Multilevel Thresholding Segmentation Based on Harmony Search Optimization

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013 Article ID 575414 24 pageshttpdxdoiorg1011552013575414

Research ArticleMultilevel Thresholding Segmentation Based onHarmony Search Optimization

Diego Oliva1 Erik Cuevas2 Gonzalo Pajares1 Daniel Zaldivar2 and Marco Perez-Cisneros2

1 Departamento de Ingenierıa del Software e Inteligencia Artificial Facultad Informatica Universidad Complutense28040 Madrid Spain

2Departamento de Ciencias Computacionales Universidad de Guadalajara CUCEI CU-TONALA Avenida Revolucion 1500CP 44430 Guadalajara JAL Mexico

Correspondence should be addressed to Erik Cuevas erikcuevascuceiudgmx

Received 14 June 2013 Revised 17 August 2013 Accepted 20 August 2013

Academic Editor Zong Woo Geem

Copyright copy 2013 Diego Oliva 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

In this paper a multilevel thresholding (MT) algorithm based on the harmony search algorithm (HSA) is introduced HSA is anevolutionary method which is inspired in musicians improvising new harmonies while playing Different to other evolutionaryalgorithms HSA exhibits interesting search capabilities still keeping a low computational overhead The proposed algorithmencodes random samples from a feasible search space inside the image histogram as candidate solutions whereas their qualityis evaluated considering the objective functions that are employed by the Otsursquos or Kapurrsquos methods Guided by these objectivevalues the set of candidate solutions are evolved through the HSA operators until an optimal solution is found Experimentalresults demonstrate the high performance of the proposed method for the segmentation of digital images

1 Introduction

Segmentation is one of the most important tasks in imageprocessing that endeavors to identifywhether a pixel intensitycorresponds to a predefined class Thresholding is the easiestmethod for segmentation as it works taking a threshold (th)value so that pixels whose intensity value is higher than thare labeled as first class while the rest correspond to a secondclass labelWhen the image is segmented into two classes thetask is called bilevel thresholding (BT) and requires only oneth value On the other hand when pixels are separated intomore than two classes the task is named asMT and demandsmore than one th value [1]

In recent years image processing has been applied todifferent areas as engineering medicine agriculture and soforth Since most of such implementations use a THmethod-ology several techniques had been studied Generally THmethods are divided into parametric and nonparametric [2ndash5] Parametric approaches need to estimate values of a prob-ability density function to model each class The estimation

process is time consuming and computationally expensiveOn the other hand the TH nonparametric employs severalcriteria such as the between-class variance the entropy andthe error rate [6ndash8] in order to verify the quality of a th valueThese metrics could also be used as optimization functionssince they result as an attractive option due their robustnessand accuracy

There exist two classical thresholding methods The firstproposed byOtsu in [6] that maximizes the variance betweenclasses while the second method submitted by Kapur et alin [7] uses the maximization of the entropy to measure thehomogeneity among classes Their efficiency and accuracyhave been already proved for a bilevel segmentation [4]Although they can be expanded for MT their computationalcomplexity increases exponentially when a new threshold isincorporated [5]

As an alternative to classical methods the MT problemhas also been handled through evolutionary optimizationmethods In general they have demonstrated to deliver betterresults than those based on classical techniques in terms

2 Journal of Applied Mathematics

of accuracy speed and robustness Numerous evolutionaryapproaches have been reported in the literature

Hammouche et al in [9] provides an interesting survey ofhow different evolutionary algorithms are used to solve theKapturrsquos and Otsursquos problems The study uses four classicalevolutionary algorithms to test their efficiency in MT Suchmethods include differential evolution (DE) [10] simulatedannealing (SA) [11] and tabu search (TS) [12]

Genetic algorithms (GA) [13] inspired on the biologicalevolution have been also used for solving segmentationtasks One interesting example is presented in [14] where aGA-based algorithm is combined with Gaussian models formultilevel thresholding Other similar works such as that ofYin [15] proposes an improved GA for optimal thresholdingIn the approach it is used as a learning strategy to increasethe speed of convergence

Evolutionary approaches inspired on swarm behaviorsuch as particle swarm optimization (PSO) [16] and artificialbee colony (ABC) [17] have been employed to face thesegmentation problem In [18] bothmethods are used to findthe optimal multilevel threshold points by using the Kapurrsquosentropy as fitness function

Finally in [19] the optimal segmentation threshold valuesare determined by using the bacterial foraging algorithm(BFA) Suchmethod aims tomaximize the Kapurrsquos andOtsursquosobjective functions by considering a set of operators thatare based on the social foraging behavior of the bacteriaEschericha Colli

On the other hand the harmony search algorithm (HSA)introduced by Geem et al [20] is an evolutionary opti-mization algorithm which is based on the metaphor of theimprovisation process that occurs when a musician searchesfor a better state of harmony The HSA generates a newcandidate solution from all existing solutions The solutionvector is analogous to the harmony in music while thelocal and global search schemes are analogous to musi-cianrsquos improvisations In comparison to other metaheuristicsmethods in the literature HSA imposes fewer mathematicalrequirements as it can be easily adapted for solving severalsorts of engineering optimization challenges [21] Further-more numerical comparisons have demonstrated that theconvergence for theHSA is faster thanGA [22] which attractsfurther attention It has been successfully applied to solve awide range of practical optimization problems such as dis-crete and continuous structural optimization [23] parameterestimation of the nonlinear Muskingum model [24] designoptimization of water distribution networks [25] vehiclerouting [26] combined heat and power economic dispatch[27] design of steel frames [28] and image processing [29]Although the standard HSA presents good search character-istics several modifications to the original HSA have beenproposed in the literature in order to enhance its own features[30]

In this paper a novel multithresholding segmentationalgorithm is introduced The proposed approach calledthe harmony search multithresholding algorithm (HSMA)combines the original harmony search algorithm (HSA) andthe Otsursquos and Kapurrsquos methodologies The proposed algo-rithm takes random samples from a feasible search space

inside the image histogram Such samples build each har-mony (candidate solution) in the HSA context whereas itsquality is evaluated considering the objective function thatis employed by the Otsursquos or the Kapurrsquos method Guidedby these objective values the set of candidate solutions areevolved using the HSA operators until the optimal solutionis found The approach generates a multilevel segmentationalgorithm which can effectively identify the threshold valuesof a digital image within a reduced number of iterationsExperimental results over several complex images have val-idated the efficiency of the proposed technique regardingaccuracy speed and robustness

The paper is organized as follows In Section 2 the HSAis introduced Section 3 gives a brief description of the Otsursquosand Kapurrsquos methods Section 4 explains the implementationof the proposed algorithm Section 5 discusses experimentalresults after testing the proposed method over a set bench-mark images Finally some conclusions are discussed inSection 6

2 Harmony Search Algorithm

21 The Harmony Search Algorithm In the basic HSA eachsolution is called a ldquoharmonyrdquo and is represented by an n-dimension real vector An initial population of harmonyvectors are randomly generated and stored within a har-mony memory (HM) A new candidate harmony is thusgenerated from the elements in the HM by using a memoryconsideration operation either by a random reinitializationor a pitch adjustment operation Finally the HM is updatedby comparing the new candidate harmony and the worstharmony vector in the HM The worst harmony vector isreplaced by the new candidate vector when the latter deliversa better solution in the HM The above process is repeateduntil a certain termination criterion is met The basic HSalgorithm consists of three main phases HM initializationimprovisation of new harmony vectors and updating theHM The following discussion addresses details about eachstage

211 Initializing the Problem and the Algorithm ParametersIn general the global optimization problem can be summa-rized as followsminimize 119891 (x) x = (119909 (1) 119909 (2) 119909 (119899)) isin R119899

subject to 119909 (119895) isin [119897 (119895) 119906 (119895)] 119895 = 1 2 119899(1)

where 119891(x) is the objective function x = (119909(1) 119909(2) 119909(119899)) is the set of design variables 119899 is the number of designvariables and 119897(119895) and 119906(119895) are the lower and upper boundsfor the design variable 119909(119895) respectively The parameters forHSA are the harmony memory size that is the numberof solution vectors lying on the harmony memory (HM)the harmony-memory consideration rate (HMCR) the pitchadjusting rate (PAR) the distance bandwidth (BW) and thenumber of improvisations (NI) which represents the totalnumber of iterations The performance of HSA is stronglyinfluenced by values assigned to such parameters which inturn depend on the application domain [31]

Journal of Applied Mathematics 3

212 Harmony Memory Initialization In this stage initialvector components at HM that is HMS vectors are con-figured Let x

119894= 119909119894(1) 119909119894(2) 119909

119894(119899) represent the 119894th

randomly-generated harmony vector 119909119894(119895) = 119897(119895) + (119906(119895) minus

119897(119895)) sdot rand(0 1) for 119895 = 1 2 119899 and 119894 = 1 2 HMSwhere rand(01) is a uniform random number between 0 and1 the upper and lower bounds of the search space are definedby 119897(119895) and 119906(119895) respectively Then the HM matrix is filledwith the HMS harmony vectors as follows

HM =[[[[

[

x1

x2

xHMS

]]]]

]

(2)

213 Improvisation of New Harmony Vectors In this phasea new harmony vector xnew is built by applying the followingthree operators memory consideration random reinitializa-tion and pitch adjustment Generating a new harmony isknown as ldquoimprovisationrdquo In thememory consideration stepthe value of the first decision variable 119909new(1) for the newvector is chosen randomly from any of the values alreadyexisting in the current HM that is from the set 119909

1(1)

1199092(1) 119909HMS(1) For this operation a uniform random

number 1199031is generated within the range [0 1] If 119903

1is

less than HMCR the decision variable 119909new(1) is gener-ated through memory considerations otherwise 119909new(1) isobtained from a random reinitialization between the searchbounds [119897(1) 119906(1)] Values of the other decision variables119909new(2) 119909new(3) 119909new(119899) are also chosen accordinglyTherefore both operations memory consideration and ran-dom reinitialization can be modeled as follows

119909new (119895)

=

119909119894(119895) isin 119909

1(119895) 119909

2(119895) 119909HMS (119895)

with probability HMCR119897 (119895) + (119906 (119895) minus 119897 (119895)) sdot rand (0 1)

with probability 1 minusHMCR

(3)

Every component obtained by memory consideration isfurther examined to determine whether it should be pitch-adjusted For this operation the pitch-adjusting rate (PAR)is defined as to assign the frequency of the adjustment andthe bandwidth factor (BW) to control the local search aroundthe selected elements of the HM Hence the pitch-adjustingdecision is calculated as follows

119909new (119895)

=

119909new (119895) = 119909new (119895) plusmn rand (0 1) sdot BW

with probability PAR119909new (119895) with probability (1 minus PAR)

(4)

Pitch adjusting is responsible for generating new potentialharmonies by slightly modifying original variable positionsSuch operation can be considered similar to the mutationprocess in evolutionary algorithms Therefore the decision

variable is either perturbed by a random number between 0and BW or left unaltered In order to protect the pitch adjust-ing operation it is important to assure that points lyingoutside the feasible range [119897 119906] must be reassigned that istruncated to the maximum or minimum values of the inter-val

214 Updating the Harmony Memory After a new harmonyvector 119909new is generated the harmony memory is updated bythe survival of the fit competition between 119909new and the worstharmony vector 119909

119908in the HMTherefore 119909new will replace 119909

119908

and become a newmember of theHM in case the fitness valueof 119909new is better than the fitness value of 119909

119908

215 Computational Procedure The computational proce-dure of the basic HSA can be summarized as in Algorithm 1[20]

This procedure is implemented for minimization If theintention is to maximize the objective function a signmodification of step 4 (x

