Research Article A Novel Enhancement Algorithm Combined ...downloads.hindawi.com/journals/mpe/2016/8598917.pdf · proposed method can enhance local contrast, restore image details,

Research ArticleA Novel Enhancement Algorithm Combined with ImprovedFuzzy Set Theory for Low Illumination Images

Hai-jiao Yun12 Zhi-yong Wu1 Guan-jun Wang12 Gang Tong1 and Hua Yang1

1Changchun Institute of Optics Fine Mechanics and Physics Chinese Academy of Sciences Changchun 130033 China2University of Chinese Academy of Sciences Beijing 100049 China

Correspondence should be addressed to Hai-jiao Yun yunhaijiao2011126com

Received 6 January 2016 Revised 22 March 2016 Accepted 27 April 2016

Academic Editor Pasquale Memmolo

Copyright copy 2016 Hai-jiao Yun et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel enhancement method of global brightness modulation and local contrast enhancement combined with the improved fuzzyset theory is proposed for color image contrast enhancementThe proposedmethod consists of three stages Firstly putting forwardnonlinear global brightness mapping model adjusts dynamic range of images for luminance component 119881 of 119867119878119881 color spaceSecondly membership function is established in stages to adjust local contrast of image details nonlinearly based on fuzzy settheory Finally the enhanced images are transformed from119867119878119881 color space into 119877119866119861 color space The experiments further showthat the proposedmethod has the shortest processing time the highest AIC values and the least NIQE values among the other fourconventional methods It has excellent effect which can enhance the global brightness and local contrast and advance visibility oflow illumination images

1 Introduction

With rapid development of information science and tech-nology digital image processing technology is more andmore widely applied in military medical and multimediatechnology and so forth Image enhancement technology isan indispensable technique and essential method to improveimage quality and visual effect in digital image processingtechnology Nowadays there exist unsaturated low signal-to-noise ratio and low contrast in color images due to cam-era defocusing nonuniform illumination and atmosphericdisturbances However low contrast is one of the mostimportant key factors for visual effects of color imagesHencelow illumination color image enhancement research has beena hot issue in recent years It is especially important toenhance the visual effect and highlight the image details Thepurposes for enhancement are denoising and improvement ofbrightness and contrast meanwhile color information alsoshould be maintained In brief the purpose is to make lowillumination color images brighter and more natural

Traditional image enhancement methods can be mainlydivided into two categories (1) the globalmethods including

logarithmic transformation Gamma correction piecewiselinear transformation and histogram equalization [1ndash4]without the brightness difference among neighborhoodthese methods changed the gray levels of pixels by one-to-one mapping when low illumination images were enhancedonly by globalmethods the contrast was effectively improvedbut the local details features were ignored easily finallyenhanced images showed fuzzy phenomenon (2) the localmethods enhancing local contrast based on the local fea-tures and mainly including multiscale Retinex with colorrestoration and gradient domain methods [5ndash7]The Retinextheory has been widely paid attention to For example theglobal dynamic ranges of original images were preliminarilyadjusted with the Retinex theory and the local characteristicswere adjusted by multiscale in the method of the literature[5] based on demands of human eyes perception imagesrsquolocal gradient field was adjusted nonlinearly in methodof literature [7] The Retinex algorithm needs to calculatedifferent scale image for processing result and large amountof calculation It is vulnerable to brightness image effectsof the other area In literature [8] Zhou et al introducedan adaptive enhancement algorithm for low illumination

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 8598917 9 pageshttpdxdoiorg10115520168598917

2 Mathematical Problems in Engineering

color image which is overall brightness and local contrastadaptive enhancement (OBLCAE) It is based on 119867119878119881 colorspace However the enhanced images by OBLCAE show haloproblem at the light and shade contrast and areas of thedistortion are serious and of poor clarity These methodscanmake enhanced images degenerate phenomenon namelybright area details are weakened then dark area details can-not be enhanced effectively Recent studies [9ndash12] stress onthe importance and necessity of having automatic methodsfor contrast enhancement and suggest that the Gray LevelGrouping (GLG) and fuzzy-logic based methods are bettersuited for automatic contrast enhancement of images

The basic objective of GLG is to achieve a uniformhistogram for a low contrast color image In GLG his-togram components in different segments of grayscale can begrouped using different criteria so they can be redistributeddifferently over the grayscale to meet specific purposes forexample certain applications may require different parts ofhistogram to be enhanced to different extents The drawbackof GLG is that it is not computationally efficient comparedto fuzzy-based methods [13] To sum up it is difficultand necessary to propose an enhancement method for lowillumination images

Fuzzy rules efficiently process data by mimicking humandecision-making Jaya and Gopikakumari [14] introducedfuzzy-rule based enhancement in the Sequency by MappedReal Transform (SMRT) domain SMRT has been an integertransform and computationally efficient Hence the fuzzyset theory can analyze human behavior system such asjudgment perception and recognition which had beenmoreand more widely applied in image enhancement algorithmsand achieved good results

With development of the fuzzy set theory it was firstlyapplied in image enhancement and got breakthrough resultsin the mid of the 1981s [15] The method of literature [16]introduced fuzzy entropy to revise grayscale fuzzy informa-tion and neighborhood statistics of images based on humaneyes perceptionThismethodnot only can effectively enhancecontrast of the local images and improve imagesrsquo visual effectbut also can enhance image edges and restrain noise Forcontrast enhancement and brightness preserving Raju andNair [17] proposed an enhancement algorithm based onfuzzy-logic and histogram in119867119878119881 color space

The proposedmethod can naturally apperceive the globalscenario content and clearly extrude the local details at thesame time On the premise of adjusting global brightness theproposed method can enhance local contrast restore imagedetails and meet the demands of human eyes perception indifferent visual areas with the fuzzy set theory

In this paper the proposed method based on 119867119878119881

color space is proposed for low illumination color imageenhancement It mainly includes three steps the first isglobal brightness adaptive iterative adjustment the secondis adaptive local contrast enhancement based on the fuzzyset theory and the last is color restoration The experimentsshow that the proposed method can not only adaptivelyenhance global brightness but also adaptively enhance localcontrast andmake the enhanced image details more clear andvivid

