Lung cancer classiﬁcation using neural networks for CT images

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jou rn al h om ep a ge :w w w . i n t l . e l s e v i e r h e a l t h . c o m / j o u r n a l s / c m p b

Lung cancer classiﬁcation using neural networks for CT images

Jinsa Kuruvilla

^∗

, K. Gunavathi

ECEDepartment,PSGCollegeofTechnology,Coimbatore641004,India

a r t i c l e i n f o

Articlehistory:

Received14March2013 Receivedinrevisedform 12September2013 Accepted8October2013

Keywords:

Computedtomography Skewness

Kurtosis Neuralnetwork

a bs t r a c t

Earlydetectionofcanceristhemostpromisingwaytoenhanceapatient’schanceforsur- vival.Thispaperpresentsacomputeraidedclassificationmethodincomputedtomography (CT)imagesoflungsdevelopedusingartificialneuralnetwork.Theentirelungissegmented fromtheCTimagesandtheparametersarecalculatedfromthesegmentedimage.Thesta- tisticalparameterslikemean,standarddeviation,skewness,kurtosis,fifthcentralmoment andsixthcentralmomentareusedforclassification.Theclassificationprocessisdoneby feedforwardandfeedforwardbackpropagationneuralnetworks.Comparedtofeedfor- wardnetworksthefeedforwardbackpropagationnetworkgivesbetterclassification.The parameterskewnessgivesthemaximumclassificationaccuracy.Amongthealreadyavail- ablethirteentrainingfunctionsofbackpropagationneuralnetwork,theTraingdxfunction givesthemaximumclassificationaccuracyof91.1%.Twonewtrainingfunctionsarepro- posedinthispaper.Theresultsshowthattheproposedtrainingfunction1givesanaccuracy of93.3%,specificityof100%andsensitivityof91.4%andameansquareerrorof0.998.The proposedtrainingfunction2givesaclassificationaccuracyof93.3%andminimummean squareerrorof0.0942.

1. Introduction

Lungcancer isthe leading cause ofcancer deathsin both womenandmen.Itisestimatedthat1.2millionpeopleare diagnosedwiththisdiseaseeveryyear(12.3%ofthetotalnum- berofcancer diagnosed),and about 1.1 millionpeople are dyingofthisdiseaseyearly(17.8%ofthetotalcancerdeath) [1].Thesurvivalrateishigherifthecancerisdetectedatearly stages.Theearlydetectionoflungcancerisnotaneasytask.

About80%patientsarediagnosedcorrectlyatthemiddleor advancedstageofcancer[2].Computer-aideddiagnosissys- temisveryhelpfulforradiologistindetectionanddiagnosing abnormalitiesearlierandfaster[3].Thecomputeraideddiag- nosisisasecondopinionforradiologistsbeforesuggestinga biopsytest[4].Inrecentresearchliterature,itisobservedthat

∗ Correspondingauthor.Tel.:+919946104098.

E-mailaddresses:jinsak@yahoo.com(J.Kuruvilla),kgunavathi2000@yahoo.com(K.Gunavathi).

principlesofneuralnetworkshavebeenwidelyusedforthe detectionoflungcancerinmedicalimages[5].

For classificationoflung cancer,few methodsbased on neuralnetworkhavebeenreportedintheliterature.Abdulla et al. [6] proposed a computer aided diagnosis based on artificial neural networks for classification of lung cancer.

Thefeaturesusedforclassiﬁcationarearea,perimeterand shape.Themaximumclassiﬁcationaccuracyobtainedis90%.

Camarlinghiet al.[7]proposed acomputer-aided detection algorithmforautomaticlungnoduleidentification.Thesensi- tivityobtainedis80%with3FP/scan.Al-Kadietal.[8]proposed aclassificationmethodbasedonfractaltexturefeatures.The classificationaccuracyobtainedis83.3%.vanGinnekenetal.