119908= xnew if 119891(xnew) gt 119891(x

119908)) is

required In this paper the HSA is used for maximizationproposes

3 Image Multilevel Thresholding (MT)

Thresholding is a process in which the pixels of a gray scaleimage are divided in sets or classes depending on their inten-sity level (119871) For this classification it is necessary to select athreshold value (th) and follow the simple rule of

1198621larr997888 119901 if 0 le 119901 lt th

1198622larr997888 119901 if th le 119901 lt 119871 minus 1

(5)

where119901 is one of the119898times119899 pixels of the gray scale image 119868119892that

can be represented in 119871 gray scale levels 119871 = 0 1 2 119871minus11198621and 119862

2are the classes in which the pixel 119901 can be located

while th is the threshold The rule in (5) corresponds to abilevel thresholding and can be easily extended for multiplesets

1198621larr997888 119901 if 0 le 119901 lt th

1

1198622larr997888 119901 if th

1le 119901 lt th

2

119862119894larr997888 119901 if th

119894le 119901 lt th

119894+1

119862119899larr997888 119901 if th

119899le 119901 lt 119871 minus 1

(6)

where th1 th2 th

119894 th119894+1 th119896 represent different thresh-

olds The problem for both bilevel and MT is to selectthe th values that correctly identify the classes AlthoughOtsursquos and Kapurrsquos methods are well-known approaches fordetermining such values both propose a different objectivefunction which must be maximized in order to find optimalthreshold values just as it is discussed below

31 Between-Class Variance (Otsursquos Method) This is a non-parametric technique for thresholding proposed by Otsu [6]that employs the maximum variance value of the different


119878119905119890119901 1 Set the parameters HMS HMCR PAR BW and NI119878119905119890119901 2 Initialize the HM and calculate the objective function value of

each harmony vector119878119905119890119901 3 Improvise a new harmony xnew as follows

for (119895 = 1 to 119899) doif (1199031ltHMCR) then

119909new(119895) = 119909119886(119895) where 119886 isin (1 2 HMS)if (1199032lt PAR) then

119909new(119895) = 119909new(119895) plusmn 1199033 sdot BW where 1199031 1199032 1199033isin rand (0 1)

end ifif 119909new(119895) lt 119897(119895)119909new(119895) = 119897(119895)end ifif 119909new(119895) gt 119906(119895)119909new(119895) = 119906(119895)end if

else119909new(119895) = 119897(119895) + 119903sdot (119906(119895) minus 119897(119895)) where 119903 isin rand (0 1)

end ifend for

119878119905119890119901 4 Update the HM as x119908= xnew if 119891(xnew) lt 119891(x119908)

119878119905119890119901 5 If NI is completed the best harmony vector x119887in the HM is returned

otherwise go back to Step3

Algorithm 1

119878119905119890119901 1 Read the image 119868 and if it is RGB separate it into 119868119877 119868119866and 119868119861 If 119868 is gray scale store it into

119868Gr 119888 = 1 2 3 for RGB images or 119888 = 1 for gray scale images119878119905119890119901 2 Obtain histograms for RGB images ℎ119877 ℎ119866 ℎ119861 and for gray scale images ℎGr119878119905119890119901 3 Calculate the probability distribution using (7) and obtain the histograms119878119905119890119901 4 Initialize the HSA parameters HMS 119896 HMCR PAR BW NI and the limits 119897 and 119906119878119905119890119901 5 Initialize a HM x119888

119894of HMS random particles with 119896 dimensions

119878119905119890119901 6 Compute the values 120596119888119894and 120583119888

119894 Evaluate each element ofHM in the objective function 119869(HM) (14)

or (20) depending on the thresholding method (Otsu or Kapur respectively)119878119905119890119901 7 Improvise a new harmony x119888new as follows

for (119895 = 1 to 119899) doif (1199031lt HCMR) then

119909119888new (119895) = 119909119888

119886(119895) where 119886 isin (1 2 HMS)

if (1199032lt PAR) then

119909119888new (119895) = 119909119888

119886(119895) plusmn 119903

3sdot BW where 119903

1 1199032 1199033isin rand (0 1)

end ifif 119909119888new (119895) lt 119897 (119895)119909119888new (119895) = 119897 (119895)

end ifif 119909119888new (119895) gt 119906 (119895)119909119888new (119895) = 119906 (119895)

end ifelse

119909119888new (119895) = 119897 (119895) + 119903 sdot (119906 (119895) minus 119897 (119895)) whew 119903 isin rand (0 1)end if

end for119878119905119890119901 8 Update the HM as x119888worst = x119888new if 119891 (x119888new) gt 119891 (x

cworst)

119878119905119890119901 9 If NI is completed or the stop criteria is satisfied then jump to Step 10 otherwise go back to Step 6119878119905119890119901 10 Select the harmony that has the best 119909119888bestobjective function value119878119905119890119901 11 Apply the thresholds values contained in 119909119888best to the image 119868 (6)

Algorithm 2


(a)

0025

002

0015

001

0005

050 100 150 200 250

Gray level

Freq

uenc

y

(b)

(c)

0012

001

0008

0006

0004

0002

050 100 150 250

Gray level200

Freq

uenc

y

(d)

(e)

0012

001

0008

0006

0004

0002

050 100 150 250

Gray level200

Freq

uenc

y

(f)

(g)

0045004

0035003

0025002

0015001

00050

50 100 150 250Gray level

200

Freq

uenc

y

(h)

Figure 1 Continued


(i)

003

0025

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y

(j)

Figure 1 (a) Camera man (c) Lena (e) Baboon (g) Hunter and (i) Butterfly the selected benchmark images (b) (d) (f) (h) and (j)histograms of the images

classes as a criterion to segment the image Taking the119871 inten-sity levels from a gray scale image or from each component ofa RGB (red green and blue) image the probability distribu-tion of the intensity values is computed as follows

Ph119888119894=

ℎ119888119894

NP

NPsum119894=1

Ph119888119894= 1

119888 = 1 2 3 if RGB Image1 if Gray scale Image

(7)

where 119894 is a specific intensity level (0 le 119894 le 119871 minus 1) 119888 is thecomponent of the image which depends if the image is grayscale or RGB whereas NP is the total number of pixels inthe image ℎ119888

119894(histogram) is the number of pixels that cor-

responds to the 119894 intensity level in 119888 The histogram is norm-alized within a probability distribution Ph119888

119894 For the simplest

segmentation (bilevel) two classes are defined as

1198621=

Ph1198881

1205961198880(th)

Ph119888th1205961198880(th)

1198622=

Ph119888th+11205961198881(th)

Ph119888119871

1205961198881(th)

(8)

where 1205960(th) and 120596

1(th) are probabilities distributions for119862

1

and 1198622 as it is shown by

1205961198880(th) =

thsum119894=1

Ph119888119894 120596119888

1(th) =

119871

sum119894=th+1

Ph119888119894 (9)

It is necessary to compute mean levels 1205831198880and 120583119888

1that define

the classes using (10) Once those values are calculated theOtsu variance between classes 1205902

119888

is calculated using (11) asfollows

1205831198880=

thsum119894=1

119894Ph119888119894

1205961198880(th)

1205831198881=119871

sum119894=th+1

119894Ph119888119894

1205961198881(th)

(10)

1205902119888

= 1205901198881+ 1205901198882 (11)

Notice that for both equations (10) and (11) 119888 depends on thetype of image In (11) the number two is part of the Otsursquosvariance operator and does not represent an exponent inthe mathematical sense Moreover 120590119888

1and 120590119888

2in (11) are the

variances of 1198621and 119862

2which are defined as

1205901198881= 1205961198880(1205831198880+ 120583119888119879)2

1205901198882= 1205961198881(1205831198881+ 120583119888119879)2

(12)

where 120583119888119879= 12059611988801205831198880+12059611988811205831198881and 120596119888

0+1205961198881= 1 Based on the values

1205901198881and 120590119888

2 (13) presents the objective function

119869 (th) = max (1205902119888

(th)) 0 le th le 119871 minus 1 (13)

where 1205902119888

(th) is the Otsursquos variance for a given th valueTherefore the optimization problem is reduced to find theintensity level (th) that maximizes (13)

Otsursquos method is applied for a single component of animage In case of RGB images it is necessary to apply separa-tion into single component images The previous descriptionof such bilevel method can be extended for the identificationofmultiple thresholds Considering 119896 thresholds it is possibleseparate the original image into 119896 classes using (6) then itis necessary to compute the 119896 variances and their respectiveelements The objective function 119869(th) in (13) can thus berewritten for multiple thresholds as follows

119869 (TH) = max (1205902119888

(TH)) 0 le th119894le 119871 minus 1 119894 = 1 2 119896

(14)

where TH = [th1 th2 th

119896minus1] is a vector containing mult-

iple thresholds and the variances are computed through

1205902119888

=119896

sum119894=1

120590119888119894=119896

sum119894=1

120596119888119894(120583119888119894minus 120583119888119879)2

(15)


Here 119894 represents the 119894 class 120596119888119894and 120583119888

119895are respectively the

probability of occurrence and themean of a class InMT suchvalues are obtained as

1205961198880(th) =

th1

sum119894=1

Ph119888119894

1205961198881(th) =

th2

sum119894=th1+1

Ph119888119894

120596119888119896minus1

(th) =119871

sum119894=th119896+1

Ph119888119894

(16)

And for the mean values

1205831198880=

th1

sum119894=1

119894Ph119888119894

1205961198880(th1)

1205831198881=

th2

sum119894=th1+1

119894Ph119888119894

1205961198880(th2)

120583119888119896minus1

=119871

sum119894=th119896+1

119894Ph119888119894

1205961198881(th119896)

(17)

Similar to the bilevel case for the MT using the Otsursquosmethod 119888 corresponds to the image components RGB 119888 =1 2 3 and gray scale 119888 = 1

32 Entropy Criterion Method (Kapurrsquos Method) Anothernonparametric method that is used to determine the optimalthreshold values has been proposed by Kapur et al [7] It isbased on the entropy and the probability distribution of theimage histogram The method aims to find the optimal ththat maximizes the overall entropy The entropy of an imagemeasures the compactness and separability among classes Inthis sense when the optimal th value appropriately separatesthe classes the entropy has the maximum value For thebilevel example the objective function of theKapurrsquos problemcan be defined as

119869 (th) = 1198671198881+ 1198671198882


(18)

where the entropies1198671and119867

2are computed by the following

model

1198671198881=

thsum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=119871

sum119894=th+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

(19)

Ph119888119894is the probability distribution of the intensity levels which

is obtained using (7) 1205960(th) and 120596

1(th) are probabilities

distributions for 1198621and 119862

2 ln(sdot) stands for the natural

logarithm Similar to the Otsursquos method the entropy-basedapproach can be extended for multiple threshold values forsuch a case it is necessary to divide the image into 119896 classesusing the similar number of thresholds Under such condi-tions the new objective function is defined as

119869 (TH) = max(119896

sum119894=1

119867119888119894)


(20)


119896minus1] is a vector that contains

the multiple thresholds Each entropy is computed separatelywith its respective th value so (21) is expanded for 119896 entropies

1198671198881=

th1

sum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=

th2

sum119894=th1+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

119867119888119896=119871

sum119894=th119896+1

Ph119888119894

120596119888119896minus1

ln(Ph119888119894

120596119888119896minus1

)

(21)

The values of the probability occurrence (1205961198880 1205961198881 120596119888

119896minus1)

of the 119896 classes are obtained using (16) and the probabilitydistribution Ph119888