The rest of this letter is organized as follows In Section 2the theory of fuzzy-logic enhancement is introduced InSection 3 the details of the proposed method are presentedto enhance images under nonuniform and uniform illumina-tion condition including global brightness modulation andlocal contrast adaptive enhancement with improved fuzzyset theory The experimental results are given in Section 4Finally a conclusion is drawn in Section 5

2 Fuzzy Image Enhancement

Fuzzy-logic is being efficiently applied in different areas ofimage processing In recent years fuzzy algorithms for imageenhancement have been developed with better performancecompared to conventional and other advanced techniqueslike GLG Fuzzy image enhancement is done by mappingimage gray level intensities into a fuzzy plane using mem-bership function According the classical fuzzy enhancementmethods by Pal and King [15] fuzzy processing consistsof mainly three stages image fuzzification (image coding)fuzzy enhancement and if necessary image defuzzification(decoding of results)

21 Image Fuzzification (Image Coding) According to (1)the image data are transformed from gray level domain tothe fuzzy membership domain based on the membershipfunction

120583119894119895= 119866 (119891

119894119895) = [1 +

119891max minus 119891119894119895

119865119889

]

minus119865119890

(1)

where 119865119890and 119865119889are conversion coefficients 119891max denotes the

maximal gray value 119891119894119895denotes the gray level of the (119894 119895)th

pixel

22 Constructing Fuzzy Membership Function This step isthe main power of fuzzy enhancement to modify the mem-bership values The membership values were modified intomembership plane with a suitable fuzzy approach

1205831015840

119894119895= 119879(119903)(120583119894119895) = 119879 (119879

(119903minus1)(120583119894119895)) 119903 = 1 2 3 (2)

where 119879(119903) is defined as successive applications of 119879 whichcan be expressed as

119879 (120583119894119895) =

2 (120583119894119895)2

0 le 120583119894119895le 05

1 minus 2 (1 minus 120583119894119895)2

05 lt 120583119894119895le 1

(3)

23 Image Defuzzification (Decoding of Results) To achievemodified gray levels the output of membership plane shouldbe decoded It means that themembership values are retrans-formed into the gray level plane

1198911015840

119894119895= 119866minus1(1205831015840

119894119895) = 119891max minus 119865

119889[(1205831015840

119894119895)(minus1119865

119890)

minus 1]

0 le 1205831015840

119894119895le 1

(4)

Mathematical Problems in Engineering 3

Inputimage I

Huecomponent H

Saturationcomponent S

Valuecomponent V

HSV

GlobalbrightnessadjustmentV998400

Local contrastenhancementV998400998400

OutputimageIe

Parameter120572

RGB

HSV

RGB

Figure 1 Flow chart of the proposed method

According to these three steps each gray level has beenassigned to a degree ofmembership depending on its locationin histogram Generally dark pixels were assigned as lowmembership values and bright pixels are assigned as highmembership values

As everyone knows in digital image processing fuzzyset theory is mainly through membership function mak-ing original image from spatial domain to fuzzy domainthen we modify grayscale pixels in fuzzy domain At lastinverse transformation goes back to spatial domain Theedge information is enhanced The key is the selectionof membership function in the procedure The segmentedmembership function can improve speed and quality of con-trast enhancement Comparedwith other fuzzy enhancementmethods using segmented membership function modifiedthe image pixels namely adjusting membership functionbased on the histogram distributions of the original images

3 Proposed Work

This letter includes the global brightness modulation withadaptive sine function and the local contrast enhancementcombined with the improved fuzzy set theory In orderto better understand the proposed method flow chart ofalgorithm is shown in Figure 1 119877119866119861 color space has highercolor correlation converting image from 119877119866119861 space to119867119878119881

spacewith small color correlationGet luminance component119881 and luminance component 119867 by using transformationequation (5)

119881 =1

radic3(119877 + 119866 + 119861)

119867 =

120579 119866 ge 119861

2120587 minus 120579 119866 lt 119861

(5)

where 119877 119866 and 119861 denote three components values respec-tively of 119877119866119861 color image and are given by

120579 = arccos (119877 minus 119866) + (119877 minus 119861)

2radic(119877 minus 119866)2+ (119877 minus 119861) (119866 minus 119861)

(6)

31 Global Brightness Adaptive Modulation The key to theglobal brightness modulation of the low illumination imagesis setting up a suitable nonlinear normalization of monotoneincreasing function [8 18] Commonly we use nonlinearmapping functions including logarithmic function expo-nential function S-shaped hyperbolic tangent function andcompound function They meet constraint conditions 119910 =

119891(119909) ge 119909 and 0 le 119891(119909) le 1 119909 isin [0 1] where 119909 denotesthe normalized119881 component value of low illumination imagepixels Literature [19ndash21] designed respectively the followingthree functions for luminance nonlinear mapping

119910 = 1 minus (119909 minus 1)2 119909 isin [0 1] (7)

119910 = 1199091205723+13

120572 isin [0 1] 119909 isin [0 1] (8)

119910 = radic120572119909 120572 isin [0 1] 119909 isin [0 1] (9)

It has been pointed out the nonlinear function of litera-ture [19] (7) is better than the other two functions (8) and (9)because there is no need for setting parameters to adaptivelyadjust the brightness for different low illumination imagesThis letter puts forward a new nonlinear global brightnessmapping model namely the sine function as shown in

119865119866= 1 minus [1 minus sin (120572119865

119881)]2

119865119881isin [0 1] 120572 isin [1

120587

2]

(10)

where 119865119881

denotes the luminance component 119881 of origi-nal images and 119865

119866denotes the luminance component 119881


01 02 03 04 05 06 07 08 09 10

(7)(10) 120572 = 12

(10) 120572 = 14

y = x

(10) 120572 = 1205872

0

01

02

03

04

05

06

07

08

09

1

Figure 2 Curves diagram of function (10) under different parame-ter values

of enhanced images by the global brightness modulationparameter 120572 denotes modulation parameter According tohuman eyes perception the letter modifies sine function bysetting parameter 120572 and ensures that the resulting imageswould not overflow Modified sine function is very flexiblemapping curve which could influence the course of mappingcurve under different values of the parameter 120572 suitable forprocessing different characteristics of images as shown inFigure 2

