An Improved Multithreshold Segmentation Algorithm Based on ...downloads.hindawi.com/journals/mpe/2019/3514258.pdf · ResearchArticle An Improved Multithreshold Segmentation Algorithm
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
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
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
4 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 5
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
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
Similarly in order to overcome the problem of isolatedpoints in segmentation Normalized Cuts (Ncut) is adopted
6 Mathematical Problems in Engineering
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
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
Mathematical Problems in Engineering 7
Start
Calculate the edge weight between pixels with the new constructed function
Generate segmentation threshold randomly
Meettermination conditions
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
The employed bees remember the location of the food sources
The employed bees become scout bees and search near the original food sources
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
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
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
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
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
4 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 5
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
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
Similarly in order to overcome the problem of isolatedpoints in segmentation Normalized Cuts (Ncut) is adopted
6 Mathematical Problems in Engineering
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
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
Mathematical Problems in Engineering 7
Start
Calculate the edge weight between pixels with the new constructed function
Generate segmentation threshold randomly
Meettermination conditions
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
The employed bees remember the location of the food sources
The employed bees become scout bees and search near the original food sources
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
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
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
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
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
4 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 5
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
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
Similarly in order to overcome the problem of isolatedpoints in segmentation Normalized Cuts (Ncut) is adopted
6 Mathematical Problems in Engineering
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
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
Mathematical Problems in Engineering 7
Start
Calculate the edge weight between pixels with the new constructed function
Generate segmentation threshold randomly
Meettermination conditions
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
The employed bees remember the location of the food sources
The employed bees become scout bees and search near the original food sources
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
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
4 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 5
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
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
Similarly in order to overcome the problem of isolatedpoints in segmentation Normalized Cuts (Ncut) is adopted
6 Mathematical Problems in Engineering
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
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
Mathematical Problems in Engineering 7
Start
Calculate the edge weight between pixels with the new constructed function
Generate segmentation threshold randomly
Meettermination conditions
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
The employed bees remember the location of the food sources
The employed bees become scout bees and search near the original food sources
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
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 5
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
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
Similarly in order to overcome the problem of isolatedpoints in segmentation Normalized Cuts (Ncut) is adopted
6 Mathematical Problems in Engineering
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
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
Mathematical Problems in Engineering 7
Start
Calculate the edge weight between pixels with the new constructed function
Generate segmentation threshold randomly
Meettermination conditions
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
The employed bees remember the location of the food sources
The employed bees become scout bees and search near the original food sources
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
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
6 Mathematical Problems in Engineering
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
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
Mathematical Problems in Engineering 7
Start
Calculate the edge weight between pixels with the new constructed function
Generate segmentation threshold randomly
Meettermination conditions
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
The employed bees remember the location of the food sources
The employed bees become scout bees and search near the original food sources
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
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 7
Start
Calculate the edge weight between pixels with the new constructed function
Generate segmentation threshold randomly
Meettermination conditions
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
The employed bees remember the location of the food sources
The employed bees become scout bees and search near the original food sources
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
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
8 Mathematical Problems in Engineering
(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
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 9
(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
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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
10 Mathematical Problems in Engineering
(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
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
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 11
(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
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
12 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 9 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
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 13
(a) (b) (c) (d) (e) (f)
Figure 10 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
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
14 Mathematical Problems in Engineering
(a) (b) (c) (d) (e) (f)
Figure 11 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
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 15
(a) (b) (c) (d) (e) (f)
Figure 12 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
16 Mathematical Problems in Engineering
Table 2 Specific segmentation thresholds of different algorithms
Image ID level Our algorithm BA MMSA IBA OTSU24077 2 141 136 138 142 145(481times321) 3 135186 131190 133181 129184 134181
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Mathematical Problems in Engineering 17
Table 3 The Information Entropy (IE) of different segmented images using various algorithm
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
24 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 25
[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
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
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Mathematical Problems in Engineering 25
[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