119894with (10) Finally it is necessary to use (6) to

separate the pixels into the corresponding classes

4 Multilevel Thresholding Using HarmonySearch Algorithm (HSMA)

41 Harmony Representation Each harmony (candidate sol-ution) uses 119896 different elements as decision variables withinthe optimization algorithm Such decision variables representa different threshold point th that is used for the segmenta-tion Therefore the complete population is represented as

HM = [x1198881 x1198882 x119888HMS]

119879

x119888119894= [th1198881 th1198882 th119888

119896]

(22)

where 119879 refers to the transpose operator HMS is the size ofthe harmony memory x

119894is the 119894th element of HM and 119888 =

1 2 3 is set for RGB images while 119888 = 1 is chosen for grayscale images For this problem the boundaries of the searchspace are set to 119897 = 0 and 119906 = 255 which correspond to imageintensity levels

42 HMA Implementation Theproposed segmentation algo-rithmhas been implemented considering two different objec-tive functions Otsu and Kapur Therefore the HSA has been


coupled with the Otsu and Kapur functions producing twodifferent segmentation algorithms The implementation ofboth algorithms can be summarized as in Algorithm 2

43 Parameter Setting The performance of HSA is stronglyinfluenced by values assigned to parameters HM HMCRPAR BW and NI Determining the most appropriate param-eter values for an arbitrary problem is a complex issue sincesuch parameters interact to each other in a highly nonlinearmanner and no mathematical models of such interactioncurrently exist The common method to find the best setof parameter values is to fix each parameter value to arandom number within the parameter limits and then HSAis executed If the final result is not satisfactory then anew set of parameter values is defined and the evolutionaryalgorithm is executed again Evidently this process can bevery expensive (in terms of computational time) since manydifferent trials may be required before reaching a set ofsatisfactory parameter values Additionally the set of valueschosen by the user are not necessarily the best possible butonly the best from the arbitrary number of trials performedby the user In order to reduce the number of experiments inthis paper it has used the factorial design method proposedin [32 33] to systematically identify the best parameters ofHSA

The factorial design method [34] is a statistical techniquethat evaluates at the same time all process variables in orderto determine which ones really exert significant influence onthe final response All variables are called factors and thedifferent values chosen to study the factors are called levelsThe factors to be considered in the factorial design are theHSA parameters the harmonymemory (HM) the harmony-memory consideration rate (HMCR) the pitch adjusting rate(PAR) the distance bandwidth (BW) and the number ofimprovisations (NI) whereas the response is the best fitnessvalue obtained as a consequence of the HSA executionTable 1 show the levels of the quantitative factors used in thefactorial design The values of zero level (central point) arebased on the suggestions of the literature [33]

Each experiment is conducted combining the two differ-ent levels that define each parameter considering as a probleman image histogram example Since the factors are five a25minus1 fractional factorial design is chosen requiring sixteenoptimization experiments plus one optimization trial for thecentral point The results obtained from seventeen runs wereanalyzed according to [32 33] using a general linear formof analysis of variance (ANOVA) [34] considering a 95 ofconfidence After such analysis it was found that the bestpossible configuration of HSA is shown in Table 2 Theseresults were consistent considering six replications usingdifferent image histograms and the Otsu (14) or Kapur (20)functions indistinctly Formore information on how to buildfractional factorial designs the reader is referred to [32 33]

5 Experimental Results

The HSMA has been tested under a set of 11 benchmarkimages Some of these images are widely used in the image

Table 1 Levels of the factors used for the factorial design method

HSA parameters (Factors) (minus) Level Central point (+) LevelHM 50 100 200HMCR 05 075 09PAR 01 05 09BW 01 03 05NI 200 250 300

Table 2 HSMA parameter values obtained by the factorial designmethod

HM HMCR PAR BW NI100 075 05 05 300

processing literature to test different methods (Lena Cam-eraman Hunter Baboon etc) [3 9] All the images havethe same size (512 times 512 pixels) and they are in JPGEformat For the sake of representation only five imageswhich are presented in Figure 1 have been used to show thevisual results however the numerical outcomes are analyzedconsidering the complete set

Since HSMA is stochastic it is necessary to employan appropriate statistical metrics to measure its efficiencyHence the results have been reported executing the algo-rithm 35 times for each image In order to maintain com-patibility with similar works reported in the literature [14 1518 19] the number of thresholds points used in the test areth = 2 3 4 5 In the experiments the stop criterion is thenumber of times in which the best fitness values remain withno changeTherefore if the fitness value for the best harmonyremains unspoiled in 10 of the total number of iterations(NI) then the HSA is stopped

To evaluate the stability and consistency it has beencomputed the standard deviation (STD) from the resultsobtained in the 35 executions Since the STD represents ameasure about how the data are dispersed the algorithmbecomes more instable as the STD value increases [19]Equation (23) shows the model used to calculate the STDvalue

STD = radicNIsum119894=1

(bf119894minus av)Ru

(23)

where bf119894is the best fitness of the 119894th iteration av is the average

value of bf and Ru is the number of total executions (Ru =35)

On the other hand as an index of quality the peak-to-signal ratio (PSNR) is used to assess the similarity of thesegmented image against a reference image (original image)based on the produced mean square error (MSE) [18 35]Both PSNR and MSE are defined as

PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)


Table 3 Result after appling the HSMA using Otsursquos function to theset of benchmark images

Image 119896 Thresholds 119909119888best PSNR STC

Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01

where 119868119888119900is the original image 119868119888th is the segmented image

119888 = 1 for gray scale and 119888 = 3 for RGB images whereas ro

co are the total number of rows and columns of the imagerespectively

51 Otsursquos Results This section analyzes the results of HSMAafter considering the variance among classes (14) as theobjective function just as it has been proposed by Otsu [6]The approach is applied over the complete set of benchmarkimages whereas the results are registered in Table 3 Suchresults present the best threshold values after testing theproposed method with four different threshold points th =2 3 4 5The table also features the PSNR and the STD valuesIt is evident that the PSNR and STD values increase theirmagnitude as the number of threshold points also increases

For the sake of representation it has been selected onlyfive images of the set to show (graphically) the segmenta-tion results Figure 1 presents the images selected from thebenchmark set and their respective histograms which possessirregular distributions (see Figure 1(j) in particular) Undersuch circumstances classical methods face great difficultiesto find the best threshold values

The processing results for the selected original imagesare presented in five tables Tables 4 5 6 7 and 8 Suchresults show the segmented images considering four differentthreshold points th = 2 3 4 5 The tables also show theevolution of the objective function during one execution

52 Kapurrsquos Results This section analyzes the performance ofHSMA after considering the entropy function (20) as objec-tive function as it has been proposed by Kapur et al in [7]Table 9 presents the experimental results after the applicationof HSMAover the entire set of benchmark imagesThe valueslisted are PSNR STD and the best threshold values of the lastpopulation (119909119861

119905)The same test procedure that was previously

applied to the Otsursquos method (Section 51) is used with theKapurrsquos method also considering the same stop criterion anda similar HSA parameter configuration

The results after appling the HSMA to the selectedbenchmark images are presented in Tables 10 11 12 13and 14 Four different threshold points have been employedth = 2 3 4 5 All tables exhibit the segmented image theapproximated histogram and the evolution of the fitnessvalue during the execution of the HSA method

From the results of both Otsursquos and Kapurrsquos methods it ispossible to appreciate that the HSMA converges (stabilizes)after a determined number of iterations depending on the thvalue For experimental purposes HSMA continues runningstill further even though the stop criterion is achieved In thisway the graphics show that convergence is often reached inthe first iterations of the optimization processThe segmentedimages provide evidence that the outcome is better with th =4 and th = 5 however if the segmentation task does notrequire to be extremely accurate then it is possible to selectth = 3

53 Comparisons In order to analyze the results of HSMAtwo different comparisons are executedThe first one involvesthe comparison between the two versions of the proposedapproach one with the Otsu function and the other with


Table 4 Results after appling the HSMA using Otsursquos over the Camera man image

HistogramThreshold 1

Threshold 2



Threshold 2

Threshold 2

Threshold 3Threshold 4

HistogramThreshold 1Threshold 2

Threshold 3Threshold 4Threshold 5

Threshold 3

0025

002

0015

001

0005

0 50 100 150 250Gray level

200Fr

eque

ncy

0025

002

0015

001

0005

0 50 100 150 250Gray level

200

Freq

uenc

y

0025

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y

0025

002

0015

001

0005

0 50 100 150 250Gray level

200

Freq

uenc

y

365236515

365136505

365036495

364936485

0 500 1000 1500 2000 2500 3000Iterations

0 500 1000 1500 2000 2500 3000

0 500 1000 1500 2000 2500 3000

0 500 1000 1500 2000 2500 3000

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

th=2

th=3

th=4

th=5

3730

37253720

3715

37103705

37003695

3785

3780

3775

3770

3765

3760

3755

3750

3815

3810

3805

3800

3795

3790

3785

3780

Iterations

Iterations

Iterations


Table 5 Results after appling the HSMA using Otsursquos over Lena image

0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200Fr

eque

ncy

0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2



0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y

0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y





196445

19644

196435

19643

196425

19642

196415

19641

0 500 1000 1500 2000 2500 3000

0 1000 2000 3000O

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

es

2140

2120

2100

2080

2060

2040

2020

2000

2195

2190

2185

2180

2175

2170

2165

2160

0 2000 4000 6000

0 1000 2000 3000 4000 5000 6000

2225

2220

2215

2210

2205

2200

2195

2190

th=2

th=3

th=4

th=5

Iterations

Iterations

Iterations

Iterations


Table 6 Results after appling the HSMA using Otsursquos over the Baboon image

0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200Fr

eque

ncy


Threshold 2

0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y



0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y



0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y



th=2

th=3

th=4

th=5

1550

1548

1546

1544

1542

1540

1538

1536

0 500 1000 1500 2000 2500 3000

0 1000 2000 3000O

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

es

1638

1640

1636

1634

1632

1630

1628

1695

1690

1685

1680

1675

1670

1665

1660

0 2000 4000 6000

1720

1715

1710

1705

1700

1695

1690

1685

1680

1675

0 2000 4000 6000 8000 10000

Iterations

Iterations

Iterations

Iterations


Table 7 Results after appling the HSMA using Otsursquos over the Hunter image

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

Freq

uenc

y

50 100 150 250Gray level

200

0045

004

0035

003

0025

002

0015

001

0005

0

Freq

uenc

y

50 100 150 250Gray level

200

0045

004

0035

003

0025

002

0015

001

0005

0

Freq

uenc

y


Threshold 2







th=2

th=3

th=4

th=5

3065

3060

3055

3050

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

0 1000 2000 3000Iterations

0 1000 2000 3000 4000 5000 6000

Iterations

0 2000 4000 6000

Iterations

0 1000 2000 3000 4000 5000

Iterations

3220

3210

3200

3190

3180

3170

3160

3150

3270

3268

3266

3264

3262

3260

3258

3256

3254

3252

3250

3310

3305

3300

3295

3290

3285

3280

3275


Table 8 Results after appling the HSMA using Otsursquos over the Butterfly image


Threshold 2

0025

003

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y

0025

003

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y

0025

003

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y

0025

003

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y







1555

1550

1545

I 540

1535

1530

0 1000 2000 3000 4000

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Iterations

Iterations

1670

1660

1650

1640

1630

1620

1610

0 2000 4000 6000 8000

Iterations0 2000 4000 6000 8000

10000

1710

1700

1690

1680

1670

1660

1650

0 1000 2000 3000 4000

Iterations

1740

1735

1730

1725

1720

1715

1710

1705

1700

th=2

th=3

th=4

th=5


Table 9 Results after appling the HSMA using Kapurrsquos function to the set of benchmark images