From the curves diagram it is an obvious advantage toprocess global brightness by function (10) With setting theparameter values the brighter area of images will not beenhanced in excess at the same time the darker area willnot be excessively weakened In Figure 2 the curves are allover function (7) which has better brightness modulationability than function (7) The image enhancement effect isbetter with function (10) Meanwhile fix on the adaptivemodulation parameter values of 120572 by

120572 =

120587

2119891 le 60

14 60 lt 119891 le 180

12 119891 gt 180

(11)

where 119891 (0 le 119891 le 255) denotes the gray levels As 30 ormore of pixels gray levels fall below 60 the image is verydark and parameter value of 120572 is set to 1205872 when 80 ormore of pixel gray level is greater than 180 the image is brightand parameter value of 120572 is set to 12 In other cases theparameter of 120572 is set to 14Therefore in view of different lowillumination image image brightness dynamic range can beadaptively adjusted through iterative calculation by function(10) and make the enhanced image more satisfying to humaneyes

32 Local Contrast Adaptive Enhancement Based on FuzzyTheory Set Through adjusting brightness the dark area ofimages gets brighter at the same time the dynamic range ofimages is compressed and the image contrast declines Basedon the research of human visual system it is sensitive to

process local contrast enhancement for human eyes percep-tion However the fuzzy set theory is on the basis of specificgrayscale pixel features and this letter proposes a novel localcontrast adaptive enhancement method based on it

321 Image Fuzzification In image fuzzification gray levelintensities are transformed to fuzzy plane whose value rangesbetween 0 and 1 The original image of size119872times119873 has pixelsgray level119891 in the range of [0 255] considered as a collectionof fuzzy singletons in the fuzzy set notationThe fuzzy matrix119865 corresponding to this image can be expressed as

119865 =

12058311

11989111

12058312

11989112

sdot sdot sdot1205831119873

1198911119873

12058321

11989121

12058322

11989122


1198912119873

1205831198721

1198911198721

1205831198722

1198911198722

sdot sdot sdot120583119872119873

119891119872119873

(12)

here 119891119894119895

is the gray level of (119894 119895)th pixel and 120583119894119895

is itsmembership value called the fuzzy property plane of theimage 120583

119894119895119891119894119895indicates the membership degree of 119891

119894119895relative

to 120583119894119895 120583119894119895= 0 indicates dark and 120583

119894119895= 1 indicates bright

322 Constructing FuzzyMembership Function Themethodof constructing fuzzy membership function is proposed Wecalculate histogram of original image and ℎ(119891

119894119895) (119891119894119895isin 119881)

indicates number of pixels gray level119891119894119895Meanwhile weighted

average can be calculated from the histogram as follows

119898 =

sum119891119891119894119895ℎ (119891119894119895)

sum119891ℎ (119891119894119895)

(13)

The parameter 119898 divides the histogram ℎ(119891119894119895) into two

parts based on the relationship between the image pixels andthe weighted average The first part 119862

1contains pixels values

in range of [0 119898minus1] and the second part1198622contains values in

range of [119898 255] The content of 119881 component is performedby two kinds of fuzzy membership functions 120583

1198621

and 1205831198622

To calculate enhanced stretching intensity it needs to

meet two rules as follows

(1) If the Difference between 119891 and 119898 Is Larger the Intensityof Stretching Should Be Smaller in the Part 119862

1 That is to

say the pixels values closer to 119898 will be enhanced higherwhereas values farther from 119898 will be extended lesser Themembership values can be used

1205831198621

=1 minus (119898 minus 119865

119866times 255)

119898 (14)

(2) If the Difference between 119891 and Maximum Value 119864 (119864 =

255) Is Larger the Intensity of Stretching Should Be Largerin the Part 119862

2 That is to say the pixels values closer to 119864


will be enhanced lesser whereas values farther from 119864 will beextended higher The membership values can be used

1205831198622

=119864 minus 119865119866times 255

119864 minus 119898 (15)

In order to reduce the amount of image fuzziness contrastintensification is applied to the fuzzy set119865 to generate anothernew fuzzy set 119865

1015840 the membership function of which isexpressed as (2) and (3)

By (2) and (3) calculate the twoparts1198621and119862

2 to obtain

the new fuzzy set

323 Image Defuzzification Image defuzzification is theinverse of fuzzification The method transformes the fuzzyplane back into the gray level intensities Finally theenhanced image 119865

119871can be obtained by following inverse

transformation respectively between the parts 1198621and 119862

2

1198651198711

=10038161003816100381610038161003816119865119866times 255 + 120583

1015840

1198621

times 11987010038161003816100381610038161003816

1198651198712

= 119865119866times 1205831015840

1198622

times 255 + (119864 minus 1205831198622

times 119870)

(16)

Here enhancing control parameter119870 decides the stretch-ing intensity It computed the enhanced intensity levels 119865

119871in

the two parts From the experimental analysis fix value 128for119870 which gave better results for the low illumination colorimages [16]

This enhanced information 119881119890can be replaced by 119865

119871

Then 119881119890can be combined with the Hue and Saturation

components of original color space to obtain enhanced image119867119878119881119890which is finally converted to 119877119866119861

119890image

33 Color Space to Restore This proposed method obtainsenhanced color images by adjusting global brightness andlocal contrast The color information of the enhanced imageis linearly restored and the proportion relationship of119877 119866 119861 three-component is consistentTherefore it can betterreserve the color information of the original image Therecovery method is shown as follows

1198651015840

119896(119894 119895) = 120573 (119894 119895) sdot 119865

119896(119894 119895) (17)

where 120573(119894 119895) = 119865119871(119894 119895)119865

119881(119894 119895) denotes enhancement factor

at the (119894 119895)th pixel119865119881(119894 119895) denotes the luminance component

119881 of original images and 119865119871(119894 119895) denotes the luminance

component 119881 of enhanced images 119865119896(119894 119895) 119896 = 119903 119892 119887

denotes 119877 119866 and 119861 three-component values of the originalimage 1198651015840

119896(119894 119895) 119896 = 119903 119892 119887 denotes 119877 119866 and 119861 three-

component values of the enhanced image

4 Experimental Results and Analysis

A lot of experiments are performed with the proposedmethod and comparedwith several other conventionalmeth-ods such as Retinex algorithm [22] fuzzy enhancement(FE) [15] Gray Level Grouping (GLG) overall brightnessand local contrast adaptive enhancement (OBLCAE) [8]These methods have been tested with several images under

nonuniform and uniform illumination conditions The testimages used for the experiments are available on the websitehttpliveeceutexaseduresearchQualityindexhtm [23]

