An Improved Multithreshold Segmentation Algorithm Based on...

Research ArticleAn Improved Multithreshold Segmentation Algorithm Based onGraph Cuts Applicable for Irregular Image

Yanzhu Hu JiaoWang Xinbo Ai and Xu Zhuang

School of Automation Beijing University of Posts and Telecommunications Beijing 100876 China

Correspondence should be addressed to Jiao Wang wangjiao0516bupteducn

Received 23 January 2019 Revised 21 March 2019 Accepted 7 April 2019 Published 13 May 2019

Academic Editor Thomas Hanne

Copyright copy 2019 Yanzhu Hu 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 order to realize themultithreshold segmentation of images an improved segmentation algorithmbased on graph cut theory usingartificial bee colony is proposed A newweight function based on gray level and the location of pixels is constructed in this paper tocalculate the probability that each pixel belongs to the same region On this basis a new cost function is reconstructed that can useboth square and nonsquare images Then the optimal threshold of the image is obtained through searching for the minimum valueof the cost function using artificial bee colony algorithm In this paper public dataset for segmentation and widely used imageswere measured separately Experimental results show that the algorithm proposed in this paper can achieve larger InformationEntropy (IE) higher Peak Signal to Noise Ratio (PSNR) higher Structural Similarity Index (SSIM) smaller Root Mean SquaredError (RMSE) and shorter time than other image segmentation algorithms

1 Introduction

Image threshold segmentation refers to dividing an imageinto two parts background and foreground under a certaingray value and target object can be easily recognized bydistinguishing between foreground and background [1 2] Atpresent target recognition based on image segmentation iswidely used in medical care military geology agricultureand many other fields [3ndash6] Due to the small differencebetween the target and the back ground of a complex imagethe results of image threshold segmentation are often farfrom satisfactory Considering the results of image segmen-tation are quite different under different thresholds [7ndash9]providing an accurate reliable and effective method foridentifying objects in complex background has a wide rangeof practical applications [10 11] On the other hand with thedevelopment of computer science and technology the real-time requirement of image segmentation is improved andfinding the exact threshold quickly is also an important part[12 13] To sum up it is important and necessary to find asuitable threshold quickly to complete the segmentation ofthe target object in an image

In the last few decades a number of image segmen-tation techniques have been devised and image threshold

segmentation is mainly divided into two categories globalthreshold segmentation and multithreshold segmentation[14 15] Both global and multithreshold segmentation selectthresholds by optimizing (maximizing or minimizing) somespecific parameters [16] Actually constructing the appro-priate parameters for image multithreshold segmentation isat the heart of solving this problem [17] And there aretwo main methods for constructing parameters entropy-based algorithm and graph cut algorithm [18] Entropy-basedThreshold Method was first proposed in 1980 by Pun [19]and is to develop extremely rapid in the next few decadesChowdhury et al used Shannons entropy and proposeda new multithreshold image segmentation method basedon minimization of bientropy function [20] Hinojosa etal used three of the most representative entropiesmdashKapurminimum cross entropy and Tsallis as objective functions[21] Mishra et al calculated the optimal threshold valuesusing bat algorithm and maximizing different objectivefunction values based on Kapurs entropy [22] Pare et alproposed an efficient multithreshold technique based onrendering minimum cross entropy [23] Application of thevarious multithreshold approaches discussed above whichare all based on entropy such as bientropy Kapurs entropyand cross entropy becomes computationally costly when

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 3514258 25 pageshttpsdoiorg10115520193514258

2 Mathematical Problems in Engineering

extended to perform multithreshold due to the constructedparameters functions to obtain optimum threshold valuesBecause of the measurement accuracy in selecting thresholdand the simplicity in dealing with the problem of image mul-tithreshold segmentation the algorithm based on graph cuttheory is being developed using a probability theorymdashthat isdifferent pixels within the same set The optimal thresholdsare gained by minimizing the cut between different pixel sets[24] Lu et al proposed an effective approach for particlesegmentation based on combing the background differencemethod and the graph cut based local threshold method [25]Jimenez et al presented a specifically designed graph cutmethodology that ensures spatial and directional consistency[26] Zhu et al developed an optimized parameter based ongraph cut to segment liver cysts [27] Deng et al obtainedthe segmentation by optimizing the cost function using graphcuts [28] Gandhimathi et al proposed an innovative spatial-spectral method for image segmentation based on graphcut [29] Guo et al presented an efficient image segmenta-tion algorithm using neutrosophic graph cut (NGC) [30]Although themethod based on graph cut discussed above canachieve effective image segmentation the weight functionof graph cut which is used to calculate the possibility thattwo pixels belong to one class does not change and it isinevitable that the segmentation effect will be unsatisfactorydue to a slow gradient drop Additionally because of thecomplexity of the weight construction function and the costfunction suitable for those algorithms the computation timeof the graph cut based method increases exponentially as thesegmentation level increases

Obviously because traditional methods based on math-ematical models are difficult to achieve ideal results somenew methods are incorporating bionic algorithms such asDragonfly algorithm [31] Artificial Bee Colony algorithm[32ndash34] Bat Algorithm [35] and Grey Wolf Algorithm [36]Moreover Gao et al demonstrated the superiority of theABC algorithm in finding an optimal value [34] Inspired bythe above algorithms we propose an image multithresholdsegmentation method based on graph cuts with artificialbee colony algorithm Through constructing a new weightfunction which is based on the location and gray value ofpixels the relationship between pixels is obtained On thisbasis a new cost function is reconstructed which can useboth regular and irregular images Then the artificial beecolony algorithm is used to search the optimalmultithresholdsegmentation values of an image By comparing the infor-mation entropy (IE) Peak Signal to Noise Ratio (PSNR)and Structural Similarity Index (SSIM) of images as well asthe time complexity of algorithm with the existing imagesegmentation methods the proposed algorithm based ongraph cuts in this paper can achieve better segmentationresults with the shortest time

The main work of this paper is given as follows Sec-tion 2 introduces the advantages of the artificial bee colonyalgorithm briefly and the general process of the algorithmSection 3 introduces the method to construct the newundirected graph Based on this new undirected graph thecost function of multithreshold segmentation is constructedSection 4 demonstrates the effectiveness of the method

through experiments At the same time qualitative and quan-titative methods are used to evaluate this method Section 5concludes this paper

2 Artificial Bee Colony Algorithm

Artificial bee colony algorithm is a global optimization algo-rithm by simulating bee foraging behavior Since Karabogaand Basturk first proposed this algorithm in 2008 theartificial bee colony algorithm (ABC) has developed rapidly[32ndash34 37] The artificial bee colony algorithm containsthree kinds of bees employed bees onlookers and scoutsEmployed bees bring nectar source back to the hive andshare the information in the dancing area By observing theinformation brought back by employed bees and calculatingthe number of food sources the onlookers can determine theprobability of selecting different nectar sources and make adecision on selection Scouts make random searches near thesources If the food source is not selected the employed beewhich carries the information of the food source becomes ascout bee and immediately searches near the original foodsource As soon as a new food source is found the scoutbee becomes an employed bee again In summary everysearch cycle of artificial bee colony algorithm includes threesteps (1) employed bees are sent to find food sources whilecalculating the amounts of nectar (2) employed bees sharethe information and onlooker bees select the optimal sourceby calculating the amount of different nectar sources (3) thescout bees are then chosen and sent out to find the new foodsources

In ABC algorithm the location of food source representsa possible optimal solution and the nectar amount of a foodsource corresponds to the quality (fitness) of the associatedsolution calculated by

fit119894 = 11 + 119891119894 (1)

where fit119894 represents the quality (fitness) of the solutionwhich is inversely proportional to 119891119894 and 119891119894is the costfunction which needs to be built for each specific problemIn this paper 119891119894 is the cost function construct based on theundirected weight map in Section 31

In the algorithm the number of employed and onlookeris equal to the number of optimal solutions Initially theartificial bee colony algorithm randomly generates P of SN asthe initial result where SN denotes the size of population andeach solution 119911119894is a vector of D dimensions of which elementsare represented as 119911119894119895 (119895 isin 1 2 119863) Here D is the numberof product of input size and cluster size for each data setAfter initialization the population of the positions (solutions)is subjected to repeated cycles C = 1 2 MCN of thesearch processes of the employed bees the onlooker beesand scout bees An employed bee produces a modificationon the position (solution) in her memory depending on thelocal information (visual information) and tests the nectaramount (fitness value) of the new source (new solution)If more nectar is found at the new food source than fromthe previous source the employed bees will remember the

Mathematical Problems in Engineering 3

Start

Initialization parametersgeneration of initial position

Find the initial source of nectar

Meettermination conditions

or not

Output the location of the food sources

End

Y

N

Calculate the number of food sources by the onlookers

The food sources is selected or not

The employed bees remember the location of the food sources

The employed bees become scout bees and search near the original food sources

YN

Figure 1 Flowchart of artificial bee colony algorithm

location of the new source otherwise they will choose toremember the location of the original source As soon asall employed bees have completed the search they share thenectar source information and location with the onlookerbees which will select the most possible food source as theoptimal solution through calculating the number of nectarThe probability of choosing a nectar source is calculated by

