image (b) enhanced with HE (c) enhanced withMSR (d) enhanced withcontourlet transform (e) enhanced with NSCT-FU and (f) enhanced with the proposed method

with formulas (13)ndash(17) Employ the Laplace operatorto enhance the details of the image

3 Results and Discussion

65 medical images were used to evaluate the efficacy ofthe proposed method The NSCT decomposition level isthree in these experiments We use 8 16 and 16 directionsin the scales from coarser to finer In this experiment wepresent results obtained by theHEmethodmultiscale retinex(MSR) [6] contourlet transform [9] improved fuzzy contrast

enhancement based onNSCT [17] and the proposedmethodto verify the effectiveness of the proposed method Bothqualitative and quantitative methods are used to demonstratethe enhanced performance of our proposed approach Foursets of medical pictures are chosen for samples and we givethe results of the comparative trial and the proposed methodwhen 119903 takes values as 045 in Figure 4 05 in Figure 5 055in Figure 6 and 05 in Figure 7

We select information entropy (119867) structural similarityindex measurement (SSIM) the peak signal to noise ratio(PSNR) mean absolute error (MAE) and time as objective


(a) (b) (c)

(d) (e) (f)


evaluation criteria The entropy represents the overall infor-mation of the image with higher entropy resulting in theimage containing more information It can be defined asfollows

119867 = minus119872

sum119894=1

119873

sum119895=1

119901 (119894 119895) log119901 (119894 119895) (18)

where119872times119873 is the size of the enhanced imageSSIM reflects the degree of distortion of the enhanced

image When the SSIM is larger the image is more clearlydefined It can be defined as follows

SSIM (119909 119910) = (2120583119909120583119910 + 1198881) (120572119909119910 + 1198882)(1205832119909 + 1205722119909 + 1198881) (1205832119909 + 1205722119909 + 1198882)

(19)

where 120583 is the estimated mean intensity of the image 120572 isthe correlation coefficient and 1198881 and 1198882 are constants derivedfrom the dynamic range of the images

The peak signal to noise ratio denotes the denoisingperformance of the algorithm When the PSNR is higher theantinoise performance of the algorithm is better It can bedefined as

PSNR = 20 times log( 119871119863MSE

) (20)

where 119871119863 is the maximum value of the pixel and MSE can bedefined as follows

MSE = 1119872119873119872

sum119894=1

119873

sum119895=1

[(1199091015840 (119894 119895) minus 119909 (119894 119895))2] (21)

where 1199091015840(119894 119895) and 119909(119894 119895) are the enhanced image pixel and theoriginal image pixel respectively MAE denotes the contrastof the enhanced image [23] A lower MAE results in bettercontrast It is computed between the original image and theenhanced image and can be defined as

MAE = 1119872 times119873

119872

sum119894=1

119873

sum119895=1

10038161003816100381610038161003816119909 (119894 119895) minus 1199091015840 (119894 119895)10038161003816100381610038161003816 (22)

Tables 1ndash3 show the information entropy PSNR MAESSIM and time of the proposedmethod and the comparativemethods A comparison of the data in the tables shows thateven though the SSIM of the medical MRI image enhancedby contourlet transformation is slightly higher than theproposed method in Table 3 the entropy and PSNR arelower in these methods than in the proposed method Onthe whole the SSIM of contourlet transformation is higherthan with HE MSR and NSCT-FU but lower than theproposedmethodThe PSNR of the proposedmethod is close


(a) (b) (c)

(d) (e) (f)


Table 1 Comparison of different methods using the objective index in Figure 4

Evaluation standard Entropy PSNR MAE SSIM TimeHE 344 2422 054 0294 071MSR 000419 2436 024 0323 776Contourlet 202 1600 022 0753 1040NSCT-FU 458 2503 008 0642 4306Proposed method 582 2732 001 0836 3558






(a)

(b) (c) (d)

(e) (f) (g)