Test 1 Figure 3 shows processing results of the five algorithmsunder nonuniform illumination condition Figures 3(a) and3(g) show the two original images and their histogramsFigures 3(b) 3(c) 3(d) and 3(e) show processing resultsby Retinex algorithm FE algorithm GLG and OBLCAErespectively Figure 3(f) is the result by the proposedmethodFigure 3(b) shows the enhanced images by the Retinex algo-rithmwhich is an algorithmof theNASA research for LangleyRetinexCenter and has been successfully applied to the PhotoFlair software in the Truview company This algorithm needsto calculate different scale image for processing result andlarge amount of calculation Because of all scales with acertainweight added to the center pixel values it is vulnerableto brightness image effects of the other area The resultingimages by FE algorithm are not clear and overall dark asshown in Figure 3(c)The resulting images by GLG algorithmshow fuzzy phenomenon as shown in Figure 3(d) Figure 3(e)shows the enhanced images by OBLCAE The processingresults show halo problem at the light and shade contrastand the areas of the distortion are serious and of poor clarityFigure 3(f) shows the enhanced images by the proposedmethod It can improve image resolution and at the sametime remove halo problems of light and shade contrast Theenhancement effects aremore naturalThe output histogramsof proposedmethod achieve a smoother distribution betweenlow and high gray level as shown in Figure 3(h) their resultsare more natural looking The histograms of the proposedmethod are successfully distributed evenly to its dynamicrange as compared to the original images as shown inFigure 3(g)

Test 2 Figure 4 shows processing results of the five algo-rithms under uniform illumination condition Figures 4(a)and 4(g) show two original images and their histogramsFigures 4(b) 4(c) 4(d) and 4(e) show processing resultsby Retinex algorithm FE algorithm GLG and OBLCAErespectively The Retinex algorithm did filter processing forthree components of 119877 119866 and 119861 respectively and combinedtogether as shown in Figure 4(b)The enhanced images by FEalgorithm are overall dark losing their original color brightcharacteristics as shown in Figure 4(c) From Figures 4(d)and 4(e) the processing results are excessively enhanced sothe distortion phenomena are serious The proposed methodretained the color information of original image only toprocess the brightness of the images making themmore clearand natural which have a better visual effect than the otherfour algorithms Compared with the histograms distributionin Figures 4(g) and 4(h) the proposed method expandedthe dynamic ranges of the gray scale distribution and thenchanged the contrast of the images

Test 3 Test the algorithmsrsquo processing time comparing thereal-time performance among the five algorithms The CPUfor test of the personal computer is Intel Core (TM) 2 DuoQ9550 whose frequency is 283GHz memory is 35 GB and


(a) (b)

(c) (d)

(e) (f)

times104 times104

012345678910

Num

ber o

f pix

els

100 20015050 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

100 20015050 2500

Gray levels

(g)

times104 times104

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)

Figure 3 Comparison of processing results of the five algorithms under nonuniform illumination condition (a) Original images (b) Retinexalgorithm (c) FE algorithm (d) GLG algorithm (e) OBLCAE algorithm (f) the proposed method (g) the histograms of the original images(h) the histograms of the proposed method

programming platform isMicrosoftVisual C++60There arethree kinds of test images whose resolutions are 256 pixelstimes 256 pixels 512 pixels times 512 pixels and 720 pixels times 576pixels respectively Test results are shown in Table 1 and theproposed method has a good real-time performance

A subjective assessment for the visual quality of theenhanced images is carried out Average information con-tents (AIC) [24] and natural image quality evaluator (NIQE)[25 26] index are used to assess the effectiveness of theproposed method


(a) (b)

(c) (d)

(e) (f)

50 150 2500 100 200

Gray levels

times104

0

05

1

15

2

25

Num

ber o

f pix

els

0

1000

2000

3000

4000

5000

6000

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(g)

times104 times104

50 100 150 200 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

0

05

1

15

2

25

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)

Figure 4 Comparison of processing results of the five algorithms under uniform illumination condition (a) Original images (b) Retinexalgorithm (c) FE algorithm (d) GLG algorithm (e) OBLCAE algorithm (f) the proposed method (g) the histograms of the original images(h) the histograms of the proposed method

The AIC is used to measure the content of an imageHigher value of the AIC indicates that more information isbrought out It is defined as

AIC = minus

119871minus1

sum

119896=0

119875 (119896) log119875 (119896) (18)

where 119875(119896) is the probability density function of the 119896th graylevel

The NIQE is used for measuring image quality It is basedon construction of a ldquoquality awarerdquo collection of statisticalfeature which can be got by a simple and successful spacedomain natural scene statistic (NSS) model The qualityof distorted image is expressed as the distance between

the quality aware NSS feature model and the multivariateGaussian (MVG) model fit to the features extracted from thedistorted image Smaller NIQE indicates better image qualityThe NIQE is defined as

119863(V1 V2 Σ1 Σ2)

= radic(V1minus V2)119879(Σ1+ Σ2

2)

minus1

(V1minus V2)

(19)

where V1and V

2and Σ

1and Σ

2are the mean vectors and

covariance matrices of the natural MVG model and thedistorted imagersquos MVG model


Table 1 Comparison of processing time with five algorithms

Image size 256 pixels times 256 pixels 512 pixels times 512 pixels 720 pixels times 576 pixelsRetinexms 368 1070 1554FEms 150 567 759GLGms 253 1150 1890OBLCAEms 980 2700 3950Proposed methodms 168 300 649

62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80

Retinex FE GLG OBLCAE ProposedOriginalmethod

Figure 5 Comparison of average AIC values

689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80

Retinex FE GLG OBLCAEOriginal Proposedmethod

Figure 6 Comparison of average NIQE values

Figures 5 and 6 show the comparisons of average AICand NIQE values between the proposed method and otherconventional methods for images under nonuniform anduniform illumination conditions Further the qualities of thetest images measured in terms of AIC and NIQE which areenhanced using the aforementioned techniques are given inTables 2 and 3 According to Table 2 the proposed methodproduces the highest AIC and shows more details Table 3shows the natural image quality evaluator index of testedimages It is found that the proposedmethod produces lowestNIQE values as compared to the others Hence the proposedmethod makes enhanced images more natural Based onqualitative and quantitative analyses the proposed methodhas been found effective in enhancing contrast of images incomparison to a few existingmethods In addition combinedwith global brightness modulation of adaptive sine functionand the local contrast enhancement based on the improved

Table 2 Comparison of AIC values

Images Original Retinex FE GLG OBLCAE Proposedmethod

Boy 61626 67689 61467 65971 64691 71308Girl 72304 7782 68704 76155 77335 76348Palace 55242 67343 44059 62541 71141 68212Room 62813 66222 65718 76816 75147 73458Average 62996 69769 59987 70371 72079 72332

Table 3 Comparison of NIQE values



fuzzy set theory the proposed method makes full dynamicrange of the pixel values formaximumcontrast Experimentalresults show that the proposed method not only outperformsall of the other methods in contrast enhancement but alsoprovides good visual representation in visual comparisonHence the proposed method gives better visual qualityimages

5 Conclusion

In this letter based on human visual system a novelenhancement method combined with the global brightnessmodulation and local contrast enhancement is proposedIt has effectively solved the problems about brightness andcontrast of the illumination images Aiming at the problemof brightness the proposedmethod combines with nonlinearsine function for global brightness modulation throughmultiple iterations to determine the best images at the sametime the letter proposes the local contrast enhancementbased on fuzzy set theory Finally we compare the proposedmethod and the other four algorithms with two performancemeasure values under two kinds of conditions nonuniformillumination and uniform illumination Meanwhile time ofthe proposed method is the shortest for different sizes ofimages and has a good real-time performance The experi-mental results show that image contrast and visual quality by


the proposed method are better than the other enhancementalgorithms Further we optimize the algorithm shorten theconsumption and improve the real-time performance Forfuture work we plan to improve the proposed methodrsquosrobustness and apply it to images obtained from optoelec-tronic theodolite to improve image visibility and clarityMeanwhile this method is simple and suitable for consumerelectronic products

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (Grant no 61405191) and theJilin Province Science Foundation for Youths of China (Grantno 20150520102JH)

References

[1] W Zhao Z Xu J Zhao F Zhao and X Han ldquoVariationalinfrared image enhancement based on adaptive dual-thresholdgradient field equalizationrdquo Infrared Physics amp Technology vol66 pp 152ndash159 2014

[2] H Yun Z Wu G Wang X Liu and M Liang ldquoEnhancementof infrared image combined with histogram equalization andfuzzy set theoryrdquo Journal of Computer-AidedDesignampComputerGraphics vol 27 no 8 pp 1499ndash1509 2015

[3] V Magudeeswaran and C G Ravichandran ldquoFuzzy logic-based histogram equalization for image contrast enhancementrdquoMathematical Problems in Engineering vol 2013 Article ID891864 10 pages 2013

[4] L Lv K Gao X Shao and G Ni ldquoAn adaptive high dynamicrange color image enhancement algorithm based on humanvision propertyrdquo Transactions of Beijing Institute of Technologyvol 32 no 4 pp 415ndash419 2012

[5] D J Jobson Z-U Rahman and G A Woodell ldquoA multiscaleretinex for bridging the gap between color images and thehuman observation of scenesrdquo IEEE Transactions on ImageProcessing vol 6 no 7 pp 965ndash976 1997

[6] H Zhao C Xiao J Yu and L Bai ldquoA Retinex algorithm fornight color image enhancement by MRFrdquo Optics and PrecisionEngineering vol 22 no 4 pp 1048ndash1055 2014

[7] F Zhang W Xie Q Shi and Q Qin ldquoA perception-inspiredcontrast enhancement method for low-light images in gradientdomainrdquo Journal of Computer-Aided Design and ComputerGraphics vol 26 no 11 pp 1981ndash1988 2014

[8] Z Zhou N Sang and X Hu ldquoGlobal brightness and localcontrast adaptive enhancement for low illumination colorimagerdquo Optik vol 125 no 6 pp 1795ndash1799 2014

[9] Y Yao and A Men ldquoImproved color image contrast enhance-ment method based on GLGrdquo Video Engineering vol 33supplement 2 pp 133ndash135 2009

[10] Z Y Chen B R Abidi D L Page and M A Abidi ldquoGray-level grouping (GLG) an automatic method for optimizedimage contrast enhancementmdashpart II the variationsrdquo IEEETransactions on Image Processing vol 15 no 8 pp 2303ndash23142006

[11] M Hanmandlu and D Jha ldquoAn optimal fuzzy system for colorimage enhancementrdquo IEEE Transactions on Image Processingvol 15 no 10 pp 2956ndash2966 2006

[12] M S Nair R Lakshmanan M Wilscy and R Tatavarti ldquoFuzzylogic-based automatic contrast enhancement of satellite imagesof oceanrdquo Signal Image and Video Processing vol 5 no 1 pp69ndash80 2011

[13] Z Chen B R Abidi D L Page and M A Abidi ldquoGray-level grouping (GLG) an automatic method for optimizedimage contrast enhancementmdashpart I the basic methodrdquo IEEETransactions on Image Processing vol 15 no 8 pp 2290ndash23022006

[14] V L Jaya andRGopikakumari ldquoFuzzy rule based enhancementin the SMRT domain for low contrast imagesrdquo Procedia Com-puter Science vol 46 pp 1747ndash1753 2015

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

[16] B-P Wang H-L Liu N-J Li andW-X Xie ldquoA novel adaptiveimage fuzzy enhancement algorithmrdquo Journal of Xidian Univer-sity Natural Science vol 32 no 2 pp 307ndash313 2005

[17] G Raju and M S Nair ldquoA fast and efficient color imageenhancement method based on fuzzy-logic and histogramrdquoAEUmdashInternational Journal of Electronics andCommunicationsvol 68 no 3 pp 237ndash243 2014

[18] X Qin H Wang Y Du H Zheng and Z Liang ldquoStructuredlight image enhancement algorithm based on retinex in HSVcolor spacerdquo Journal of Computer-Aided Design amp ComputerGraphics vol 25 no 4 pp 488ndash493 2013

[19] S-J Wang X-H Ding Y-H Liao and D-H Guo ldquoA novelbio-inspired algorithm for color image enhancementrdquo ActaElectronica Sinica vol 36 no 10 pp 1970ndash1973 2008

[20] J Zheng J Jiang and Z Huang ldquoColor image enhancementbased on RGB gray value scalingrdquo Computer Engineering vol38 no 2 pp 226ndash228 2012

[21] P Guo P Yang Y Liu and L Chen ldquoAn adaptive enhancementalgorithm for low-illumination image based on hue reservingrdquoin Proceedings of the Cross Strait Quad-Regional Radio Scienceand Wireless Technology Conference (CSQRWC rsquo11) pp 1247ndash1250 Harbin China July 2011

[22] M Bertalmıo V Caselles and E Provenzi ldquoIssues about retinextheory and contrast enhancementrdquo International Journal ofComputer Vision vol 83 no 1 pp 101ndash119 2009

[23] H R Sheikh Z Wang and A C Bovik ldquoLIVE image qual-ity assessment database Release 2rdquo httpliveeceutexaseduresearchQualityindexhtm

[24] Y-C Chang and C-M Chang ldquoA simple histogram modifica-tion scheme for contrast enhancementrdquo IEEE Transactions onConsumer Electronics vol 56 no 2 pp 737ndash742 2010

[25] A K Moorthy and A C Bovik ldquoBlind image quality assess-ment from natural scene statistics to perceptual qualityrdquo IEEETransactions on Image Processing vol 20 no 12 pp 3350ndash33642011

[26] A Mittal R Soundararajan and A C Bovik ldquoMaking alsquocompletely blindrsquo image quality analyzerrdquo IEEE Signal Process-ing Letters vol 20 no 3 pp 209ndash212 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


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OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


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Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


color image which is overall brightness and local contrastadaptive enhancement (OBLCAE) It is based on 119867119878119881 colorspace However the enhanced images by OBLCAE show haloproblem at the light and shade contrast and areas of thedistortion are serious and of poor clarity These methodscanmake enhanced images degenerate phenomenon namelybright area details are weakened then dark area details can-not be enhanced effectively Recent studies [9ndash12] stress onthe importance and necessity of having automatic methodsfor contrast enhancement and suggest that the Gray LevelGrouping (GLG) and fuzzy-logic based methods are bettersuited for automatic contrast enhancement of images

The basic objective of GLG is to achieve a uniformhistogram for a low contrast color image In GLG his-togram components in different segments of grayscale can begrouped using different criteria so they can be redistributeddifferently over the grayscale to meet specific purposes forexample certain applications may require different parts ofhistogram to be enhanced to different extents The drawbackof GLG is that it is not computationally efficient comparedto fuzzy-based methods [13] To sum up it is difficultand necessary to propose an enhancement method for lowillumination images

Fuzzy rules efficiently process data by mimicking humandecision-making Jaya and Gopikakumari [14] introducedfuzzy-rule based enhancement in the Sequency by MappedReal Transform (SMRT) domain SMRT has been an integertransform and computationally efficient Hence the fuzzyset theory can analyze human behavior system such asjudgment perception and recognition which had beenmoreand more widely applied in image enhancement algorithmsand achieved good results

With development of the fuzzy set theory it was firstlyapplied in image enhancement and got breakthrough resultsin the mid of the 1981s [15] The method of literature [16]introduced fuzzy entropy to revise grayscale fuzzy informa-tion and neighborhood statistics of images based on humaneyes perceptionThismethodnot only can effectively enhancecontrast of the local images and improve imagesrsquo visual effectbut also can enhance image edges and restrain noise Forcontrast enhancement and brightness preserving Raju andNair [17] proposed an enhancement algorithm based onfuzzy-logic and histogram in119867119878119881 color space

The proposedmethod can naturally apperceive the globalscenario content and clearly extrude the local details at thesame time On the premise of adjusting global brightness theproposed method can enhance local contrast restore imagedetails and meet the demands of human eyes perception indifferent visual areas with the fuzzy set theory

In this paper the proposed method based on 119867119878119881

color space is proposed for low illumination color imageenhancement It mainly includes three steps the first isglobal brightness adaptive iterative adjustment the secondis adaptive local contrast enhancement based on the fuzzyset theory and the last is color restoration The experimentsshow that the proposed method can not only adaptivelyenhance global brightness but also adaptively enhance localcontrast andmake the enhanced image details more clear andvivid

The rest of this letter is organized as follows In Section 2the theory of fuzzy-logic enhancement is introduced InSection 3 the details of the proposed method are presentedto enhance images under nonuniform and uniform illumina-tion condition including global brightness modulation andlocal contrast adaptive enhancement with improved fuzzyset theory The experimental results are given in Section 4Finally a conclusion is drawn in Section 5

2 Fuzzy Image Enhancement

Fuzzy-logic is being efficiently applied in different areas ofimage processing In recent years fuzzy algorithms for imageenhancement have been developed with better performancecompared to conventional and other advanced techniqueslike GLG Fuzzy image enhancement is done by mappingimage gray level intensities into a fuzzy plane using mem-bership function According the classical fuzzy enhancementmethods by Pal and King [15] fuzzy processing consistsof mainly three stages image fuzzification (image coding)fuzzy enhancement and if necessary image defuzzification(decoding of results)

21 Image Fuzzification (Image Coding) According to (1)the image data are transformed from gray level domain tothe fuzzy membership domain based on the membershipfunction

120583119894119895= 119866 (119891

119894119895) = [1 +

119891max minus 119891119894119895

119865119889

]

minus119865119890

(1)

where 119865119890and 119865119889are conversion coefficients 119891max denotes the

maximal gray value 119891119894119895denotes the gray level of the (119894 119895)th

pixel

22 Constructing Fuzzy Membership Function This step isthe main power of fuzzy enhancement to modify the mem-bership values The membership values were modified intomembership plane with a suitable fuzzy approach

1205831015840

119894119895= 119879(119903)(120583119894119895) = 119879 (119879

(119903minus1)(120583119894119895)) 119903 = 1 2 3 (2)

where 119879(119903) is defined as successive applications of 119879 whichcan be expressed as

119879 (120583119894119895) =

2 (120583119894119895)2

0 le 120583119894119895le 05

1 minus 2 (1 minus 120583119894119895)2

05 lt 120583119894119895le 1

(3)

23 Image Defuzzification (Decoding of Results) To achievemodified gray levels the output of membership plane shouldbe decoded It means that themembership values are retrans-formed into the gray level plane

1198911015840

119894119895= 119866minus1(1205831015840

119894119895) = 119891max minus 119865

119889[(1205831015840

119894119895)(minus1119865

119890)

minus 1]

0 le 1205831015840

119894119895le 1

(4)


Inputimage I

Huecomponent H


Valuecomponent V

HSV



OutputimageIe

Parameter120572

RGB

HSV

RGB




3 Proposed Work



119881 =1

radic3(119877 + 119866 + 119861)

119867 =

120579 119866 ge 119861

2120587 minus 120579 119866 lt 119861

(5)




(6)



119910 = 1 minus (119909 minus 1)2 119909 isin [0 1] (7)

119910 = 1199091205723+13

120572 isin [0 1] 119909 isin [0 1] (8)

119910 = radic120572119909 120572 isin [0 1] 119909 isin [0 1] (9)


119865119866= 1 minus [1 minus sin (120572119865

119881)]2

119865119881isin [0 1] 120572 isin [1

120587

2]

(10)

where 119865119881




01 02 03 04 05 06 07 08 09 10

(7)(10) 120572 = 12

(10) 120572 = 14

y = x

(10) 120572 = 1205872

0

01

02

03

04

05

06

07

08

09

1




120572 =

120587

2119891 le 60

14 60 lt 119891 le 180

12 119891 gt 180

(11)





119865 =

12058311

11989111

12058312

11989112


1198911119873

12058321

11989121

12058322

11989122


1198912119873

1205831198721

1198911198721

1205831198722

1198911198722

sdot sdot sdot120583119872119873

119891119872119873

(12)

here 119891119894119895








119894119895) (119891119894119895isin 119881)



119898 =

sum119891119891119894119895ℎ (119891119894119895)

sum119891ℎ (119891119894119895)

(13)






1198621

and 1205831198622




1 That is to


1205831198621

=1 minus (119898 minus 119865

119866times 255)

119898 (14)






1205831198622

=119864 minus 119865119866times 255

119864 minus 119898 (15)




2 to obtain

the new fuzzy set




2

1198651198711

=10038161003816100381610038161003816119865119866times 255 + 120583

1015840

1198621

times 11987010038161003816100381610038161003816

1198651198712

= 119865119866times 1205831015840

1198622

times 255 + (119864 minus 1205831198622

times 119870)

(16)


119871in



119871



119890image


1198651015840

119896(119894 119895) = 120573 (119894 119895) sdot 119865

119896(119894 119895) (17)

where 120573(119894 119895) = 119865119871(119894 119895)119865















(a) (b)

(c) (d)

(e) (f)

times104 times104

012345678910

Num

ber o

f pix

els

100 20015050 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

100 20015050 2500

Gray levels

(g)

times104 times104

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)





(a) (b)

(c) (d)

(e) (f)

50 150 2500 100 200

Gray levels

times104

0

05

1

15

2

25

Num

ber o

f pix

els

0

1000

2000

3000

4000

5000

6000

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(g)

times104 times104

50 100 150 200 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

0

05

1

15

2

25

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)



AIC = minus

119871minus1

sum

119896=0

119875 (119896) log119875 (119896) (18)




119863(V1 V2 Σ1 Σ2)


2)

minus1

(V1minus V2)

(19)

where V1and V

2and Σ

1and Σ






62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80



689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80











5 Conclusion




Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Inputimage I

Huecomponent H


Valuecomponent V

HSV



OutputimageIe

Parameter120572

RGB

HSV

RGB




3 Proposed Work



119881 =1

radic3(119877 + 119866 + 119861)

119867 =

120579 119866 ge 119861

2120587 minus 120579 119866 lt 119861

(5)




(6)



119910 = 1 minus (119909 minus 1)2 119909 isin [0 1] (7)

119910 = 1199091205723+13

120572 isin [0 1] 119909 isin [0 1] (8)

119910 = radic120572119909 120572 isin [0 1] 119909 isin [0 1] (9)


119865119866= 1 minus [1 minus sin (120572119865

119881)]2

119865119881isin [0 1] 120572 isin [1

120587

2]

(10)

where 119865119881




01 02 03 04 05 06 07 08 09 10

(7)(10) 120572 = 12

(10) 120572 = 14

y = x

(10) 120572 = 1205872

0

01

02

03

04

05

06

07

08

09

1




120572 =

120587

2119891 le 60

14 60 lt 119891 le 180

12 119891 gt 180

(11)





119865 =

12058311

11989111

12058312

11989112


1198911119873

12058321

11989121

12058322

11989122


1198912119873

1205831198721

1198911198721

1205831198722

1198911198722

sdot sdot sdot120583119872119873

119891119872119873

(12)

here 119891119894119895








119894119895) (119891119894119895isin 119881)



119898 =

sum119891119891119894119895ℎ (119891119894119895)

sum119891ℎ (119891119894119895)

(13)






1198621

and 1205831198622




1 That is to


1205831198621

=1 minus (119898 minus 119865

119866times 255)

119898 (14)






1205831198622

=119864 minus 119865119866times 255

119864 minus 119898 (15)




2 to obtain

the new fuzzy set




2

1198651198711

=10038161003816100381610038161003816119865119866times 255 + 120583

1015840

1198621

times 11987010038161003816100381610038161003816

1198651198712

= 119865119866times 1205831015840

1198622

times 255 + (119864 minus 1205831198622

times 119870)

(16)


119871in



119871



119890image


1198651015840

119896(119894 119895) = 120573 (119894 119895) sdot 119865

119896(119894 119895) (17)

where 120573(119894 119895) = 119865119871(119894 119895)119865















(a) (b)

(c) (d)

(e) (f)

times104 times104

012345678910

Num

ber o

f pix

els

100 20015050 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

100 20015050 2500

Gray levels

(g)

times104 times104

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)





(a) (b)

(c) (d)

(e) (f)

50 150 2500 100 200

Gray levels

times104

0

05

1

15

2

25

Num

ber o

f pix

els

0

1000

2000

3000

4000

5000

6000

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(g)

times104 times104

50 100 150 200 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

0

05

1

15

2

25

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)



AIC = minus

119871minus1

sum

119896=0

119875 (119896) log119875 (119896) (18)




119863(V1 V2 Σ1 Σ2)


2)

minus1

(V1minus V2)

(19)

where V1and V

2and Σ

1and Σ






62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80



689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80











5 Conclusion




Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










01 02 03 04 05 06 07 08 09 10

(7)(10) 120572 = 12

(10) 120572 = 14

y = x

(10) 120572 = 1205872

0

01

02

03

04

05

06

07

08

09

1




120572 =

120587

2119891 le 60

14 60 lt 119891 le 180

12 119891 gt 180

(11)





119865 =

12058311

11989111

12058312

11989112


1198911119873

12058321

11989121

12058322

11989122


1198912119873

1205831198721

1198911198721

1205831198722

1198911198722

sdot sdot sdot120583119872119873

119891119872119873

(12)

here 119891119894119895








119894119895) (119891119894119895isin 119881)



119898 =

sum119891119891119894119895ℎ (119891119894119895)

sum119891ℎ (119891119894119895)

(13)






1198621

and 1205831198622




1 That is to


1205831198621

=1 minus (119898 minus 119865

119866times 255)

119898 (14)






1205831198622

=119864 minus 119865119866times 255

119864 minus 119898 (15)




2 to obtain

the new fuzzy set




2

1198651198711

=10038161003816100381610038161003816119865119866times 255 + 120583

1015840

1198621

times 11987010038161003816100381610038161003816

1198651198712

= 119865119866times 1205831015840

1198622

times 255 + (119864 minus 1205831198622

times 119870)

(16)


119871in



119871



119890image


1198651015840

119896(119894 119895) = 120573 (119894 119895) sdot 119865

119896(119894 119895) (17)

where 120573(119894 119895) = 119865119871(119894 119895)119865















(a) (b)

(c) (d)

(e) (f)

times104 times104

012345678910

Num

ber o

f pix

els

100 20015050 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

100 20015050 2500

Gray levels

(g)

times104 times104

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)





(a) (b)

(c) (d)

(e) (f)

50 150 2500 100 200

Gray levels

times104

0

05

1

15

2

25

Num

ber o

f pix

els

0

1000

2000

3000

4000

5000

6000

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(g)

times104 times104

50 100 150 200 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

0

05

1

15

2

25

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)



AIC = minus

119871minus1

sum

119896=0

119875 (119896) log119875 (119896) (18)




119863(V1 V2 Σ1 Σ2)


2)

minus1

(V1minus V2)

(19)

where V1and V

2and Σ

1and Σ






62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80



689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80











5 Conclusion




Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1205831198622

=119864 minus 119865119866times 255

119864 minus 119898 (15)




2 to obtain

the new fuzzy set




2

1198651198711

=10038161003816100381610038161003816119865119866times 255 + 120583

1015840

1198621

times 11987010038161003816100381610038161003816

1198651198712

= 119865119866times 1205831015840

1198622

times 255 + (119864 minus 1205831198622

times 119870)

(16)


119871in



119871



119890image


1198651015840

119896(119894 119895) = 120573 (119894 119895) sdot 119865

119896(119894 119895) (17)

where 120573(119894 119895) = 119865119871(119894 119895)119865















(a) (b)

(c) (d)

(e) (f)

times104 times104

012345678910

Num

ber o

f pix

els

100 20015050 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

100 20015050 2500

Gray levels

(g)

times104 times104

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)





(a) (b)

(c) (d)

(e) (f)

50 150 2500 100 200

Gray levels

times104

0

05

1

15

2

25

Num

ber o

f pix

els

0

1000

2000

3000

4000

5000

6000

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(g)

times104 times104

50 100 150 200 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

0

05

1

15

2

25

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)



AIC = minus

119871minus1

sum

119896=0

119875 (119896) log119875 (119896) (18)




119863(V1 V2 Σ1 Σ2)


2)

minus1

(V1minus V2)

(19)

where V1and V

2and Σ

1and Σ






62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80



689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80











5 Conclusion




Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)

(c) (d)

(e) (f)

times104 times104

012345678910

Num

ber o

f pix

els

100 20015050 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

100 20015050 2500

Gray levels

(g)

times104 times104

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

0

2

4

6

8

10

12

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)





(a) (b)

(c) (d)

(e) (f)

50 150 2500 100 200

Gray levels

times104

0

05

1

15

2

25

Num

ber o

f pix

els

0

1000

2000

3000

4000

5000

6000

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(g)

times104 times104

50 100 150 200 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

0

05

1

15

2

25

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)



AIC = minus

119871minus1

sum

119896=0

119875 (119896) log119875 (119896) (18)




119863(V1 V2 Σ1 Σ2)


2)

minus1

(V1minus V2)

(19)

where V1and V

2and Σ

1and Σ






62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80



689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80











5 Conclusion




Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)

(c) (d)

(e) (f)

50 150 2500 100 200

Gray levels

times104

0

05

1

15

2

25

Num

ber o

f pix

els

0

1000

2000

3000

4000

5000

6000

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(g)

times104 times104

50 100 150 200 2500

Gray levels

0

05

1

15

2

25

3

Num

ber o

f pix

els

0

05

1

15

2

25

Num

ber o

f pix

els

50 100 150 200 2500

Gray levels

(h)



AIC = minus

119871minus1

sum

119896=0

119875 (119896) log119875 (119896) (18)




119863(V1 V2 Σ1 Σ2)


2)

minus1

(V1minus V2)

(19)

where V1and V

2and Σ

1and Σ






62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80



689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80











5 Conclusion




Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












62996

69769

59987

7037172079 72332

50

55

60

65

70

75

80



689435

60819

72905

641455

5812625

450725

40

45

50

55

60

65

70

75

80











5 Conclusion




Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Competing Interests


Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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Research Article A Novel Enhancement Algorithm Combined ...downloads.hindawi.com/journals/mpe/2016/8598917.pdf · proposed method can enhance local contrast, restore image details,