Biomedical Signal Processing and Control

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Biomedical Signal Processing and Control

j ou rn a l h o m e pa g e :w w w . e l s e v i e r . c o m / l o c a t e / b s p c

A study about evolutionary and non-evolutionary segmentation techniques on hand radiographs for bone age assessment

Shreyas Simu, Shyam Lal

^∗

DepartmentofElectronics&CommunicationEngineering,NationalInstituteofTechnologyKarnataka,Surathkal,Mangaluru-575025,India

a r t i c l e i n f o

Articlehistory:

Received4June2016

Receivedinrevisedform22October2016 Accepted16November2016

Keywords:

Handbonesegmentation Boneageassessment Evolutionaryalgorithms Non-evolutionaryalgorithms

a b s t r a c t

Inthispaper,astudyandperformancecomparisonofvariousevolutionaryandnon-evolutionaryseg- mentationtechniquesondigitalhandradiographsforboneageassessmentispresented.Thesegmented handbonesareofvitalimportanceinprocessofautomatedboneageassessment(ABAA).Boneage assessmentisatechniqueofcheckingtheskeletaldevelopmentanddetectinggrowthdisorderinaper- son.However,itisverydifficulttosegmentoutthebonefromthesofttissue.Theproblemarisesfrom overlappingpixelintensitiesbetweenboneregionandsofttissueregionandalsobetweensofttissue regionandbackground.Thusthereisarequirementforarobustsegmentationtechniqueforhandbone segmentation.Takingthisintoconsiderationwemakeacomparisonbetweennon-evolutionaryand evolutionarysegmentationalgorithmsimplementedonhandradiographstorecognizebonebordersand shapes.Thesimulationandexperimentalresultsdemonstratethatmultiplicativeintrinsiccomponent optimization(MICO)algorithmprovidesbetterresultsascomparedtootherexistingevolutionaryand non-evolutionaryalgorithms.

©2016ElsevierLtd.Allrightsreserved.

1. Introduction

Boneageassessment(BAA)isoneofthemostimportantpro- ceduresfortheevaluationofbiologicalmaturityofchildrenwhose ageisunknown.Alsodefinedasaclinicalmethodforevaluating thestageofskeletalmaturationofachild,henceitisalsocalled asskeletalageassessment.Skeletalmaturitygivesthemeasureof developmentofaboneincorporatingitsshape,sizeanddegreeof mineralization[1].Boneageassessmentisusedtodeterminethe differencebetweenskeletalboneageandthechronologicalage.In normalconditions,theboneageshouldbeapproximately10%of chronologicalage[1].Thedifferencebetweentwoages,i.e.bone ageandchronologicalage,showsthatthereareabnormalitiesin theskeletalgrowthofchildrenorthereisahormonalimbalance.

Themostimportantmethodsfortheestimationofagebased onradiologicalanalysiswere definedby Greulichand Pyle (GP method)[2]andTannerandWhitehouse(TW1method)[3]respec- tively.GPmethodisanatlasmatchingmethod,andisstillthemost commonlyusedtechnique,becausethemethodisveryeasyand lesstimeconsuming.TheTW1methodismoreflexibleandhas beenderivedfromasolidmathematicalbase.TheTW1methodhas

∗Correspondingauthor.

E-mailaddresses:shreyas.simu@gmail.com(S.Simu),shyam.mtec@gmail.com (S.Lal).

beenmodifiedthroughouttheyears,evolvingtoTW3method[4].

Theonlydifferencemadewascalibratingthescoringmethodon NorthAmericanandEuropeanchildren.InTW3methodeachbone inregionofinterestisgivenascore.Anoverallscoreofallthese bonesiscalculated.Overallscoreindicatestoaparticularboneage asmentionedinthetablesandgraphsofTW3method.Theprocess iscomplex,soitisseldomused,yetitsmodularstructuremakesit suitableforautomation.Theagesthatcanbepredictedusingthese methodsisintherangeof0–18years,asaftertheageof18years thebonesarecompletelymaturedandfusioniscomplete.

Whenthehandradiographsaretobeprocesseddigitally,one oftheproblemsthat occuris non-uniformcontrastvariation of thebackground.Thisisanintrinsiceffectintheprocessofdig- italacquisitionofradiograph. Itposes amajor challengetothe segmentationalgorithmalongwiththeproblemofpixelintensity overlappingbetweenboneandsofttissueregion.Variousmethods havebeendesigned toremovethebackgroundofradiographas pre-processing[5,6].Themostchallengingpartisremovalofsoft tissueregion.Inordertosolvetheproblem,imagesegmentation techniquesarerequired.Imagesegmentationtechniquescanbe classifiedinto,thresholding,clustering,edge-based,region-based, deformablemodelsandhybridtechniques.

Thresholdingistheoldestandfirstsegmentationtechnique,also themostwidelyappliedsegmentationtechnique.Itpresumesthat bothforegroundandbackgroundregionshavemutuallyexclusive rangeofpixelintensities.Segmentingthebonesfromsofttissue http://dx.doi.org/10.1016/j.bspc.2016.11.016

1746-8094/©2016ElsevierLtd.Allrightsreserved.

regioncanbeachievedbySobelgradient[5,7].Thismethodhas limitationsas thegradientimagecan’t befurtherusedforseg- mentation.Alsooverlappingofpixelsispresent intheresulting image.SimilarsegmentationtechniqueslikeDerivativeofGauss- ian(DoG)anddynamicthresholdinghavealsobeenimplemented onhandradiographs[8–10].Butthesetechniquesholdthesame problemsastheprevioustechnique.Otsuthresholdingwhichis basedonmaximizingtheinterclassvariancewasimplementedon handradiographs,butthemajorproblemwiththetechniquewas thatresultswerenotaccurate[11,12].

Clusteringisanunsupervisedlearningstrategythatgroupssim- ilarpatternsintoclusters.Mostpopularclusteringtechniqueused forsegmentationisk-meansclusteringtechniquewhereinthepix- elsareclassifiedintokclusters,basedondistancemeasuresuchas Euclideandistance.Clusteringprocessdependsuponoptimization ofanobjectivefunction,suchasminimizationofasquarederror function.Adaptiveclustering algorithmbased onk-meansclus- teringalongwithGibbsrandomfieldswasformulatedbyPappas [13].Thisclusteringtechniquewasimplementedonhandradio- graphsbymanyresearchers,buttheresultswereappallingasit wasnoteffectiveonslowlyvaryingtextures,[14–17].Thek-means clusteringalgorithmalongwithgray-levelco-occurrencematrix wasusedbyChaietal.forsegmentation[18].Thedrawbackswere thatnumberofgraylevelshadtobemanuallydecidedanditwas computationallyintensiveandtimeconsuming.