Figure 7 (a) Original image (b) noisy image with noise level 120590 = 02 (c) noisy image enhanced byHE (d) noisy image enhanced byMSR (e)noisy image enhanced by contourlet transform (f) noisy image enhanced by NSCT-FU and (g) noisy image enhanced by proposed method

to NSCT-FU while it is significantly higher than the otherthree algorithms The MAE of the proposed method is lowerthan in the other four methods which demonstrates that theproposed algorithm can obtain better contrast than the otheralgorithms Although the proposed method has a slowerprocessing time than the other algorithms it is faster thanNSCT-FU We can analyze the enhanced results objectivelyusing the four sets of pictures used in the above experimentsAs can be seen in the enhanced images the HE method canimprove the contrast of images globally however it doesnot take into account relationships among neighborhoods

and leads to poor visual effects At the same time somedetails are submerged in the process of enhancement Thecontrast enhancement is not obvious in the enhancementresults of contourlet transformation especially in cases wherethe input image yields low brightness MSR can improvethe luminance of an image effectively while the enhancedimage faces overenhancement and noise amplification andthe entropy becomes very low after processingThe enhancedeffect of NSCT-FU is close to the proposed method but itsdefinition and contrast are not better than the proposedmethod


Table 4 Comparison of different methods using the average objective index of 65 medical images


Table 5 PSNR values for Figure 7(a) with the different noise level of the different algorithms

120590119873 01 02 03 04 05HE 2471 2331 2265 2121 2011MSR 2567 2505 2461 2431 2382Contourlet 1203 1103 1015 940 847NSCT-FU 1907 1767 1485 1367 1258Proposed method 2802 2742 2700 2592 2503

Table 6 SSIM values for Figure 7(a) with the different noise level of the different algorithms


The average value of 65 medical images is shown inTable 4 To analyze the effectiveness of the proposed methodin medical image denoising a white Gaussian noise with var-ious standard deviations has been added to the experimentalimages The experimental results are shown in Figure 7and the PSNR and SSIM of the different methods aregiven in Tables 5 and 6 The effectiveness of the proposedmethod is further demonstrated When analyzed using bothquantitative and qualitative methods the proposed methodhas a better effect than the four other enhancement methods

4 Conclusion

This paper proposed an algorithmbased onNSCT combiningadaptive threshold and improved fuzzy set that followsthe demands for medical image enhancement We improvethe fuzzy contrast function and change its normal inverseAt the same time a new function is designed which cancalculate the enhanced pixel gray membership which is thencombined with the Laplace operator to enhance the detailsExperimental results show that the proposed method is ableto highlight the details and contours of an image enhancethe general contrast of an image and significantly improvean imagersquos visual effect Further studies should focus on theadaptability of the algorithm

Conflicts of Interest

The authors declare no competing financial interests

Authorsrsquo Contributions

Fei Zhou and ZhenHong Jia conceived and designed theexperiments Fei Zhou carried out the experiment and wrotethe paper Professor ZhenHong Jia Jie Yang and NikolaKasabov worked on text and language correction All authorsreviewed the manuscript

Acknowledgments

This work was supported in part by the International Coop-erative Research and Personnel Training Projects of theMinistry of Education of China [Grants nos DICE2014-2029and DICE2016-2196]References

[1] Y Yang Y Que S Huang and P Lin ldquoMultimodal SensorMedical Image Fusion Based on Type-2 Fuzzy Logic in NSCTDomainrdquo IEEE Sensors Journal vol 16 no 10 pp 3735ndash37452016

[2] H Lidong Z Wei W Jun and S Zebin ldquoCombination ofcontrast limited adaptive histogram equalisation and discretewavelet transform for image enhancementrdquo IET Image Process-ing vol 9 no 10 pp 908ndash915 2015

[3] T Celik and T Tjahjadi ldquoAutomatic image equalization andcontrast enhancement usingGaussianmixturemodelingrdquo IEEETransactions on Image Processing vol 21 no 1 pp 145ndash156 2012

