BrainTumorSegmentationusinghybridofboth NetrosopicModifiedNonlocalFuzzyC-meanand ModifiedLevelsets
ShaimaElnazer1,MohamedMorsy2,MohyEldinA.Abo-Elsoud3
1LectureAssistant,Communicationdapartment, NileAcademy,Mans.univ,Mansoura,Egypt. Shaima_elnazer@yahoo.com
2Doctor,Communicationdapartment, Mans.univ,Mansoura,Egypt.
3Professor,Communicationdapartment, Mans.univ,Mansoura,Egypt.
Abstract:animprovedsegmentationapproachbasedonNeutrosophicsets(NS)andModifiedNonlocalFuzzyc-meanclustering (NLFCM)isproposed.ThebraintumorMRIimageistransformedintoNSdomain,whichisdescribedusingthreesubsetsnamely;the percentageoftruthinasubsetT%,thepercentageofindeterminacyinasubsetI%,andthepercentageoffalsityinasubsetF%.The entropyinNSisdefinedandemployedtoevaluatetheindeterminacy.NSimageisadaptedalsousingModifiedNonlocalFuzzyCmeanalgorithm(MNLFCM).Finally,MRIbraintumorimageissegmentedandtumorisselectedusingModifiedLevelSets(MLS). TheproposedapproachdenotedasNS-MNLFCM-MLSandcomparedwithanotherpaperusingJaccardIndexandDice Coefficient.TheexperimentalresultsdemonstratethattheproposedapproachislesssensitivetonoiseandperformsbetteronMRI brainimage.
Keywords:Magneticresonanceimaging,Netrosophic,Nonlocalfuzzycmean,Directionalα-meanoperation,modifiedlevelsets
1.Introduction
TheBraintumorsegmentationmethodscanbecome classifiedintothreeclassesinlinewiththelevelofrequired humanbeinginteractionasdescribedsimplybyFooetal. [1],Olabarrigaetal.[2],andYao[3]:manualsegmentation, semiautomaticsegmentation,andtotallyprogrammed segmentation.Braintumorsarehardtosegmentsincethey haveavarietyofpresenceandeffectonadjoiningstructures. Followingareseveralofthetypicalcharacteristicsofbrain tumors:(A)changegreatlyindimensionsandplacement,(B) varygreatlyinthewaytheybepresentinMRI,(C)might haveoverlappingintensitieswithnormaltissue,(D)canbe spaceoccupying(newtissuesthatmovesnormalstructure)or infiltrating(changingrealestateofexistingtissue),(E)may enhancefully,somewhat,ornotatevery,withcontrastagent.
Clusteringisknownasagenerallyusedmathematical procedurewhichinturnperformssegmentationprocessto distinguishthestructuresandmaternityshapespresentina greatinputimageordataset[4]Itcouldbecategorizedinto twogroups:hierarchicalanddividing[5].Theoutputof hierarchicalclusteringareliketreeandtheydon'tneedto specifythenumberoftheamountoftheclustersand independentofthefirstcondition.However,itmightfailto separateoverlappingclustersduetonotenoughinformation regardingthesizeofclustersoritsglobalcondition.Dividing clusteringalgorithmonfixthedisadvantageofhierarchical clusteringalgorithmpartitionsthedatasetintospecific numberofgroupings.Fuzzybasedclusteringallowspartition
aninputphotointoseveralhomogenousclassesorclusters, bywhichinturnidenticalconditionsaregroupedfoundina sameclassandnon-identicalitemsbelongtodifferent classes
Themajorityofthealgorithmsfoundinimageprocessing aresusceptibletoseveraluncertainties,pertainingto instance,graynessambiguity(uncertaintyinsidetheinput detailsitself).Thekeyaimofthisworkshouldbetolessen uncertaintywhileclustering.Generallytherearetwomain tacticsinclusteringtechniqueparticularlycrispandfuzzy clusteringtechnique.Duetodifferentsituations,forimages, problemslikesmallscaleofspatialresolution,poorlight, occurrenceofnoise,powerimbricationsleadscrisp segmentationahardtask.Betweennumerousclustering techniques,fuzzyc-means(FCM)[6]algorithmisusually moresignificantasaresultoftherobustness
Althoughitisdefinitelyrobustitworksjustontheimages withnonoise.Manyresearchersexperienceanalyzedbrain MRIsegmentationusingFSs,seeZhao[7]Agrawal[8].Yet thesealgorithmsstillincludeproblemsduetodifferent situations,forinstance,takingbrainimagesunderlowofthe illuminationmakeitunclear.Ingeneral,FCMcriteriahave greaterdatamanagingcapacityandhavebetteroperability afterdiversifiedinforange.Duetotheapplicationofpixel neighborhoodinformation,RFCMalgorithmhasniceoverall performanceofnoiserestraining,andgetsgoodsegmentation benefitscomparingwithstandardFCM.Yet,wefoundthat withalltheincreaseofnormaldeviationofnoise,theability ofnoisereductionsofFCMalgorithmmightbecomeweaken. V.P.Ananthi[9]useSegmentationofbraintumorbasedon
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interval-respectedintunisticfuzzysetsfeaturesDice coefficientequalzero.967.M.Zarinbal[10]workin astrocytomasextractiononlyusingtype2fuzzyandhavegot accuracyof89%.
Inrespecttothissituation,allofusputforwardclustering algorithmbasedinnon-localinformationNON-LOCAL unclearC-meansclustering,(NLFCM),agreaterweighted neighborhooddetailscanbeused,soitisdefinitelybetterto suppresssoundsthanthatofRFCMalgorithm.Non-local regularizationwasfirstformerlyusedforpicturedenoising, callednon-localindicatedenoising[11].Thealgorithm essentiallyusestheredundantinformationofnormal structure,franklyneighborhoodaboutapixelandaswell otherneighborpixelsfoundinthesamescenemaymatch witheachvariousother.TheNLFCMalgorithmidentifiesa weightedgraphofallpixelsintheimage,inwhichtheweight valueisreceivedbysimilaritycalculationoftwo neighborhoodpixels
Theconvergencerategetsaffectedifthenumberof clustersanditerationsaresubsequentlyincreased. Diminishingthenumberofiterationsandclusterstoobtain fasterconvergenceratehasanadverseeffectuponthe segmentationaccuracy.Toovercomethesekindsof hindrances,anovelsegmentationalgorithmwhichcombines Neutrosophystudiesthefoundation,characteristics,scopeof neutralities,andtheirinteractionswithdistinctideational spectra.Itisusuallyanewphilosophythatextendsfuzzy logicandisthebasisofneutrosophiclogic,neutrosophic likelihood,neutrosophicsettheory,andneutrosophic statistics.Becausetheworldisfilledwithindeterminacy,the imperfection of understanding that a human receives/observesfromtheexternaluniversealsocauses imprecision.Neutrosophyintroducesanewprinciple <Neut-A>,whichisdefinitelytherepresentationof indeterminacy.However,thistheorycanbemostlydiscussed inphysiologyandmathematics.Thus,applicationstoprove thistheorycanresolverealchallengesareneeded.Inthis kindofdissertation,Iapplyneutrosophytobraintumor segmentation.Inbraintumorsegmentation,neutrosophy helpsreducenoises.InMRIbraintumoursegmentation, neutrosophyintegratestwocontroversialopinionsabout noise.
2.Proposedalgorithm
Ansuperiorsegmentationapproachbasedupon Neutrosophicsets(NS)andNonlocalFuzzyc-mean clustering(NLFCM)isrecommended.ThebraintumorMRI imageisbecomeNSdomain,whichisdefinedusingthree subsetsparticularly.TheentropyinNSisdefinedand employedtogaugetheindeterminacy.NSimageismodified usingMovingMeanOperation(MMO)andalsousing ModifiedNotlocalFuzzyC-meanalgorithm(MNLFCM). Finally,MRIbraingrowthimageissegmentedandtumoris selectedapplyingModifiedLevelSets(MLS).Theproposed approachdenotedasNS-MNLFCM-MLSandusing MaximaMorphologicalTransform(MMT)tofindaccurate tumorboundary.Wecomparedwithanothernewspaperusing
sensitivity,SpecificityandDiceCoefficient.Thetrialand errorresultsdemonstratethefactthatofferedapproachisless hypersensitivetonoiseandfunctionsbetteronMRIbrain image.Figure1showtheflowchartoftheproposedapproach.
2.1NeutrosophicMRIbraintumorImage
LetUgetanuniverseoftalk,andWbeasetincludedin Circumstance,whichiscomposedsimplybybrightpixels.A neutrosophicimagePisindicatedbythreesubsetTo,Iand F.ApixelPintheimageisidentifiedasP(T,Myspouseand i,F)andbelongstoWinthenextway:itist%trueinthe dazzlingpixelset,i%indeterminate,andf%bogus,wheret variesinTvariesI,andfvariesinN.ThepixelP(i,j)inthe imagewebsiteistransformedintoneutrosophicdomainP NS(i,j)=T(i,j),I(i,j),F(i,j).WhereT(i,j),I(i,j)andF(i, j)willbetheprobabilitiesbelongtobrightwhiteset, indeterminatesetandnon-whiteset,respectively[12],which aredescribedas:equationbelow:
ThepixelP(i,j)intheimagedomainistransformedinto NeutrosophicdomainPN
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S(i,j)={T(i,j),I(i,j),F(i,j)}. WhereT(i,j),I(i,j)andF(i,j)aretheprobabilitiesbelong towhiteset,indeterminatesetandnon-white set, respectively,whicharedefinedinthefollowingequations.
PNS(i,j)={T(i,j),I(i,j),F(i,j)} (1)
Ho(i,j)=abs(g(i,j)g(i,j)) (2) F(i,j)=1T(i,j) (3) (4) (5) (6)
Whereg(i,j)isthelocalmeanvalueoftheimage,Ho(i,j)is thehomogeneityvalueofTat(i,j)whichisdescribedby theabsolutevalueofdifferencebetweenintensityg(i,j) anditslocalmeanvalueg(i,j)Figureshowinputimageand ifoftheenhancedMRIimagethenNSImageareshownin fig(D)
2.2EnhancementofNSMRIbraintumorImage
TheMRIbraintumorpictureinNSdomainmightincreased usingintensificationtransformationenhancementtechnique (ITET)toincreasethetopqualityandemphasizescertain featuresofapicturetomakessegmentationeasierandmore effective[13].Figure3showresultofusing(ITET)
entropyisoptimum,theseveralintensitieshaveeven probabilityandthefeaturesdistributeuniformly.Ifthe entropyissmall,theintensitieshavedifferentpossibilities andtheirdistributionsareactuallynon-uniform.
Definition1(Neutrosophicimageentropy)NSpicture entropyisdefinedwhilethesummationoftheentropiesof threesubsection,subdivision,subgroup,subcategory, subclassF,TandI,whichisemployedtoevaluatethe distributioninthecomponentsinNSsite[14]:
EnT=−PT(i)lnPT(i) (9)
EnF=−PF(i)lnPF(i) (10) EnI=−PI(i)lnPI(i) (11) EnNS=EnT+EnI+EnF (12) WhereEnI,EnTandEnFaretheentropyofsubsetsT,Iand F,respectivelyasshowninfig4.
Fig4:GUIResultofentropycalculation
2.4Directionalα-meanoperation
In[14],anα-meanfunctioningwasdefinedona neutrosophicimage,andittakenoffnoiseefficiently However,itcouldblurringtheimageandlessenthecontrast, whichcanreducetheperformanceofthesegmentationto overcomethiskindofdrawback,directionalα-mean operationdenotedasDAMisusuallynewlyproposedto removethenoiseeffectandconservetheedgesatthesame time.ThefunctionofthedirectionalmeanfilterDAMis identifiedas[16]: WhereG(i,j)ThandG(i,j)TVarethenormofthe gradientat(,atthehorizontalandverticaldirection, respectively.
2.3EntropyofNSbraintumorMRIImage
Entropyisutilizedtoassessthedistributionofdiversegray levelinmindtumorMRIimages.Intheeventthatthe
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3.4ModifiedNonLocalFuzzyCmean:
Asshowninabove,NONlocalFCM(NLFCM)isextremely sensitivetotheoutliers.Themembershipfunctionofthe Nonlocalunclearismodifiedbylookingattheoutliers rejection;Frequency.(10)becomes:16
vicinityofapoorlydefinedborder,theborder-stopfunction (BSF)doesnotstopthecontour[22].
Thepartoftheexponentisdefinitelytolimitthepartially distributionwiththepointsbetweentwoneighboringclusters somewhatthantoallgroupings.Isdefinedas: ExactlywhereXmaxandTimesminarerespectively,the maximumandtheminimalintensityintheimageisbetween 1and2Ifthegraphichasabigintensityselectionthepartial distributionofthepixelsbetween2surroundingclustersis reduced.Notlikely,iftheimageincludesasmallintensity range,isusuallycloseto1andthepartialdistributionofthe pixelsisbasicallyamongtheadjacentgroupings.
ThemembershipfunctionofNLFCMismodifiedbysimply replacingtheoriginallengthfromequation8in[11]
ToovercomethelimitationwiththetraditionalBSFsin borderbasedactivecontourtypes,weproposeaconstruction toconstructagroupofrobustBSFsthatmakeuseof probabilityscoresratherthanthepredictedclassbrandsfrom aclassifier.Seeingthatthescoresfallin[0,1],thiskindof taskisjustlikefuzzysegmentation.Unlikethetechniquesof [23],[24],whichinturnrelyonlyoncategoryprobability usingBayes'guideline,ourframeworkisconsiderablymore flexiblesinceitutilizestheprobabilityscoresbyany classifier.Atthesametime,wemaintaingradientinformation toendcontourevolutionwhenpresentlytherearenofuzzy principlesduetodistinctlimitations.Theseideas differentiatetheworkfrom[25],whichreliesonenergyand isalsoconsideredaregion-basedlevelsettechnique.The traditionalBSFneedsreinititializationtoavoidirregularities duringitsevolution[20],[21].Asreinitializationoftenbrings aboutproblems,Lietal.[22]proposedthelengthregularized levelsetdevelopment(DRLSE)whichremovesthe advantagesofreinitialization.ThattheyappliedtheDRLSE toanedge-basedactivecurvemodelbyintroducingthe gradientflowasequation(19) WeusethefuzzyESF
CombiningNSbraintumorimagewithMNLFCMweget accurateplaceofbraintumorasshowninfigure6 a
2.5Modifiedlevelsets:
AfterusingnetrosophicwithModifiedNonlocalFuzzyC Mean(MNLFCM)wehavetomakeuseofboundarymethod togetaccuratetumor.InGeneral,picturesegmentation modelsusinglevelsetsmethod(LSM)canalwaysbe classifiedasedge-basedtypesorregion-basedmodels[17][18].Theformerutilizesedgedetails[19]althoughthelatter employsaregiondescriptortocontrolthedisplacementof theactivecontour[20],[21].Edge-basedtypesarenot sensitivetoinhomogeneityofimagefeatures.Butare sensitivetoobjectswithpoorlydescribedtumorsboundaries. Inimagesinwhichtheintensitieschangesteadilyinthe
WherePistheprobabilityscorefortheforeground Subsequently,thefuzzyESFisusedtoregularizefunctionin (4)toobtainwhichcanbesimplyexpressedby =
(17) (19)
ThefuzzyESF,willcompeltobenear0whenisnearzero despitethefactthatismuchhigherthan0,i.e.,whenthe pictureforcedropsbitbybit.Consequently,willbenear0 whichwillstopashapeatthefanciedlimit.Itisclearthat capacityassumesanimperativepartwhenaninadequately characterizedlimitisavailable.Itproducesabaseworth whenthescoresareatthechoicelimit.Besides,holdingthe inclinationdataishelpfulatclearlimitssubsequenttothere arenofluffyqualities.Capacityfusesbothofthesefavorable circumstancestogiveexactdivisionresults.What'smore,the proposedstructureisadaptable
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2.6MaximatransformEnhancement
Forangraphicisdefinitelymadeusingmorphological operationssuchasiterateddilationsoftheimageandlaterit iscamouflaged.Kohetal[29]havedefinedHtransformas whereRI(I-h)istheretracedimagebydilatingIwith respecttoI-h.Thissortofrestrainsallpixelsinwhose powerrateislittlerthanthelimitifmaybetheworthisrather thantheirneighbors.Wellthenlocateallterritorialidealof pictureandindividualthepixelsofsuccessiveforce.Maxima strategyistakenoututilizingtheequationRegionalmaxima ofH-maximachangedgrouppicturehavingtumorcanbe utilizedtouprootneighborhoodpixelsofpowerunderneathh fromthecapabilities.UtilizingEq.(9),lastparticulartumor localeisunquestionablyseparatedwithoutedemaandother non-tumorarea.H-maximachangehappentobeshownin Fig.8.
ADSCestimationofzeroshowsnocover;anestimationof onedemonstratesperfectdivision.Highernumbersshow betterdivision,whichimpliesthatthedivisionresults coordinatethegroundtruthsuperiortoanythingresultswith lowerqualitiesDSCvalues.
Table1:Accuracyoftheproposedsegmentationapproach foreachsubjectusingdicesimilaritycoefficient(DSC(%)). &Accuracyoftheproposedsegmentationapproachforeach subjectusingthe98percentilemodifiedHausdorffdistance
Patient number DSC Hausdroff p.1 98.403 2.05 P.2 96.56 5.13 p.3 97.34 1.78 p.4 96.76 12.43 (20) (21)
Fig8:SegmentedtumorusingHtransform
2.7PerformanceEvaluationMetric:
Thedatasetsforexperimentalanalysiswereobtainedfrom MansouraHospitalUniversityMRIScan.Testsareexecuted onnumerousbrainMRimagedatasetshavingtumor.To evaluatethesegmentationaccuracy,weusedthreemetrics, namely,(i)theDiceSimilarityCoefficient(DSC),(ii)the98percentilemodifiedHausdorffdistance(H98)[30].The followingsubsectionswilldescribeeachusedmetricinmore detail.
A)DiceSimilarityCoefficientTheDicesimilaritycoefficient (DSC)measuressetagreementbetweentwosets(S,G),andis definedastheunionsizeofthetwosetsdividedbythe averagesizeofthetwosets
DSC(S,G)=(2|S∩G|/(S∩G+SG))×100 (22)
Insegmentationvalidation,theDSCisusuallyexpressedin termsoffalsepositive(FP),falsenegative(FN),true negative(TN),andtruepositive(TP)counts,whichwere obtainedbycomparingthesegmentationresultstotheground truth(goldstandard)(seeFigure31).Thesevaluescanbe usedtocalculatetheDSCasshownby[30]:
DSC=2TP/(2TP+FP+FN)×100 (23)
Fig9:Diagramillustratingthemeaningofsegmentationerrors,namely, truepositive(TP),falsepositive(FP),truenegative(TN),andfalsepositive (FP).Thesesegmentationerrors,obtainedbycomparingthesegmentedand thegroundtruthobjects,areusedtocalculatethedicesimilaritycoefficient (DSC).
B)ModifiedHausdorffDistance
Distancemeasuresareanothertypeofperformancemetric usedforevaluatingsegmentationmethods.TheEuclidean distanceisoftenutilized,butanothercommonmeasureisthe Hausdorffdistance(H).TheHvaluefromasetStoasetGis definedasthemaximumdistanceofthesetStothenearest pointinthesetG(seeFigure6[30]):
H(S,G)=maxsS{mingG{d(s,g)}}, (24)
wheresandgarepointsofsetsSandG,respectively,and d(s,g)isEuclideandistancebetweenthesepoints.The bidirectionalHausdorffdistance,denotedbyH(S,G), betweenthesegmentedregion(S)anditsgroundtruth(G)is definedas:
HBi(S,G)=max{H(S,G),H(G,S)}. (25)
Inthispaper,toeliminatetheeffectofsegmentationoutliers, the98-percentilemodifiedHausdorffdistance(MH)was usedtoassesstheproposedsegmentationframework accuracy.Metricswerecomputedbycomparingaground truthsegmentationtoresultsfromtheproposedsegmentation technique.Thedetailedsegmentationresultsforeachsubject aregiveninTables1
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AsdemonstratedinTable1,theDSCforsegmentationofthe braintumorisgivesgoodresultusingourproposed algorithm.Performanceshowninfig(9)andintable2.
Conclusion:
Inthispaper,theproposedfullautomaticbraintumor segmentationtechniquehasbeendenotedasNS-MNLFCMMLSandusingMaximaMorphologicalTransform(MMT) tofindaccuratetumorboundary.Itisbasedonneutrosophic preprocessingmethodandModifiednonlocalfuzzycmea ClusteringmethodComparedwithanothernewpaperusing JaccardIndexandDiceCoefficient.Resultsdemonstratethe factthatofferedapproachislesshypersensitivetonoiseand functionsbetteronMRIbrainimageProposedalgorithm givehighaccuracyresultcomparedwithanothermethods. Theresultsoftheproposedmethodshowthatthe100% detectionrateinall34caseswithaverageofhighdice 99.37%,highspecificity99.26%andlowermissingrate 0.52,andmodifiedHausdroffdistance1.302.
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