[9] compared and combined six computer aided detection algorithms forpulmonarynodules.Thecombination ofsix algorithmsisabletodetect80%ofallnodulesattheexpense

http://dx.doi.org/10.1016/j.cmpb.2013.10.011

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Fig.1–CTimageoflungswithcancer.

ofonlytwofalsepositivedetectionsperscanand65%ofall noduleswithonly0.5falsepositives.Cascioetal.[10]proposed acomputer-aideddetection(CAD)systemfortheselectionof lungnodulesincomputertomography(CT)images.Thedetec- tionrateofthesystemis88.5%with6.6FPs/CTon15CTscans.

Areductionto2.47FPs/CTisachievedat80%efﬁciency.

2. Segmentation

The images are collected from a database of Lung Image Database Consortium(LIDC) and also from reputedhospi- tal.CTimages of155patients are collected including both menand women. The average age ofthe patients consid- eredis64.2years(ageoftheyoungestpatientis18yearsand theoldestpatientis85years).ThelowdoseCTscanimages areobtainedatkilovoltagepeakdistributionof120–140KVp withacurrentvaryingfrom25to40mAsdependinguponthe ageofthepatient.Thereconstructiondiametervariesfrom 260to400mm withaslice thickness of0.75–1.25mm. The totalnumber of110 nodulesofsize >3mmare considered inthis study and the nodules are referred bytwo radiolo- gists.Theﬁnalresponsewastheconsensusdecisionofthe tworadiologists.ThetworadiologistshavereferredtheLIDC CTscanswithoutconsideringtheannotationsavailableinthe LIDCdatabase.Bothprimaryandsecondarystagecancernod- ules(classiﬁedbytworadiologistsdependingonthesizeof thenodules)withfourdifferentkindsofnoduleslikeWell- circumscribed nodules, Vascularized nodules, Juxta-pleural nodulesandPleural-tailnodulesareconsideredinthework [11].Fig.1showstheCTimageoflungswithcancerousregion.

ThelungissegmentedfromtheCTimagesusingmorpho- logicaloperations.Thegrayscaleimageisﬁrstconvertedto binaryimage.Allthepixelsintheinputimagewithainten- sitygreaterthanathresholdlevelisreplacedwithvalue‘1’

andallpixelvalueswithaintensitylessthanthresholdlevel isreplacedwithvalue‘0’.Thethresholdleveliscalculated byOtsumethod[12].TheOtsumethodchoosesthethresh- oldleveltominimizetheintraclassvarianceoftheblackand white pixels.Fig. 2givesthe grayscale tobinary converted image.

Fig.2–Binaryimage.

Fig.3–Morphologicalopeningoutput.

Themorphologicalopeningoperationisperformedtothe binaryimagewithastructuringelement.Thestructuringis ashape,usedtoprobeorinteractwithagivenimage,with the purposeofdrawingconclusionson howthis shapefits ormissestheshapesintheimage.Thestructuringelement usedis‘periodicline’.Itisaflatstructuringelementcontain- ing2×(P+1)members.Thevalueof‘P’specifiesthesizeof the structuringelement. ThePvalue isselected as 2.One structuring element is located at the origin. Fig. 3 shows theoutputaftermorphologicaloperation.Theimageisthen invertedandclearborderoperationisperformed.Theclear borderoperationsuppressesstructuresthatarelighterthan theirsurroundings andthat areconnectedtotheborderof theimage.Thesegmentationmethodusesonlymorphologi- caloperationsandanaverageof98%ofimagesissegmented correctly.Thesegmentedimagesareindependentlyreferred bytworadiologists.Mainadvantageofmorphologicalopera- tionistheirspeedandsimplicityofimplication.Fig.4shows thefinalsegmentedoutput.

3. Statistical parameters

Thestatistical parametersare extractedfrom theregionof interest.Theregionofinterestisthesegmentedsingleslices containing 2 lungs. The parameters considered are mean, standarddeviation,skewnessandkurtosis[13].Inthispaper

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Fig.4–Segmentedoutput.

thehigherordermomentslikeﬁfthcentralmomentandsixth centralmomentarealsoconsidered.

