FluidsegmentationinNeutrosophicdomain
ElyasRashno
DepartmentofComputerEngineering IranUniversityOfScienceandTechnology Tehran,Iran elyas.rashno@gmail.com
AbdolrezaRashno
DepartmentofComputerEngineering EngineeringFaculty LorestanUniversity Khorramabad,Iran rashno.a@lu.ac.ir
SadeghFadaei DepartmentofElectricalEngineering FacultyofEngineering YasoujUniversity Yasouj,Iran,7591874934 s.fadaei@yu.ac.ir
Abstract—Opticalcoherencetomography(OCT)asretina imagingtechnologyiscurrentlyusedbyophthalmologistas anon-invasiveandnon-contactmethodfordiagnosisofagerelateddegeneration(AMD)anddiabeticmacularedema(DME) diseases.FluidregionsinOCTimagesrevealthemainsignsof AMDandDME.Inthispaper,anefficientandfastclustering inneutrosophic(NS)domainreferredasneutrosophicC-means isadaptedforfluidsegmentation.Forthistask,aNCMcost functioninNSdomainisadaptedforfluidsegmentationandthen optimizedbygradientdescendmethodswhichleadstobinary segmentationofOCTBscanstofluidandtissueregions.The proposedmethodisevaluatedinOCTdatasetsofsubjectswith DMEabnormalities.Resultsshowedthattheproposedmethod outperformsexistingfluidsegmentationmethodsby6%indice coefficientandsensitivitycriteria.
IndexTerms—Opticalcoherencetomography;Neutrosophic theory;Fluidsegmentation;Retinadiseases
I.INTRODUCTION
Ophthalmologistsuseopticalcoherencetomography(OCT) asanon-contactmethodtodiagnosisandfollowupof retinadisease.FluidregionsaredetectableinOCTimages andrevealabnormalitiesofretinadiseaseincludingdiabetic maculaedema(DME)andage-relatedmaculardegeneration (AMD)[1].Imageprocessinganddataminingapplications havebeenwidelyusedinmanyapplication[2]–[7].Fluid regionscanbesegmentedautomaticallybyimageprocessing anddataminingtools.Manyfluiddetectionmethodshave beenproposedintheliteraturesuchaskernelregression basedsegmentationofOCTimageswithDME[8],fluid-filled regiondelineationofboundariesinOCT[9],semi-automatic segmentationmethodforretinalOCTimagestestedinpatients withdiabeticmacularedema[10],labelpropagationand higher-orderconstraint-basedsegmentationoffluidregionsin OCTimagesofDMEsubjects[11],computerizedassessment ofintraretinalandsubretinalfluidregionsinOCTimages oftheretina[12],automatedsegmentationofpathological cavitiesinOCTscans[13],three-dimensionalanalysisof retinallayerandfluid-filledregionsinOCTofthemacula [14],probabilityconstrainedgraph-search-graph-cutmethod forthree-dimensionalsegmentationoffluid-associatedabnormalities[15],fluidsegmentationwithshortest-pathmethods andneutrosophic(NS)theory[16]–[21],fluidsegmentation withdeepconvolutionalnetworks(CNNs)[22]–[25].
SmarandacheproposedNStheoryin1995,abranchofphilosophywhichstudiestheorigin,natureandscopeofneutralities,aswellastheirinteractionswithdifferentideationalspectra[26].Thistheoryhasbeenappliedonmanyapplications includingimagesegmentation[27]–[30],imagethresholding [31],imageedgedetection[32],content-basedimageretrieval [33]–[37],retinalimageanalysis[16]–[20],speechprocessing [38],dataclustering[39],[40]anduncertaintyhandling[41], [42].Themaincontributionofthisworkistooptimizeacost functioninNSdomaintobinarizeretinaOCTscanstofluid andtissueregions.Thecostfunctionisderivedfromfuzzycmeans(FCM)andisoptimizedbygradientdescendmethods insubsequenceiterations.Therestofthispaperisorganized asfollows:SectionIIreviewsFCMandNStheory.Section IIIpresentstheproposedmethod.Experimentalresultsand conclusionarediscussedinsectionsIVandV,respectively.
II.REVIEWOF NS AND FCM
SincethecostfunctioninthisworkisanextensionofFCM andisdefinedinNSdomain,here,areviewonFCMandNS isdiscussedshortly.