[4] C Lee C Lee Y Y Lee and C S Kim ldquoPower-constrainedcontrast enhancement for emissive displays based on histogram


equalizationrdquo IEEETransactions on Image Processing vol 21 no1 pp 80ndash93 2012

[5] ZWei H LidongW Jun and S Zebin ldquoEntropymaximisationhistogram modification scheme for image enhancementrdquo IETImage Processing vol 9 no 3 pp 226ndash235 2015

[6] Y Li C Z Hou F Tian H L Yu L Guo G Z Xu et alldquoEnhancement of infrared image based on the retinex theoryrdquoin Proceedings of the 29th Annual International Conference ofthe IEEE Engineering in Medicine Biology Society pp 3315ndash33182007

[7] J H Jang S D Kim and J B Ra ldquoEnhancement of opticalremote sensing images by subband-decomposed multiscaleretinex with hybrid intensity transfer functionrdquo IEEE Geo-science and Remote Sensing Letters vol 8 no 5 pp 983ndash9872011

[8] H S Bhadauria and M L Dewal ldquoMedical image denoisingusing adaptive fusion of curvelet transform and total variationrdquoComputers and Electrical Engineering vol 39 no 5 pp 1451ndash1460 2013

[9] M H Asmare V S Asirvadam and A F M Hani ldquoImageenhancement based on contourlet transformrdquo Signal Image andVideo Processing vol 9 no 7 pp 1679ndash1690 2014

[10] A L da Cunha J Zhou and M N Do ldquoNonsubsampled con-tourlet transform filter design and applications in denoisingrdquoin Proceedings of the IEEE International Conference on ImageProcessing (ICIP rsquo05) vol 1 pp 749ndash752 September 2005

[11] M Sajjadi R Amirfattahi and M R Ahmadzadeh ldquoA newNSCT based contrast enhancement algorithm for amplificationof early signs of ischemic stroke in brain CT imagesrdquo inProceedings of the 7th Iranian conference on Machine Vision andImage Processing (MVIP) 2011

[12] L Liu Z Jia J Yang et al ldquoA medical image enhance-ment method using adaptive thresholding in NSCT domaincombined unsharp maskingrdquo International Journal of ImagingSystems amp Technology vol 25 no 3 pp 199ndash205 2015

[13] S A Pal and R A King ldquoImage enhancement using smoothingwith fuzzy setsrdquo IEEE Transactions on Systems Man andCybernetics vol 11 no 7 pp 494ndash501 1981

[14] L J Wang and T Yan ldquoA new approach of image enhancementbased on improved fuzzy domain algorithmrdquo in Proceedingsof the International Conference on Multisensor Fusion andInformation Integration for Intelligent Systems (MFI) pp 1ndash52014

[15] K Hasikin and N A M Isa ldquoEnhancement of the low contrastimage using fuzzy set theoryrdquo in Proceedings of the UKSim 14thConference on Modelling and Simulation pp 371ndash386 2012

[16] M Liu X Sun H Deng et al ldquoImage enhancement based onintuitionistic fuzzy sets theoryrdquo Iet Image Processing vol 10 no10 2016

[17] J J Wang Z H Jia X Z Qin J Yang and N KasabovldquoMedical image enhancement algorithm based on NSCT andthe improved fuzzy contrastrdquo International Journal of ImagingSystems and Technology vol 25 no 1 pp 7ndash14 2014

[18] A L da Cunha J Zhou and M N Do ldquoThe nonsubsampledcontourlet transform theory design and applicationsrdquo IEEETransactions on Image Processing vol 15 no 10 pp 3089ndash31012006

[19] A P Dhawan G Buelloni and R Gordon ldquoEnhancement ofMammographic Features by Optimal Adaptive NeighborhoodImage Processingrdquo IEEE Transactions on Medical Imaging vol5 no 1 pp 8ndash15 1986