Image 119896 Thresholds 119909119888best PSNR STD

Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02


Table 10 Results after appling the HSMA using Kapurrsquos over the Camera man image


Threshold 2

0025

002

0015

001

0005

0500 100 150 250

Gray level200

Freq

uenc

y

0025

002

0015

001

0005

0500

0

0

100 150 300250Gray level

200

Freq

uenc

y

0025

002

0015

001

0005

050 100 150 300250

Gray level200

Freq

uenc

y

0025

002

0015

001

0005

050 100 150 300250

Gray level200

Freq

uenc

y







th=2

th=3

th=4

th=5

176

1755

175

1745

174

1735

173

1725

172

1715

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000

Iterations

222

22

218

216

214

212

21

268

266

264

262

26

258

256

254

252

25

306

304

302

30

298

296

294


Table 11 Results after appling the HSMA using Kapurrsquos over Lenarsquos image

0012

001

0008

0006

0004

0002

0

50

0

0

0

0

100 150 250Gray level

200Fr

eque

ncy

0012

001

0008

0006

0004

0002

0

Freq

uenc

y


Threshold 2

50 100 150 300250Gray level

200



0012

001

0008

0006

0004

0002

0

Freq

uenc

y

50 100 150 300250Gray level

200

0012

001

0008

0006

0004

0002

0

Freq

uenc

y

50 100 150 300250Gray level

200





1781

178

1779

1778

1777

1776

1775

1774

1773

1772

1771

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

0 1000 2000 3000 4000 5000

Iterations

224

223

222

221

22

219

218

0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000 60005000

Iterations

2665

266

2655

265

2645

264

2635

263

2625

262

2615

0 1000 2000 3000 4000

Iterations

308

306

304

302

30

298

296

294

292

29

288

th=2

th=3

th=4

th=5


Table 12 Results after appling the HSMA using Kapurrsquos over the Baboon image

0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200Fr

eque

ncy

0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200

Freq

uenc

y

0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200

Freq

uenc

y

0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2





17635

1763

17625

1762

17615

1761

17605

176

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

0 1000 2000 3000 4000

Iterations

2206

2204

2202

22

2198

2196

2194

2192

219

2188

0 1000 2000 3000 4000 60005000

Iterations

0 2000 4000 80006000

Iterations

Iterations0 2000 4000 6000 8000 10000 12000

268

266

264

262

26

258

256

254

31

308

306

304

302

30

298

296

294

292

29

th=2

th=3

th=4

th=5




Table 13 Results after appling the HSMA using Kapurrsquos over the Hunter image

0045

004

0035

003

0025

002

0015

001

0005

0 50 100 150 250Gray level

200Fr

eque

ncy

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2







17865

1786

17855

1785

17845

1784

17835

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000

Iterations

226

225

224

223

222

221

22

219

218

0 1000 2000 3000 4000 5000

Iterations

269

268

267

266

265

264

263

262

0 2000 4000 80006000

Iterations

306

3055

305

3045

304

3035

303

3025

302

th=2

th=3

th=4

th=5


Table 14 Results after appling the HSMA using Kapurrsquos over the Butterfly image

th=2

th=3

th=4

th=5

50 100 150 300250Gray level

200


Threshold 2

0025

003

002

0015

001

0005

0Fr

eque

ncy

50 100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

500

0

0

0

100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

50 100 150 250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y







168

166

164

162

16

158

156

154

152

0 1000 2000 3000 4000

Iterations

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

215

205

20

19

21

195

0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000 5000

Iterations

255

25

245

24

235

23

225

0 2000 4000 80006000

Iterations

29

285

28

275

27

265

26

255

25


Table 15 119875 values produced by Wilcoxonrsquos test comparing Otsuversus Kapur over the averaged PSNR from Tables 3 and 9

Image 119896 P-value Otsu versus Kapur

Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14

the Kapur criterion The second analyses the comparisonbetween the HSMA and other state-of-the-art approaches

531 Comparison between Otsu and Kapur HSMA In orderto statistically compare the results fromTables 3 and 9 a non-parametric significance proof known as the Wilcoxonrsquos ranktest [36 37] for 35 independent samples has been conductedSuch proof allows assessing result differences among tworelated methods The analysis is performed considering a 5significance level over the peak-to-signal ratio (PSNR) datacorresponding to the five threshold points Table 15 reportsthe 119875 values produced by Wilcoxonrsquos test for a pairwisecomparison of the PSNR values between the Otsu and Kapurobjective functions As a null hypothesis it is assumed thatthere is no difference between the values of the two objectivefunctions The alternative hypothesis considers an existentdifference between the values of both approaches All119875 valuesreported in Table 15 are less than 005 (5 significance level)which is a strong evidence against the null hypothesis indi-cating that the Otsu PSNR mean values for the performanceare statistically better and it has not occurred by chance

532 Comparison among HSMA and Other MT ApproachesThe results produced by HSMA have been compared withthose generated by state-of-the-art thresholding methodssuch genetic algorithms (GA) [15] particle swarm optimiza-tion (PSO) [18] and bacterial foraging (BF) [19]

All the algorithms run 35 times over each selected imageThe images at this test are the same as in Sections 52 and51 (Camera man Lena Baboon Hunter and Butterfly) Foreach image the PSNR the STD and themean of the objectivefunction values are calculated Moreover the entire test isperformed using both Otsursquos and Kapurrsquos objective functions

Table 16 presents the computed values for a reducedbenchmark test (five images) It is clear that the HSMAdelivers better performance than the others Such values arecomputed using the Otsursquos method as the objective functionOn the other hand the same experiment has been performedusing the Kapurrsquos method Using the same criteria (as thosedescribed for the Otsursquos method) the algorithm runs over35 times at each image The results of this experiment arepresented in Table 17 and show that the proposed HSMAalgorithm is better in comparison with the GA PSO and BF

6 Conclusions

In this paper a MT-based method on the original harmonysearch algorithm (HSA) is presentedThe approach combinesthe good search capabilities of HSA algorithm and the useof some objective functions that have been proposed by thepopularMTmethods of Otsu and Kapur In order tomeasurethe performance of the proposed approach the peak signal-to-noise ratio (PSNR) is used to assess the segmentationquality by considering the coincidences between the seg-mented and the original images In this work a simple HSAimplementation without any modification is considered inorder to demonstrate that it can be applied to image process-ing tasks

The study explores the comparison between two versionsof HSMA one employs the Otsu objective function whilethe other uses the Kapur criterion Results show that the


Table 16 Comparisons between HSMA GA PSO and BF applied over the selected test images using Otsursquos method

Image 119896HSMA GA PSO BF

PSNR STD Mean PSNR STD Mean PSNR STD Mean PSNR STD Mean

Camera man

2 17247 230119864 minus 12 36519 17048 00232 36045 17033 00341 35983 17058 00345 359093 20211 155119864 minus 02 37274 17573 01455 36783 19219 02345 36627 20035 02459 365754 21533 276119864 minus 12 37824 20523 02232 37815 21254 03142 37774 21209 04560 376145 23282 530119864 minus 03 38137 21369 04589 37664 22095 05089 37416 22237 05089 37898

Lena

2 15401 922119864 minus 13 19644 15040 00049 19609 15077 00033 19614 15031 299119864 minus 04 196153 17427 299119864 minus 02 21314 17304 01100 21264 17276 00390 21277 17401 00061 212804 18763 277119864 minus 01 21949 17920 02594 21737 18305 01810 21806 18507 00081 218905 19443 304119864 minus 01 22187 18402 03048 21962 18770 02181 22125 19001 00502 22156

Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330

Table 17 Comparison between HSMA GA PSO and BF applied over selected test images using Kapurrsquos method



Camera man


Lena


Baboon


Hunter


Butterfly



Otsu function delivers better results than the Kapur criterionSuch conclusion has been statistically proved considering theWilcoxon test

The proposed approach has been compared to othertechniques that implement different optimization algorithmslikeGA PSO andBFThe efficiency of the algorithmhas beenevaluated in terms of the PSNR index and the STD valueExperimental results provide evidence on the outstandingperformance accuracy and convergence of the proposedalgorithm in comparison to other methods Although theresults offer evidence to demonstrate that the standard HSAmethod can yield good results on complicated images theaim of our paper is not to devise an MT algorithm thatcould beat all currently available methods but to show thatharmony search algorithms can be effectively considered asan attractive alternative for this purpose

Acknowledgment

The proposed algorithm is part of the vision system usedby a biped robot supported under the Grant CONACYT CB181053 The first author acknowledges The National Councilof Science and Technology of Mexico (CONACyT) for thedoctoral Grant number 215517 and The Youth Institute ofJalisco (IJJ) for partially support this research

References

[1] R C Gonzalez and R E Woods Digital Image ProcessingAddison Wesley Reading Mass USA 1992

[2] R Guo and S M Pandit ldquoAutomatic threshold selection basedon histogram modes and a discriminant criterionrdquo MachineVision and Applications vol 10 no 5-6 pp 331ndash338 1998

[3] N R Pal and S K Pal ldquoA review on image segmentationtechniquesrdquo Pattern Recognition vol 26 no 9 pp 1277ndash12941993

[4] P K Sahoo S Soltani and A K C Wong ldquoA survey ofthresholding techniquesrdquoComputer Vision Graphics and ImageProcessing vol 41 no 2 pp 233ndash260 1988

[5] W Snyder G Bilbro A Logenthiran and S Rajala ldquoOptimalthresholding a new approachrdquo Pattern Recognition Letters vol11 no 12 pp 803ndash809 1990

[6] N Otsu ldquoA threshold selection method from gray-level his-togramsrdquo IEEE Transactions on Systems Man Cybernetics vol9 no 1 pp 62ndash66 1979

[7] J N Kapur P K Sahoo and A K C Wong ldquoA new methodfor gray-level picture thresholding using the entropy of thehistogramrdquo Computer Vision Graphics amp Image Processing vol29 no 3 pp 273ndash285 1985

[8] J Kittler and J Illingworth ldquoMinimum error thresholdingrdquoPattern Recognition vol 19 no 1 pp 41ndash47 1986

[9] K Hammouche M Diaf and P Siarry ldquoA comparative studyof various meta-heuristic techniques applied to the multilevelthresholding problemrdquo Engineering Applications of ArtificialIntelligence vol 23 no 5 pp 676ndash688 2010

[10] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic for global optimization over continuousspacesrdquo Journal of Global Optimization vol 11 no 4 pp 341ndash359 1997

[11] S Kirkpatrick C D Gelatt Jr andM P Vecchi ldquoOptimizationby simulated annealingrdquo Science vol 220 no 4598 pp 671ndash6801983

[12] F Glover ldquoTabu Searchmdashpart Irdquo ORSA Journal on Computingvol 1 article 3 pp 190ndash206 1989

[13] J H Holland Adaptation in Natural and Artificial SystemsUniversity of Michigan Press Ann Arbor Mich USA 1975

[14] C Lai and D Tseng ldquoA hybrid approach using Gaussiansmoothing and genetic algorithm for multilevel thresholdingrdquoInternational Journal of Hybrid Intelligent Systems vol 1 pp143ndash152 2004

[15] P-Y Yin ldquoA fast scheme for optimal thresholding using geneticalgorithmsrdquo Signal Processing vol 72 no 2 pp 85ndash95 1999

[16] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995

[17] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Computer EngineeringDepartment Engineering Faculty Erciyes University 2005

[18] B Akay ldquoA study on particle swarm optimization and artificialbee colony algorithms for multilevel thresholdingrdquo Applied SoftComputing vol 13 no 6 pp 3066ndash3091 2012

[19] PD Sathya andRKayalvizhi ldquoOptimalmultilevel thresholdingusing bacterial foraging algorithmrdquo Expert Systems with Appli-cations vol 38 no 12 pp 15549ndash15564 2011

[20] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001

[21] M Mahdavi M Fesanghary and E Damangir ldquoAn improvedharmony search algorithm for solving optimization problemsrdquoAppliedMathematics and Computation vol 188 no 2 pp 1567ndash1579 2007

[22] K S Lee and Z W Geem ldquoA new meta-heuristic algorithm forcontinuous engineering optimization harmony search theoryand practicerdquo Computer Methods in Applied Mechanics andEngineering vol 194 no 36-38 pp 3902ndash3933 2005

[23] K S Lee Z W Geem S-H Lee and K-W Bae ldquoThe harmonysearch heuristic algorithm for discrete structural optimizationrdquoEngineering Optimization vol 37 no 7 pp 663ndash684 2005

[24] J H Kim Z W Geem and E S Kim ldquoParameter estimationof the nonlinear Muskingum model using harmony searchrdquoJournal of the AmericanWater Resources Association vol 37 no5 pp 1131ndash1138 2001

[25] Z W Geem ldquoOptimal cost design of water distribution net-works using harmony searchrdquo Engineering Optimization vol38 no 3 pp 259ndash280 2006

[26] Z W Geem K S Lee and Y J Park ldquoApplication of harmonysearch to vehicle routingrdquoAmerican Journal of Applied Sciencesvol 2 pp 1552ndash1557 2005

[27] A VasebiM Fesanghary and SM T Bathaee ldquoCombined heatand power economic dispatch by harmony search algorithmrdquoInternational Journal of Electrical Power andEnergy Systems vol29 no 10 pp 713ndash719 2007

[28] S O Degertekin ldquoOptimum design of steel frames using har-mony search algorithmrdquo Structural and Multidisciplinary Opti-mization vol 36 no 4 pp 393ndash401 2008

[29] E Cuevas N Ortega-Sanchez D Zaldivar and M Perez-Cisneros ldquoCircle detection by harmony search optimizationrdquoJournal of Intelligent and Robotic Systems pp 1ndash18 2011

[30] OMAlia andRMandava ldquoThevariants of the harmony searchalgorithm an overviewrdquo Artificial Intelligence Review vol 36no 1 pp 49ndash68 2011


[31] F G Lobo C F Lima and Z Michalewicz Eds ParameterSetting in Evolutionary Algorithms vol 54 of Studies in Com-putational Intelligence Springer Berlin Germany 2007

[32] C B B Costa M R W MacIel and R M Filho ldquoFactorialdesign technique applied to genetic algorithm parameters ina batch cooling crystallization optimisationrdquo Computers andChemical Engineering vol 29 no 10 pp 2229ndash2241 2005

[33] A Khadwilard P Luangpaiboon and P Pongcharoen ldquoFull fac-torial experimental design for parameters selection of harmonysearch Algorithmrdquo The Journal of Industrial Technology vol 8no 2 pp 1ndash10 2012

[34] G E P Box W G Hunter and J S Hunter Statistic for Experi-mentersmdashAn Introduction to Design Data Analysis and ModelBuilding John Wiley amp Sons New York NY USA 1978

[35] S K Pal D Bhandari and M K Kundu ldquoGenetic algorithmsfor optimal image enhancementrdquo Pattern Recognition Lettersvol 15 no 3 pp 261ndash271 1994

[36] F Wilcoxon ldquoIndividual comparisons by ranking methodsrdquoBiometrics vol 1 pp 80ndash83 1945

[37] S Garcia D Molina M Lozano and F Herrera ldquoAstudy onthe use of non-parametric tests for analyzing the evolutionaryalgorithmsrsquo behaviour a case study on the CECrsquo2005 Specialsession on real parameter optimizationrdquo Journal of Heuristicsvol 15 no 6 pp 617ndash644 2008

Submit your manuscripts athttpwwwhindawicom

OperationsResearch

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2013


Mathematical Problems in Engineering

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2013

ISRN Applied Mathematics


Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2013

International Journal of

Combinatorics


Journal of Function Spaces and Applications

International Journal of Mathematics and Mathematical Sciences


ISRN Geometry


Discrete Dynamics in Nature and Society



Volume 2013

Advances in

Mathematical Physics

ISRN Algebra


ProbabilityandStatistics

Journal of


ISRN Mathematical Analysis


Journal ofApplied Mathematics


Advances in

DecisionSciences



Stochastic AnalysisInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013

The Scientific World Journal


ISRN Discrete Mathematics


Differential EquationsInternational Journal of

Volume 2013


of accuracy speed and robustness Numerous evolutionaryapproaches have been reported in the literature

Hammouche et al in [9] provides an interesting survey ofhow different evolutionary algorithms are used to solve theKapturrsquos and Otsursquos problems The study uses four classicalevolutionary algorithms to test their efficiency in MT Suchmethods include differential evolution (DE) [10] simulatedannealing (SA) [11] and tabu search (TS) [12]

Genetic algorithms (GA) [13] inspired on the biologicalevolution have been also used for solving segmentationtasks One interesting example is presented in [14] where aGA-based algorithm is combined with Gaussian models formultilevel thresholding Other similar works such as that ofYin [15] proposes an improved GA for optimal thresholdingIn the approach it is used as a learning strategy to increasethe speed of convergence

Evolutionary approaches inspired on swarm behaviorsuch as particle swarm optimization (PSO) [16] and artificialbee colony (ABC) [17] have been employed to face thesegmentation problem In [18] bothmethods are used to findthe optimal multilevel threshold points by using the Kapurrsquosentropy as fitness function

Finally in [19] the optimal segmentation threshold valuesare determined by using the bacterial foraging algorithm(BFA) Suchmethod aims tomaximize the Kapurrsquos andOtsursquosobjective functions by considering a set of operators thatare based on the social foraging behavior of the bacteriaEschericha Colli

On the other hand the harmony search algorithm (HSA)introduced by Geem et al [20] is an evolutionary opti-mization algorithm which is based on the metaphor of theimprovisation process that occurs when a musician searchesfor a better state of harmony The HSA generates a newcandidate solution from all existing solutions The solutionvector is analogous to the harmony in music while thelocal and global search schemes are analogous to musi-cianrsquos improvisations In comparison to other metaheuristicsmethods in the literature HSA imposes fewer mathematicalrequirements as it can be easily adapted for solving severalsorts of engineering optimization challenges [21] Further-more numerical comparisons have demonstrated that theconvergence for theHSA is faster thanGA [22] which attractsfurther attention It has been successfully applied to solve awide range of practical optimization problems such as dis-crete and continuous structural optimization [23] parameterestimation of the nonlinear Muskingum model [24] designoptimization of water distribution networks [25] vehiclerouting [26] combined heat and power economic dispatch[27] design of steel frames [28] and image processing [29]Although the standard HSA presents good search character-istics several modifications to the original HSA have beenproposed in the literature in order to enhance its own features[30]

In this paper a novel multithresholding segmentationalgorithm is introduced The proposed approach calledthe harmony search multithresholding algorithm (HSMA)combines the original harmony search algorithm (HSA) andthe Otsursquos and Kapurrsquos methodologies The proposed algo-rithm takes random samples from a feasible search space

inside the image histogram Such samples build each har-mony (candidate solution) in the HSA context whereas itsquality is evaluated considering the objective function thatis employed by the Otsursquos or the Kapurrsquos method Guidedby these objective values the set of candidate solutions areevolved using the HSA operators until the optimal solutionis found The approach generates a multilevel segmentationalgorithm which can effectively identify the threshold valuesof a digital image within a reduced number of iterationsExperimental results over several complex images have val-idated the efficiency of the proposed technique regardingaccuracy speed and robustness

The paper is organized as follows In Section 2 the HSAis introduced Section 3 gives a brief description of the Otsursquosand Kapurrsquos methods Section 4 explains the implementationof the proposed algorithm Section 5 discusses experimentalresults after testing the proposed method over a set bench-mark images Finally some conclusions are discussed inSection 6

2 Harmony Search Algorithm

21 The Harmony Search Algorithm In the basic HSA eachsolution is called a ldquoharmonyrdquo and is represented by an n-dimension real vector An initial population of harmonyvectors are randomly generated and stored within a har-mony memory (HM) A new candidate harmony is thusgenerated from the elements in the HM by using a memoryconsideration operation either by a random reinitializationor a pitch adjustment operation Finally the HM is updatedby comparing the new candidate harmony and the worstharmony vector in the HM The worst harmony vector isreplaced by the new candidate vector when the latter deliversa better solution in the HM The above process is repeateduntil a certain termination criterion is met The basic HSalgorithm consists of three main phases HM initializationimprovisation of new harmony vectors and updating theHM The following discussion addresses details about eachstage

211 Initializing the Problem and the Algorithm ParametersIn general the global optimization problem can be summa-rized as followsminimize 119891 (x) x = (119909 (1) 119909 (2) 119909 (119899)) isin R119899

subject to 119909 (119895) isin [119897 (119895) 119906 (119895)] 119895 = 1 2 119899(1)

where 119891(x) is the objective function x = (119909(1) 119909(2) 119909(119899)) is the set of design variables 119899 is the number of designvariables and 119897(119895) and 119906(119895) are the lower and upper boundsfor the design variable 119909(119895) respectively The parameters forHSA are the harmony memory size that is the numberof solution vectors lying on the harmony memory (HM)the harmony-memory consideration rate (HMCR) the pitchadjusting rate (PAR) the distance bandwidth (BW) and thenumber of improvisations (NI) which represents the totalnumber of iterations The performance of HSA is stronglyinfluenced by values assigned to such parameters which inturn depend on the application domain [31]



119894= 119909119894(1) 119909119894(2) 119909

119894(119899) represent the 119894th



HM =[[[[

[

x1

x2

xHMS

]]]]

]

(2)


1(1)



1is


119909new (119895)

=

119909119894(119895) isin 119909

1(119895) 119909

2(119895) 119909HMS (119895)



(3)


119909new (119895)

=



(4)





119908


119908



119908= xnew if 119891(xnew) gt 119891(x

119908)) is




1198621larr997888 119901 if 0 le 119901 lt th


(5)





1198621larr997888 119901 if 0 le 119901 lt th

1

1198622larr997888 119901 if th

1le 119901 lt th

2

119862119894larr997888 119901 if th

119894le 119901 lt th

119894+1

119862119899larr997888 119901 if th

119899le 119901 lt 119871 minus 1

(6)

where th1 th2 th












end ifend for




Algorithm 1








119909119888new (119895) = 119909119888

119886(119895) where 119886 isin (1 2 HMS)


119909119888new (119895) = 119909119888

119886(119895) plusmn 119903


1 1199032 1199033isin rand (0 1)



end ifelse



cworst)


Algorithm 2


(a)

0025

002

0015

001

0005

050 100 150 200 250

Gray level

Freq

uenc

y

(b)

(c)

0012

001

0008

0006

0004

0002

050 100 150 250

Gray level200

Freq

uenc

y

(d)

(e)

0012

001

0008

0006

0004

0002

050 100 150 250

Gray level200

Freq

uenc

y

(f)

(g)

0045004

0035003

0025002

0015001

00050

50 100 150 250Gray level

200

Freq

uenc

y

(h)

Figure 1 Continued


(i)

003

0025

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y

(j)



Ph119888119894=

ℎ119888119894

NP

NPsum119894=1

Ph119888119894= 1


(7)






1198621=

Ph1198881

1205961198880(th)

Ph119888th1205961198880(th)

1198622=

Ph119888th+11205961198881(th)

Ph119888119871

1205961198881(th)

(8)

where 1205960(th) and 120596


1


1205961198880(th) =

thsum119894=1

Ph119888119894 120596119888

1(th) =

119871

sum119894=th+1

Ph119888119894 (9)


1that define


119888


1205831198880=

thsum119894=1

119894Ph119888119894

1205961198880(th)

1205831198881=119871

sum119894=th+1

119894Ph119888119894

1205961198881(th)

(10)

1205902119888

= 1205901198881+ 1205901198882 (11)


1and 120590119888

2in (11) are the



1205901198881= 1205961198880(1205831198880+ 120583119888119879)2

1205901198882= 1205961198881(1205831198881+ 120583119888119879)2

(12)

where 120583119888119879= 12059611988801205831198880+12059611988811205831198881and 120596119888


1205901198881and 120590119888


119869 (th) = max (1205902119888

(th)) 0 le th le 119871 minus 1 (13)

where 1205902119888



119869 (TH) = max (1205902119888

(TH)) 0 le th119894le 119871 minus 1 119894 = 1 2 119896

(14)




1205902119888

=119896

sum119894=1

120590119888119894=119896

sum119894=1

120596119888119894(120583119888119894minus 120583119888119879)2

(15)





1205961198880(th) =

th1

sum119894=1

Ph119888119894

1205961198881(th) =

th2

sum119894=th1+1

Ph119888119894

120596119888119896minus1

(th) =119871

sum119894=th119896+1

Ph119888119894

(16)


1205831198880=

th1

sum119894=1

119894Ph119888119894

1205961198880(th1)

1205831198881=

th2

sum119894=th1+1

119894Ph119888119894

1205961198880(th2)

120583119888119896minus1

=119871

sum119894=th119896+1

119894Ph119888119894

1205961198881(th119896)

(17)



119869 (th) = 1198671198881+ 1198671198882


(18)



model

1198671198881=

thsum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=119871

sum119894=th+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

(19)







119869 (TH) = max(119896

sum119894=1

119867119888119894)


(20)




1198671198881=

th1

sum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=

th2

sum119894=th1+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

119867119888119896=119871

sum119894=th119896+1

Ph119888119894

120596119888119896minus1

ln(Ph119888119894

120596119888119896minus1

)

(21)


119896minus1)






HM = [x1198881 x1198882 x119888HMS]

119879

x119888119894= [th1198881 th1198882 th119888

119896]

(22)















HM HMCR PAR BW NI100 075 05 05 300






(23)




PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















Threshold 2



Threshold 2

Threshold 2




Threshold 3

0025

002

0015

001

0005

0 50 100 150 250Gray level

200Fr

eque

ncy

0025

002

0015

001

0005

0 50 100 150 250Gray level

200

Freq

uenc

y

0025

002

0015

001

0005

050 100 150 250

Gray level200

Freq

uenc

y

0025

002

0015

001

0005

0 50 100 150 250Gray level

200

Freq

uenc

y

365236515

365136505

365036495

364936485

0 500 1000 1500 2000 2500 3000Iterations

0 500 1000 1500 2000 2500 3000

0 500 1000 1500 2000 2500 3000

0 500 1000 1500 2000 2500 3000

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

th=2

th=3

th=4

th=5

3730

37253720

3715

37103705

37003695

3785

3780

3775

3770

3765

3760

3755

3750

3815

3810

3805

3800

3795

3790

3785

3780

Iterations

Iterations

Iterations



0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200Fr

eque

ncy

0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2



0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y

0012

001

0008

0006

0004

0002

0

50 100 150 250Gray level

200

Freq

uenc

y





196445

19644

196435

19643

196425

19642

196415

19641

0 500 1000 1500 2000 2500 3000

0 1000 2000 3000O

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

esO

bjec

tive f

unct

ion

valu

es

2140

2120

2100

2080

2060

2040

2020

2000

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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



119894= 119909119894(1) 119909119894(2) 119909

119894(119899) represent the 119894th



HM =[[[[

[

x1

x2

xHMS

]]]]

]

(2)


1(1)



1is


119909new (119895)

=

119909119894(119895) isin 119909

1(119895) 119909

2(119895) 119909HMS (119895)



(3)


119909new (119895)

=



(4)





119908


119908



119908= xnew if 119891(xnew) gt 119891(x

119908)) is




1198621larr997888 119901 if 0 le 119901 lt th


(5)





1198621larr997888 119901 if 0 le 119901 lt th

1

1198622larr997888 119901 if th

1le 119901 lt th

2

119862119894larr997888 119901 if th

119894le 119901 lt th

119894+1

119862119899larr997888 119901 if th

119899le 119901 lt 119871 minus 1

(6)

where th1 th2 th












end ifend for




Algorithm 1








119909119888new (119895) = 119909119888

119886(119895) where 119886 isin (1 2 HMS)


119909119888new (119895) = 119909119888

119886(119895) plusmn 119903


1 1199032 1199033isin rand (0 1)



end ifelse



cworst)


Algorithm 2


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(d)

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(f)

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(h)

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(j)



Ph119888119894=

ℎ119888119894

NP

NPsum119894=1

Ph119888119894= 1


(7)






1198621=

Ph1198881

1205961198880(th)

Ph119888th1205961198880(th)

1198622=

Ph119888th+11205961198881(th)

Ph119888119871

1205961198881(th)

(8)

where 1205960(th) and 120596


1


1205961198880(th) =

thsum119894=1

Ph119888119894 120596119888

1(th) =

119871

sum119894=th+1

Ph119888119894 (9)


1that define


119888


1205831198880=

thsum119894=1

119894Ph119888119894

1205961198880(th)

1205831198881=119871

sum119894=th+1

119894Ph119888119894

1205961198881(th)

(10)

1205902119888

= 1205901198881+ 1205901198882 (11)


1and 120590119888

2in (11) are the



1205901198881= 1205961198880(1205831198880+ 120583119888119879)2

1205901198882= 1205961198881(1205831198881+ 120583119888119879)2

(12)

where 120583119888119879= 12059611988801205831198880+12059611988811205831198881and 120596119888


1205901198881and 120590119888


119869 (th) = max (1205902119888

(th)) 0 le th le 119871 minus 1 (13)

where 1205902119888



119869 (TH) = max (1205902119888

(TH)) 0 le th119894le 119871 minus 1 119894 = 1 2 119896

(14)




1205902119888

=119896

sum119894=1

120590119888119894=119896

sum119894=1

120596119888119894(120583119888119894minus 120583119888119879)2

(15)





1205961198880(th) =

th1

sum119894=1

Ph119888119894

1205961198881(th) =

th2

sum119894=th1+1

Ph119888119894

120596119888119896minus1

(th) =119871

sum119894=th119896+1

Ph119888119894

(16)


1205831198880=

th1

sum119894=1

119894Ph119888119894

1205961198880(th1)

1205831198881=

th2

sum119894=th1+1

119894Ph119888119894

1205961198880(th2)

120583119888119896minus1

=119871

sum119894=th119896+1

119894Ph119888119894

1205961198881(th119896)

(17)



119869 (th) = 1198671198881+ 1198671198882


(18)



model

1198671198881=

thsum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=119871

sum119894=th+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

(19)







119869 (TH) = max(119896

sum119894=1

119867119888119894)


(20)




1198671198881=

th1

sum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=

th2

sum119894=th1+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

119867119888119896=119871

sum119894=th119896+1

Ph119888119894

120596119888119896minus1

ln(Ph119888119894

120596119888119896minus1

)

(21)


119896minus1)






HM = [x1198881 x1198882 x119888HMS]

119879

x119888119894= [th1198881 th1198882 th119888

119896]

(22)















HM HMCR PAR BW NI100 075 05 05 300






(23)




PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013









end ifend for




Algorithm 1








119909119888new (119895) = 119909119888

119886(119895) where 119886 isin (1 2 HMS)


119909119888new (119895) = 119909119888

119886(119895) plusmn 119903


1 1199032 1199033isin rand (0 1)



end ifelse



cworst)


Algorithm 2


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(d)

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(f)

(g)

0045004

0035003

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0015001

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200

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(h)

Figure 1 Continued


(i)

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(j)



Ph119888119894=

ℎ119888119894

NP

NPsum119894=1

Ph119888119894= 1


(7)






1198621=

Ph1198881

1205961198880(th)

Ph119888th1205961198880(th)

1198622=

Ph119888th+11205961198881(th)

Ph119888119871

1205961198881(th)

(8)

where 1205960(th) and 120596


1


1205961198880(th) =

thsum119894=1

Ph119888119894 120596119888

1(th) =

119871

sum119894=th+1

Ph119888119894 (9)


1that define


119888


1205831198880=

thsum119894=1

119894Ph119888119894

1205961198880(th)

1205831198881=119871

sum119894=th+1

119894Ph119888119894

1205961198881(th)

(10)

1205902119888

= 1205901198881+ 1205901198882 (11)


1and 120590119888

2in (11) are the



1205901198881= 1205961198880(1205831198880+ 120583119888119879)2

1205901198882= 1205961198881(1205831198881+ 120583119888119879)2

(12)

where 120583119888119879= 12059611988801205831198880+12059611988811205831198881and 120596119888


1205901198881and 120590119888


119869 (th) = max (1205902119888

(th)) 0 le th le 119871 minus 1 (13)

where 1205902119888



119869 (TH) = max (1205902119888

(TH)) 0 le th119894le 119871 minus 1 119894 = 1 2 119896

(14)




1205902119888

=119896

sum119894=1

120590119888119894=119896

sum119894=1

120596119888119894(120583119888119894minus 120583119888119879)2

(15)





1205961198880(th) =

th1

sum119894=1

Ph119888119894

1205961198881(th) =

th2

sum119894=th1+1

Ph119888119894

120596119888119896minus1

(th) =119871

sum119894=th119896+1

Ph119888119894

(16)


1205831198880=

th1

sum119894=1

119894Ph119888119894

1205961198880(th1)

1205831198881=

th2

sum119894=th1+1

119894Ph119888119894

1205961198880(th2)

120583119888119896minus1

=119871

sum119894=th119896+1

119894Ph119888119894

1205961198881(th119896)

(17)



119869 (th) = 1198671198881+ 1198671198882


(18)



model

1198671198881=

thsum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=119871

sum119894=th+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

(19)







119869 (TH) = max(119896

sum119894=1

119867119888119894)


(20)




1198671198881=

th1

sum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=

th2

sum119894=th1+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

119867119888119896=119871

sum119894=th119896+1

Ph119888119894

120596119888119896minus1

ln(Ph119888119894

120596119888119896minus1

)

(21)


119896minus1)






HM = [x1198881 x1198882 x119888HMS]

119879

x119888119894= [th1198881 th1198882 th119888

119896]

(22)















HM HMCR PAR BW NI100 075 05 05 300






(23)




PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















Threshold 2



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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013


(a)

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Figure 1 Continued


(i)

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(j)



Ph119888119894=

ℎ119888119894

NP

NPsum119894=1

Ph119888119894= 1


(7)






1198621=

Ph1198881

1205961198880(th)

Ph119888th1205961198880(th)

1198622=

Ph119888th+11205961198881(th)

Ph119888119871

1205961198881(th)

(8)

where 1205960(th) and 120596


1


1205961198880(th) =

thsum119894=1

Ph119888119894 120596119888

1(th) =

119871

sum119894=th+1

Ph119888119894 (9)


1that define


119888


1205831198880=

thsum119894=1

119894Ph119888119894

1205961198880(th)

1205831198881=119871

sum119894=th+1

119894Ph119888119894

1205961198881(th)

(10)

1205902119888

= 1205901198881+ 1205901198882 (11)


1and 120590119888

2in (11) are the



1205901198881= 1205961198880(1205831198880+ 120583119888119879)2

1205901198882= 1205961198881(1205831198881+ 120583119888119879)2

(12)

where 120583119888119879= 12059611988801205831198880+12059611988811205831198881and 120596119888


1205901198881and 120590119888


119869 (th) = max (1205902119888

(th)) 0 le th le 119871 minus 1 (13)

where 1205902119888



119869 (TH) = max (1205902119888

(TH)) 0 le th119894le 119871 minus 1 119894 = 1 2 119896

(14)




1205902119888

=119896

sum119894=1

120590119888119894=119896

sum119894=1

120596119888119894(120583119888119894minus 120583119888119879)2

(15)





1205961198880(th) =

th1

sum119894=1

Ph119888119894

1205961198881(th) =

th2

sum119894=th1+1

Ph119888119894

120596119888119896minus1

(th) =119871

sum119894=th119896+1

Ph119888119894

(16)


1205831198880=

th1

sum119894=1

119894Ph119888119894

1205961198880(th1)

1205831198881=

th2

sum119894=th1+1

119894Ph119888119894

1205961198880(th2)

120583119888119896minus1

=119871

sum119894=th119896+1

119894Ph119888119894

1205961198881(th119896)

(17)



119869 (th) = 1198671198881+ 1198671198882


(18)



model

1198671198881=

thsum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=119871

sum119894=th+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

(19)







119869 (TH) = max(119896

sum119894=1

119867119888119894)


(20)




1198671198881=

th1

sum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=

th2

sum119894=th1+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

119867119888119896=119871

sum119894=th119896+1

Ph119888119894

120596119888119896minus1

ln(Ph119888119894

120596119888119896minus1

)

(21)


119896minus1)






HM = [x1198881 x1198882 x119888HMS]

119879

x119888119894= [th1198881 th1198882 th119888

119896]

(22)















HM HMCR PAR BW NI100 075 05 05 300






(23)




PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013


(i)

003

0025

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Freq

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y

(j)



Ph119888119894=

ℎ119888119894

NP

NPsum119894=1

Ph119888119894= 1


(7)






1198621=

Ph1198881

1205961198880(th)

Ph119888th1205961198880(th)

1198622=

Ph119888th+11205961198881(th)

Ph119888119871

1205961198881(th)

(8)

where 1205960(th) and 120596


1


1205961198880(th) =

thsum119894=1

Ph119888119894 120596119888

1(th) =

119871

sum119894=th+1

Ph119888119894 (9)


1that define


119888


1205831198880=

thsum119894=1

119894Ph119888119894

1205961198880(th)

1205831198881=119871

sum119894=th+1

119894Ph119888119894

1205961198881(th)

(10)

1205902119888

= 1205901198881+ 1205901198882 (11)


1and 120590119888

2in (11) are the



1205901198881= 1205961198880(1205831198880+ 120583119888119879)2

1205901198882= 1205961198881(1205831198881+ 120583119888119879)2

(12)

where 120583119888119879= 12059611988801205831198880+12059611988811205831198881and 120596119888


1205901198881and 120590119888


119869 (th) = max (1205902119888

(th)) 0 le th le 119871 minus 1 (13)

where 1205902119888



119869 (TH) = max (1205902119888

(TH)) 0 le th119894le 119871 minus 1 119894 = 1 2 119896

(14)




1205902119888

=119896

sum119894=1

120590119888119894=119896

sum119894=1

120596119888119894(120583119888119894minus 120583119888119879)2

(15)





1205961198880(th) =

th1

sum119894=1

Ph119888119894

1205961198881(th) =

th2

sum119894=th1+1

Ph119888119894

120596119888119896minus1

(th) =119871

sum119894=th119896+1

Ph119888119894

(16)


1205831198880=

th1

sum119894=1

119894Ph119888119894

1205961198880(th1)

1205831198881=

th2

sum119894=th1+1

119894Ph119888119894

1205961198880(th2)

120583119888119896minus1

=119871

sum119894=th119896+1

119894Ph119888119894

1205961198881(th119896)

(17)



119869 (th) = 1198671198881+ 1198671198882


(18)



model

1198671198881=

thsum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=119871

sum119894=th+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

(19)







119869 (TH) = max(119896

sum119894=1

119867119888119894)


(20)




1198671198881=

th1

sum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=

th2

sum119894=th1+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

119867119888119896=119871

sum119894=th119896+1

Ph119888119894

120596119888119896minus1

ln(Ph119888119894

120596119888119896minus1

)

(21)


119896minus1)






HM = [x1198881 x1198882 x119888HMS]

119879

x119888119894= [th1198881 th1198882 th119888

119896]

(22)















HM HMCR PAR BW NI100 075 05 05 300






(23)




PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013





1205961198880(th) =

th1

sum119894=1

Ph119888119894

1205961198881(th) =

th2

sum119894=th1+1

Ph119888119894

120596119888119896minus1

(th) =119871

sum119894=th119896+1

Ph119888119894

(16)


1205831198880=

th1

sum119894=1

119894Ph119888119894

1205961198880(th1)

1205831198881=

th2

sum119894=th1+1

119894Ph119888119894

1205961198880(th2)

120583119888119896minus1

=119871

sum119894=th119896+1

119894Ph119888119894

1205961198881(th119896)

(17)



119869 (th) = 1198671198881+ 1198671198882


(18)



model

1198671198881=

thsum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=119871

sum119894=th+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

(19)







119869 (TH) = max(119896

sum119894=1

119867119888119894)


(20)




1198671198881=

th1

sum119894=1

Ph119888119894

1205961198880

ln(Ph119888119894

1205961198880

)

1198671198882=

th2

sum119894=th1+1

Ph119888119894

1205961198881

ln(Ph119888119894

1205961198881

)

119867119888119896=119871

sum119894=th119896+1

Ph119888119894

120596119888119896minus1

ln(Ph119888119894

120596119888119896minus1

)

(21)


119896minus1)






HM = [x1198881 x1198882 x119888HMS]

119879

x119888119894= [th1198881 th1198882 th119888

119896]

(22)















HM HMCR PAR BW NI100 075 05 05 300






(23)




PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















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Threshold 2







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3065

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0 1000 2000 3000Iterations

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Threshold 2

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1555

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th=2

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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




Threshold 2

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176

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1715

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50

0

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Threshold 2

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0 1000 2000 3000 4000

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17635

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176

Obj

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th=2

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Freq

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Threshold 2







17865

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Obj

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Threshold 2

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500

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100 150 300250Gray level

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0025

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50 100 150 250Gray level

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168

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16

158

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0 1000 2000 3000 4000

Iterations

Obj

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265

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25




Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013











HM HMCR PAR BW NI100 075 05 05 300






(23)




PSNR = 20 log10(

255

RMSE) (dB)

RMSE = radicsum

ro119894=1sum

co119895=1

(119868119888119900(119894 119895) minus 119868119888th (119894 119895))

ro times co

(24)




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















Threshold 2



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Threshold 3

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Gray level200

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365236515

365136505

365036495

364936485

0 500 1000 1500 2000 2500 3000Iterations

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0 500 1000 1500 2000 2500 3000

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th=2

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3730

37253720

3715

37103705

37003695

3785

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3775

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3765

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Threshold 2



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Freq

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200

Freq

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196445

19644

196435

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19642

196415

19641

0 500 1000 1500 2000 2500 3000

0 1000 2000 3000O

bjec

tive f

unct

ion

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ion

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ion

valu

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tive f

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es

2140

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2100

2080

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2040

2020

2000

2195

2190

2185

2180

2175

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0 2000 4000 6000

0 1000 2000 3000 4000 5000 6000

2225

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2195

2190

th=2

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Iterations

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200Fr

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th=2

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1550

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1536

0 500 1000 1500 2000 2500 3000

0 1000 2000 3000O

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1638

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1636

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1695

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50 100 150 250Gray level

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0045

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Threshold 2







th=2

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3065

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Obj

ectiv

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Obj

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Obj

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ctio

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Obj

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0 1000 2000 3000Iterations

0 1000 2000 3000 4000 5000 6000

Iterations

0 2000 4000 6000

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0 1000 2000 3000 4000 5000

Iterations

3220

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3190

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3270

3268

3266

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3258

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3310

3305

3300

3295

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3275




Threshold 2

0025

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0015

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050 100 150 250

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uenc

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0025

003

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0015

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050 100 150 250

Gray level200

Freq

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0025

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0015

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050 100 150 250

Gray level200

Freq

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0025

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y







1555

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I 540

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0 1000 2000 3000 4000

Obj

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Iterations

Iterations

1670

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0 2000 4000 6000 8000

Iterations0 2000 4000 6000 8000

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0 1000 2000 3000 4000

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1740

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1705

1700

th=2

th=3

th=4

th=5




Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013




Camera man

2 70 144 17247 230119864 minus 12

3 59 119 156 20211 155119864 minus 02

4 42 95 140 170 21533 276119864 minus 12

5 36 82 122 149 173 23282 530119864 minus 03

Lena

2 91 150 15401 922119864 minus 13

3 79 125 170 17427 299119864 minus 02

4 73 112 144 179 18763 277119864 minus 01

5 71 107 134 158 186 19443 304119864 minus 01

Baboon

2 97 149 15422 692119864 minus 13

3 85 125 161 17709 192119864 minus 02

4 71 105 136 167 20289 582119864 minus 02

5 66 97 123 147 173 21713 440119864 minus 01

Hunter

2 51 116 17875 230119864 minus 12

3 36 86 135 20350 230119864 minus 12

4 27 65 104 143 22203 122119864 minus 02

5 22 53 88 112 152 23703 184119864 minus 12

Airplane

2 113 173 15029 922119864 minus 13

3 92 144 190 18854 483119864 minus 01

4 84 129 172 203 20735 724119864 minus 01

5 68 106 143 180 205 23126 838119864 minus 01

Peppers

2 72 138 16299 138119864 minus 12

3 65 122 169 18359 461119864 minus 13

4 50 88 128 171 20737 461119864 minus 13

5 48 85 118 150 179 22310 184119864 minus 012

Living room

2 87 145 15999 115119864 minus 12

3 76 123 163 18197 692119864 minus 12

4 56 97 132 168 20673 922119864 minus 12

5 49 88 120 146 178 22225 286119864 minus 02

Blonde

2 106 155 14609 692119864 minus 13

3 53 112 158 19157 923119864 minus 13

4 50 103 139 168 20964 548119864 minus 01

5 49 92 121 152 172 22409 650119864 minus 01

Bridge

2 91 56 13943 461119864 minus 13

3 72 120 177 17019 710119864 minus 01

4 63 103 145 193 18872 291119864 minus 01

5 56 91 124 159 201 20539 357119864 minus 01

Butterfly

2 99 151 13934 730119864 minus 02

3 82 119 160 16932 617119864 minus 01

4 71 102 130 163 19259 307119864 + 00

5 62 77 109 137 167 21450 387119864 + 00

Lake

2 85 154 14638 461119864 minus 13

3 78 140 194 15860 184119864 minus 12

4 67 110 158 198 17629 268119864 minus 01

5 57 88 127 166 200 19416 112119864 minus 01
















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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




Threshold 2

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Obj

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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013




Threshold 2



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Threshold 2







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3065

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0 1000 2000 3000Iterations

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Threshold 2

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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




Threshold 2

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0 1000 2000 3000 4000 5000

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0 1000 2000 3000 4000

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Threshold 2







17865

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Obj

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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