Edgesarepixelswhichgothroughasuddenchangeingraylevel intensity,alsoknownasdiscontinuities.Theseedgesareconnected intoaclosedboundaryandthepixelsinsidethisclosedbound- ary arecalled objects.Thistechnique isreferred as edge-based segmentation.Region-basedsegmentationtechniquessegmentan image by classifyingit into two sets of pixels, foreground and background.Thetheorybehindthistechniqueisthattheregion tobesegmentedhassimilarimagepropertiessuchasanalogous rangeofpixelintensities,textureandpattern[19].Regiongrow- ingand regionmerging techniquewasappliedby Manoset al.

onhandradiographs[20].Thistechniqueisinsensitivetoimage semanticsandisunabletoseparatemultipledisconnectedobjects simultaneously.

A class of techniques that generates an approximate model ofthetargetedobjectusingsomepriorinformation iscalledas deformablemodels.Thepriorinformationusedtocreateamodel canbeedgeinformation,shapeofanobjectorimagetexture.Three majorclassesofdeformablemodelsarisefromthetypeofprior informationused,theyareactivecontourmodel(edgeinformation) (ACM),activeshapemodel(shapeinformation)(ASM)andactive appearancemodel(imagetexture)(AAM)[21].Niemeijeretal.had segmentedmiddlephalanxofthethirdfingerusingASM[22].The datasetconsistedofimagesofagegroup9–17years.Otherauthors alsotriedusingASMandACMforsegmentation[23].Thodbergetal.

proposedacompleteBAAsystemcalledasBoneXpertmethod[24].

ThebonereconstructionisbasedonAAM.Howevertheagegroups 17–18and0–2wereomittedfromthedataset.Alsoradiusandulna boneswerepoorlyreconstructed.

Hybridtechniquesare basicallycombination oftwo ormore aforementioned techniques. Watershed algorithm is a classic exampleofhybridsegmentationtechnique.Itisbasedonthebasic conceptsthresholding,regiongrowingandedge detectiontech- niques.Hanetal.implementeditonhandradiographsbutithad limitationsduetosensitivitytowardsnoiseandheavydependence ongradientoftheimage[25].ParticleSwarmOptimizationwas usedalongwithedgedetectors[26]andalsowithgraph-basedseg- mentation[27].ThedrawbackofPSOisthatthesolutionsometimes getscorneredinalocaloptimum.Henceitmightworkwellinsome situationsbutmightfailinother.

Thispaperfocusesoncomparisonbetweenvariousevolutionary andnon-evolutionarysegmentationtechniquesondifferenthand

radiographs.Asoundcomparisonisdonebyperformingqualitative andquantitativeanalysisonhandradiographs,which waslack- ingintheliterature.Noveltyofpaperliesinwideandin-depth analysisdonebyapplyingvariousrobust,popularandwidelyused segmentationtechniquesonhandradiographs.

Thepaperisorganizedasfollows:Section2discussesthevar- iousnon-evolutionaryandevolutionarysegmentationtechniques.

Abriefdiscussionaboutmethodshasbeendone.InSection3we describethematerialsandmethods.InSection4wediscussthe resultsand compare thesegmentation resultsof differentevo- lutionary and non-evolutionary segmentation techniques using standardqualitymetrics.FinallyweconcludetheworkinSection5.

2. Segmentationtechniques

The hand radiograph can be divided into 3 distinct regions namely, background, soft tissue region and the bones. Since composition of radiograph is made of these regions, evaluat- ingsegmentationtechniqueslikethresholdingandclusteringfor extractionofbonesontheradiographisjustified.Therehavebeen severaltechniquesdevisedforsegmentation ofimage basedon multi-level thresholding. We have covered some of the popu- larthresholdingtechniquesnamely,Otsu’sthresholding[11]and Tsallisentropybasedthresholding[28].Othersegmentationtech- niquescoveredinthispaperinclude,adaptiveclusteringalgorithm based on k-meansclustering with Gibbs random fields (KGRF) [13], adaptively regularized kernel-based fuzzy C-means clus- tering (ARKFCM)[29],k-meansclusteringusingGLCM[18] and bi-convexfuzzyvariationalimagesegmentationmethod[30].The previous mentioned segmentation techniques can be classified asnon-evolutionarysegmentationtechniques.Whereasoptimiza- tion techniques usedfor multi-level thresholding are classified asevolutionarysegmentationtechniques,suchasParticleSwarm Optimization(PSO)[31] andDarwinianPSO(DPSO)[32].Multi- plicativeintrinsiccomponentoptimization(MICO)technique[33]

wasrecentlydevelopedforMRIimagesegmentationhasbeenalso explored.MICOisbasedonestimatingthebiasfieldandsimulta- neouslysegmentingtherequiredregions.

2.1. Non-evolutionarysegmentationtechniques

2.1.1. SegmentationbasedonOtsu’sthresholdingmethod

ThresholdingusingOtsu’smethod,wetrytofindathreshold valuethatminimizestheintraclassvariance_w²(t_h)givenbythe weightedsumofvariancesofthetwoclasses[11]:

_w²(t_h)=ω₁(t_h)²₁(t_h)+ω₂(t)₂²(t) (1) whereω_i(t_h)areprobabilitiesoftwoclassesseparatedbythresh- oldt_h.Otsuhasshownthatminimizingtheintraclassvarianceis equivalenttomaximizingtheinter-classvariance_b²(t_h):

_b²(t_h)=²(t)−_w²(t_h)=ω₁(t_h)ω₂(t_h)[₁(t_h)−₂(t_h)]² (2) whichisgivenintermsofclassprobabilityω_i(t_h)andclassmean _i(t_h).Theclassprobabilityω_i(t)iscalculatedfromhistogram:

ω₁(t_h)=

t_h−1

i=0

p(i) (3)

ω₂(t_h)=

L−1 i=t_h

p(i) (4)

whiletheclassmeanare:

₁(t_h)=

t_h−1

i=0

p(i)x(i) (5)

₂(t_h)=

L−1 th

p(i)x(i) (6)

x(i)isthevalueatcenteroftheithhistogramandListhenumber oflevelsinanimage.

Thisalgorithmassumesthatimagescontaintwoclassesofpix- elsresultinginbimodalhistogram(foregroundandbackground).It calculatestheoptimumthresholdwhichseparatesthetwoclasses sothatthecombinedspreadisminimal.Theextensionofthisis multi-levelthresholdingcalledasmulti-Otsu[11].

Algorithm1. AlgorithmforsegmentationusingOtsu’sthreshold- ingmethod

Step1 Calculatethehistogramandprobabilitiesateachinten- sitylevelfrom0toL-1.

Step2 Initializeω_i(0)and_i(0).

Step3 Iteratethroughallthresholdvaluesfromt=1tomaxi- mumintensityvalue.

Step4 Compute_b²(t_h).

Step5 Requiredthresholdvaluecorrespondstothemaximum valueof_b²(t_h).

2.1.2. SegmentationbasedonTsallisentropy

deAlbuquerqueetal.proposedasegmentationtechniquebased onTsallisentropy[28].Consideranimagewithlgraylevels.The probabilitydistributionofthelevelsisgivenbyp_i=p1,p2,...,p_l. Wedividethisdistributionintotwoprobabilitydistributions,one forforegroundandanotherforbackground[28].Theprobability distributionsoftheforegroundandbackgroundclasses,calledA andBrespectively,aregivenby:

p_A= p₁ P^A,p₂

P^A,...,pt_h

P^A and p_B= p_th+1 P^B ,p_th+2

P^B ,...,p_l

P^B (7)

whereP^A=

t_h

i=1p(i)andP^B=

l

i=th+1p(i).

ForeachdistributiontheaprioriTsallisentropyisdefinedas:

E_x^A(t_h)= 1−

t_h

i=1(p_i/p^A)^x

x−1 and E^B_x(t_h)= 1−

l

i=th+1(p_i/p^B)^x x−1

(8) Theentropicindexxdistinguishesthedegreeofnonextensivity.

TsallisentropyEx(t_h)reliesonthethresholdvaluet_hforthedivision intoforegroundandbackgroundregions[28].Itisgeneralizedas thesumofeachentropy:

Ex(t_h)= 1−

th i=1(p_A)^x

x−1 +1−

l

i=t_h+1(pB)^x x−1 +(1−x).1−

t_h

i=1(p_A)^x x−1 .1−

l

i=t_h+1(pB)^x

x−1 (9)

WhenEx(t_h)ismaximized,thevalueoft_hisconsideredtobethe optimumthresholdvalue.Thiscanbeachievedbyoptimizingthe objectivefunction[28]:

t_hopt=argmax[E^A_x(t_h)+E^B_x(t_h)+(1−x).E_x^A(t_h).E^B_x(t_h)] (10) Theaboveprocesscanbeeasilyextendedtomulti-levelthreshold- ing.

Algorithm2. AlgorithmforsegmentationusingTsallisentropy Step1 Dividetheimageintoforeground andbackgroundand

calculatethe probability distributionof each intensity levelgivenbyEq.(7).

Step2 CalculatetheTsallisentropyforeachregionusingEq.(8).

Step3 MaximizetheobjectivefunctiongiveninEq.(10).

Step4 Iteratethroughallthresholdvaluesfromt_h=1tomaxi- mumintensityvalue.

2.1.3. Segmentationusingadaptiveclusteringalgorithmbasedon k-meansclusteringwithGibbsrandomfields

Thissegmentationalgorithmconsistsoftwostages.Firststageis clusteringusingthek-meansalgorithmandsecondstageisusing Gibbsrandomfieldsforestimationoftheintensityfunctionseg- mentation.

Thek-meansalgorithmusestheEuclideandistancesbetween samplesandclustercentersctocalculatethesimilarity.Eachpixel ocanbeidentifiedbythreevalues,it’simagecoordinatesandthe graylevel intensityvalue.Using this algorithmthesamplesare clubbedtogetherintoapredefinednumberofclassesn.Thisclas- sificationiscompletelybasedontheminimization ofdifference betweensampleandclustercenters[19].

Inthesecondstageweassigntheimagepixelstooneofthe classesbasedontheirintensityandrelativelocation.Lettheinten- sityofpixelolocatedatibedenotedasoi.Wedenotesegmentation ofimageintoclassesbyx,wherex_i=z,zisoneoftheclassamongn numberofclasses.Weassumethateveryclassisaslowlyvarying intensityfunction.Gibbsrandommodelfieldsareusedforspatial informationwhichdescribethelocaldistributionofgraylevels.The probabilitydensityfunctionisnowdefinedas:

p(x_i|g,xq for all q=/i)=p(x_i|g_i,xq,q∈W_i)∝exp

×

− 1

2²[g_i−^(x_iⁱ⁾]²−˙_xi∈CV_C(x)

(11) whereqisthecliquepixel,_iisagraylevelofintensityfunctionfor eachclassx_i,g_iisthepixelgraylevelvalue,²inthenoisevariance, Wiisawindowsizearoundpixeli,VCisacliquepotentialinGibbs model.

Theintensitiesvaluesareupdatedcontinuouslybyaveraging graylevelvaluesofpixelsbelongingtotheconsideredclassesin theslidingwindowwhosesizeisdecreasedineveryiteration.The algorithm maximizesthis probabilitydensity functionand esti- matestheintensityfunctions,interchangeably. Amore detailed descriptionofthissegmentationalgorithmcanbefoundin[13,14].

Thetwo-pointandone-pointcliquepotentialsaredefinedas:

VC ={−,x_i=xq i,q∈C} or VC={+,x_i=/xq i,q∈C} (12) whereCisthesummationofallcliquevaluesinthatregion.The valuecliquepotentialissetto0.5.Anegativevalueofsaysthat twopixelsdonotbelongtosameclass[13].

Algorithm3. ClusteringalgorithmbasedonKGRF Step1 Performk-meansclusteringonthegivenimage.

Step2 Initializethewindow sizeWto thesizeofimage and numberofiterationsmto1.

Step3 Estimatethevalueof_i.

Step4 Fromthenewvalueofi,performk-meanssegmenta- tion,m=m+1.

Step5 Repeatsteps3and4tillm=mmax.Whenvalueofm=mmax

reducethewindowsizeWandrepeatsteps3and4.

Step6 IfwindowsizeW=W_minterminatethealgorithm.

2.1.4. GLCMbasedadaptivecrossedreconstruction(ACR) k-meansclusteringforsegmentation

Chai et al. proposed segmentation using gray level co- occurrence matrix and k-means clustering algorithm [18]. The GLCMisusedfortextureanalysiswhichwasproposedbyHaral- ick[34].Inthismethodtheimageisfirstdividedintonumberof verticalandhorizontalbands.Unsupervisedk-meansclusteringis thenappliedwithk=2andk=3onthesub-image.Thecontrastand homogeneityvaluesoftheseimagesarefoundusingGLCM.Maxi- mumvalueofhomogeneityischeckedandthesub-imageswhich givehighestvaluesarethususedtoreconstructtheimage.

Algorithm4. GLCMbasedACRk-meansalgorithm

Step1 Divide the image into pre-defined number of vertical bands.

Step2 Dividetheresultingimagesintopre-definednumberof horizontalbands.

Step3 Performk-meansclusteringoneachsub-imagewithk=2 andk=3.

Step4 Performtextureanalysisonresultingsub-imagesusing GLCMdefinedbyHaralick[34].

Step5 Check the contrast and homogeneity values of these GLCMresults.

Step6 Useonlythoseimageswhichgivehighesthomogeneity valuesforreconstructionofimages.

2.1.5. Segmentationbasedonadaptivelyregularized kernel-basedfuzzyC-meansclustering(ARKFCM)algorithm

ThefuzzyC-means(FCM)algorithmfromwhichARKFCMhas beendesigned,assignsamembershipvaluetoeachpixelforall clustersintheimagespace[35].AssumeanimageIwithsetof grayscalevaluesx_iatpixeli(i=1,2,...,N),whereNistotalnumber ofpixels.X=x₁,x₂,...,x_Nink-dimensionalspaceandwithcluster centersd=d1,d2,...,dcwherecbeingapositiveinteger(2<cN), thereisamembershipvalueuijforeachpixeliinthejthcluster (j=1,2,...,c).TheobjectivefunctionoftheFCMalgorithmis[35]

OFCM=

N i=1

c j=1

u^q_ij||x_i−d_j||² (13)

whereqisaweightingexponenttothedegreeoffuzziness,i.e.q>1, and||x_i−d_j||²isthegray-scaleEuclideandistancebetweenpixeli andcenterd_j.TheFCMalgorithmisverysensitivetonoiseandthe accuracydecreasesinthepresenceofnoise.

Elazabetal.[29] haveintroducedanadaptive regularization parameter , to enhance segmentation robustness, also devise aweightedimage,andadopt theGaussian radialbasisfunction (GRBF)forbetteraccuracy.

Theobjectivefunctionisdefinedas:

O_ARKFCM=2

⎡

⎣

^N

i=1

c j=1

u^q_ij(1−K(x_i,d_j))+

c j=1

_iu^q_ij(1−K(x_i,d_j))

⎤

⎦

(14) wherexicanbeanaverage(ARKFCM-avg)ormedian(ARKFCM- med)filteredoraweighted(ARKFCM-wtd)image.Intheabove objectivefunction,aGRBFkernelKisusedinsteadofEuclidean distancemeasure:

||(x_i)−(d_j)||²=2(1−K(x_i,d_j)) (15)

whereKiskernelfunctionwithwidthω:

K(x_i,d_j)=exp

||x_i−d_j||² 2ω²

(16) Fordetailedmathematicalanalysisreferto[29].

Algorithm5. ARKFCMalgorithm

Step1 Initializeloopcountert=0,andothervariablesd,uand. Step2 Calculate x_i basedtype of filteringaverage, medianor

weightedimage.

Step3 Calculatetheclustercentersd_iusingequation:

d_j=

N

i=1u^q_ij(K(x_i,d_j)x_i+_iK(x_i,d_j)x_i)

N

i=1u^q_ij(K(x_i,d_j)+_iK(x_i,d_j)) (17) Step4 Calculatethemembershipfunctionu_ijusingequation:

u_ij= ((1−K(x_i,d_j)+_i(1−K(x_i,d_j)))^{−(1/(q−1))}

c

i=1((1−K(x_i,d_j)+_i(1−K(x_i,d_j)))^{−(1/(q−1))} (18) Step5 Ifmaximumnumberofiterationareoverthenstop,oth-

erwise,updatet=t+1andgotostep(3).

2.1.6. Segmentationbasedonbi-convexfuzzyvariational(BFV) imagesegmentationalgorithm:

This algorithm combines fuzzy logic with Chan–Vese (CV) model [36] to make a bi-convex objective function. CV model belongstotheclass ofpartialdifferentialequation(PDE)model equationsforsolvingimagesegmentationproblems.Therehave beenthreemajorproblemswithCVmodel,viz.(1)convergence to local optima, (2) highly dependent on parameter selection, and(3)computationallyexpensive.WhereasBFValgorithm[30]

efficiently combinesnumericalremedytechniques andlengthly penalty termstogivebetterresults. Thus reducing thecompu- tationalcostsandalsobringingalotofrobustnesstoparameter settings.

Thefuzzyenergyfunctionusedis:

E=w₁

R

u^m(I−b₁)²dx+w₂

R

(1−u)^m(I−b₂)²dx (19) whereuisthemembershipfunction,misaconstantpositiveinte- ger,w1,w2areweightsandb1,b2areaveragevaluesofgivenimage Iinsideandoutsidethecurve.

Algorithm6. Bi-convexfuzzyvariationalalgorithm

Step1Initializeb1,b2,andurandomlytocalculateg(r(|∇I|,S)):

g(x,S)=(S−S0)e^−x2+(1−(S−S0)) 1

1+x² (20) r(|∇I|,S)=(S−S0)|∇I|+(1−(S−S0))|G∗∇I| (21) whereSistheSNRoftestimage,(S)=(1/(1+e^−S)),Gisa Gaussiankernel.

Step2Calculateb₁andb₂usingequations:

b₁=

Ru^mIdx

Ru^mdx and b₁=

R(1−u)^mIdx

R(1−u)^mdx (22)

Step3Sett₁=0.Calculateu_n+1/2usingequation:

∂u

∂t =m(−w₁u^m−1(I−b₁)²+w₂(1−u)^m−1(I−b₂)²) (23) Ift₁+ t₁≤T₁thent₁=t₁+ t₁,uⁿ=u^n+1/2andmovetostep 2,elsecontinue.

Step4Calculateu_n+1usingequation:

un=u_n+1/2+ t2g(r(|∇^I|,S),S) u_n+1/2 (24)

Step5Ifu_n+1satisfiesstationaryconditionthenstop,otherwisego tostep2.

Therearetwo stationaryconditions, oneis predefined numberofiterationsandotherismax|u_n+1−u₁|≤εwhere εisanysmallpositiveconstant.

2.2. Evolutionarysegmentationtechniques 2.2.1. SegmentationbasedonPSOalgorithm

EberhartandKennedydevelopedParticleSwarmOptimization algorithminwhichthecontestantsolutionsareknownasparticles.

Ateverystep,a fitnessfunctionisevaluatedtofindtheparticle success[31].Eqs.(25)and(26)showhoweachparticleinavigates throughaspacebasedonthepositionx_iandvelocityvivalueswhich relyonlocalbest(lbest),andglobalbest(gbest)information.

ThePSOalgorithmevaluateseachparticleforthefitnessfunc- tion, which is defined as the inter-class variance given in Eq.

(1). The local and global best values are initialized with the random possible values. Population size and stopping criteria are the other two parameters which need tobe adjusted. The population size is very critical factor to optimize and achieve anoverall goodsolution.Basedontheproblem, stoppingcrite- ria can be a predefined number of iterations or any other criteria[37].

Algorithm7. AlgorithmforsegmentationbasedonPSO

Step1 Particlesarerandomlygeneratedbetweenthelimitsof thresholdvaluesforapopulationsizeP.

Step2 Objectivefunctionsoftheseparticlesarecalculated.

Fig.1. Testradiographsusedfromtheimagedatabase.

Step3 Thevaluesobtainedfrompreviousstepareusedtosetthe lbestandgbest.

Step4 Velocityiscomputedusingtheequation:

v(i+1)=v(i)+1∗r(i)∗(lbest(i)−x(i))

+₂∗r(i)∗(gbest(i)−x(i)) (25)

where1and2arelearningfactorsandr(i)isarandom numberbetween0and1.

Step5 Positionofeachparticleisupdatedusingtheequation:

x(i+1)=x(i)+v(i+1) (26)

Step6 Objectivefunctionsarecalculatedforupdatedvalues.If thenewvaluesisbetterthanthepreviousvaluethenitis setaslbestandgbestrespectively.

Step7 Repeattheaboveprocessuntilstoppingcriteriaissatis- fied.

2.2.2. SegmentationbasedonDPSOalgorithm

ThemajordrawbackofPSOtechniqueisthat,solutiongetscor- neredinalocaloptimum[37].TheconceptofDarwinianParticle Swarm Optimization(DPSO)wasexpressedbyTilletet al.[32].

AtagivenpointoftimeinDPSOmanyswarmsoftestsolutions exist.EachoftheswarmsbehavelikeanordinaryPSOalgorithm whichusesnaturalselection tobreakoutfromlocaloptima.Ifa searchgetstrappedinalocaloptimum,thesearchinthatregionis discardedandanotherregionissearched.InDPSO,ateverystep, swarmsthatimprovearerewardedandswarmswhichhinderare punished[32,37].Thestateofeachswarmandthefitnessofallpar- ticlesiscalculated.Theneighborhoodandindividualbestpositions ofeachparticleisalsoupdated.Anewparticleisspawnedonlyif anewglobalsolutionarises.Whereasaparticleisdeletedifthe swarmfailstoupdatetoabetterstateinapre-definednumberof iterations[32,37].

Algorithm8. AlgorithmforsegmentationbasedonDPSO Step1 Evolveeachswarminthegroup.

Fig.2.Segmentationresultsofdifferentalgorithmsonhandradiographtakenfrom2yearoldperson[5329.jpg].

Step2 Updateparticlefitnessandupdateparticlebestforeach particle.

Step3 Updatethevelocityvector.

Step4 Findobjectivevalues,checkthefitness,iffitnesscriteria notmet,deletetheparticle.

Step5 If the swarm gets better results, reward the swarm (extendswarmlife)ifnot,punishswarm(reduceswarm lifeordelete).Theconditionisgivenby:

s_min≤s≤smax (27)

wheres isswarm’spopulation, s_min and smax aretheminimum andmaximumswarmpopulationconsidered.Whenthe populationgoesbelows_minswarmisdeleted.

Step6 Spawneachswarminthecollection.

Step7 Deletefailedswarms.

2.2.3. Multiplicativeintrinsiccomponentoptimization(MICO) Lietal.[33]proposedanenergyminimizationmethodnamed asmultiplicativeintrinsiccomponentoptimization(MICO)forbias fieldestimationandsegmentationofMRimages.Thistechnique

essentiallydivides theimageinto2 multiplicativecomponents, whicharebiasfieldandthetrueimagealongwithadditivenoise.

M(x)=b(x)I(x)+n(x) (28)

Thebiasfieldissaidtobealinearcombinationofasetofsmooth basisfunctionsf₁,...,fm.biasfieldisestimatedbyfindingtheopti- malcoefficientsw₁,...,wm.

b(x)=w^TF(x) (29)

whereF(x)isacolumnvectorofbasisfunctionsf1,...,fm.assuming thatthereareNtypesofclassesintheimagedomainR.Eachclass isdefinedbyamembershipfunctionu(i).thetrueimagecanbe approximatedby:

I(x)=

N i=1

c_iu_i(x) (30)

wherec(i)areconstants.Thustheenergyminimizationformulation isgivenby,

E(b,I)=

R

|M(x)−b(x)I(x)|²dx (31)

Fig.3.Segmentationresultsofdifferentalgorithmsonhandradiographtakenfrom4yearoldperson[5121.jpg].

Theenergy functionE(b,I)canbearticulatedin termsof three variablesu,candw andoptimizationofband Icanbeaccom- plishedbyminimizingtheenergyfunctionwithrespecttothese threevariables:

Eq(u,c,w)=

R

N i=1

|M(x)−w^TF(x)c_i|²u^q_i(x)dx (32)

Toachievefuzzysegmentation(softsegmentation)resultsfuzzifier q≥1hasbeenintroduced.Forq>1thefuzzymembershipfunctions cantakevaluebetween0and1.Detailedmathematicalanalysisof energyminimizationfunctioncanbereadin[33].

ToachieveenergyminimizationweneedtominimizeEq(u,c,w) withrespecttoeachvariablekeepingothertwofixed.

Algorithm 9. Multiplicative intrinsic component optimization algorithm

Step1 MinimizeEwithrespecttow,initializecandu.

Step2 Updatethevalueofbaccordingtoequation:

b(x)ˆ =wˆ^TF(x) (33)

Step3 Updatethevalueofcaccordingtotheequation:

ˆ c_i=

RM(x)b(x)u^q_i(x)dx

Rb²(x)u^q_i(c) (34)

Step4 Updatethevalueofuaccordingtotheequation:

ˆ

u_i(x)= (|M(x)−w^TF(x)c_i|²)^1/(1−q)

N

j=1(|M(x)−w^TF(x)c_j|²)^1/(1−q)

(35)

Step5 Checkifconvergencehasbeenreachedorthenumberof iterationshaveexceeded,stoptheiterationorelsegoto step2.

3. Materialsandmethods

3.1. Imagedatabase

Thedatabaseusedwasacquiredfromonlinewebsite,http://

www.ipilab.org/BAAweb/.Theimagesonthiswebsitehavebeen collected from Children’s Hospital Los Angeles (CHLA), United States of America. The manual segmentation or ground truth imageswereconstructedwiththehelpoforthopediciansfromGoa MedicalCollege(GMC),Bambolim,Goa,India.

Inthispaper,wehavepresentedresultsof9imagestakenfrom thedatabaseofAsianmaleimagesfromthewebsitementioned previously.Eachimageselectedhasagegapof2yearsbetween theagerangeof2–18years.TheTW3method[4]estimatesbone ageuptotheageof18yearsasafterthatagethebonesofhand arecompletelymaturedandtherearenosignificantchangesinthe shapeandstructurethatcanbetracked.

Fig.4.Segmentationresultsofdifferentalgorithmsonhandradiographtakenfrom6yearoldperson[5072.jpg].

3.2. Segmentationandanalysisprocedure

Thesegmentationofbonesfromhandradiographsandresult analysisinvolves4simplesteps.

1ThehandradiographofaparticularageisreadinMATLABscript.

2Anisotropicdiffusionisperformedontheradiographimageas pre-processingstep.

3Segmentationtechniquesdiscussedintheprevioussectionare thenappliedonebyone.

4Segmented imageand ground truth imageis then compared usingvariousimagequalitymetrics.

Beforesegmentationofthebonesweapplyanisotropicdiffusion.

Perona and Malik [38] introduced anisotropic diffusion, which is also called as non-linear anisotropic diffusion. Unlike other isotropicdiffusionalgorithmsusedfornoiseremoval,anisotropic diffusionalgorithmpreservestheedgeswhilediffusingthenoise.

Itwillsmoothentheimagewheregradientis lessandpreserve thehighgradientregionoredges.This pre-processingstep not onlyhelpsinnoiseremovalbutalsomakessegmentationofbones easier.

3.3. Quantitativeperformancemetrics

Thesegmentation resultshavebeenevaluated usingvarious performancemetricslikePSNR andMSE [19],Jaccardsimilarity index(JSI),structuresimilarityindex(SSIM),dicesimilarityand accuracy[39].Thecomputationalcostintermsoftimetakenby CPUforexecutionofeachsegmentationtechniquehasalsobeen calculated.

ThemathematicalexpressionforPSNRis:

PSNR (dB)=10∗log₁₀

255² MSE

(36) MSEisgivenby:

MSE= 1 mn

m i=1

n j=1

(S−G)² (37)

whereSstandsforsegmentedimageandGforgroundtruthimage.

Structuresimilarityindex(SSIM)isgivenbyequation:

SSIM(S,G)= (2_SG+₁)(2_SG+₂)

(²_S+²_G+₁)(_S²+_G²+₂) (38)

Fig.5.Segmentationresultsofdifferentalgorithmsonhandradiographtakenfrom8yearoldperson[5097.jpg].

Table1

Qualitymetricresultsforsegmentationofhandradiographtakenfrom2yearold person[5329.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 46.19 1.56 0.83 0.14 0.19 0.49 2.68 Tsallis[28] 56.90 0.13 0.98 0.41 0.58 0.70 1.18 KGRF[13] 56.90 0.13 0.98 0.42 0.60 0.71 28.56 GLCM-ACR[18] 8.23 9784.99 0.00 0.14 0.00 0.01 16.13 ARKFCM-avg[29] 55.38 0.19 0.98 0.41 0.58 0.71 128.75 ARKFCM-med[29] 56.90 0.13 0.98 0.45 0.62 0.72 124.76 ARKFCM-wtd[29] 56.91 0.13 0.98 0.44 0.61 0.72 127.33 BFV[30] 54.43 0.23 0.97 0.37 0.54 0.68 43.52 PSO[31] 56.90 0.13 0.98 0.41 0.58 0.71 7.02 DPSO[32] 56.90 0.13 0.98 0.41 0.58 0.70 7.02 MICO[33] 56.74 0.14 0.98 0.50 0.66 0.75 23.09 Highlightedvaluesignifiesthebestresultamongallalgorithms.

where_S,_Sisthemeanandvarianceofsegmentedimageand G,Gisthemeanandvarianceofgroundtruthimage.SGisthe covarianceand₁,₂aresmallconstantstostabilizethedenomi- nator.

Jaccardsimilarityindex(JSI)[39]usedforperformanceanalysis, JSI= |S∩G|

|S∪G| (39)

Dicesimilarity[39]isgivenbyequation, Dice=2|S∩G|

|S+G| (40)

Accuracy(ACC)[39]givesinformationabouttheratioofthepix- elscontainedwithinthesegmentedregionachievedbythetest algorithmwiththepixelsofthemanuallysegmentedregion.The segmentationaccuracyisdefinedas,

ACC= tp+tn

tp+fp+tn+fn

(41) where tp=truepositive,tn=truenegative,fp=false positive and fn=falsenegative.The range ofvalues takenby qualitymetrics SSIM,JDI,Dice,ACCis between0to1,where 1denotesperfect segmentation.

4. Experimentalresultsanddiscussion

The quantitative and qualitative performance evaluation of different non-evolutionary segmentation techniques such as Otsu’s thresholding [11], Tsallis entropy [28], adaptive cluster- ingalgorithm based onk-meansclustering withGibbs random fields(KGRF) [13], adaptive crossedreconstruction usingGLCM (GLCM-ACR) [18], ARKFCM algorithm [29], BFV algorithm [30]

andevolutionarysegmentationtechniquessuchasPSOalgorithm [31], DPSO algorithm [32], MICO algorithm [33] implemented on digital hand radiographs are discussed in this section. The segmentationresultsobtainedforvariousdigitalhandradiographs at ages 2 [5329.jpg (1063×1507)], 4 [5121.jpg(1209×1616)], 6 [5072.jpg(1558×1788)], 8 [5097.jpg(1520×1950)], 10 [5217.jpg(1619×2018)], 12 [5322.jpg(1592×2081)], 14 [5225.jpg(1910×2419)], 16 [5208.jpg(1841×2248)] and 18 [6145.jpg(1616×2376)]aregiveninTables1–9.

Allsegmentationresultswereobtainedona64-bitsystemwith MATLAB2015asoftware,havinga4GBRAMandanInteli7proces- sorwithclockspeedof2.93GHz.

4.1. Quantitativeanalysis

The quantitative analysis of various evolutionary and non- evolutionarysegmentationtechniquesusingthequalitymetrics discussed is presented in tabular form. Tables 1–9 show the

Table2

Qualitymetricresultsforsegmentationofhandradiographtakenfrom4yearold person[5121.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 46.23 1.55 0.83 0.15 0.20 0.49 2.67 Tsallis[28] 56.59 0.14 0.98 0.37 0.54 0.69 1.89 KGRF[13] 56.50 0.15 0.98 0.39 0.57 0.70 34.90 GLCM-ACR[18] 7.34 12003.50 0.00 0.15 0.00 0.01 9.33 ARKFCM-avg[29] 55.82 0.17 0.98 0.44 0.61 0.72 151.23 ARKFCM-med[29] 56.52 0.14 0.98 0.39 0.57 0.70 166.00 ARKFCM-wtd[29] 55.82 0.17 0.98 0.44 0.61 0.72 157.75 BFV[30] 54.71 0.22 0.97 0.40 0.57 0.70 51.17 PSO[31] 56.52 0.14 0.98 0.40 0.57 0.70 7.71 DPSO[32] 56.53 0.14 0.98 0.40 0.57 0.70 7.72 MICO[33] 56.19 0.16 0.98 0.48 0.65 0.74 31.64 Highlightedvaluesignifiesthebestresultamongallalgorithms.

Table3

Qualitymetricresultsforsegmentationofhandradiographtakenfrom6yearold person[5072.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 46.59 1.43 0.84 0.14 0.20 0.50 3.47 Tsallis[28] 58.00 0.10 0.99 0.43 0.60 0.72 1.35 KGRF[13] 58.37 0.09 0.99 0.51 0.68 0.76 52.35 GLCM-ACR[18] 8.32 9578.28 0.00 0.14 0.00 0.01 12.70 ARKFCM-avg[29] 58.33 0.10 0.99 0.51 0.67 0.75 221.25 ARKFCM-med[29] 56.62 0.14 0.98 0.50 0.66 0.75 230.36 ARKFCM-wtd[29] 58.34 0.10 0.99 0.51 0.67 0.75 227.51 BFV[30] 56.64 0.14 0.98 0.50 0.66 0.75 75.46 PSO[31] 58.32 0.10 0.99 0.51 0.67 0.75 9.04 DPSO[32] 58.30 0.10 0.99 0.50 0.67 0.75 9.19 MICO[33] 57.56 0.11 0.99 0.55 0.71 0.78 38.02 Highlightedvaluesignifiesthebestresultamongallalgorithms.

Table4

Qualitymetricresultsforsegmentationofhandradiographtakenfrom8yearold person[5097.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 46.75 1.37 0.84 0.16 0.22 0.51 3.93 Tsallis[28] 57.88 0.11 0.99 0.43 0.61 0.72 2.66 KGRF[13] 58.28 0.10 0.99 0.53 0.70 0.77 52.82 GLCM-ACR[18] 7.56 11401.31 0.00 0.16 0.00 0.01 13.21 ARKFCM-avg[29] 58.24 0.10 0.99 0.52 0.69 0.76 227.57 ARKFCM-med[29] 57.47 0.12 0.99 0.57 0.73 0.78 246.83 ARKFCM-wtd[29] 57.47 0.12 0.99 0.57 0.73 0.78 228.04 BFV[30] 57.03 0.13 0.98 0.55 0.71 0.78 74.02 PSO[31] 57.66 0.11 0.99 0.58 0.73 0.79 10.53 DPSO[32] 57.70 0.11 0.99 0.58 0.73 0.79 10.38 MICO[33] 59.68 0.07 0.99 0.69 0.82 0.85 44.73 Highlightedvaluesignifiesthebestresultamongallalgorithms.

Table5

Qualitymetricresultsforsegmentationofhandradiographtakenfrom10yearold person[5217.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 46.74 1.38 0.84 0.17 0.23 0.51 3.85 Tsallis[28] 57.88 0.11 0.99 0.44 0.61 0.72 2.36 KGRF[13] 57.65 0.11 0.99 0.60 0.75 0.80 60.35 GLCM-ACR[18] 8.70 8775.48 0.01 0.17 0.00 0.01 14.72 ARKFCM-avg[29] 57.58 0.11 0.99 0.60 0.75 0.80 250.07 ARKFCM-med[29] 58.59 0.09 0.99 0.54 0.70 0.77 289.81 ARKFCM-wtd[29] 57.59 0.11 0.99 0.60 0.75 0.80 267.66 BFV[30] 57.15 0.13 0.98 0.57 0.73 0.79 86.98 PSO[31] 58.96 0.08 0.99 0.59 0.74 0.79 11.15 DPSO[32] 58.96 0.08 0.99 0.59 0.74 0.79 11.63 MICO[33] 60.84 0.05 0.99 0.76 0.86 0.88 48.45 Highlightedvaluesignifiesthebestresultamongallalgorithms.

segmentationresultsforhandradiographsofages2,4,6,8,10,12, 14,16and18respectively.

Table 1 shows that PSNR value of ARKFCM-weighted algo- rithm is highest, with Tsallis, KGRF, PSO, DPSO and MICO

Table6

Qualitymetricresultsforsegmentationofhandradiographtakenfrom12yearold person[5322.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 46.57 1.43 0.84 0.18 0.24 0.51 4.07 Tsallis[28] 57.90 0.11 0.99 0.63 0.77 0.81 5.56 KGRF[13] 58.02 0.10 0.99 0.63 0.78 0.82 63.87 GLCM-ACR[18] 7.59 11324.66 0.00 0.18 0.00 0.01 13.89 ARKFCM-avg[29] 57.73 0.11 0.99 0.62 0.76 0.81 254.04 ARKFCM-med[29] 57.73 0.11 0.99 0.62 0.76 0.81 256.33 ARKFCM-wtd[29] 57.73 0.11 0.99 0.62 0.76 0.81 292.08 BFV[30] 56.60 0.14 0.98 0.56 0.72 0.78 86.15 PSO[31] 58.29 0.10 0.99 0.64 0.78 0.82 11.22 DPSO[32] 58.33 0.10 0.99 0.64 0.78 0.82 13.47 MICO[33] 59.28 0.08 0.99 0.70 0.82 0.85 49.37 Highlightedvaluesignifiesthebestresultamongallalgorithms.

algorithmhavingcloservalues.ButJSI,Diceandaccuracyvalues whichdenotethesegmentationqualityandaccuracyarehighest forMICOalgorithm.SegmentationaccuracyislowestforGLCM- ACR algorithm. The time taken for segmentation is lowest for TsallisalgorithmandhighestforARKFCMalgorithms.InTable2 weseethat PSNR valuesof PSO, DPSO,Tsallis,KGRF,ARKFCM- median,MICOalgorithmsarecomparablewithDPSObeinghighest amongthem. Structural similarity(SSIM) values aresimilar for thesealgorithmsbutJSI,Diceandaccuracyvaluesarehighestfor

Table7

Qualitymetricresultsforsegmentationofhandradiographtakenfrom14yearold person[5225.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 46.71 1.39 0.84 0.19 0.26 0.51 5.54 Tsallis[28] 58.34 0.10 0.99 0.65 0.79 0.82 2.64 KGRF[13] 58.75 0.09 0.99 0.65 0.79 0.82 85.69 GLCM-ACR[18] 6.09 16005.70 0.00 0.19 0.00 0.01 20.38 ARKFCM-avg[29] 57.34 0.12 0.98 0.61 0.76 0.81 399.46 ARKFCM-med[29] 57.34 0.12 0.98 0.61 0.76 0.81 388.03 ARKFCM-wtd[29] 57.34 0.12 0.98 0.61 0.76 0.81 371.62 BFV[30] 57.13 0.13 0.98 0.60 0.75 0.80 133.63 PSO[31] 58.75 0.09 0.99 0.65 0.78 0.82 14.34 DPSO[32] 58.79 0.09 0.99 0.65 0.78 0.82 14.16 MICO[33] 60.84 0.05 0.99 0.77 0.87 0.89 419.16 Highlightedvaluesignifiesthebestresultamongallalgorithms.

MICO algorithm. Tsallisalgorithm has least computationalcost withOtsu’sthresholdingmethodbeingsecondhighestandARK- FCMalgorithmstakenthemaximumtime.

Table3hasresultsderivedfromhandradiographof6yearold personandshowsthatsegmentation accuracymetricsarehigh- estforMICOalgorithm.ThetimetakenbyTsallisalgorithmisleast andARKFCMbeinghighest.Thereisahugetimedifferencebetween thetwo.Otsu’sthresholdingalgorithmtakesclosertimevalueto Tsallisalgorithm followedby PSO,DPSO, GLCM-ACRandMICO.

Fig.6.Segmentationresultsofdifferentalgorithmsonhandradiographtakenfrom10yearoldperson[5217.jpg].

Table8

Qualitymetricresultsforsegmentationofhandradiographtakenfrom16yearold person[5208.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 47.01 1.30 0.85 0.21 0.28 0.52 5.54 Tsallis[28] 57.52 0.12 0.99 0.47 0.64 0.73 2.84 KGRF[13] 58.85 0.08 0.99 0.65 0.79 0.83 79.99 GLCM-ACR[18] 7.07 12775.13 0.00 0.21 0.00 0.01 16.54 ARKFCM-avg[29] 58.35 0.10 0.99 0.68 0.81 0.84 355.43 ARKFCM-med[29] 58.35 0.09 0.99 0.68 0.81 0.84 351.39 ARKFCM-wtd[29] 58.35 0.10 0.99 0.68 0.81 0.84 356.44 BFV[30] 58.03 0.10 0.99 0.67 0.80 0.83 109.65 PSO[31] 58.82 0.09 0.99 0.65 0.79 0.83 13.76 DPSO[32] 58.82 0.09 0.99 0.65 0.79 0.83 12.70 MICO[33] 62.28 0.04 1.00 0.84 0.91 0.92 109.54 Highlightedvaluesignifiesthebestresultamongallalgorithms.

PSNRvalueofKGRFalgorithmishighest,withTsallis,PSO,DPSO andARKFCMalgorithmhavingcloservalues.Table4showsresults obtainedfromhandradiographof8yearoldperson.Wecanseethat MICOalgorithmhashighestsegmentationaccuracyvaluesbutTsal- lisalgorithmtakesleasttime.ThetimetakenbyMICOalgorithmis almost10timesthanthatofTsallisalgorithm.InTables5,6,7,8and 9weseethatMICOalgorithmgivesthebestresultsforsegmenta- tionaccuracyandnoneoftheotheralgorithmshavecomparable

Table9

Qualitymetricresultsforsegmentationofhandradiographtakenfrom18yearold person[6145.jpg].

Techniques PSNR MSE SSIM JSI Dice ACC Time(s) Otsu[11] 58.60 0.09 0.99 0.73 0.84 0.86 4.06 Tsallis[28] 57.77 0.11 0.99 0.70 0.82 0.85 1.46 KGRF[13] 58.45 0.09 0.99 0.72 0.84 0.86 65.35 GLCM-ACR[18] 6.75 13758.6 0.01 0.26 0.01 0.01 16.01 ARKFCM-avg[29] 58.08 0.10 0.99 0.71 0.83 0.86 294.32 ARKFCM-med[29] 58.09 0.10 0.99 0.71 0.83 0.86 295.30 ARKFCM-wtd[29] 58.08 0.10 0.99 0.71 0.83 0.86 293.23 BFV[30] 56.37 0.15 0.98 0.63 0.77 0.81 106.89 PSO[31] 58.57 0.09 0.99 0.73 0.84 0.86 11.08 DPSO[32] 58.60 0.09 0.99 0.73 0.84 0.86 10.76 MICO[33] 61.57 0.05 0.99 0.85 0.92 0.92 69.55 Highlightedvaluesignifiesthebestresultamongallalgorithms.

values.AlsothetimetakenbyTsallisisleastforallthehandradio- graphswithMICOtaking10timesmoretime.Thetimetakenby algorithmisvaryingbecausethehandradiographimagesareof differentsizes.

4.2. Qualitativeanalysis

The qualitative analysis of various evolutionary and non- evolutionary segmentation techniques have been shown in

Fig.7.Segmentationresultsofdifferentalgorithmsonhandradiographtakenfrom12yearoldperson[5322.jpg].

followingfigures.Fig.2showsresultsfor2yearsoldperson.Except forMICOalgorithmallothersegmentationtechniqueshavefailed.

Allbonesarenotsegmentedandlostintheprocedure.GLCM-ACR algorithmhascompletelyfailedbytrackingboundaryofhandand notthebones.

Fig.3showsthesegmentationresultsfor4yearsoldperson.

HerealsoweseethatMICOalgorithmgivesbestresultascompared toothersastheyhavefailedtosegmentoutallthebones.

FromthesegmentationresultsshowninFig.4forahandradio- graph of 6 year old person we cansay that, apart from MICO algorithmPSOandDPSOalgorithmshavefairedwell.Buttheyhave failedtosegmentthebonesofpinky/smallfinger.Restallresults havesegmentedsofttissueregionoverthepalmofhand.

InFig.9alsowecanseethatPSOandDPSOalgorithmshave fairedwellbutlostthebonesofsmallandringfingers.Allother algorithmshavetrackedtheboundaryonhandratherthanseg- mentingthebones.MICOalgorithmhasgivenbestrestforthishand radiographof8yearoldperson.

Fig.6showssegmentationresultsevaluatedonhandradiograph of10yearoldperson.MICOalgorithmhasperformedbestamong allalgorithms.Allotheralgorithmshavetrackedonlytheboundary ofhandexceptforPSOandDPSOalgorithmswhichsegmentedthe bonesbutnotall.KGRFandBFValgorithmshavetrackedthebones offingerswellbutrestofthebonesarenotdelineated.

ForhandradiographshowninFig.7thesegmentationresults showthat MICOalgorithmhassegmented theboneswithhigh accuracycomparedtoalltheotheralgorithms.

FromFig.8wecanseethatTsallisalgorithmalongwithPSOand DPSOalgorithmshavegivenfairresultsbutstillhaveoverlapping regions.KGRFalgorithmhasperformedwellbutfailedtosegment bonesofpinkyfingerandofthepalm.MICOalgorithmhasgiven bestresultsonthishandradiographof14yearoldperson.

FromFig.9whichshowssegmentationresultsforhandradio- graph of 16 year old person we can see that PSO and DPSO techniques have given good results but still have overlapping regionsandmissedoutabonesoflastfinger.MICOtechniquehas givenbestresult.

InFig.10whichshowssegmentationresultsforhandradiograph of18yearoldpersonwecanseethatTsallis,KGRF,ARKFCM,PSO andDPSOsegmentation techniqueshavegivengoodresultsbut stillhaveoverlappingregionsoverthepalmregionofhand.MICO techniqueagain hasgiven bestresultamong allthealgorithms compared.

4.3. Segmentationaccuracy

Thevariousquality metricsusednamelyJSI,Dice and Accu- racy give sound information about the segmentation accuracy

Fig.8.Segmentationresultsofdifferentalgorithmsonhandradiographtakenfrom14yearoldperson[5225.jpg].