3.1. Mean

Themean,ofthepixelvaluesinthedeﬁnedwindow,esti- mates the value in the image in which central clustering occurs.

= 1 MN

M

i=1

N

j=1

p(i,j)

wherep(i,j)istheintensityvalueofthepixelatthepoint(i,j).

M×Nisthesizeoftheimage.

3.2. Standarddeviation

Thestandarddeviation,istheestimateofthemeansquare deviationofgraypixelvaluep(i,j)fromitsmeanvalue.

=

¹

MN

M

i=1

N

j=1

(p(i,j)−)²

3.3. Skewness

Skewness,Scharacterizesthedegreeofasymmetryofapixel distributioninthespeciﬁedwindowarounditsmean.Skew- nessisapurenumberthatcharacterizesonlytheshapeofthe distribution.

S= 1 MN

M

i=1

N

j=1

p(i,j)−

3

3.4. Kurtosis

Kurtosis,Kmeasuresthepeaknessorﬂatnessofadistribution relativetoanormaldistribution.

K= 1 MN

M

i=1

N

j=1

p(i,j)−

4

Fifthcentralmoment= 1 MN

M

i=1

N

j=1

p(i,j)−

5

Sixthcentralmoment= 1 MN

M

i=1

N

j=1

p(i,j)−

6

4. Artiﬁcial neural network

The neural nets can be trained to perform pattern classification [14].Thesimplest neuralnetworkused forpattern classificationconsistsofalayerofinputunitandasingleout- putunit.Bothfeedforwardandfeedforwardbackpropagation neuralnetworksareusedforclassification.

4.1. Feedforwardneuralnetwork

Infeedforwardneuralnetworksinformationalwaysmoves inonedirectiononly,thereisnofeedback.Theinformation movesforwardfrominputlayerthroughhiddenlayertothe outputlayer.ThenetworksusedareHebb,Perceptron,Ada- lineandMadalinenetworks.InHebbnetworklearningisdone bymodiﬁcation ofthe weightsofthe neurons.Theweight isinformationusedbyneuralnetworktosolveaproblem.If twointerconnectedneuronsareboth‘on’atthesametime, then the weightbetweenthose neuronsare increased[15].

ThePerceptronnetworkissupervisedclassifierforclassify- inganinputintooneoftwopossibleoutputs.Itisatypeof linearclassifier.Theclassificationalgorithmmakesitspredic- tionsbasedonalinearpredictorfunctioncombiningasetof weightswiththefeaturevectordescribingagiveninput.Both biasandthresholdareneededinthisnetwork.TheAdaline (AdaptiveLinearNeuron)networkusesbipolaractivationsfor itsinputsignalsandtargetoutput.Theweightsontheconnec- tionfromtheinputunitstotheadalinenetworkareadjustable.

Thenetworkhasabias,whichactslikeanadjustableweight onaconnectionfromaunitwhoseactivationisalways1.A Madaline networkconsistsofadalines arrangedinamulti- layernet.Itisatwolayerneuralnetworkwithasetofadalines inparallelasitsinputlayerandasingleprocessingelement initsoutputlayer.

4.2. Feedforwardbackpropagationneuralnetwork Thebackpropagationisasystematicmethodoftrainingmul- tilayer neural networks in asupervised manner. The back propagationmethod,alsoknownastheerrorbackpropaga- tionalgorithm,isbasedontheerror-correctionlearningrule.

Thebackpropagationnetworkconsistsofatleastthreelayers ofunits:aninputlayer,atleastoneintermediatehiddenlayer andoneoutputlayer.Theunitsareconnectedinfeedforward fashionwithinputsunitsconnectedtothehiddenlayerunits andthehiddenlayerunitsareconnectedtotheoutputlayer

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units.Aninputpatternisforwarded tothe outputthrough inputtohiddenandhiddentooutputweights.Theoutputof thenetworkistheclassiﬁcationdecision.