A.FCM
TheFCMisaclusteringmethodthatassignsamembership degreeininterval[0-1]toeachdatapoint,Therefore,each datapointisassignedtoallclusterswithdifferentmembership degreesandthesumofmembershipstoallclustersshouldbe 1.FCMcostfunctionisdefinedasfollows:
tothe
th clusterwithcenter v
.
and m areanorm metricandaconstantvariablefordeterminingthefuzziness oftheresultingpartition,respectively.MinimizingFCMcost functionleadstothefollowingequationsforthecomputation ofmembershipdegreesandclustercenters:
Firstly,membershipdegreesareinitializedrandomlyand clustercentersarecomputedbyEq.(3).Then,membership degreesandclustercentersarecomputedrepeatedly,untilthere isnosignificantchangesoftheseparametersinsubsequent iterations.
B.Neutrosophic
NStheoryisanewlybroughtupbranchesofphilosophy.In thistheory,setA,Anti-A(contemplatesAinacorrelationwith itsopposite),Neut-A(neutralityofA,neitherAnorAnti-A) aredefined[26].Ineachapplication,NSsetsshouldbedefined foralldatapointsaswellasrelationsbetweensets.Forexample,inourproblemofinterestasimagesegmentation,each pixelinNSdomainismodeledas P (t,i,f ) meaningthatitis t percenttrue, i percentindeterministic,and f percentfalse. Therefore,threesets PNS (i,j)= {T (i,j),I(i,j),F (i,j)} are definedforpixelsinNSdomainasfollows[27]:
T (i,j)= g(i,j) gmin gmax gmin (4)
g(i,j)= 1 w × w
i+ w 2 m=i w 2
j+ w 2 n=j w 2
g(m,n) (5)
I(i,j)= δ(i,j) δmin δmax δmin (6)
δ(i,j)= |g(i,j) g(i,j)| (7)
F (i,j)=1 T (i,j) (8)
where, g(i,j) representstheintensityvalueofthepixel P (i,j), g isimagematrix g filteredbyaveragefilterwith windowsize w.Differenceoftwomatrixes g and g is computedandstoredin δ
III.PROPOSED METHOD
Inthiswork,NCMcostfunctionisusedandadaptedfor OCTfluidsegmentation.SinceOCTscanscontainnoiseand thereisambiguitybetweenfluidpixelsandmanypixelsin backgroundandtissue,indeterminacyset I inNSdomaincan beveryusefulandmodelssuchambiguitieseasily.Here,each pixelinOCTscansaretransferredtothreesets T , I and F by Eqs.(4),(6)and(8),respectively.Then,NSsetsarepresented forclusteringcostfunctionasfollows:
(T,I,F,C
Cqi = argmax(Tij ) ,j = pi ∩ j =1, 2, ,C (12)
Gradientdescentmethodisusedforcostfunctionoptimizationwhichleadstothefollowingrelationsforthecomputation of T , I and F setsinNSdomainandclustercenters.
Tij = K w1 (Xi Cj ) ( 2 m 1) (13)
Ii = K w2 (Xi Cimax ) ( 2 m 1) (14)
Fi = K w3 δ ( 2 m 1) (15) Cj = N i=1(¯ w1Tij )mXi N i=1(¯ w1Tij )m (16)
K = 1 w1
C j=1 (Xi Cj ) ( 2 m 1) + 1 w2 (Xi Cimax ) ( 2 m 1) + 1 w3 δ ( 2 m 1) 1 (17)
Parameter K isacommonpartinEqs.(13)-(15).Itis computedonceandusedthreetimeswhichleadstospeedupin eachiterationofoptimization.Inthefirststep, 12 clustersare consideredforclustering.Thereasonisthatthereis 11 layers inretinaandeachlayercanbeassignedtooneclusterbasedon itstextureandgraylevel.Oneextraclusterisconsideredfor fluidregionsasfluidcluster.Afterconvergence,clustersare sortedascendinglybasedonthegraylevelofclustercenters. Thefirstclusterisconsideredasfluidclusterwithlabel1and otherclustersareconsideredastissueclusterswithlabel 0 Therefore,theproposedclusteringschemeleadstoabinary segmentationofOCTscans.
IV.EXPERIMENTAL RESULTS
A.EvaluationMetrics
Toshowtheeffectivenessoftheproposedmethod,ithas beenevaluatedwiththreemetrics;dicecoefficient,precision andsensitivity;computedfromtruepositive(TP)fluidpixels detectedasfluid,falsepositive(FP)tissuepixelsdetectedas fluid,truenegative(TN)tissuepixelsdetectedastissueand falsenegative(FN)fluidpixelsdetectedastissue.
Dice Coeff = 2TP 2TP + FP + FN (18)
Sensitivity = TP TP + FN (19)
Precision = TP TP + FP (20)
Thesecriteriaareusedtoevaluatefluidsegmentationresultsofautomatedmethodsincomparisonwithmanually segmentedfluidregionsbyophthalmologistexperts.
B.Dataset
Theproposedfluidsegmentationmethodistestedona datasetfromOPTIMACystSegmentationChallengewhich contains 4 subjectswith 49 imagespersubjectwheretheimage resolutionvariesfrom 512 × 496 to 512 × 1024.Thefluid regionsofeachOCTimagearemanuallysegmentedbytwo ophthalmologistexpertsasgroundtruthimages.Thisdataset ispubliclyavailableandcanbefoundonline1
C.Resultes
Segmentedfluidregionsbytheproposedmethodarecomparedwithgroundtruthimages.Fig.1depictsfluidregions segmentedbyexpertandtheproposedmethodfortwoscans, eachscaninonerow.Theproposedfluidsegmentationmethod iscomparedwith4fluidsegmentationmethodsproposedin [17]and[44]–[46].Theresultsofthesemethodsareshownin Fig.2.Itisclearvisuallythattheproposedmethodhaslower numberoffalsenegaiveswhichleadstohigheraccuracy.
Fig.2:Segmentedfluidby:(a)expert,(b)methodin[17], (c)methodin[44],(d)methodin[45]and(e)theproposed method
TABLEI:Dicecoefficient,sensitivityandprecisionofthe proposedmethodandothermethodsincomparisonwithexpert 1.
Expert1 Sub. Method in[44] Method in[45] Method in[46] Method in[17] Prop. Method
DiceCoeff
Sensitivity
1 73.49 80.43 71.40 82.96 83.17 2 73.90 55.10 45.49 78.11 74.61 3 78.46 75.35 69.54 82.23 84.85 4 78.12 71.78 71.15 80.75 86.32 Ave. 75.99 70.66 64.39 81.01 82.23
1 70.81 82.19 72.49 84.43 86.95 2 96.79 99.04 70.45 98.94 98.42 3 75.72 85.13 47.38 85.18 86.58 4 78.78 80.59 77.79 84.49 90.51 Ave. 80.52 86.73 67.02 88.26 90.59
1 93.00 85.06 54.87 84.03 82.12
Fig.1:Fluidsegmentationresultsfor2scans:(a)InputOCT image,(b)manuallysegmentatedbyexpertand(c) segmentedbytheproposedmethod.
Precision
2 74.36 54.18 51.12 78.48 69.31 3 94.89 79.88 30.93 85.45 83.43 4 96.97 88.62 54.98 93.20 75.01 Ave. 89.80 76.93 47.97 85.29 77.46
TableIreportsthedicecoefficient,sensitivityandprecision oftheproposedmethodandmethodsin[17]and[44]–[46]. ReportedresultsinTableIarethecomparisonbetweenall methodsandfluidregionsmanuallysegmentedbyexpert1. TableIIreportsthesameresultsbutincomparisonwithexpert 2.Incomparisonwiththeresultsofexpert1,theproposed methodoutperformsothermethodswithrespecttodicecoefficientandsensitivityof 82.23% and 90.59%,respectively. Thesemeasuresoftheproposedmethodincomparisonwith expert2are 81 62% and 90 11% whichalsooutperforms othermethods.Forprecisionmeasure,methodsin[17]with 85 29% and[44]with 90 87% havethebestperformancein comparisonwithexpert1and2,respectively.
(a) (b) (c) (a) (b) (c)
V.CONCLUSION
(a) (b) (c) (d) (e)
Thispaperpresentedafluidsegmentationmethodbased onNCMcostfunctioninNSdomain.Minimizingthecost
1https://optima.meduniwien.ac.at/research/challenges/
functionresultedinbinarysegmentationofOctimagesinto tissueandfluidregions.SegmentationresultsonOptima datasetshowedthattheproposedmethodoutperformsother segmentationmethodsindicecoefficientandsensitivitymeasureswhileforprecisioncriteria,othermethodshadthebest performance.Futureeffortswillbedirectedtowardsproposing acostfunctioninNSdomainforbettermodelingofnoiseand uncertaintyinOCTpixels.NScanmodeluncertaintyofOCT pixelsindeepconvolutionalnetworksandleadstomorerobust networkagainstnoiseandimagingdevice.Therefore,using NStheoryforfluidsegmentationbyCNNcanbeproposedas anotherfuturework.
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