119901119894 = fit119894sum119878119873119894=1 fit119894 (2)

where 119901119894 is the probability of choosing nectar source SNis the number of food sources which is equal to the numberof employed bees and fit119894 is the fitness of the solution givenin (1)

In order to produce a candidate food position from theold one in memory the new source is obtained by

V119894119895 = 119911119894119895 + 120593119894119895 (119911119894119895 minus 119911119896119895) (3)

where V119894119895 represents the candidate food position 119911119894119895 isthe original resource location and 119911119896119895 is a generated resourcelocation through choosing the indexes 119896 (119896 isin 1 2 119878119873)and 119895 (119895 isin 1 2 119863) randomly Although 119896 is determinedrandomly it has to be different from 119894 and 120601119894119895 is randomlygenerated in [minus1 1]

If the location of the nectar source cannot be updated bythe previous lsquolimitrsquo of bees the location of the nectar source119911119894 is discarded and the employed bees are turned into scoutbees It is assumed that the location of the abandoned nectarsource is 119911119894 and 119895 isin 1 2 119863 and then the scouts found anew food source of food to replace 119911119894 The above steps can beexpressed by

119911119894119895 = 119911119895min + rand (0 1) (119911119895max minus 119911119895min) (4)

where 119911119895max and 119911119895min are the upper and lower limits of thejth component of all solutions If the new solution is betterthan the original the scout bee will become an employedbee again All employed bees onlooker bees and scout beesrepeat the above steps until the termination criteria are metThe flow of the artificial bee colony algorithm is shown inFigure 1 and the search result of ABC algorithm is shown inFigure 2 At last the fake code is given in Algorithm 1

3 Threshold SegmentationModel Construction

According to the analysis above the artificial bee colonyalgorithm can obtain the optimal solution of a certainproblem by searching the location of the optimal nectar


Input MCNNumber of iterations for optimizationSN Number of food sources equal to the number of employed bees

(1) Initialize parameters and generate initial position(2) Find the initial source of nectar(3)While Stopping criteria not met do(4) calculate the number of food sources by the onlookers(5) if the food sources is selected(6) the employed bees remember the location of the food sources(7) else(8) the employed bees become scout bees and search near the original food sources(9) end if(10) end whileOutput The location of the food sources

Algorithm 1 Algorithm ABC

Artificial Bee Colony algorithm for function optimization

14

12

10

8

6

4

2

0

func

tion

valu

e

optimal valueaverage value

0 200 400 600 800 1000

Iteration

Figure 2 Search for the optimal value using the ABC algorithm

source In this section we first converted an image undirectedweight map based on graph spectra theory On this basis

we constructed a cost function suitable for multithresholdsegmentation Finally the artificial bee colony algorithm isused to search the minimum cut of undirected weight map toachieve threshold segmentation of the image

31 Construction of Undirected Weight Map Based on GrayValue According to undirected graph theory the point setsof any feature space can be represented by 119866 = (119881 119864) whereV represents the set of points and E represents the set ofconnecting edges between points In undirected weightedmap there is only one connecting edge between two pointsWeight w (u v) is given to the edge which indicates thesimilarity between points u and v In summary the smallerthe value the less likely points u and v belong to the same set

When constructing an undirected weighted map of animage considering that the larger the distance betweenpixelsthe less likely they belong to the same set the weight functionconstructed is required to have a fast descent gradientwhich means when the denominator of the weight functionincreases the weight value decreases rapidly implying thepossibility that two pixel points belong to the same set quicklydecreases At the same time the weight valuew represents theprobability which is nonnegative To sum up the edge weightbetween pixel point u and pixel point v is as follows

119908 (119906 V) = 1

119889119905 119865 (119906) minus 119865 (V) 22 + 119889119883 119883 (119906) minus 119883 (V) 100381710038171003817100381722 119883 (119906) minus 119883 (V) 2 lt 1199030 others

(5)

where 119865(∙) is the gray value of pixel points 119883(∙) is thespatial position of pixel points ∙ 22 is the two norm 119889119894and 119889119883 are positive scale factors and 119903 is positive integerrepresenting the range of pixel points involved in calculatingtheweightTheweight function is visualized for several valuesof 119903 isin [1 5] in Figure 3

In this paper 119903 = 2 119889119894 = 125 and 119889119883 = 14 is taken as anexample to test the effectiveness of the algorithm Meanwhilethe weight function constructed in this paper is lower than

the original function in time complexity and its analysis isput in Section 4

32 e Cost Function Construct Based on the UndirectedWeight Map For any threshold 119905 = 1199051 1199052 119905119899 0 lt 1199051 lt1199052 119905119899 lt 119879 where 119879 is dynamic which depends on the bitsper pixel occupied (T=255 if 8 bits per pixel while T=65535 if16 bits per pixel) We can get a multithreshold partition 119881 =1198671 1198672 119867119899 of the corresponding undirected weighted


map 119866 = (119881 119864) of the image which can be expressed as

1198671 = 1199051minus1⋃119896=0

1198811198961198672 = 1199052⋃

119896=1199051

119881119896∙ ∙ ∙

119867119899 = 255⋃119896=119905119899

119881119896119896 isin 119871

(6)

where 119881 represents the collection of pixels119864 represents thecollection of edges between pixels and 119867119899 represents a pixelcollection belonging to class119899 According to the graph cutstheory when the image is segmented by multithresholds thedifference between pixels belonging to different divisions isthe largest while the difference between pixels belonging tothe same division is the smallest The cut between 1198671 and 1198672is defined as

cut (1198671 1198672) = sum119906isin1198671 Visin1198672

119908 (119906 V) = sum119906isin1198671

[ sumVisin1198672

119908 (119906 V)]

= 1199051sum119894=0

sum119906isin119881119894

[[1199052sum119895=1199051+1

sumVisin119881119895

119908 (119906 V)]]= 1199051sum119894=0

1199052sum119895=1199051+1

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]]

(7)

Similarly the cut between 1198671and 1198671 is defined as

asso (1198671 1198671) = sum119906isin1198671Visin1198671

119908 (119906 V)

= 1199051sum119894=0

1199051sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](8)

In the same way

asso (1198672 1198672) = sum119906isin1198672 Visin1198672

119908 (119906 V)

= 1199052sum119894=1199051

1199052sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](9)

For image multithreshold segmentation it is to find 119905 =1199051 1199052 119905119899 0 lt 1199051 lt 1199052 119905119899 lt 119879 making the value ofcut(1198671 1198672) + cut(11986711198673) + + cut(1198671 119867119899) + cut(1198672 1198673) +cut(119867119899minus1 119867119899) minimum while the value of asso(11986711198671) +asso(1198672 1198672) + + asso(119867119899 119867119899) maximum

In order to facilitate further analysis we define

cut (119881119894 119881119895) = sum119906isin119881119894Visin119881119895

119908 (119906 V) (10)

0 5 10 15 20 25 300

1

2

3

4

5

Less possibility belong to the same set

dt = 125 dx = 14 X (u)-X()2 = 1

dt = 125 dx = 14 X (u)-X()2 = 2

dt = 125 dx = 14 X (u)-X()2 = 3

dt = 125 dx = 14 X (u)-X()2 = 4

dt = 125 dx = 14 X (u)-X()2 = 5

F (u)-F ()2

w(u

)

Figure 3 Graphical display of the weight function results con-structed in this paper

Then (7) can be transformed into

cut (1198671 1198672) = 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) (11)

Similarly

cut (1198671 1198673) = 1199051sum119894=0

1199053sum119895=1199052

cut (119881119894 119881119895) (12)

Therefor (13) is established

cut (11986711198672) + cut (11986711198673)= 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) + 1199051sum119894=0

1199053sum119895=1199052+1

cut (119881119894 119881119895)

= 1199051sum119894=0

1199053sum119895=1199051+1

cut (119881119894 119881119895) = cut (1198671 1198672 + 1198673)(13)

By parity of reasoning (14) also holds

cut (1198671 1198672) + cut (1198671 1198673) + sdot sdot sdot + cut (1198671 119867119899)+ cut (1198672 1198673) + sdot sdot sdot cut (119867119899minus1119867119899)

= cut (1198671 1198672) + cut (1198671 + 11986721198673) + sdot sdot sdot+ cut (1198671 + 1198672 + sdot sdot sdot + 119867119899minus1 119867119899)

(14)

Similarly in order to overcome the problem of isolatedpoints in segmentation Normalized Cuts (Ncut) is adopted


Input An image with gray valueSegmented threshold level

(1) Calculate the edge weight between pixels with the new constructed function(2) Generate segmentation threshold randomly(3) Calculate the value of Ncut under the threshold(4) Calculate the value of new cost function (fit119894) based on Ncut(5)While Stopping criteria not met do(6) Search new threshold near the original threshold using artificial bee colony algorithm(7) Recalculate the value of Ncut under the new threshold(8) Recalculate he value of new cost function (fit119894) based on Ncut(9) if the cost function becomes smaller(10) Continue searching new threshold near the original threshold(11) else(12) Break(13) end if(14) end whileOutputMulti-level image segmentation threshold

Algorithm 2 Multithreshold image segmentation algorithm based on graph cuts

to describe the degree of separation between the two classes[38] which is defined as follows

Ncut (119860 119861) = cut (119860 119861)asso (119860 119881) + cut (119860 119861)

asso (119861119881) (15)

Equation (16) can be obtained by transforming (15)

Ncut (1198671 1198672) = cut (1198671 1198672)asso (1198671 1198671 + 1198672)+ cut (1198671 1198672)asso (1198672 1198671 + 1198672)

= cut (1198671 1198672)asso (1198671 1198671) + cut (1198671 1198672)+ cut (11986711198672)asso (1198672 1198672) + cut (1198671 1198672)

(16)

After normalization (17) can be obtained from (14)

Ncut (1198671 1198672) + Ncut (1198671 + 1198672 1198673) + sdot sdot sdot+ Ncut (1198671 + 1198672 + sdot sdot sdot + 119867119899minus1 119867119899)= cut (1198671 1198672)asso (1198671 1198671 + 1198672) + cut (1198671 1198672)

asso (1198672 1198671 + 1198672)+ cut (1198671 + 1198672 1198673)asso (1198671 + 1198672 1198671 + 1198672 + 1198673)

+ cut (1198671 + 11986721198673)asso (11986731198671 + 1198672 + 1198673) + sdot sdot sdot

+ cut (1198671 + 1198672 + sdot sdot sdot + 119867119899minus1 119867119899)asso (1198671 + 1198672 + sdot sdot sdot + 119867119899minus1 1198671 + 1198672 + sdot sdot sdot + 119867119899)

+ cut (1198671 + 1198672 + sdot sdot sdot + 119867119899minus1119867119899)asso (119867119899 1198671 + 1198672 + sdot sdot sdot + 119867119899)

(17)

Therefore the key of image segmentation is to find a setof N thresholds so that (18) can achieve the smallest valuewhich is mentioned in (1)

119891 ([1199051 1199052 119905119899])= Ncut (1198671 1198672) + Ncut (1198671 + 1198672 1198673) + sdot sdot sdot

+ Ncut (1198671 + 1198672 + sdot sdot sdot + 119867119899minus1 119867119899)(18)

The flowchart of image segmentation algorithm proposedin this paper is shown in Figure 4 and the fake code is givenin Algorithm 2

4 Experiments

In this section we will evaluate the performance of thealgorithm proposed in this paper comprehensively Firstlypublic dataset for segmentation and widely used images areevaluated separately using the proposed algorithm in thispaper to segment each image into two three four and fivelevels of threshold And at the same time quantitative meth-ods are used to demonstrate the advantages of the proposedalgorithm through comparing the Information Entropy (IE)Root Mean Squared Error (RMSE) Peak Signal to NoiseRatio (PSNR) and Structural Similarity Index (SSIM) ofimages with other widely used algorithms such as BA (BatAlgorithm) [35] IBA (Improved Bat Algorithm) [39]MMSA(Meta-heuristic Moth Swarm Algorithm) [40] and OTUS[41] algorithms Finally the time advantage of the algorithm isconfirmed via analyzing the time complexity of the algorithm

41 Qualitative Comparison and Analysis of Different Algo-rithms In this part we will compare the performance ofour algorithm using the new weight and cost function withother algorithms Firstly we selected five images commonlyused in the image field to verify the effectiveness of thealgorithm proposed in this paper Figures 5 6 7 and 8 are


Start

Calculate the edge weight between pixels with the new constructed function

Generate segmentation threshold randomly


or not

Output multi-level image segmentation threshold

End

Y

N

Calculate the value of Ncut under the threshold

The cost function becomes smaller or not



YN

Search new threshold near the original threshold using artificial bee colony algorithm

Recalculate the value of Ncut under the new threshold

Calculate the value of new cost function (fiti) based on Ncut

Recalculate the value of new cost function (fiti) based on Ncut

Figure 4 Flowchart of image segmentation algorithm proposed in this paper

the segmentation results obtained by different algorithmsFigure 5 shows the two-level segmentation results Figure 6shows the three-level segmentation results Figure 7 showsthe four-level segmentation results and Figure 8 shows thefive-level segmentation results

The specific segmentation thresholds of different algo-rithms are given in Table 1 As can be seen from Table 1the segmentation results given by our method are slightlydifferent from those of other methods

Further we selected ten images from the data set [42] tojustify the superiority of proposed method Figures 9 10 11and 12 are the segmentation results obtained by different algo-rithms Figure 9 shows the two-level segmentation resultsFigure 10 shows the three-level segmentation results Figure 11shows the four-level segmentation results and Figure 12shows the five-level segmentation results

The specific segmentation thresholds of different algo-rithms are given in Table 2 and qualitative analysis of theadvantages and disadvantages of those algorithms is put inSection 42

42 Quantitative Comparison and Analysis of Different Algo-rithms In this part we will evaluate the performance of thealgorithm quantitatively by calculating Information Entropy(IE) Root Mean Squared Error (RMSE) Peak Signal toNoise Ratio (PSNR) and Structural Similarity Index (SSIM)of images Generally speaking the entropy of an imagerepresents the information contained in the image Accordingto the theory of Information Entropy (IE) the better seg-mentation results are the greater the value of informationentropy is The entropy of an image can be calculated asfollows


(a) (b) (c) (d) (e) (f)

Figure 5 Two-level segmentation results of different algorithms (a) origin image (b) segmented image using our method (c) segmentedimage using BA algorithms (d) segmented image using MMSA algorithms (e) segmented image using IBA algorithms and (f) segmentedimage using OTSU algorithms

H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)

where 119901(119896) is the probability density of pixel value kand M is largest pixel value For the convenience of readingwe put the results of the two data sets in one table TheInformation Entropy (IE) of different segmented imagesusing various algorithms is given in Table 3

As shown in Table 3 the image segmented by the algo-rithm proposed in this paper can obtain a larger informationentropy (IE) which means the algorithm proposed in thispaper has the best segmentation effect compared with otheralgorithms mentioned above What is more the value ofinformation entropy (IE) of multithreshold segmented imageis greater than that of two-level threshold segmentationmeaning the more threading levels there are the less infor-mation lost is

Root Mean Squared Error (RMSE) is a mathematicalmodel established based on the visual system of human eyeswhich determines the degree of distortion of the image by

calculating the mean square value of the pixel differencebetween the original image and the processed image Theentropy of an image can be calculated as follows

RMSE = radic 1119872 times 119873 sum0le119894lt119873

sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)

where M and N represents the length and width of theimage 119891119894119895 represents the gray value of the point (119894 119895) in theoriginal image and 1198911198941198951015840 represents the pixel value of the point(119894 119895) in the image after segmentation We put the resultsof the two datasets in one table The Root Mean SquaredError (RMSE) of different segmented images using variousalgorithms is given in Table 4

As shown in Table 4 the image segmented by thealgorithm proposed in this paper can obtain smaller RootMean Squared Error (RMSE) which means the proposedalgorithm has the least degree of distortion compared withother algorithms The value ofThe Root Mean Squared Error(RMSE) of the multithreshold segmentation image is greater


(a) (b) (c) (d) (e) (f)

Figure 6 Three-level segmentation results of different algorithms (a) origin image (b) segmented image using our method (c) segmentedimage using BA algorithms (d) segmented image using MMSA algorithms (e) segmented image using IBA algorithms and (f) segmentedimage using OTSU algorithms

Table 1 Specific segmentation thresholds of different algorithms

Image level Our algorithm BA MMSA IBA OTSU

LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179

PEPPERS(512times512)

2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169

GOLDHILL(256times256)

2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)

Figure 7 Four-level segmentation results of different algorithms (a) origin image (b) segmented image using our method (c) segmentedimage using BA algorithms (d) segmented image using MMSA algorithms (e) segmented image using IBA algorithms and (f) segmentedimage using OTSU algorithms

than that of two-threshold segmentation meaning that themore threading level there are the less degree of distortion is

Peak Signal to Noise Ratio (PSNR) is another importantindicator to measure image quality It is based on com-munication theory which represents the ratio of maximumsemaphore to noise intensity Since digital images representimage pixels in discrete numbers the maximum pixel valueof the image is used instead of the maximum semaphoreThespecific formula is as follows

PSNR = 10 times lg119871 times 119871MSE

(21)

where L is the maximum gray value of the pixels in theimage generally 255 andMSE is the square ofRMSE We alsoonly used one table to present the results The Peak Signalto Noise Ratio (PSNR) of different segmented images usingvarious algorithms is given in Table 5

As shown in Table 5 the image segmented by thealgorithm proposed in this paper can obtain a higher PeakSignal to Noise Ratio (PSNR) which means the algorithmproposed in this paper has the best background noise filtering

compared with other algorithms whether it is in two-levelthreshold segmentation or multithreshold segmentation

Structural Similarity Index (SSIM) is an indicator thatmeasures the similarity of two images The method was firstproposed by the University of Texas at Austins Laboratoryfor Image and Video Engineering If the two images are oneafter segmentation and the other before segmentation SSIMalgorithm can be used to evaluate the segmentation effectThe calculation formula is as follows

SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)

where 119868119874 represents the original image and 119868119878 representsthe segmented image 120583119868119874 and 120583119868119878 respectively representthe mean values of images 119868119874 and 119868119878 120590119868119874 and 120590119868119878 representthe standard deviations of images 119868119874and 119868119878 respectivelyand 1205832119868119874and 1205832119868119878 are the square of 120583119868119874 and 120583119868119878 1205902119868119874 and 1205902

119868119878

represent the variance of the images 119868119874 and 119868119878 and 1198881 and1198882 are constants to maintain stability in order to avoid the


(a) (b) (c) (d) (e) (f)

Figure 8 Five-level segmentation results of different algorithms (a) origin image (b) segmented image using our method (c) segmentedimage using BA algorithms (d) segmented image using MMSA algorithms (e) segmented image using IBA algorithms and (f) segmentedimage using OTSU algorithms

denominator being zero Normally 1198881 = (1198701 lowast 119871)2 and1198882 = (1198702 lowast 119871)2 where 1198701 = 001 and 1198702 = 003 119871 is thedynamic range of pixel values generally taken as 255 Weput the results of two datasets together and the StructuralSimilarity Index (SSIM) of different segmented images usingvarious algorithms is given in Table 6

As shown in Table 6 the image segmented by the algo-rithm proposed in this paper can obtain a higher StructuralSimilarity Index (SSIM) which means the algorithm pro-posed in this paper has the highest similarity to the originalimage compared with other algorithms The value of Struc-tural Similarity Index (SSIM) of multithreshold segmentedimage is higher than that of two-threshold segmentationmeaning the more the threading levels there are the higherthe similarity is

43 Time Complexity Analysis of Different Algorithm Inthis part we show the time advantage of the algorithm byanalyzing the time complexity of the algorithm

The computing of the algorithm proposed in this papercan be divided into two parts the first part is the compu-tational time T1 needed to construct the undirected weight

map based on gray level and the second part is the timeneeded to search the optimal solution using artificial beecolony algorithm according to the undirected weight mapThe analysis of the time complexity of the second part hasbeen given in literature [29] therefore it will not be involvedin the essay For the first part the computation of structuringthe undirected weight map depends on the parameter r Withthe increase of r there are more edges connecting the pointsinweightmapG and the corresponding calculation increasesas well Obviously in (4) r=1 ismeaningless while r=2meansfor every pixel we must calculate the weight value betweenthis pixel and every other pixel in its 3lowast3 neighborhood Thetotal amount of calculation frequency needed to calculate allpixels in undirected weight map G is (8 lowastN)2=4 lowastN whereN represents the total number of pixels Division by lsquo2rsquo isbecause the weight between pixel point v and pixel point u isrepeatedly calculated twice when pixel point v and pixel pointu are respectively centered

Generally speaking when rgt1 every pixel has [2(119903 minus 1) +1]2minus1 neighborhood pixels except the pixels on the boundaryof an image Therefore the number of weights needed tocalculate in the undirected weight map is


(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)




Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181

4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228

1199051 = [2 (119903 minus 1) + 1]2 minus 12 times 119873 = 2119903 (119903 minus 1)119873 (23)

The time complexity of t1 is O (r2 N) and the time costof various algorithm compared with our method is given inTable 7

As shown in Table 7 the image segmented by thealgorithm proposed in this paper can reduce the computationload which means the algorithm proposed in this paperhas the shortest computation time compared with otheralgorithms

5 Conclusion

In this paper we have proposed an improved segmentationalgorithm based on graph cut theory using artificial beecolony This approach uses a new weight function basedon gray level and the location of pixels to calculate theprobability that each pixel belongs to the same region Thenthe optimal threshold of the image is obtained throughsearching for the minimum value of the cost functionwhich is constructed based on the weight function usingartificial bee colony algorithm Experiment results show that


Table 3 The Information Entropy (IE) of different segmented images using various algorithm


LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued

Image level Our algorithm BA MMSA IBA OTSU37073 2 264 262 263 259 264(481times321) 3 430 426 425 426 428

4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518

Table 4 Root Mean Squared Error (RMSE) of different segmented images using various algorithm


LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602

Table 5 Peak Signal to Noise Ratio (PSNR) of different segmented images using various algorithm


LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404


Table 6 Structural Similarity Index (SSIM) of different segmented images using various algorithm


LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082

Table 7 Time cost of diffident methods (unit millisecond)


LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017

the algorithm proposed in this paper can achieve largerInformation Entropy (IE) higher Peak Signal to Noise Ratio(PSNR) higher Structural Similarity Index (SSIM) smallerRoot Mean Squared Error (RMSE) and shorter time thanother image segmentation algorithms

Data Availability

The data used to support the research findings of thisstudy have been deposited in ldquohttpspanbaiducoms1UhHjhFnvfqS2Po0QUPIxzArdquo and ldquohttpswww2eecsber-keleyeduResearchProjectsCSvisionbsdsBSDS300htmldatasetimageshtmlrdquo

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported by Subproject of Key Projectof Beijing China (Nos Z181100000618006 and

D161100004916002) Beijing Natural Science Foundation(No 4192042) and National Natural Science Foundation ofChina (No 61627816)

Supplementary Materials

Test all the 100 pictures in the test dataset of Berkeley Seg-mentation Dataset to justify the superiority of the proposedapproach (Supplementary Materials)

References

[1] T Wang J Yang Z Ji and Q Sun ldquoProbabilistic diffusion forinteractive image segmentationrdquo IEEE Transactions on ImageProcessing vol 28 no 1 pp 330ndash342 2019

[2] Y Zhou and H Q Zhu ldquoImage segmentation using a trimmedlikelihood estimator in the asymmetricmixturemodel based ongeneralized gamma and gaussian distributionsrdquo MathematicalProblems in Engineering vol 2018 Article ID 3468967 17 pages2018

[3] S Kotte R K Pullakura and S K Injeti ldquoOptimal multilevelthresholding selection for brainMRI image segmentation based


on adaptive wind driven optimizationrdquo Measurement vol 130pp 340ndash361 2018

[4] M A Hossam H M Ebied M H Abdel-Aziz andM F TolbaldquoAccelerated hyperspectral image recursive hierarchical seg-mentation using GPUs multicore CPUs and hybrid CPUGPUclusterrdquo Journal of Real-Time Image Processing vol 14 no 2 pp413ndash432 2018

[5] Z Li and G Zhang ldquoFracture segmentation method basedon contour evolution and gradient direction consistency insequence of coal rock CT imagesrdquo Mathematical Problems inEngineering vol 2019 Article ID 2980747 8 pages 2019

[6] M Sharif M A Khan Z Iqbal M F Azam M I Lali andM Y Javed ldquoDetection and classification of citrus diseasesin agriculture based on optimized weighted segmentation andfeature selectionrdquoComputers and Electronics in Agriculture vol150 pp 220ndash234 2018

[7] V P Ananthi P Balasubramanian and P Raveendran ldquoAthresholding method based on interval-valued intuitionisticfuzzy sets an application to image segmentationrdquo PAA PatternAnalysis and Applications vol 21 no 4 pp 1039ndash1051 2018

[8] M I Daoud A A Atallah and F Awwad ldquoAutomaticsuperpixel-based segmentation method for breast ultrasoundimagesrdquo Expert Systems with Applications vol 121 pp 78ndash962019

[9] Z Fan J Lu C Wei H Huang X Cai and X Chen ldquoA hier-archical image matting model for blood vessel segmentation infundus imagesrdquo IEEE Transactions on Image Processing vol 28no 5 pp 2367ndash2377 2019

[10] J Olveres D E Carbaajal R B Escalante et al ldquoDeformablemodels for segmentation based on local analysisrdquoMathematicalProblems in Engineering vol 2017 Article ID 1646720 13 pages2017

[11] B Han and Y Wu ldquoActive contours driven by global and localweighted signed pressure force for image segmentationrdquoPatternRecognition vol 88 pp 715ndash728 2019

[12] R Panda S Agrawal L Samantaray et al ldquoAn evolutionarygray gradient algorithm for multilevel thresholding of brainMR images using soft computing techniquesrdquo Applied SoComputing vol 50 pp 94ndash108 2017

[13] A K Jumaat and K Chen ldquoA reformulated convex andselective variational image segmentation model and its fastmultilevel algorithmrdquoNumerical Mathematics eory Methodsand Applications vol 12 no 2 pp 403ndash437 2019

[14] E Essa and X Xie ldquoAutomatic segmentation of cross-sectionalcoronary arterial imagesrdquo Computer Vision and Image Under-standing vol 165 pp 97ndash110 2017

[15] H Liang H Jia Z Xing J Ma and X Peng ldquoModifiedgrasshopper algorithm-based multilevel thresholding for colorimage segmentationrdquo IEEE Access vol 7 pp 11258ndash11295 2019

[16] Y T Chen ldquoMedical image segmentation using independentcomponent analysis-based kernelized fuzzy c -means cluster-ingrdquoMathematical Problems in Engineering vol 2017 Article ID5892039 21 pages 2017

[17] A R J Fredo R S Abilash and C Suresh Kumar ldquoSegmenta-tion and analysis of damages in composite images using multi-level threshold methods and geometrical featuresrdquo Measure-ment vol 100 pp 270ndash278 2017

[18] W William A Ware A H Basaza-Ejiri and J Obungoloch ldquoAreview of image analysis and machine learning techniques forautomated cervical cancer screening from pap-smear imagesrdquoComputer Methods and Programs in Biomedicine vol 164 pp15ndash22 2018

[19] T Pun ldquoAnewmethod for grey-level picture thresholding usingthe entropy of the histogramrdquo Signal Processing vol 2 no 3 pp223ndash237 1980

[20] K Chowdhury D Chaudhuri and A K Pal ldquoA new image seg-mentation technique using bi-entropy function minimizationrdquoMultimedia Tools and Applications vol 77 no 16 pp 20889ndash20915 2018

[21] S Hinojosa K G Dhal M A Elaziz D Oliva and E CuevasldquoEntropy-based imagery segmentation for breast histologyusing the stochastic fractal searchrdquo Neurocomputing vol 321pp 201ndash215 2018

[22] S Mishra and M Panda ldquoBat algorithm for multilevel colourimage segmentation using entropy-based thresholdingrdquo Ara-bian Journal for Science and Engineering vol 43 no 12 pp7285ndash7314 2018

[23] S Pare A Kumar V Bajaj and G K Singh ldquoAn efficientmethod for multilevel color image thresholding using cuckoosearch algorithm based on minimum cross entropyrdquo AppliedSo Computing vol 61 pp 570ndash592 2017

[24] J W Long X Feng X F Zhu J Zhang and G Gou ldquoEfficientsuperpixel-guided interactive image segmentation based ongraph theoryrdquo Symmetry-Basel vol 10 no 5 p 169 2018

[25] ZM Lu F C Zhu X YGao B C Chen andZGGao ldquoIn-situparticle segmentation approach based on average backgroundmodeling and graph-cut for the monitoring of L-glutamicacid crystallizationrdquo Chemometrics and Intelligent LaboratorySystems vol 178 pp 11ndash23 2018

[26] C D Jimenez P D Bermejo and P Nardelli ldquoA graph-cutapproach for pulmonary artery-vein segmentation in noncon-trast CT imagesrdquo Medical Image Analysis vol 52 pp 144ndash1592019

[27] H Zhu Z Zhuang J Zhou et al ldquoImproved graph-cutsegmentation for ultrasound liver cyst imagerdquoMultimedia Toolsand Applications vol 9 pp 1ndash19 2018

[28] X Deng Y Zheng Y Xu X Xi N Li and Y Yin ldquoGraph cutbased automatic aorta segmentation with an adaptive smooth-ness constraint in 3D abdominal CT imagesrdquo Neurocomputingvol 310 pp 46ndash58 2018

[29] S G A Usha and S Vasuki ldquoImproved segmentation andchange detection of multi-spectral satellite imagery using graphcut based clustering andmulticlass SVMrdquoMultimedia Tools andApplications vol 77 no 12 pp 15353ndash15383 2018

[30] Y H Guo Y M Akbulut A Sengur et al ldquoAn efficientimage segmentation algorithm using neutrosophic graph cutrdquoSymmetry vol 9 no 9 p 185 2017

[31] MADiaz-Cortes S NOrtega SHinojosa et al ldquoAmulti-levelthresholding method for breast thermo grams analysis usingdragonfly algorithmrdquo Infrared Physics amp Technology vol 93 pp346ndash361 2018

[32] J C Bansal A Gopal and A K Nagar ldquoStability analysisof artificial bee colony optimization algorithmrdquo Swarm andEvolutionary Computation vol 41 pp 9ndash19 2018

[33] L B Ma X W Wang H Shen et al ldquoA novel artificial beecolony optimiser with dynamic population size for multi-levelthreshold image segmentationrdquo International Journal of Bio-Inspired Computation vol 13 no 1 pp 32ndash44 2019

[34] H Gao Z Fu and C M Pun ldquoA multi-level thresholdingimage segmentation based on an improved artificial bee colonyalgorithmrdquo Computers and Electrical Engineering vol 70 pp931ndash938 2018


[35] S Mishra and M Panda ldquoBat algorithm for multilevel colourimage segmentation using entropy-based thresholdingrdquo Ara-bian Journal for Science and Engineering vol 6 pp 1ndash30 2018

[36] M Q Li L P Xu N Xu T Huang and B Yan ldquoSAR image seg-mentation based on improved greywolf optimization algorithmand fuzzy c-meansrdquoMathematical Problems in Engineering vol2018 Article ID 4576015 11 pages 2018

[37] S Zhang W Jiang and S Satoh ldquoMultilevel thresholdingcolor image segmentation using a modified artificial bee colonyalgorithmrdquo IEICE Transaction on Information and Systems volE101D no 8 pp 2064ndash2071 2018

[38] Y Zhong R Gao and L Zhang ldquoMultiscale and multifeaturenormalized cut segmentation for high spatial resolution remotesensing imageryrdquo IEEE Transactions on Geoscience and RemoteSensing vol 54 no 10 pp 6061ndash6075 2016

[39] A Alihodzic and M Tuba ldquoImproved bat algorithm applied tomultilevel image thresholdingrdquoeScientificWorld Journal vol2014 Article ID 176718 16 pages 2014

[40] Y Zhou X Yang Y Ling and J Zhang ldquoMeta-heuristic mothswarm algorithm for multilevel thresholding image segmen-tationrdquo Multimedia Tools and Applications vol 77 no 18 pp23699ndash23727 2018

[41] S C Satapathy N S M Raja V Rajinikanth et al ldquoMulti-level image thresholding using Otsu and chaotic bat algorithmrdquoNeural Computing and Applications vol 29 no 12 pp 1285ndash1307 2018

[42] httpswww2eecsberkeleyeduResearchProjectsCSvisionbsdsBSDS300htmldatasetimages

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


extended to perform multithreshold due to the constructedparameters functions to obtain optimum threshold valuesBecause of the measurement accuracy in selecting thresholdand the simplicity in dealing with the problem of image mul-tithreshold segmentation the algorithm based on graph cuttheory is being developed using a probability theorymdashthat isdifferent pixels within the same set The optimal thresholdsare gained by minimizing the cut between different pixel sets[24] Lu et al proposed an effective approach for particlesegmentation based on combing the background differencemethod and the graph cut based local threshold method [25]Jimenez et al presented a specifically designed graph cutmethodology that ensures spatial and directional consistency[26] Zhu et al developed an optimized parameter based ongraph cut to segment liver cysts [27] Deng et al obtainedthe segmentation by optimizing the cost function using graphcuts [28] Gandhimathi et al proposed an innovative spatial-spectral method for image segmentation based on graphcut [29] Guo et al presented an efficient image segmenta-tion algorithm using neutrosophic graph cut (NGC) [30]Although themethod based on graph cut discussed above canachieve effective image segmentation the weight functionof graph cut which is used to calculate the possibility thattwo pixels belong to one class does not change and it isinevitable that the segmentation effect will be unsatisfactorydue to a slow gradient drop Additionally because of thecomplexity of the weight construction function and the costfunction suitable for those algorithms the computation timeof the graph cut based method increases exponentially as thesegmentation level increases

Obviously because traditional methods based on math-ematical models are difficult to achieve ideal results somenew methods are incorporating bionic algorithms such asDragonfly algorithm [31] Artificial Bee Colony algorithm[32ndash34] Bat Algorithm [35] and Grey Wolf Algorithm [36]Moreover Gao et al demonstrated the superiority of theABC algorithm in finding an optimal value [34] Inspired bythe above algorithms we propose an image multithresholdsegmentation method based on graph cuts with artificialbee colony algorithm Through constructing a new weightfunction which is based on the location and gray value ofpixels the relationship between pixels is obtained On thisbasis a new cost function is reconstructed which can useboth regular and irregular images Then the artificial beecolony algorithm is used to search the optimalmultithresholdsegmentation values of an image By comparing the infor-mation entropy (IE) Peak Signal to Noise Ratio (PSNR)and Structural Similarity Index (SSIM) of images as well asthe time complexity of algorithm with the existing imagesegmentation methods the proposed algorithm based ongraph cuts in this paper can achieve better segmentationresults with the shortest time

The main work of this paper is given as follows Sec-tion 2 introduces the advantages of the artificial bee colonyalgorithm briefly and the general process of the algorithmSection 3 introduces the method to construct the newundirected graph Based on this new undirected graph thecost function of multithreshold segmentation is constructedSection 4 demonstrates the effectiveness of the method

through experiments At the same time qualitative and quan-titative methods are used to evaluate this method Section 5concludes this paper

2 Artificial Bee Colony Algorithm

Artificial bee colony algorithm is a global optimization algo-rithm by simulating bee foraging behavior Since Karabogaand Basturk first proposed this algorithm in 2008 theartificial bee colony algorithm (ABC) has developed rapidly[32ndash34 37] The artificial bee colony algorithm containsthree kinds of bees employed bees onlookers and scoutsEmployed bees bring nectar source back to the hive andshare the information in the dancing area By observing theinformation brought back by employed bees and calculatingthe number of food sources the onlookers can determine theprobability of selecting different nectar sources and make adecision on selection Scouts make random searches near thesources If the food source is not selected the employed beewhich carries the information of the food source becomes ascout bee and immediately searches near the original foodsource As soon as a new food source is found the scoutbee becomes an employed bee again In summary everysearch cycle of artificial bee colony algorithm includes threesteps (1) employed bees are sent to find food sources whilecalculating the amounts of nectar (2) employed bees sharethe information and onlooker bees select the optimal sourceby calculating the amount of different nectar sources (3) thescout bees are then chosen and sent out to find the new foodsources

In ABC algorithm the location of food source representsa possible optimal solution and the nectar amount of a foodsource corresponds to the quality (fitness) of the associatedsolution calculated by

fit119894 = 11 + 119891119894 (1)

where fit119894 represents the quality (fitness) of the solutionwhich is inversely proportional to 119891119894 and 119891119894is the costfunction which needs to be built for each specific problemIn this paper 119891119894 is the cost function construct based on theundirected weight map in Section 31

In the algorithm the number of employed and onlookeris equal to the number of optimal solutions Initially theartificial bee colony algorithm randomly generates P of SN asthe initial result where SN denotes the size of population andeach solution 119911119894is a vector of D dimensions of which elementsare represented as 119911119894119895 (119895 isin 1 2 119863) Here D is the numberof product of input size and cluster size for each data setAfter initialization the population of the positions (solutions)is subjected to repeated cycles C = 1 2 MCN of thesearch processes of the employed bees the onlooker beesand scout bees An employed bee produces a modificationon the position (solution) in her memory depending on thelocal information (visual information) and tests the nectaramount (fitness value) of the new source (new solution)If more nectar is found at the new food source than fromthe previous source the employed bees will remember the


Start




or not


End

Y

N





YN



119901119894 = fit119894sum119878119873119894=1 fit119894 (2)



V119894119895 = 119911119894119895 + 120593119894119895 (119911119894119895 minus 119911119896119895) (3)












14

12

10

8

6

4

2

0

func

tion

valu

e


0 200 400 600 800 1000

Iteration






119908 (119906 V) = 1


(5)







1198671 = 1199051minus1⋃119896=0

1198811198961198672 = 1199052⋃

119896=1199051

119881119896∙ ∙ ∙

119867119899 = 255⋃119896=119905119899

119881119896119896 isin 119871

(6)



119908 (119906 V) = sum119906isin1198671

[ sumVisin1198672

119908 (119906 V)]

= 1199051sum119894=0

sum119906isin119881119894

[[1199052sum119895=1199051+1


119908 (119906 V)]]= 1199051sum119894=0

1199052sum119895=1199051+1

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]]

(7)



119908 (119906 V)

= 1199051sum119894=0

1199051sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](8)

In the same way


119908 (119906 V)

= 1199052sum119894=1199051

1199052sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](9)




119908 (119906 V) (10)

0 5 10 15 20 25 300

1

2

3

4

5


dt = 125 dx = 14 X (u)-X()2 = 1

dt = 125 dx = 14 X (u)-X()2 = 2

dt = 125 dx = 14 X (u)-X()2 = 3

dt = 125 dx = 14 X (u)-X()2 = 4

dt = 125 dx = 14 X (u)-X()2 = 5

F (u)-F ()2

w(u

)



cut (1198671 1198672) = 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) (11)

Similarly

cut (1198671 1198673) = 1199051sum119894=0

1199053sum119895=1199052

cut (119881119894 119881119895) (12)


cut (11986711198672) + cut (11986711198673)= 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) + 1199051sum119894=0

1199053sum119895=1199052+1

cut (119881119894 119881119895)

= 1199051sum119894=0

1199053sum119895=1199051+1

cut (119881119894 119881119895) = cut (1198671 1198672 + 1198673)(13)




(14)







Ncut (119860 119861) = cut (119860 119861)asso (119860 119881) + cut (119860 119861)

asso (119861119881) (15)




(16)



asso (1198672 1198671 + 1198672)+ cut (1198671 + 1198672 1198673)asso (1198671 + 1198672 1198671 + 1198672 + 1198673)




(17)





4 Experiments




Start




or not


End

Y

N





YN












(a) (b) (c) (d) (e) (f)


H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)






sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)




(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









Start




or not


End

Y

N





YN



119901119894 = fit119894sum119878119873119894=1 fit119894 (2)



V119894119895 = 119911119894119895 + 120593119894119895 (119911119894119895 minus 119911119896119895) (3)












14

12

10

8

6

4

2

0

func

tion

valu

e


0 200 400 600 800 1000

Iteration






119908 (119906 V) = 1


(5)







1198671 = 1199051minus1⋃119896=0

1198811198961198672 = 1199052⋃

119896=1199051

119881119896∙ ∙ ∙

119867119899 = 255⋃119896=119905119899

119881119896119896 isin 119871

(6)



119908 (119906 V) = sum119906isin1198671

[ sumVisin1198672

119908 (119906 V)]

= 1199051sum119894=0

sum119906isin119881119894

[[1199052sum119895=1199051+1


119908 (119906 V)]]= 1199051sum119894=0

1199052sum119895=1199051+1

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]]

(7)



119908 (119906 V)

= 1199051sum119894=0

1199051sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](8)

In the same way


119908 (119906 V)

= 1199052sum119894=1199051

1199052sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](9)




119908 (119906 V) (10)

0 5 10 15 20 25 300

1

2

3

4

5


dt = 125 dx = 14 X (u)-X()2 = 1

dt = 125 dx = 14 X (u)-X()2 = 2

dt = 125 dx = 14 X (u)-X()2 = 3

dt = 125 dx = 14 X (u)-X()2 = 4

dt = 125 dx = 14 X (u)-X()2 = 5

F (u)-F ()2

w(u

)



cut (1198671 1198672) = 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) (11)

Similarly

cut (1198671 1198673) = 1199051sum119894=0

1199053sum119895=1199052

cut (119881119894 119881119895) (12)


cut (11986711198672) + cut (11986711198673)= 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) + 1199051sum119894=0

1199053sum119895=1199052+1

cut (119881119894 119881119895)

= 1199051sum119894=0

1199053sum119895=1199051+1

cut (119881119894 119881119895) = cut (1198671 1198672 + 1198673)(13)




(14)







Ncut (119860 119861) = cut (119860 119861)asso (119860 119881) + cut (119860 119861)

asso (119861119881) (15)




(16)



asso (1198672 1198671 + 1198672)+ cut (1198671 + 1198672 1198673)asso (1198671 + 1198672 1198671 + 1198672 + 1198673)




(17)





4 Experiments




Start




or not


End

Y

N





YN












(a) (b) (c) (d) (e) (f)


H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)






sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)




(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018













14

12

10

8

6

4

2

0

func

tion

valu

e


0 200 400 600 800 1000

Iteration






119908 (119906 V) = 1


(5)







1198671 = 1199051minus1⋃119896=0

1198811198961198672 = 1199052⋃

119896=1199051

119881119896∙ ∙ ∙

119867119899 = 255⋃119896=119905119899

119881119896119896 isin 119871

(6)



119908 (119906 V) = sum119906isin1198671

[ sumVisin1198672

119908 (119906 V)]

= 1199051sum119894=0

sum119906isin119881119894

[[1199052sum119895=1199051+1


119908 (119906 V)]]= 1199051sum119894=0

1199052sum119895=1199051+1

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]]

(7)



119908 (119906 V)

= 1199051sum119894=0

1199051sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](8)

In the same way


119908 (119906 V)

= 1199052sum119894=1199051

1199052sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](9)




119908 (119906 V) (10)

0 5 10 15 20 25 300

1

2

3

4

5


dt = 125 dx = 14 X (u)-X()2 = 1

dt = 125 dx = 14 X (u)-X()2 = 2

dt = 125 dx = 14 X (u)-X()2 = 3

dt = 125 dx = 14 X (u)-X()2 = 4

dt = 125 dx = 14 X (u)-X()2 = 5

F (u)-F ()2

w(u

)



cut (1198671 1198672) = 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) (11)

Similarly

cut (1198671 1198673) = 1199051sum119894=0

1199053sum119895=1199052

cut (119881119894 119881119895) (12)


cut (11986711198672) + cut (11986711198673)= 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) + 1199051sum119894=0

1199053sum119895=1199052+1

cut (119881119894 119881119895)

= 1199051sum119894=0

1199053sum119895=1199051+1

cut (119881119894 119881119895) = cut (1198671 1198672 + 1198673)(13)




(14)







Ncut (119860 119861) = cut (119860 119861)asso (119860 119881) + cut (119860 119861)

asso (119861119881) (15)




(16)



asso (1198672 1198671 + 1198672)+ cut (1198671 + 1198672 1198673)asso (1198671 + 1198672 1198671 + 1198672 + 1198673)




(17)





4 Experiments




Start




or not


End

Y

N





YN












(a) (b) (c) (d) (e) (f)


H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)






sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)




(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018










1198671 = 1199051minus1⋃119896=0

1198811198961198672 = 1199052⋃

119896=1199051

119881119896∙ ∙ ∙

119867119899 = 255⋃119896=119905119899

119881119896119896 isin 119871

(6)



119908 (119906 V) = sum119906isin1198671

[ sumVisin1198672

119908 (119906 V)]

= 1199051sum119894=0

sum119906isin119881119894

[[1199052sum119895=1199051+1


119908 (119906 V)]]= 1199051sum119894=0

1199052sum119895=1199051+1

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]]

(7)



119908 (119906 V)

= 1199051sum119894=0

1199051sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](8)

In the same way


119908 (119906 V)

= 1199052sum119894=1199051

1199052sum119895=119894

[[

sum119906isin119881119894Visin119881119895

119908 (119906 V)]](9)




119908 (119906 V) (10)

0 5 10 15 20 25 300

1

2

3

4

5


dt = 125 dx = 14 X (u)-X()2 = 1

dt = 125 dx = 14 X (u)-X()2 = 2

dt = 125 dx = 14 X (u)-X()2 = 3

dt = 125 dx = 14 X (u)-X()2 = 4

dt = 125 dx = 14 X (u)-X()2 = 5

F (u)-F ()2

w(u

)



cut (1198671 1198672) = 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) (11)

Similarly

cut (1198671 1198673) = 1199051sum119894=0

1199053sum119895=1199052

cut (119881119894 119881119895) (12)


cut (11986711198672) + cut (11986711198673)= 1199051sum119894=0

1199052sum119895=1199051+1

cut (119881119894 119881119895) + 1199051sum119894=0

1199053sum119895=1199052+1

cut (119881119894 119881119895)

= 1199051sum119894=0

1199053sum119895=1199051+1

cut (119881119894 119881119895) = cut (1198671 1198672 + 1198673)(13)




(14)







Ncut (119860 119861) = cut (119860 119861)asso (119860 119881) + cut (119860 119861)

asso (119861119881) (15)




(16)



asso (1198672 1198671 + 1198672)+ cut (1198671 + 1198672 1198673)asso (1198671 + 1198672 1198671 + 1198672 + 1198673)




(17)





4 Experiments




Start




or not


End

Y

N





YN












(a) (b) (c) (d) (e) (f)


H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)






sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)




(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018













Ncut (119860 119861) = cut (119860 119861)asso (119860 119881) + cut (119860 119861)

asso (119861119881) (15)




(16)



asso (1198672 1198671 + 1198672)+ cut (1198671 + 1198672 1198673)asso (1198671 + 1198672 1198671 + 1198672 + 1198673)




(17)





4 Experiments




Start




or not


End

Y

N





YN












(a) (b) (c) (d) (e) (f)


H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)






sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)




(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









Start




or not


End

Y

N





YN












(a) (b) (c) (d) (e) (f)


H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)






sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)




(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)


H = minus119872sum119894=119900

119901 (119896) log2119901 (119896) (19)






sum0le119895lt119872

(119891119894119895 minus 1198911198941198951015840)2 (20)




(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)




LENA(512times512)

2 121 118 120 121 1193 78146 80150 80150 80150 771454 58108160 60109160 60109160 60109160 561061595 60105144180 56100144182 56100144182 56100144182 74112144179


2 128 128 130 129 1263 70140 74146 74146 74146 671344 61115164 61112164 72135193 61112164 611171655 55104150194 57104148194 58105148194 57104148194 4685125168

BIRD(256times256)

2 105 108 106 109 1043 70125 71138 71138 71138 681244 67128177 70129177 70129177 70130177 651161595 5596139177 5196139177 5194138177 5196140177 5896131163

CAMERA(256times256)

2 76 75 76 77 763 71150 128193 128193 128193 691434 58120156 44104193 44104193 44104193 581181555 4095146195 4497146197 4497146197 4497146197 4194139169


2 115 113 116 115 1143 92158 90157 90157 90157 931604 80126178 79132178 79132178 79132178 821251785 70108150192 67108151191 66107151191 65104144186 69102137185


(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)





(21)





SSIM (119868119874 119868119878) = SSIM (119868119878 119868119874)= (2120583119868119874120583119868119878 + 1198881) (2120590119868119874120590119868119878 + 1198882)

(1205832119868119874 + 1205832119868119878 + 1198881) (1205902119868119874

+ 1205902119868119878

+ 1198882)(22)


119868119878



(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)



(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c) (d) (e) (f)





4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018











4 121167201 117160196 119162203 123171204 1181642055 89141181230 84136179224 86137183239 91145183235 88139183226

89072 2 134 131 132 134 132(321times481) 3 104154 101152 99157 103159 105156

4 97137181 91132180 92135183 94134184 931361865 84143175236 81137171232 79136172231 82135177239 80140172234

42049 2 88 84 85 86 85(481times321) 3 66165 62161 63162 64167 64163

4 41124221 42128218 45130215 39129224 421262255 4591161235 4093167228 4186158229 4896168231 4289159231

86016 2 95 91 92 91 93(481times321) 3 87121 83119 84116 82123 85125

4 82124152 81126151 84123147 79119143 811261515 71129152201 73132156205 69128153206 74131156206 76132149204

54082 2 73 71 72 72 73(321times481) 3 4887 4586 4689 4586 4788

4 3552121 3254125 3656124 3351118 32501245 5093130192 4889126188 4691135196 4796126190 4891128195

21077 2 102 104 105 103 103(481times321) 3 95130 91129 92134 94135 93133

4 84142216 81143219 82145214 80139215 821452195 80117143225 78114147227 77115141221 76115149220 78119141224

160068 2 119 116 117 117 118(481times321) 3 117169 112170 115172 120168 119171

4 82120158 80124160 79121162 78123159 801241605 90121150200 91125153204 92123154203 87118151197 88120154201

37073 2 86 84 85 84 86(481times321) 3 5491 5194 5295 5088 5189

4 56102162 54103165 52106159 5399159 571041655 5186147201 4984144199 5384150197 5189149204 5383145200

66053 2 75 72 73 73 74(481times321) 3 71148 70146 73145 69145 68146

4 62143186 61141189 59140185 60147188 601421895 60112177205 63115179201 61116174208 58114180201 61115179201

304074 2 136 134 135 135 136(321times481) 3 127173 124170 130171 129173 127173

4 115164199 114161201 113159197 111161195 1131682015 104153190229 105149187225 106151188226 103151190227 104156187228




5 Conclusion





LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018











LENA(512times512)

2 263 261 261 263 2623 448 439 439 439 4454 557 545 545 545 5515 622 605 605 605 614


2 284 284 283 283 2833 450 443 443 443 4464 555 553 551 553 5555 615 610 608 610 607

BIRD(256times256)

2 233 231 234 234 2333 362 362 362 362 3594 442 438 438 438 4415 481 478 477 478 475

CAMERA(256times256)

2 227 223 224 227 2263 385 381 381 381 3844 461 445 445 445 4605 469 468 468 468 469


2 316 318 315 315 3163 471 468 468 468 4704 570 562 562 562 5645 624 617 617 618 616

24077 2 287 285 284 285 287(481times321) 3 391 388 388 288 289

4 464 459 458 458 4615 512 504 505 505 509

89072 2 302 301 301 301 302(321times481) 3 436 433 434 433 434

4 523 520 521 521 5235 598 591 592 592 593

42049 2 219 218 217 217 218(481times321) 3 324 321 322 322 322

4 398 394 395 395 3965 445 439 438 439 441

86016 2 223 222 221 222 223(481times321) 3 341 339 338 338 340

4 412 408 408 409 4105 467 462 463 462 462

54082 2 235 234 234 234 235(321times481) 3 423 421 421 422 423

4 552 548 549 549 5515 631 625 624 625 628

21077 2 276 275 275 275 276(481times321) 3 363 361 362 362 362

4 432 428 429 428 4305 486 481 480 480 479

160068 2 231 230 231 230 230(481times321) 3 383 381 380 381 380

4 476 471 470 471 4725 556 549 551 549 550


Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









Table 3 Continued


4 495 493 492 491 4905 528 525 523 518 524

66053 2 316 315 314 315 315(481times321) 3 456 451 451 452 451

4 543 538 537 539 5395 619 612 613 612 614

304074 2 313 312 310 314 313(321times481) 3 409 407 406 408 409

4 476 470 471 473 4735 521 516 515 515 518



LENA(512times512)

2 1796 1797 1807 1803 18013 1721 1753 1767 1734 17304 1647 1676 1683 1661 16525 1567 1607 1618 1616 1589


2 1814 1816 1815 1814 18153 1741 1758 1760 1757 17524 1651 1668 1670 1666 16575 1611 1618 1621 1620 1614

BIRD(256times256)

2 1816 1817 1822 1817 18193 1763 1775 1773 1774 17714 1607 1616 1624 1621 16155 1526 1547 1541 1538 1532

CAMERA(256times256)

2 1806 1808 1807 1807 18063 1661 1673 1684 1676 16644 1604 1622 1622 1621 16105 1563 1574 1586 1581 1576


2 1770 1778 1780 1776 17723 1719 1727 1731 1729 17234 1678 1684 1686 1680 16785 1583 1603 1606 1601 1596

24077 2 1721 1724 1725 1721 1722(481times321) 3 1692 1705 1710 1696 1695

4 1682 1694 1699 1687 16855 1656 1663 1679 1666 1663

89072 2 1810 1811 1812 1810 1811(321times481) 3 1802 1800 1808 1801 1803

4 1734 1738 1743 1740 17345 1696 1712 1719 1717 1705

42049 2 1803 1809 1813 1811 1805(481times321) 3 1772 1779 1782 1776 1773

4 1672 1671 1672 1673 16735 1590 1592 1592 1593 1592


Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









Table 4 Continued


4 1721 1731 1731 1725 17225 1569 1581 1578 1583 1574

54082 2 1792 1795 1800 1800 1792(321times481) 3 1711 1714 1716 1714 1713

4 1533 1549 1567 1551 15335 1476 1480 1496 1489 1480

21077 2 1706 1717 1722 1712 1712(481times321) 3 1635 1653 1656 1648 1641

4 1612 1617 1622 1619 16125 1515 1521 1529 1522 1517

160068 2 1821 1823 1824 1824 1822(481times321) 3 1789 1795 1798 1996 1789

4 1661 1674 1679 1678 16715 1559 1562 1581 1565 1559

37073 2 1850 1853 1855 1853 1850(481times321) 3 1809 1816 1821 1812 1809

4 1627 1638 1648 1637 16275 1541 1581 1592 1570 1540

66053 2 1847 1850 1852 1850 1849(481times321) 3 1801 1807 1805 1806 1802

4 1689 1697 1713 1703 16945 1631 1642 1651 1646 1633

304074 2 1772 1774 1776 1773 1772(321times481) 3 1728 1735 1747 1731 1728

4 1630 1638 1646 1644 16355 1601 1604 1609 1604 1602



LENA(512times512)

2 2306 2304 2299 2301 23023 2360 2326 2319 2335 23374 2389 2365 2361 2372 23775 2410 2401 2395 2396 2411


2 2323 2295 2295 2296 22953 2367 2323 2322 2324 23264 2392 2369 2368 2370 23745 2417 2395 2394 2394 2397

BIRD(256times256)

2 2318 2294 2292 2294 22933 2357 2315 2316 2315 23174 2392 2396 2392 2394 23975 2415 2434 2437 2439 2443

CAMERA(256times256)

2 2301 2299 2299 2299 23003 2342 2366 2360 2365 23714 2375 2393 2393 2394 23995 2392 2419 2412 2415 2418


Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









Table 5 Continued



2 2266 2313 2312 2314 23163 2287 2338 2336 2337 23414 2308 2360 2359 2362 23635 2320 2403 2402 2404 2407

24077 2 2301 2340 2340 2342 2341(481times321) 3 2344 2350 2347 2354 2355

4 2375 2355 2353 2359 23605 2399 2371 2363 2370 2371

89072 2 2298 2297 2297 2298 2297(321times481) 3 2334 2303 2299 2302 2301

4 2357 2333 2330 2332 23355 2367 2346 2343 2344 2350

42049 2 2390 2298 2296 2297 2300(481times321) 3 2434 2313 2311 2314 2316

4 2446 2367 2367 2366 23665 2458 2409 2409 2409 2409

86016 2 2268 2303 2302 2303 2302(481times321) 3 2302 2324 2323 2324 2329

4 2333 2336 2336 2340 23415 2348 2415 2417 2414 2419

54082 2 2323 2305 2303 2303 2306(321times481) 3 2342 2345 2344 2345 2346

4 2358 2433 2423 2432 24425 2365 2473 2463 2467 2473

21077 2 2277 2344 2341 2346 2346(481times321) 3 2301 2377 2375 2379 2383

4 2324 2396 2393 2395 23985 2332 2449 2444 2448 2451

160068 2 2274 2292 2291 2291 2292(481times321) 3 2308 2305 2304 2213 2308

4 2330 2366 2363 2363 23675 2337 2426 2415 2424 2427

37073 2 2341 2277 2276 2277 2279(481times321) 3 2368 2295 2292 2297 2298

4 2382 2384 2379 2385 23905 2387 2415 2409 2421 2438

66053 2 2267 2279 2278 2279 2279(481times321) 3 2299 2299 2300 2300 2302

4 2325 2354 2346 2351 23555 2328 2382 2378 2380 2387

304074 2 2297 2315 2314 2316 2316(321times481) 3 2315 2334 2328 2336 2338

4 2330 2384 2380 2381 23865 2335 2403 2400 2403 2404




LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018











LENA(512times512)

2 056 054 055 054 0553 074 072 073 072 0744 081 078 079 078 0805 090 087 088 087 089


2 063 061 061 062 0633 078 075 075 077 0784 085 082 082 083 0845 094 090 091 092 093

BIRD(256times256)

2 057 056 055 056 0573 068 066 065 066 0684 087 084 083 085 0865 091 088 087 089 090

CAMERA(256times256)

2 071 069 070 069 0703 081 077 078 077 0794 094 091 092 091 0935 097 094 093 094 096


2 055 054 054 053 0553 078 076 076 075 0774 085 083 084 082 0845 091 088 089 088 090

24077 2 079 079 078 078 078(481times321) 3 084 083 083 084 082

4 088 086 086 085 0865 094 093 093 092 093

89072 2 062 062 062 062 062(321times481) 3 076 075 074 075 074

4 082 081 080 081 0825 088 087 086 087 087

42049 2 076 075 076 076 076(481times321) 3 083 082 081 082 083

4 092 092 091 092 0925 097 095 096 096 097

86016 2 054 054 054 054 054(481times321) 3 066 065 064 064 066

4 073 073 071 071 0735 092 090 091 090 089

54082 2 032 031 031 031 030(321times481) 3 038 037 037 037 036

4 060 059 059 058 0565 092 091 091 091 090

21077 2 048 048 048 047 047(481times321) 3 073 072 071 071 071

4 089 088 088 087 0875 093 092 092 091 091

160068 2 061 060 059 059 060(481times321) 3 067 065 064 064 064

4 072 069 069 069 0685 077 074 073 073 073


Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









Table 6 Continued


4 082 080 080 080 0815 089 087 087 087 088

66053 2 047 044 044 044 045(481times321) 3 079 077 077 077 078

4 084 082 082 081 0835 088 086 086 085 087

304074 2 055 054 055 054 054(321times481) 3 069 065 066 065 066

4 078 075 077 076 0775 086 082 083 082 082



LENA(512times512)

2 138 168 154 162 1493 239 268 257 264 2514 3094 3478 3314 3357 31895 20439 24138 23425 23814 22464


2 146 182 167 174 1543 279 312 297 304 2844 3164 3578 3379 3451 32595 24241 28412 27125 27949 26141

BIRD(256times256)

2 112 143 137 141 1243 198 224 214 219 2074 1864 2174 2091 2142 19755 13425 15224 14598 14862 14091

CAMERA(256times256)

2 119 149 141 145 1263 214 238 227 231 2214 2856 3285 3171 3224 29835 18425 21739 20795 21124 19927


2 142 178 163 170 1493 246 298 261 289 2614 3425 3941 3781 3845 35785 22135 25147 23718 24691 23043

24077 2 151 183 169 177 159(481times321) 3 243 290 273 279 263

4 2943 3412 3143 3264 30575 17689 19319 18627 18257 17995

89072 2 146 181 164 176 155(321times481) 3 241 284 269 276 261

4 2967 3412 3149 3268 30415 16684 18396 17666 17991 17309

42049 2 125 153 142 147 135(481times321) 3 216 247 231 238 223

4 2314 2706 2542 2671 24585 15412 16822 16259 16436 15871


Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018









Table 7 Continued


4 2516 2945 2764 2885 26745 15954 17621 16766 17165 16439

54082 2 141 176 161 168 152(321times481) 3 234 279 263 270 252

4 2862 3255 3006 3143 29595 16459 18064 17401 17739 17042

21077 2 155 189 171 183 162(481times321) 3 249 299 276 283 269

4 3009 3507 3216 3318 31555 16746 18503 17814 18267 17324

160068 2 149 179 163 172 154(481times321) 3 238 281 266 272 258

4 2914 3345 3094 3209 30175 16601 18273 17610 17893 17223

37073 2 139 171 158 164 144(481times321) 3 236 280 261 273 255

4 2904 3301 3058 3191 29915 16504 18236 17510 17827 17134

66053 2 158 193 176 188 165(481times321) 3 253 308 281 292 275

4 3059 3589 3277 3381 31985 19847 22755 21113 22134 20623

304074 2 162 203 182 196 274(321times481) 3 261 318 293 306 282

4 3318 3869 3518 3687 34185 23164 26431 25234 24923 24017


Data Availability




Acknowledgments





References





















































Journal of












Journal of







Volume 2018






Volume 2018

























































Journal of












Journal of







Volume 2018






Volume 2018








An Improved Multithreshold Segmentation Algorithm Based on...

Documents

Transcript of An Improved Multithreshold Segmentation Algorithm Based on...