4.3. Typesoftrainingfunctionsusedforclassiﬁcation The back propagation neural networks are trained with thirteen training algorithms or functions [16]. The training functions used are Gradient descent back propagation (traingd), Gradient descent with variable learning rate (traingda),Gradientdescentwithmomentum(traingdm),Gra- dient descent with variable learning rate and momentum (traingdx),Resilientbackpropagation(trainrp),ConjugateGra- dientAlgorithms(traincgf,traincgp,traincgb,trainscg),Quasi NewtonBFGS(trainbfg),OneStepSecantAlgorithm(trainoss), Levenberg–Marquardt (trainlm) and Automated Regulariza- tion(trainbr).

4.4. Gradientdescentbackpropagation(traingd)

Traingdisatrainingfunctionwhichupdatesweightandbias valuesaccordingtogradientdescent.Anetworkcanbetrained whenitsweight,netinput,andtransferfunctionshavederiva- tivefunctions. The weightsand biases are updated inthe directionofthenegativegradientoftheperformancefunc- tion[17].Thelearningrate‘lr’ismultipliedwiththenegative ofthegradienttodeterminethechangestotheweightsand biases.Backpropagationisusedtocalculatederivativesofper- formance(dperf)withrespecttotheweightandbiasvariables X.Eachvariableisadjustedaccordingtogradientdescent:

dX=lr×dprf dX

4.5. Gradientdescentwithvariablelearningrate (traingda)

Traingdaisatrainingfunctionthatupdatesweightandbias valuesdependingonthegradientdescentwithadaptivelearn- ing rate. Theperformance of the back propagation neural networkissensitivetothe learningrate. Itisnotpractical todeterminetheoptimalsettingforthelearningratebefore training.Theoptimallearningratechangesduringthetraining process,asthealgorithmmovesacrosstheperformancesur- face.Anynetworkcanbetrainedwhenitsweight,netinput, andtransferfunctionsarederivativefunctions.Backpropaga- tionalgorithmisusedtocalculatederivativesofperformance (dperf)withrespecttotheweightandbiasvariablesX.Ifper- formancedecreasestowardthegoal,thenthelearningrate isincreasedbyaconstantfactor.Ifperformanceincreasesby morethanthemaximumperformanceﬁxed,thelearningrate isdecreasedbyaconstantfactor.

4.6. Gradientdescentwithmomentum(traingdm) Traingdm is a network training function that updates weightand biasvalues accordingto gradientdescent with

momentum.Eachvariableisadjustedaccordingtogradient descentwithmomentum,

dX=mc×dXprev+lr×(1−mc)×dperf dX

where‘dXprev’isthepreviouschangetotheweightorbias,

‘mc’ismomentumconstantand‘lr’islearningrate.

4.7. Gradientdescentwithvariablelearningrateand momentum(traingdx)

Traingdxisanetworktrainingfunctionthatupdatesweight andbiasvaluesaccordingtogradientdescentmomentumand adaptivelearningrate.Eachvariableisadjustedaccordingto thegradientdescentwithmomentum[18].Theperformance canbeincreasedifthelearningrateisallowedtochangedur- ingthetrainingprocess.Theinitialnetworkoutputanderror arecalculatedﬁrst.Ateachepochnewweightsandbiasesare calculatedusingthecurrentlearningrate.Newoutputsand errorsarethencalculated.Eachvariableisadjustedaccording tothegradientdescentwithmomentum.

dX=mc×dXprev+lr×mc×dperf dX

Whenmomentumisconsidered,ifthenewerrorexceeds theolderrorbymorethanapredeﬁnedratio,thenewweights andbiasesarediscarded.

4.8. Resilientbackpropagation(trainrp)

Trainrp isanetworktraining functionthat updatesweight and bias values accordingto the resilient backpropagation algorithm [19]. The purpose of the resilient backpropagation(Rprop)trainingalgorithmistoeliminatetheeffectsof the magnitudesof the partialderivatives. Thesign of the derivative determines the direction of the weight update.