[20] A Thakur and D Mishra ldquoFuzzy contrast mapping for imageenhancementrdquo in Proceedings of the 2nd International Confer-ence on Signal Processing and Integrated Networks (SPIN) pp549ndash552 2015

[21] H Wang H Cai and W Lu ldquoLocally adaptive bivariateshrinkage algorithm for image denoising based on nonsubsam-pled contourlet transformrdquo in Proceedings of the InternationalConference on Computer Mechatronics Control and ElectronicEngineering pp 33ndash36 2010

[22] C H Yu and W L Feng ldquoImage detection method basedon fuzzy set theoryrdquo in Proceedings of the 2nd InternationalConference on Multimedia Technology pp 364ndash367 2011

[23] T Chaira ldquoAn improved medical image enhancement schemeusing Type II fuzzy setrdquo Applied Soft Computing Journal vol25 pp 293ndash308 2014

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of


Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 201


Molecular Biology International

GenomicsInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


BioinformaticsAdvances in

Marine BiologyJournal of



Signal TransductionJournal of


BioMed Research International

Evolutionary BiologyInternational Journal of



Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Genetics Research International


Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational



Enzyme Research



Microbiology


image enhancement in the transform domain are appliedincluding the wavelet curvelet and contourlet methodsCurvelet transformations are able to best represent salientimage features like edges and details [8] The construction ofthe curvelet is not directly built into the discrete domain socurvelet transformations fail to achieve an optimal nonlinearapproximation for a higher order canonical singular edgeScratches appear at the edges of the image after imageprocessing A 2-dimensional discrete wavelet transformationis extended from the one-dimensional function thereforeit can only capture limited directions and it is not ableto effectively represent the directional information of theimage Contourlet transform is proposed in order to over-come this shortcoming of wavelet transform [9] Howevercontourlet transform is limited in shift-invariance becauseof the downsampling process in the Laplacian pyramid anddirectional filter bank and this drawback may cause pseudo-Gibbs phenomena around singularities which reduces thelocal information and weakens the features of the directionalselection da Cunha et al [10] proposed the nonsubsampledcontourlet transform (NSCT) which has the characteristic ofshift-invariance so that each pixel of the transform subbandscorresponds to that of the initial image in same spatiallocation It can isolate the noise from texture effectivelywhile refraining from the interference of new noise Sajjadiet al [11] put forward a set of simpler and more efficientfilters for nonsubsampled pyramid inNSCT and introduce animproved method for modification of directional subbandsrsquocoefficient which remove the noise while retaining a largeamount of detail information However the textures andedges of the processed image will be blurred Liu et al [12]proposed a method in NSCT domain combining unsharpmasking which can highlight the local region of textureinformation but the overall contrast has not been improvedPal andKing first employed fuzzy sets for image enhancementin 1981 and they received satisfactory results [13] Wang andYan [14] have designed an image enhancement algorithmbased on improved fuzzy domain in which an improvedfuzzy shrink function was used to conduct denoising butthe process of this algorithm is complex so that it will bringdifficulty to its application Hasikin and Isa [15] proposeda fuzzy technique to enhance low contrast images where Smembership function was used and the parameters in themembership function were computed using entropy and theindex of fuzziness Liu et al [16] presented a method basedon intuitionistic fuzzy sets theory in which the restrictedequivalence function is used to find themembership functionto avoid the defect of Pal-Kingrsquos algorithm and the newfuzzification hyperbolisation and defuzzification functionare used to deal with the object and background areasof the image in parallel but the problem of averting theamplification of noise and highlighting the textures anddetails at the same time has not been solved Wang et al[17] designed a medical image enhancement method basedon improved fuzzy contrast and adaptive threshold but themean membership function is included in the fuzzy contrastwhich makes the algorithm more complex and the fuzzycontrast value would be not accurate A constant is usedto replace the mean function which makes the calculation

simpler and the traditional threshold function has betterdenoising effect in this paper

The Laplacian filter is an isotropic filter which has beencommonly used as an enhancement operator to enhanceimage details Adaptive threshold function is adopted todistinguish image details and noises in high-frequency sub-bands of the NSCT domain which is used to remove noisesThis paper proposes an algorithm based on the aboveanalysis that combines the adaptive threshold function basedon NSCT and the improved fuzzy contrast enhancementThe adaptive threshold is implemented on high-frequencysubbands to eliminate the noise in order to avoid the ampli-fication of the noise when enhancing the edges and detailsThe core contribution lies in the improved fuzzy contrastenhancement which can dispel the quantization error insmall neighborhood and reduce the loss of the details inlarge neighborhood The combination of these methods canreserve more details of the initial image and thus increase thequality of the enhanced image Experiments demonstrate thatimages produced by the proposed enhancement method areobserved to be superior to the images obtained from othercomparative enhancement algorithms

2 Material and Methods

21 Figures Consent and Permissions The figures used inthis study were taken from several medical image resourcesmentioned in the acknowledgement sectionThe experimen-tal protocol of this study was reviewed and approved by theCollege of Information Science and Engineering XinjiangUniversity After fully carrying out the procedure of themethod proposed in this study all study subjects signedan informed consent form All methods in this study werestrictly executed in accordance with the approval guidelinesand regulations

22 Theoretical Analysis

221 The Theory of NSCT NSCT is an overcomplete trans-formation which has shift-invariant multiscale and multidi-rection features [18] The NSCT is built upon a 2D nonsub-sampled pyramid and nonsubsampled directional filter bank(NSDFB) The nonsubsampled pyramid can be obtained byremoving the downsamplers and upsamplers in the Laplacianpyramid which decides the multiscale decomposition ofthe NSCT The NSDFB is constructed by eliminating thedownsamplers and upsamplers in the directional filter bankwhich decides the directional decomposition of the NSCTThe NSCT can suppress the pseudo-Gibbs phenomena effec-tively capture the intrinsic geometrical structures accuratelyand separate the noise from the weak edge The overallstructure of the NSCT is shown in Figure 1(a) Figure 1(b)illustrates an example of the idealized frequency decomposi-tion

222 The Traditional Fuzzy Enhancement Algorithm andAnalysis In light of conventional fuzzy enhancement theoryassume that 119868 is a fuzzymatrix the size of an image119883 is119898times 119899


Inputimage



Low-pass subband

(a)

휔2

휔1

(minus휋 minus휋)

(휋 휋)

(b)



119868 =119872

⋃119898=1

119873

⋃119899=1

120583119898119899119909119898119899 (1)




1205831015840119898119899 = 119879119903 (120583119898119899) = 119879119903 (119879119903minus1 (120583119898119899)) 119903 = 1 2 (3)



(4)




119865119888 (119898 119899) =100381610038161003816100381610038161003816100381610038161003816120583119898119899 minus 120583119898119899120583119898119899 + 120583119898119899

100381610038161003816100381610038161003816100381610038161003816 (5)






119879119861 = 1198881205902

1205902119909 (7)


120590 = median 10038161003816100381610038161003816119889119894119895 (119897 119896)1003816100381610038161003816100381606745

120590119909 = radicmax (1003816100381610038161003816119904119897119896 minus 12059021003816100381610038161003816 0)

119904119897119896 = 1119898119899119898

sum119894=1

119899

sum119895=1

1198892119897119896 (119894 119895)

(8)




119904119897 = (sum119899119896=1 119904119897119896)2119897 (9)


120582 = 119904119897119904119897119896 (10)


119879 = 120582119879119861 (11)


1198891015840119894119895 = 119889119894119895 119889119894119895 gt 1198790 119889119894119895 lt 119879

(12)



119906119894119895 = 119909119894119895 minus 119909min

119909max minus 119909min (13)



119865 =10038161003816100381610038161003816119906119894119895 minus 1199031003816100381610038161003816100381610038161003816100381610038161003816119906119894119895 + 11990310038161003816100381610038161003816

(14)







(16)

r = 02

r = 05

r = 08


0

01

02

03

04

05

06

07

08

09

1

Enha

ncem

ent o

pera

tor



1199091015840119894119895 = 1199061015840119894119895 (119909max minus 119909min) + 119909min (17)











(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



119867 = minus119872

sum119894=1

119873

sum119895=1

119901 (119894 119895) log119901 (119894 119895) (18)



SSIM (119909 119910) = (2120583119909120583119910 + 1198881) (120572119909119910 + 1198882)(1205832119909 + 1205722119909 + 1198881) (1205832119909 + 1205722119909 + 1198882)

(19)




) (20)


MSE = 1119872119873119872

sum119894=1

119873

sum119895=1

[(1199091015840 (119894 119895) minus 119909 (119894 119895))2] (21)


MAE = 1119872 times119873

119872

sum119894=1

119873

sum119895=1

10038161003816100381610038161003816119909 (119894 119895) minus 1199091015840 (119894 119895)10038161003816100381610038161003816 (22)



(a) (b) (c)

(d) (e) (f)









(a)

(b) (c) (d)

(e) (f) (g)












4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Inputimage



Low-pass subband

(a)

휔2

휔1

(minus휋 minus휋)

(휋 휋)

(b)



119868 =119872

⋃119898=1

119873

⋃119899=1

120583119898119899119909119898119899 (1)




1205831015840119898119899 = 119879119903 (120583119898119899) = 119879119903 (119879119903minus1 (120583119898119899)) 119903 = 1 2 (3)



(4)




119865119888 (119898 119899) =100381610038161003816100381610038161003816100381610038161003816120583119898119899 minus 120583119898119899120583119898119899 + 120583119898119899

100381610038161003816100381610038161003816100381610038161003816 (5)






119879119861 = 1198881205902

1205902119909 (7)


120590 = median 10038161003816100381610038161003816119889119894119895 (119897 119896)1003816100381610038161003816100381606745

120590119909 = radicmax (1003816100381610038161003816119904119897119896 minus 12059021003816100381610038161003816 0)

119904119897119896 = 1119898119899119898

sum119894=1

119899

sum119895=1

1198892119897119896 (119894 119895)

(8)




119904119897 = (sum119899119896=1 119904119897119896)2119897 (9)


120582 = 119904119897119904119897119896 (10)


119879 = 120582119879119861 (11)


1198891015840119894119895 = 119889119894119895 119889119894119895 gt 1198790 119889119894119895 lt 119879

(12)



119906119894119895 = 119909119894119895 minus 119909min

119909max minus 119909min (13)



119865 =10038161003816100381610038161003816119906119894119895 minus 1199031003816100381610038161003816100381610038161003816100381610038161003816119906119894119895 + 11990310038161003816100381610038161003816

(14)







(16)

r = 02

r = 05

r = 08


0

01

02

03

04

05

06

07

08

09

1

Enha

ncem

ent o

pera

tor



1199091015840119894119895 = 1199061015840119894119895 (119909max minus 119909min) + 119909min (17)











(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



119867 = minus119872

sum119894=1

119873

sum119895=1

119901 (119894 119895) log119901 (119894 119895) (18)



SSIM (119909 119910) = (2120583119909120583119910 + 1198881) (120572119909119910 + 1198882)(1205832119909 + 1205722119909 + 1198881) (1205832119909 + 1205722119909 + 1198882)

(19)




) (20)


MSE = 1119872119873119872

sum119894=1

119873

sum119895=1

[(1199091015840 (119894 119895) minus 119909 (119894 119895))2] (21)


MAE = 1119872 times119873

119872

sum119894=1

119873

sum119895=1

10038161003816100381610038161003816119909 (119894 119895) minus 1199091015840 (119894 119895)10038161003816100381610038161003816 (22)



(a) (b) (c)

(d) (e) (f)









(a)

(b) (c) (d)

(e) (f) (g)












4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology




119904119897 = (sum119899119896=1 119904119897119896)2119897 (9)


120582 = 119904119897119904119897119896 (10)


119879 = 120582119879119861 (11)


1198891015840119894119895 = 119889119894119895 119889119894119895 gt 1198790 119889119894119895 lt 119879

(12)



119906119894119895 = 119909119894119895 minus 119909min

119909max minus 119909min (13)



119865 =10038161003816100381610038161003816119906119894119895 minus 1199031003816100381610038161003816100381610038161003816100381610038161003816119906119894119895 + 11990310038161003816100381610038161003816

(14)







(16)

r = 02

r = 05

r = 08


0

01

02

03

04

05

06

07

08

09

1

Enha

ncem

ent o

pera

tor



1199091015840119894119895 = 1199061015840119894119895 (119909max minus 119909min) + 119909min (17)











(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



119867 = minus119872

sum119894=1

119873

sum119895=1

119901 (119894 119895) log119901 (119894 119895) (18)



SSIM (119909 119910) = (2120583119909120583119910 + 1198881) (120572119909119910 + 1198882)(1205832119909 + 1205722119909 + 1198881) (1205832119909 + 1205722119909 + 1198882)

(19)




) (20)


MSE = 1119872119873119872

sum119894=1

119873

sum119895=1

[(1199091015840 (119894 119895) minus 119909 (119894 119895))2] (21)


MAE = 1119872 times119873

119872

sum119894=1

119873

sum119895=1

10038161003816100381610038161003816119909 (119894 119895) minus 1199091015840 (119894 119895)10038161003816100381610038161003816 (22)



(a) (b) (c)

(d) (e) (f)









(a)

(b) (c) (d)

(e) (f) (g)












4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology




(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



119867 = minus119872

sum119894=1

119873

sum119895=1

119901 (119894 119895) log119901 (119894 119895) (18)



SSIM (119909 119910) = (2120583119909120583119910 + 1198881) (120572119909119910 + 1198882)(1205832119909 + 1205722119909 + 1198881) (1205832119909 + 1205722119909 + 1198882)

(19)




) (20)


MSE = 1119872119873119872

sum119894=1

119873

sum119895=1

[(1199091015840 (119894 119895) minus 119909 (119894 119895))2] (21)


MAE = 1119872 times119873

119872

sum119894=1

119873

sum119895=1

10038161003816100381610038161003816119909 (119894 119895) minus 1199091015840 (119894 119895)10038161003816100381610038161003816 (22)



(a) (b) (c)

(d) (e) (f)









(a)

(b) (c) (d)

(e) (f) (g)












4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b) (c)

(d) (e) (f)



119867 = minus119872

sum119894=1

119873

sum119895=1

119901 (119894 119895) log119901 (119894 119895) (18)



SSIM (119909 119910) = (2120583119909120583119910 + 1198881) (120572119909119910 + 1198882)(1205832119909 + 1205722119909 + 1198881) (1205832119909 + 1205722119909 + 1198882)

(19)




) (20)


MSE = 1119872119873119872

sum119894=1

119873

sum119895=1

[(1199091015840 (119894 119895) minus 119909 (119894 119895))2] (21)


MAE = 1119872 times119873

119872

sum119894=1

119873

sum119895=1

10038161003816100381610038161003816119909 (119894 119895) minus 1199091015840 (119894 119895)10038161003816100381610038161003816 (22)



(a) (b) (c)

(d) (e) (f)









(a)

(b) (c) (d)

(e) (f) (g)












4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b) (c)

(d) (e) (f)









(a)

(b) (c) (d)

(e) (f) (g)












4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a)

(b) (c) (d)

(e) (f) (g)












4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology









4 Conclusion






Acknowledgments


































Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





























Volume 201






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

Method of Improved Fuzzy Contrast Combined Adaptive...

Documents

Transcript of Method of Improved Fuzzy Contrast Combined Adaptive...