0012

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0002

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uenc

y


Threshold 2



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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




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17865

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Obj

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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



0045

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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




Threshold 2

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Threshold 2

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17865

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Obj

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215

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265

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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013




Threshold 2

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Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




Threshold 2

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Threshold 2

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Obj

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Threshold 2







17865

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Obj

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168

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0 1000 2000 3000 4000

Iterations

Obj

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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013




Camera man

2 128 196 13626 360119864 minus 15

3 44 103 196 14460 140119864 minus 03

4 44 96 146 196 20153 120119864 minus 03

5 24 60 98 146 196 20661 275119864 minus 02

Lena

2 96 163 14638 360119864 minus 15

3 23 96 163 16218 766119864 minus 02

4 23 80 125 173 19287 144119864 minus 14

5 23 71 109 144 180 21047 122119864 minus 02

Baboon

2 79 143 16016 108119864 minus 14

3 79 143 231 16016 719119864 minus 02

4 44 98 152 231 18485 847119864 minus 02

5 33 74 114 159 231 20507 108119864 minus 14

Hunter

2 92 179 15206 144119864 minus 14

3 59 117 179 18500 416119864 minus 04

4 44 89 133 179 21065 431119864 minus 04

5 44 89 133 179 222 21086 343119864 minus 02

Airplane

2 70 171 15758 330119864 minus 03

3 68 126 182 18810 108119864 minus 14

4 68 126 182 232 18810 182119864 minus 01

5 64 104 143 184 232 20321 180119864 minus 01

Peppers

2 66 143 16265 721119864 minus 15

3 62 112 162 18367 180119864 minus 14

4 62 112 162 227 18376 239119864 minus 02

5 48 86 127 171 227 18827 417119864 minus 04

Living room

2 89 170 14631 140119864 minus 03

3 47 103 175 17146 270119864 minus 03

4 47 98 149 197 19144 134119864 minus 02

5 42 85 125 162 197 21160 189119864 minus 02

Blonde

2 125 203 12244 144119864 minus 14

3 65 134 203 16878 100119864 minus 03

4 65 113 155 203 20107 550119864 minus 03

5 65 113 155 203 229 20107 448119864 minus 02

Bridge

2 94 171 13529 740119864 minus 03

3 65 131 195 16806 144119864 minus 02

4 53 102 151 199 18902 247119864 minus 02

5 40 85 131 171 211 20268 212119864 minus 02

Butterfly

2 27 213 81930 225119864 minus 02

3 27 120 213 13415 860119864 minus 04

4 27 96 144 213 16725 380119864 minus 03

5 27 83 118 152 213 19413 390119864 minus 03

Lake

2 91 163 14713 144119864 minus 14

3 73 120 170 16441 305119864 minus 04

4 69 112 156 195 17455 453119864 minus 02

5 62 96 131 166 198 18774 366119864 minus 02




Threshold 2

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Threshold 2

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Threshold 2





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Obj

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Threshold 2







17865

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Obj

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Obj

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0025

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Obj

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215

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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013




Threshold 2

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Threshold 2





17635

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176

Obj

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Obj

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Threshold 2







17865

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Obj

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50 100 150 300250Gray level

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0025

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001

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0

Freq

uenc

y

500

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0

0

100 150 300250Gray level

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0025

003

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001

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50 100 150 250Gray level

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168

166

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0 1000 2000 3000 4000

Iterations

Obj

ectiv

e fun

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Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



0012

001

0008

0006

0004

0002

0

50

0

0

0

0


200Fr

eque

ncy

0012

001

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Freq

uenc

y


Threshold 2

50 100 150 300250Gray level

200



0012

001

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0

Freq

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50 100 150 300250Gray level

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0012

001

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Freq

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y

50 100 150 300250Gray level

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1781

178

1779

1778

1777

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1775

1774

1773

1772

1771

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

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0 1000 2000 3000 4000

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th=2

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0 50 100 150 250Gray level

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0 50 100 150 250Gray level

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Freq

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0012

001

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0 50 100 150 250Gray level

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Freq

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Threshold 2





17635

1763

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176

Obj

ectiv

e fun

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Obj

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Obj

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0 1000 2000 3000 4000

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2206

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2198

2196

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0 2000 4000 80006000

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268

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308

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th=2

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0045

004

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0 50 100 150 250Gray level

200Fr

eque

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0045

004

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002

0015

001

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50 100 150 250Gray level

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Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2







17865

1786

17855

1785

17845

1784

17835

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

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Obj

ectiv

e fun

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Obj

ectiv

e fun

ctio

n va

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0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000

Iterations

226

225

224

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221

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0 1000 2000 3000 4000 5000

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269

268

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0 2000 4000 80006000

Iterations

306

3055

305

3045

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303

3025

302

th=2

th=3

th=4

th=5



th=2

th=3

th=4

th=5

50 100 150 300250Gray level

200


Threshold 2

0025

003

002

0015

001

0005

0Fr

eque

ncy

50 100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

500

0

0

0

100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

50 100 150 250Gray level

200

0025

003

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0015

001

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Freq

uenc

y







168

166

164

162

16

158

156

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0 1000 2000 3000 4000

Iterations

Obj

ectiv

e fun

ctio

n va

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Obj

ectiv

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Obj

ectiv

e fun

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Obj

ectiv

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215

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29

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255

25




Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200Fr

eque

ncy

0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200

Freq

uenc

y

0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200

Freq

uenc

y

0012

001

0008

0006

0004

0002

0 50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2





17635

1763

17625

1762

17615

1761

17605

176

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

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Obj

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e fun

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Obj

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e fun

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0 1000 2000 3000 4000

Iterations

2206

2204

2202

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2198

2196

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2192

219

2188

0 1000 2000 3000 4000 60005000

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0 2000 4000 80006000

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Iterations0 2000 4000 6000 8000 10000 12000

268

266

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262

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258

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31

308

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30

298

296

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th=2

th=3

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0045

004

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003

0025

002

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0 50 100 150 250Gray level

200Fr

eque

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0045

004

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003

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001

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50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

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0

50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2







17865

1786

17855

1785

17845

1784

17835

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

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lues

Obj

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e fun

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n va

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Obj

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e fun

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0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000

Iterations

226

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0 1000 2000 3000 4000 5000

Iterations

269

268

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0 2000 4000 80006000

Iterations

306

3055

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3045

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303

3025

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th=2

th=3

th=4

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th=2

th=3

th=4

th=5

50 100 150 300250Gray level

200


Threshold 2

0025

003

002

0015

001

0005

0Fr

eque

ncy

50 100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

500

0

0

0

100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

50 100 150 250Gray level

200

0025

003

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0015

001

0005

0

Freq

uenc

y







168

166

164

162

16

158

156

154

152

0 1000 2000 3000 4000

Iterations

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

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n va

lues

Obj

ectiv

e fun

ctio

n va

lues

215

205

20

19

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0 1000 2000 3000 4000

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0 1000 2000 3000 4000 5000

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255

25

245

24

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0 2000 4000 80006000

Iterations

29

285

28

275

27

265

26

255

25




Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



0045

004

0035

003

0025

002

0015

001

0005

0 50 100 150 250Gray level

200Fr

eque

ncy

0045

004

0035

003

0025

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0015

001

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0

50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y

0045

004

0035

003

0025

002

0015

001

0005

0

50 100 150 250Gray level

200

Freq

uenc

y


Threshold 2







17865

1786

17855

1785

17845

1784

17835

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

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lues

Obj

ectiv

e fun

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Obj

ectiv

e fun

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0 1000 2000 3000 4000

Iterations

0 1000 2000 3000 4000

Iterations

226

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0 1000 2000 3000 4000 5000

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269

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0 2000 4000 80006000

Iterations

306

3055

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3025

302

th=2

th=3

th=4

th=5



th=2

th=3

th=4

th=5

50 100 150 300250Gray level

200


Threshold 2

0025

003

002

0015

001

0005

0Fr

eque

ncy

50 100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

500

0

0

0

100 150 300250Gray level

200

0025

003

002

0015

001

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0

Freq

uenc

y

50 100 150 250Gray level

200

0025

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168

166

164

162

16

158

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0 1000 2000 3000 4000

Iterations

Obj

ectiv

e fun

ctio

n va

lues

Obj

ectiv

e fun

ctio

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Obj

ectiv

e fun

ctio

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lues

Obj

ectiv

e fun

ctio

n va

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215

205

20

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0 1000 2000 3000 4000

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0 1000 2000 3000 4000 5000

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255

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245

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29

285

28

275

27

265

26

255

25




Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013



th=2

th=3

th=4

th=5

50 100 150 300250Gray level

200


Threshold 2

0025

003

002

0015

001

0005

0Fr

eque

ncy

50 100 150 300250Gray level

200

0025

003

002

0015

001

0005

0

Freq

uenc

y

500

0

0

0

100 150 300250Gray level

200

0025

003

002

0015

001

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0

Freq

uenc

y

50 100 150 250Gray level

200

0025

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y







168

166

164

162

16

158

156

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0 1000 2000 3000 4000

Iterations

Obj

ectiv

e fun

ctio

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Obj

ectiv

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ctio

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Obj

ectiv

e fun

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Obj

ectiv

e fun

ctio

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215

205

20

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0 1000 2000 3000 4000

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245

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29

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26

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25




Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013




Camera man

2 10425119864 minus 16

3 21435119864 minus 15

4 26067119864 minus 16

5 62260119864 minus 16

Lena

2 10425119864 minus 16

3 94577119864 minus 15

4 97127119864 minus 15

5 12356119864 minus 12

Baboon

2 10425119864 minus 16

3 17500119864 minus 02

4 53417119864 minus 14

5 14013119864 minus 14

Hunter

2 10425119864 minus 16

3 26067119864 minus 16

4 66386119864 minus 14

5 64677119864 minus 15

Airplane

2 10425119864 minus 16

3 46500119864 minus 02

4 17438119864 minus 13

5 62475119864 minus 13

Peppers

2 10425119864 minus 16

3 10425119864 minus 16

4 60498119864 minus 15

5 53194119864 minus 15

Living room

2 32405119864 minus 15

3 14223119864 minus 15

4 13175119864 minus 14

5 62220119864 minus 14

Blonde

2 10425119864 minus 16

3 26067119864 minus 16

4 40480119864 minus 13

5 78167119864 minus 04

Bridge

2 73588119864 minus 06

3 11300119864 minus 04

4 19400119864 minus 02

5 21900119864 minus 02

Butterfly

2 11615119864 minus 14

3 25697119864 minus 14

4 37190119864 minus 13

5 17941119864 minus 06

Lake

2 10425119864 minus 16

3 56120119864 minus 16

4 98174119864 minus 14

5 22292119864 minus 14






6 Conclusions







Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013





Camera man


Lena


Baboon


Hunter


Butterfly

2 13934 730119864 minus 02 15530 13007 00426 15530 13092 00846 15530 13890 00643 155303 16932 617119864 minus 01 16692 15811 03586 16690 17261 26268 16657 17285 12113 166724 19259 307119864 + 00 17083 17104 06253 17099 17005 37976 17029 17128 22120 170705 21450 387119864 + 00 17280 18593 05968 17344 18099 60747 17307 189061 35217 17330




Camera man


Lena


Baboon


Hunter


Butterfly





Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013




Acknowledgment


References








































OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013










OperationsResearch

Advances in








Volume 2013


Combinatorics





ISRN Geometry





Volume 2013

Advances in


ISRN Algebra



Journal of






Advances in

DecisionSciences










Volume 2013

Multilevel Thresholding Segmentation Based on Harmony Search Optimization

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Transcript of Multilevel Thresholding Segmentation Based on Harmony Search Optimization