Themagnitudeofthederivativehasnoeffectontheweight update.Ifthederivativeiszero,thentheupdatevalueremains thesame.Whenevertheweightsareoscillating,theweight changeisreduced.Iftheweightcontinuestochangeinthe samedirectionforseveraliterations,thenthemagnitudeof theweightchangeisincreased.

4.9. Conjugategradientalgorithms

Inthe conjugategradientalgorithmsasearchisperformed alongconjugatedirections.Inconjugategradientalgorithms, thestepsizeisadjustedateachiteration[20].Asearchismade alongtheconjugategradientdirectiontodeterminethestep sizethatminimizestheperformancefunctionalongthatline.

(a) Fletcher-ReevesUpdate(traincgf):Thesteepestdescentdirec- tion (negative of the gradient) is searched by the ﬁrst iteration.

P0=−g0

whereP₀istheinitialsearchgradientandg₀istheinitial gradient.Theoptimaldistancetomovealongthecurrent searchdirectionisobtainedbylinesearch.

X_k+1=X_k+˛_kp_k

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sothatitisconjugatetotheprevioussearchdirections.

Thenewsearchdirectionisdeterminedbycombiningthe newsteepestdescentdirectionwiththeprevioussearch direction.

p_k=−g_k+ˇ_kp_k₋₁

wherep_k−1 isthe previoussearch directionand ˇ_kis a constant.

ForFletcherReevesupdate,theconstantˇ_kisobtainedby

ˇ_k= g^T_kg_k g^T_k−tg_k−1

Thisistheratioofthesquareofthecurrentgradienttothe squareofthepreviousgradient.Eachvariableisadjusted accordingtothefollowing:

X=X+a×dX

where dX is the search direction.The parameter ‘a’ is selectedtominimizethe performancealong thesearch direction.

(b) PolakandRibiere(traincgp)

InPolakandRibiereupdate,theconstantˇ_kisobtainedby

ˇ_k= g^T_kg_k g^T_k₋_tg_k−1

Thisistheinnerproductofthepreviouschangeinthe gradientwiththecurrentgradientdividedbythesquare ofthepreviousgradient.

(c) PowellandBealeRestarts(traincgb)

Thesearchdirectionisperiodicallyresettothenegativeof thegradientforallconjugategradientalgorithms[21].The standardresetpointoccurswhenthenumberofiterations isequaltothenumberofnetworkparameters.ThePowell andBealeproposedanewresetmethodtoincreasethe efﬁciencyofthetrainingprocess.Thistechniquerestarts ifthereisverylittleorthogonalityleftbetweenthecurrent gradientandthepreviousgradient.Thisistestedwiththe followinginequality:

|g^T_k−1g_k|≥0.2×||g_k||²

Iftheconditionissatisﬁed,thesearchdirectionisresetto thenegativeofthegradient.

(d) ScaledConjugateGradientAlgorithm(trainscg)

Eachoftheconjugategradientalgorithmsrequiresaline searchateachiteration.Thislinesearchiscomputation- allyexpensive.Itrequiresthatthenetworkresponseto all training inputsbe computed several times foreach search. Thescaled conjugate gradient algorithm (SCG), wasdesignedtoavoidthetime-consuminglinesearch.

4.10. QuasiNewtonBFGS(trainbfg)

Trainbfgisanetworktraining functionthatupdatesweight andbiasvaluesaccordingtotheBFGSquasi-Newtonmethod.

updateofNewton’smethodisgivenby W_k+1=W_k−A⁻¹_k g_k

whereA_kistheHessianmatrixoftheperformanceindexin the current valuesof the weights and biases.As A_k value increasesthecomplexityandtimeconsumptionincomput- ingW_k+1increases.Itiscomplexandexpensivetocomputethe Hessianmatrix.QuasiNewtonmethodisbasedonNewton’s methodbutdoesnotrequirethecalculationofHessianmatrix.

AnapproximationofHessianmatrixisupdatedateachiter- ationofthealgorithm.Theupdateiscomputedasafunction ofthegradient.

4.11. Onestepsecantalgorithm(trainoss)

Trainossisanetworktrainingfunctionthatupdatesweight and bias values according to the one step secant method [22].TheBFGSalgorithmrequiresmorestorageandcomputa- tionineachiterationthantheconjugategradientalgorithms.

Theone stepsecant(OSS) methodisanattempt tobridge thegapbetweentheconjugategradientalgorithmsandthe quasi-Newtonalgorithms.Thisalgorithmdoesnotstorethe complete Hessianmatrix.Itassumesthatateachiteration, thepreviousHessianwastheidentitymatrix.Theadditional advantageisthatthenewsearchdirectioncanbecalculated withoutcomputingamatrixinverse.

4.12. Levenberg–Marquardt(trainlm)

Trainlmisanetworktrainingfunctionthatupdatesweight andbiasstatesaccordingtoLevenberg–Marquardtoptimiza- tion [23]. Trainlmisthe fastest backpropagationalgorithm, andishighlyrecommendedasaﬁrstchoicesupervisedalgo- rithm, although it does require more memory than other algorithms.Whentheperformancefunctionhastheformofa sumofsquares,thentheHessianmatrixcanbeapproximated as

H=J^TJ

Thegradientcanbecomputedas g=J^Te

whereJistheJacobianmatrixthatcontainsﬁrstderivatives ofnetworkerrorswithrespecttotheweightsandbiasesand

‘e’isavectorofnetworkerrors.TheJacobianmatrixcanbe computedusingbackpropagationalgorithm.Itismuchless complexthancomputingtheHessianmatrix.

TheLevenberg–Marquardtalgorithmusesanapproxima- tiontotheHessianmatrix.

X_k+1=X_k−(J^TJ+I)⁻¹J^Te whereIistheidentitymatrix.

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4.13. Automatedregularization(trainbr)

Trainbrisanetworktrainingfunctionthatupdatestheweight andbiasvaluesaccordingtoLevenberg–Marquardtoptimiza- tion. It minimizes a combination of squared errors and weightsand,thendeterminesthecorrectcombinationsoas toproduceanetworkwhichgeneralizeswell.Theprocessis calledBayesianregularization[24].Itisdesirabletodetermine theoptimalregularizationparametersinanautomatedfash- ion.Theweightsandbiasesofthenetworkareassumedto berandomvariables withspeciﬁeddistributions. Theregu- larizationparametersare relatedtotheunknownvariances associatedwiththesedistributions.TheBayesianregulariza- tiontakesplacewithintheLevenberg–Marquardtalgorithm.

BackpropagationisusedtocalculatetheJacobianjXofperfor- mancePERFwithrespecttotheweightandbiasvariablesX.

EachvariableisadjustedaccordingtoLevenberg–Marquardt jj=jX×jX

je=jX×E

dX=−jj+I×mu je

whereEisallerrorsandIistheidentitymatrix.

Twonewtrainingfunctionsareproposedinthispaper.

4.14. Proposedtrainingfunctions

4.14.1. Trainingfunction1

Themomentumvalueandthelearningrateinﬂuencetheclas- siﬁcationaccuracyandthemeansquareerroroftheneural network.Anewtrainingfunctionwhichincludesthemomen- tumfactorandthelearningrateisproposed.Inthetraining function1eachvariableisadjustedaccordingtothegradient descentwithmomentumgivenby

dX=mc×dXprev+lr×(1−mc)×mc×dperf dX

where‘dXprev’isthepreviouschangetotheweightorbias,

‘mc’ismomentumconstant,‘lr’islearningrateand‘dperf’is thederivativeofperformancewithrespecttotheweightand biasvariablesX.Theclassiﬁcationaccuracyisincreasedbythe trainingfunction1.

4.14.2. Trainingfunction2

Thetrainingfunction1ismodiﬁedtoreducethemeansquare error. In the training function 2 each variable is adjusted accordingtothegradientdescentwithmomentumgivenby

dX=3.7×mc×dXprev+lr×(1−mc)×mc×dperf dx

where‘dXprev’isthepreviouschangetotheweightorbias,‘mc’

ismomentumconstant,‘lr’islearningrateand‘dperf’isthe derivativeofperformancewithrespecttotheweightandbias variablesX.Themeansquareerrorisminimumfortraining function2.

5. Experimental results

Thestatisticalparametersarecalculatedforsegmentedsin- gleslicescontaining2lungsandgivenasinputtotheneural network.Thetrainingsetfortheneuralnetworkconsistsof 70%ofthetotalimagesandthetestingsetis30%ofthetotal images.Imagesfortrainingandtestingrefertothesegmented singleslicescontaining2lungs.Thesensitivity,speciﬁcityand accuracyarecalculatedforeachnetwork.

5.1. Sensitivity

Itmeasurestheproportionofactualpositiveswhicharecor- rectlyidentiﬁed.Thatisthepercentageofsegmentedslices containingcancerousnoduleiscorrectlyclassiﬁedascancer- ous.

Sensitivity= TP TP+FN

TruePositive(TP):Segmentedslicecontainingcancernodule isclassiﬁedascancerous.

FalsePositive(FP):Segmentedslicewithoutcancernoduleis classiﬁedascancerous.

TrueNegative(TN):Segmentedslicewithoutcancernodule isclassiﬁedasnon-cancerous.

FalseNegative(FN):Segmentedslicecontainingcancernod- uleisclassiﬁedasnon-cancer

5.2. Speciﬁcity

Itmeasurestheproportionofnegativeswhichare correctly identiﬁed.Thepercentageofsegmentedsliceswithoutcan- cerousnoduleiscorrectlyidentiﬁedasnoncancerous.

Speciﬁcity= TN TN+FP 5.3. Accuracy

Accuracyisastatisticalmeasureofhowwellaclassiﬁercor- rectlyidentiﬁesorexcludesacondition.Theaccuracyisthe proportionoftrueresults(bothtruepositiveandtruenegative) inthepopulation.

Accuracy= TP+TN TP+TN+FP+FN

Theresultshowsthattheparameterskewnessgivesmaxi- mumclassificationaccuracy.Thehigherordermomentsare considered, but nosignificant improvement inthe classifi- cationaccuracyisobserved.Comparedtothefeed forward networks, the classification accuracy of back propagation neuralnetworkismore.Theclassificationaccuracyoffeed forwardnetworksandbackpropagationnetworkisshownin Fig.5.Allthethirteentrainingfunctionsofthebackpropa- gationnetworkaretrainedwithdifferentmomentumfactor andlearningrate.Themomentumandlearningratearevar- iedfrom0.1to0.9.Keepingoneoftheseparametersconstant andvaryingtheother,theperformanceofthenetworkisstud- ied.Thebestclassificationaccuracyandleastmeansquare errorofdifferenttrainingfunctionsfordifferentmomentum

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Traingd 0.4 0.6 86.7 0.1242

Traingda 0.3 0.5 88.89 0.118

Traingdm 0.4 0.7 88.89 0.115

Traingdx 0.3 0.7 91.11^a 0.112^a

Traincgf 0.3 0.5 75.5 0.164

Traincgb 0.6 0.3 73.3 0.198

Traincgp 0.4 0.8 75.56 0.162

Trainlm NA 0.8 82.2 0.144

Trainoss 0.6 0.6 73.3 0.196

Trainrp 0.4 0.7 80 0.154

Trainscg 0.6 0.3 73.3 0.197

Trainbfg NA 0.5 80 0.156

Trainbr 0.4 0.6 88.89 0.115

a Themaximumclassiﬁcationrateobtainedamongthe13trainingfunctions.

andlearningrateare showninTable1.Table1showsthat the training function Traingdx gives the maximum classi- ﬁcationaccuracy of91.11%.The Speciