Research Article An Image Segmentation by BFV and...

Research ArticleAn Image Segmentation by BFV and TLBO

Mohammad Heidari

Department of Mechanical Engineering Abadan Branch Islamic Azad University Abadan Iran

Correspondence should be addressed to Mohammad Heidari moh104337yahoocom

Received 3 August 2016 Accepted 13 October 2016

Academic Editor Mehmet Onder Efe

Copyright copy 2016 Mohammad HeidariThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents the establishing of a biconvex fuzzy variational (BFV) method with teaching learning based optimization(TLBO) for geometric image segmentation (GIS) Firstly a biconvex object function is adopted to process GIS Then TLBO isintroduced tomaximally optimize the length penalty item (LPI) which will be changed under teaching and learner phase of TLBOmaking the LPI closer to the target boundary Afterward the LPI can be adjusted based on fitness function namely the evaluationstandards of image quality Finally the LP is combined item with the numerical order to get better results Different GIS strategiesare compared with various fitness functions in terms of accuracy Simulations show that the presented method is more effective inthis area

1 Introduction

Image segmentation is very important in image processingIt is also an important research direction of computer visiontechnology and has been highly appreciated by people formany years On the one hand it is the foundation of targetexpression and has an important influence on the measure-ment of characteristics on the other hand because of theimage segmentation and expression of segmentation featureextraction and target parameter measurement based on seg-mentation will convert the original image into more abstractandmore compact formmaking it possible for higher level ofimage analysis and understanding There are many methodsin the field of image segmentation such as thresholding[1] edge detection of image [2] clustering for image [34] regional active contour [5] and specific mathematicaltheory tools [6] Some new segmentation methods were alsoproposed such as anterior cruciate ligament [7] improvedfirefly algorithm [8] and fuzzy c-means clustering for imagedetection [9] They are relatively simple image segmentationmethods and most widely used but there are still variousdeficiencies The active contour model without edges namedCVmodel is one of the most successful models in image seg-mentation However CV model also has drawbacks (1) con-verging to local optima [10] (2) being sensitive to selectionof parameters [11] and (3) computational inefficiency [12]In order to overcome these drawbacks a novel BFV image

can be proposed [13] but the BFVmethod is only suitable forsome special images and the LPI is randomly initialized thereis no universality The paper proposes an efficient biconvexfuzzymethodwith TLBO for image segmentationTheTLBOapproaches [14ndash16] used to maximally optimize the LPI willbe changed under teaching phase and learner phase to getbetter results Rao [17 18] presented the Jaya algorithm in thisarea for optimization of the problem

The article is organized as follows Section 2 describes theCVmodel and the BFVmodel Section 3 describes the TLBOstrategy Section 4 presents GIS algorithm based on BFV byTLBO In Section 5 experimental results of the proposedmodel are given Section 6 depicts the conclusion of thispaper

2 CV Model and the BFV Model

Chan and Vese [11] simplified theMumford-Shahmodel andthey presented a novel active contour model based on regionnamely the CV model [19ndash21] The model assumes that theimage is divided into two types of target and backgroundTheenergy function is defined as follows

119864 (119862) = 120583119871 (119862) + ]119860 (119862) + 1205821 int119894(119862)

1003816100381610038161003816119868 (119909 119910) minus 119862110038161003816100381610038162 119889119909+ 1205822 int

119900(119862)

1003816100381610038161003816119868 (119909 119910) minus 119862210038161003816100381610038162 119889119910 (1)

Hindawi Publishing CorporationAdvances in Fuzzy SystemsVolume 2016 Article ID 8109686 7 pageshttpdxdoiorg10115520168109686

2 Advances in Fuzzy Systems

where 119864 119868(119909 119910) and 119862 are the energy of image originalimage and contour of the original image respectively 119894(119862)and 119900(119862) show the region which are inside and outside thecontour The latter two items are fitted to detect the targetregion and background region 119871(119862) indicates the length ofthe contour 119860(119862) shows the area inside the contour 1198621indicates the average gray inside the contour and 1198622 showsthe average gray outside the contour Also120583 V 1205821 and1205822 areall nonnegative numbers where 1205821 and 1205822 are weights for theLPI and the fitting item respectively To minimize the energyfunction and achieve the best effect fuzzy energy functionalis used as follows

119864 = 1205821 intΩ120583119898 (119868 minus 1198621)2 119889119909

+ 1205822 intΩ(1 minus 120583)119898 (119868 minus 1198622)2 119889119910 (2)

In formula (2) 120583 and 119898 are the membership function anda constant positive integer respectively In this paper 1205821 =1205822 = 1 The first-order partial derivatives in formula (2) arecalculated with respect to 1198621 and 1198622 and then they are set tobe zero 1198621 and 1198622 are as follows

1198621 = intΩ120583119898119868 119889119909intΩ120583119898119889119909

1198622 = intΩ(1 minus 120583)119898 119868 119889119909intΩ(1 minus 120583)119898 119889119909 (3)

Another shortcoming of theCVmodel is that the LPI restrictsthe choice of the initial value for level set function Alsothe selection of initial level set function depends on 120583 sothe proposed method is using TLBO to optimize the lengthitem Calculating the Gateaux derivative to energy functionalaccording to formula (1) and derivative function on variables120575 the level set function is expressed as 120601 which shows theinitial surface of the contour It should be noted that the zerolevel set is the contour The evolution process is to get thederivative of the function 120601 on variable 119905 as shown in thefollowing120597120601120597119905 = 120575 (120601) [120583 div( nabla1206011003816100381610038161003816nabla1206011003816100381610038161003816) minus ] minus 1205821 (1 minus 1198621)2

+ 1205822 (1 minus 1198622)2] (4)

In formula (4) div 120575(120601) and nabla are divergence operatorapproximating solution of Dirac function and gradientoperator respectively

In the experiment V = 0 and 1205821 = 1205822 = 1 In the sameway the evolution function for level set of formula (1) is120597120583120597119905= 119898 (minus1205821120583119898minus1 (119868 minus 1198621)2 + 1205822 (1 minus 120583)119898minus1 (119868 minus 1198622)2) (5)

Start

Initialization parameters and members

Calculate the fitness value

Select the teacher calculate average grades

Calculate the gap of value update teaching phase

No Yes

No

No

Yes

Yes

Save theoriginal solution

Accept theupdate solution

Update learning phaseLearning

Finishcondition

Finish

Xnew gt Xold



Xnew gt Xold

phase

phase

Teaching

Figure 1 Algorithm of TLBO

In this paper standard Von Neumann analysis is applied forstudying the time stability [22]The following formula is usedfor calculation

120583119899 = 120583119899+1 + Δ119905119892 (119901 (|nabla119868 119904|) 119904) Δ120583119899+12 119901 (|nabla119868 119904|) = 120576 (119904 minus 1199040) |nabla119868| + (1 minus 120576 (119904 minus 1199040)) |119866 lowast nabla119868| 120576 (119904) = 11 + 119890minus119904 119892max = max 119892 (119901 (|nabla119868|))

(6)

where 119904 119866 and lowast are the SNR of test image Gaussian kerneland operation of convolution respectively

Advances in Fuzzy Systems 3

(a) (b)

(c) (d)

Figure 2 (a) Primary image (b) CV segmentation (c) BFV segmentation (d) TLBO-BFV segmentation

3 TLBO

TheTLBO put forward by Rao et al [14ndash16] is a novel heuris-tic algorithm The model can be described that it randomlygenerated a series of solutions in the constraints space Thesesolutions can be regarded as a group of ldquostudentsrdquo and oneof the best is recognized as a ldquoteacherrdquo The teacher impartsknowledge and answers studentsrsquo questions Students enrichtheir knowledge from the teacher This is the first process ofTLBO algorithm [19] called the teaching phaseThe learningphase which is the second process can be described ascommunicating with others and exchanging experience topromote each other After a period of time the studentsrsquoknowledge is higher and higher that is to say it is more andmore tending to the optimal solution in the constraint spaceThe whole process is shown in Figure 1The optimal model isas follows

min 119891 (119883) or max119891 (119883)Subject to 119883 isin 119878

119892119894 (119883) le 0(119894 = 1 2 119898) (7)

where 119891(119883) is optimized objective function searching anypoint119883119895 = (1199091 1199092 119909119889) 119895 = 1 2 119878119901 119878119901 is the numberof species and 119889 are dimensions of 119883 Continuous variables119878 = 119883 | 119909119871119902 le 119909119902 le 119909119880119902 119902 = 1 2 119889 and 119909119871119902 and 119909119880119902are lower and upper bound of each dimension weight of 119883respectively Discrete variable 119909119902 isin 119878 = 1198831 1198832 119883119901and 119901 is a number of discrete set In the TLBO algorithmthe relations of class students and teacher are as follows

Class set 119883119895 119895 = 1 2 119878119901Students set 119883119895 = (1199091 1199092 119909119889) where 119889 is thesubject of teaching

Teacher the best fitness value 119891(119883) of set 119883119895 119895 =1 2 119878119901


(a) (b)

(c) (d)


The class matrix is defined as follows

((

119891(1198831) 1198831119891 (1198832) 1198832 119891 (119883119878119901) 119883119878119901))

=((

11990911 11990912 sdot sdot sdot 119909111988911990921 11990922 sdot sdot sdot 1199092119889 sdot sdot sdot 1199091198781199011 1199091198781199012 sdot sdot sdot 119909119878119901119889

))119883teacher = min119891 (119883119895) 119895 = 1 2 119878119901

(8)

Themarks distribution curve of the class is a normal distribu-tion as in formulation (6) in spite of having certain deviationwith the actual it still be helpful for analysis The definitionabove can be described as

119891 (119883) = 1120590radic2120587119890minus(119909minus120583)221205902 (9)

In formula (9)120590 x and120583 are the variance the value in certainrange and the mean value respectively

31 Teaching and Learner Phase In the beginning of teachingphase studentsrsquo values are relatively scattered and the averagegrades are 119878119860 at the same time the teacherrsquo is 119879119860 Aftera period of teaching studentsrsquo results gradually concentratedistribution and the average grade is increasing to 119878119861 andthe teacher is also updated to 119879119861 Students learn knowledgefrom the teacher through the difference between the averageof teacher and the student in the teaching phase In short thesolution is updated with formula (9) If the new solution isbetter than the existing one replace the existing solution withthe new one

Difference Meannew119894 = 119903119894 (119872new119894 minus 119879119865119872119894) (10)

where 119903119894 is a random number 119903119894 isin [0 1] and 119879119865 is a teachingfactor which decides how the mean value is to be changedBecause 119879119865 is either 1 or 2 it can be presented as follows

119879119865 = round [1 + rand (0 2)] (11)

Solutions of the problem are updated based on the followingstrategy At first the value of objective function is obtainedIf the new solution is better than the existing one replace it


(a) (b)

(c) (d)


with the new one

iilarr random (pop rize) (119894119894 = 119894)if119883119894 is better than119883119894119894 then119883119894new = 119883119894 + 119903 sdot (119883119894 minus 119883119894119894)else119883119894new = 119883119894 + 119903 sdot (119883119894119894 minus 119883119894)end if

evaluate (119883119894new)if119883119894new is better than119883119894 then119883119894 larr 119883119894newend if

Figure 1 show the flowchart of TLBO algorithm

4 GIS Strategy Based on BFV with TLBO

In this paper the fitness function applies Jaccard Similarity(JS) [23] value and standard deviation (Std) as the quantita-tive indexes to evaluate the results The JS value is explainedas

JS (1198781 1198782) = 10038161003816100381610038161198781 cap 1198782100381610038161003816100381610038161003816100381610038161198781 cup 11987821003816100381610038161003816 (12)

In (12) 1198782 and 1198781 are the ground truth data and thesegmentation results respectively The Std is defined as

Std = 100 times 1((1 (119899 minus 1))sum119899119894=1 (119909119894 minus 119909)2)12 (13)

where 119909 and 119909119894 are the mean of image pixels and the valueof image pixels respectively From the discussion above itis not necessary to record experimental results each timeWe can take a reaction part to 119879 with step Δ119905 (119879 = 119899Δ119905where 119899 is a positive integer) In summary the flowchart of


084620796107944

09392

06691

08296

09921098420918

Fig4Fig3Fig20

02

04

06

08

1

JS

CVBFVTLBO-BFV

Figure 5 JS of methods

050960499404591

080110822308622096310983309909

Fig4Fig3Fig2

CVBFVTLBO-BFV

0

02

04

06

08

1

12

Std

Figure 6 Standard deviation of methods

the proposed algorithm (TLBO-BFV) can be summed up asin the following steps

(1) Set 119899 = 0 It uses the TLBOmethod to optimize 119906 andcalculate 119892 using formula (6)

(2) Calculate 1198621 and 1198622 using formula (3)(3) Set 119905 = 0 Compute120583119899+12 using formula (5) If 119905+Δ119905 le119879 then set 119905 = 119905 + Δ119905 and 120583119899 = 120583119899+12 and it goes to

step (2) otherwise it continues(4) It computes 120583119899+1 using formula (6)(5) If 120583119899+1 satisfy termination condition it stops other-

wise set 119899 = 119899 + 1 and it returns to step (2)

5 Simulation

The CV model and BFV segmentation method are selectedto compare with TLBO-BFVmethod In the experiments thesame iteration number is set

Tables 1 2 and 3 demonstrate the results of Figures 2 3and 4 respectively

Table 1 Results of Figure 2

Model Std JSCV 04591 07944BFV 08622 08296TLBO-BFV 09909 0918





Figures 2 3 and 4 show the value of JS and Std of the threemethods

Figures 5 and 6 demonstrate the JS and Std of the threemethods respectively

6 Conclusion

This paper presents a new image segmentation methodnamedTLBO-BFVTheTLBO approach is used tomaximallyoptimize the LPI so as to improve the accuracy of seg-mentation Simulations indicate that the proposed methodimproves the robustness and the recognition rate and thealgorithm has advantages in stability and effectiveness

Competing Interests

The author declares that they have no competing interests

References

[1] S Patra R Gautam and A Singla ldquoA novel context sensitivemultilevel thresholding for image segmentationrdquo Applied SoftComputing Journal vol 23 pp 122ndash127 2014

[2] C I Gonzalez P Melin J R Castro O Castillo and OMendoza ldquoOptimization of interval type-2 fuzzy systems forimage edge detectionrdquo Applied Soft Computing Journal vol 47pp 631ndash643 2016

[3] J Hou W Liu X Ex and H Cui ldquoTowards parameter-independent data clustering and image segmentationrdquo PatternRecognition vol 60 pp 25ndash36 2016

[4] X Fan L Ju X Wang and S Wang ldquoA fuzzy edge-weightedcentroidal Voronoi tessellation model for image segmentationrdquoComputers amp Mathematics with Applications vol 71 no 11 pp2272ndash2284 2016

[5] F Y Shih and K Zhang ldquoLocating object contours in complexbackground using improved snakesrdquo Computer Vision andImage Understanding vol 105 no 2 pp 93ndash98 2007


[6] O Hadjerci A Hafiane N Morette C Novales P Vieyresand A Delbos ldquoAssistive system based on nerve detection andneedle navigation in ultrasound images for regional anesthesiardquoExpert Systems with Applications vol 61 pp 64ndash77 2016

[7] H Lee H Hong and J Kim ldquoSegmentation of anterior cruciateligament in knee MR images using graph cuts with patient-specific shape constraints and label refinementrdquo Computers inBiology and Medicine vol 55 pp 1ndash10 2014

[8] B Krawczyk and P Filipczuk ldquoCytological image analysiswith firefly nuclei detection and hybrid one-class classificationdecompositionrdquo Engineering Applications of Artificial Intelli-gence vol 31 pp 126ndash135 2014

[9] X L Jiang Q Wang B He S J Chen and B L Li ldquoRobustlevel set image segmentation algorithmusing local correntropy-based fuzzy c-means clustering with spatial constraintsrdquoNeuro-computing vol 207 pp 22ndash35 2016

[10] G Aubert and P Kornprobst Mathematical Problems in ImageProcessing Partial Differential Equations and the Calculus ofVariations Springer New York NY USA 2006

[11] T F Chan and L A Vese ldquoActive contours without edgesrdquo IEEETransactions on Image Processing vol 10 no 2 pp 266ndash2772002

[12] T-T Tran V-T Pham and K-K Shyu ldquoImage segmentationusing fuzzy energy-based active contour with shape priorrdquoJournal of Visual Communication and Image Representation vol25 no 7 pp 1732ndash1745 2014

[13] M Gong D Tian L Su and L Jiao ldquoAn efficient bi-convexfuzzy variational image segmentation methodrdquo InformationSciences vol 293 pp 351ndash369 2015

[14] R V Rao V J Savsani and D P Vakharia ldquoTeaching-learning-based optimization a novelmethod for constrainedmechanicaldesign optimization problemsrdquoComputer Aided Design vol 43no 3 pp 303ndash315 2011

[15] R V Rao V J Savsani and D P Vakharia ldquoTeaching-learning-based optimization an optimization method for continuousnon-linear large scale problemsrdquo Information Sciences vol 183no 1 pp 1ndash15 2012

[16] R V Rao Teaching Learning Based Optimization and ItsEngineering Applications Springer Basel Switzerland 2016

[17] R V Rao ldquoJaya a simple and new optimization algorithm forsolving constrained and unconstrained optimization problemsrdquoInternational Journal of Industrial Engineering Computationsvol 7 no 1 pp 19ndash34 2016

[18] R V Rao K More J Taler and P Ocłon ldquoDimensional opti-mization of a micro-channel heat sink using Jaya algorithmrdquoApplied Thermal Engineering vol 103 pp 572ndash582 2016

[19] R V Rao ldquoReview of applications of tlbo algorithm and a tuto-rial for beginners to solve the unconstrained and constrainedoptimization problemsrdquo Decision Science Letters vol 5 no 1pp 1ndash30 2016

[20] B Al-Diri A Hunter andD Steel ldquoAn active contourmodel forsegmenting and measuring retinal vesselsrdquo IEEE Transactionson Medical Imaging vol 28 no 9 pp 1488ndash1497 2009

[21] S K Nath K Palaniappan and F Bunyak ldquoCell segmentationusing coupled level sets and graph-vertex coloringrdquo MedicalImage Computing and Computer-Assisted Inter- Vention vol 9no 1 pp 101ndash108 2006

[22] K Zhang L Zhang H Song and D Zhang ldquoReinitialization-free level set evolution via reaction diffusionrdquo IEEETransactionson Image Processing vol 22 no 1 pp 258ndash271 2013

[23] S Jimenez F A Gonzalez and A Gelbukh ldquoMathematicalproperties of soft cardinality enhancing Jaccard Dice andcosine similarity measures with element-wise distancerdquo Infor-mation Sciences vol 367-368 pp 373ndash389 2016

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Distributed Sensor Networks


Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

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HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

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Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

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Biomedical Imaging


ArtificialNeural Systems

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Advances in

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where 119864 119868(119909 119910) and 119862 are the energy of image originalimage and contour of the original image respectively 119894(119862)and 119900(119862) show the region which are inside and outside thecontour The latter two items are fitted to detect the targetregion and background region 119871(119862) indicates the length ofthe contour 119860(119862) shows the area inside the contour 1198621indicates the average gray inside the contour and 1198622 showsthe average gray outside the contour Also120583 V 1205821 and1205822 areall nonnegative numbers where 1205821 and 1205822 are weights for theLPI and the fitting item respectively To minimize the energyfunction and achieve the best effect fuzzy energy functionalis used as follows

119864 = 1205821 intΩ120583119898 (119868 minus 1198621)2 119889119909

+ 1205822 intΩ(1 minus 120583)119898 (119868 minus 1198622)2 119889119910 (2)

In formula (2) 120583 and 119898 are the membership function anda constant positive integer respectively In this paper 1205821 =1205822 = 1 The first-order partial derivatives in formula (2) arecalculated with respect to 1198621 and 1198622 and then they are set tobe zero 1198621 and 1198622 are as follows

1198621 = intΩ120583119898119868 119889119909intΩ120583119898119889119909

1198622 = intΩ(1 minus 120583)119898 119868 119889119909intΩ(1 minus 120583)119898 119889119909 (3)

Another shortcoming of theCVmodel is that the LPI restrictsthe choice of the initial value for level set function Alsothe selection of initial level set function depends on 120583 sothe proposed method is using TLBO to optimize the lengthitem Calculating the Gateaux derivative to energy functionalaccording to formula (1) and derivative function on variables120575 the level set function is expressed as 120601 which shows theinitial surface of the contour It should be noted that the zerolevel set is the contour The evolution process is to get thederivative of the function 120601 on variable 119905 as shown in thefollowing120597120601120597119905 = 120575 (120601) [120583 div( nabla1206011003816100381610038161003816nabla1206011003816100381610038161003816) minus ] minus 1205821 (1 minus 1198621)2

+ 1205822 (1 minus 1198622)2] (4)

In formula (4) div 120575(120601) and nabla are divergence operatorapproximating solution of Dirac function and gradientoperator respectively

In the experiment V = 0 and 1205821 = 1205822 = 1 In the sameway the evolution function for level set of formula (1) is120597120583120597119905= 119898 (minus1205821120583119898minus1 (119868 minus 1198621)2 + 1205822 (1 minus 120583)119898minus1 (119868 minus 1198622)2) (5)

Start

Initialization parameters and members

Calculate the fitness value

Select the teacher calculate average grades

Calculate the gap of value update teaching phase

No Yes

No

No

Yes

Yes



Update learning phaseLearning

Finishcondition

Finish

Xnew gt Xold



Xnew gt Xold

phase

phase

Teaching

Figure 1 Algorithm of TLBO

In this paper standard Von Neumann analysis is applied forstudying the time stability [22]The following formula is usedfor calculation

120583119899 = 120583119899+1 + Δ119905119892 (119901 (|nabla119868 119904|) 119904) Δ120583119899+12 119901 (|nabla119868 119904|) = 120576 (119904 minus 1199040) |nabla119868| + (1 minus 120576 (119904 minus 1199040)) |119866 lowast nabla119868| 120576 (119904) = 11 + 119890minus119904 119892max = max 119892 (119901 (|nabla119868|))

(6)

where 119904 119866 and lowast are the SNR of test image Gaussian kerneland operation of convolution respectively


(a) (b)

(c) (d)


3 TLBO



119892119894 (119883) le 0(119894 = 1 2 119898) (7)





(a) (b)

(c) (d)



((

119891(1198831) 1198831119891 (1198832) 1198832 119891 (119883119878119901) 119883119878119901))

=((


))119883teacher = min119891 (119883119895) 119895 = 1 2 119878119901

(8)







119879119865 = round [1 + rand (0 2)] (11)



(a) (b)

(c) (d)


with the new one






JS (1198781 1198782) = 10038161003816100381610038161198781 cap 1198782100381610038161003816100381610038161003816100381610038161198781 cup 11987821003816100381610038161003816 (12)





084620796107944

09392

06691

08296

09921098420918

Fig4Fig3Fig20

02

04

06

08

1

JS

CVBFVTLBO-BFV


050960499404591

080110822308622096310983309909

Fig4Fig3Fig2

CVBFVTLBO-BFV

0

02

04

06

08

1

12

Std







5 Simulation











6 Conclusion


Competing Interests


References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




(a) (b)

(c) (d)


3 TLBO



119892119894 (119883) le 0(119894 = 1 2 119898) (7)





(a) (b)

(c) (d)



((

119891(1198831) 1198831119891 (1198832) 1198832 119891 (119883119878119901) 119883119878119901))

=((


))119883teacher = min119891 (119883119895) 119895 = 1 2 119878119901

(8)







119879119865 = round [1 + rand (0 2)] (11)



(a) (b)

(c) (d)


with the new one






JS (1198781 1198782) = 10038161003816100381610038161198781 cap 1198782100381610038161003816100381610038161003816100381610038161198781 cup 11987821003816100381610038161003816 (12)





084620796107944

09392

06691

08296

09921098420918

Fig4Fig3Fig20

02

04

06

08

1

JS

CVBFVTLBO-BFV


050960499404591

080110822308622096310983309909

Fig4Fig3Fig2

CVBFVTLBO-BFV

0

02

04

06

08

1

12

Std







5 Simulation











6 Conclusion


Competing Interests


References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




(a) (b)

(c) (d)



((

119891(1198831) 1198831119891 (1198832) 1198832 119891 (119883119878119901) 119883119878119901))

=((


))119883teacher = min119891 (119883119895) 119895 = 1 2 119878119901

(8)







119879119865 = round [1 + rand (0 2)] (11)



(a) (b)

(c) (d)


with the new one






JS (1198781 1198782) = 10038161003816100381610038161198781 cap 1198782100381610038161003816100381610038161003816100381610038161198781 cup 11987821003816100381610038161003816 (12)





084620796107944

09392

06691

08296

09921098420918

Fig4Fig3Fig20

02

04

06

08

1

JS

CVBFVTLBO-BFV


050960499404591

080110822308622096310983309909

Fig4Fig3Fig2

CVBFVTLBO-BFV

0

02

04

06

08

1

12

Std







5 Simulation











6 Conclusion


Competing Interests


References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




(a) (b)

(c) (d)


with the new one






JS (1198781 1198782) = 10038161003816100381610038161198781 cap 1198782100381610038161003816100381610038161003816100381610038161198781 cup 11987821003816100381610038161003816 (12)





084620796107944

09392

06691

08296

09921098420918

Fig4Fig3Fig20

02

04

06

08

1

JS

CVBFVTLBO-BFV


050960499404591

080110822308622096310983309909

Fig4Fig3Fig2

CVBFVTLBO-BFV

0

02

04

06

08

1

12

Std







5 Simulation











6 Conclusion


Competing Interests


References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




084620796107944

09392

06691

08296

09921098420918

Fig4Fig3Fig20

02

04

06

08

1

JS

CVBFVTLBO-BFV


050960499404591

080110822308622096310983309909

Fig4Fig3Fig2

CVBFVTLBO-BFV

0

02

04

06

08

1

12

Std







5 Simulation











6 Conclusion


Competing Interests


References
































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article An Image Segmentation by BFV and...

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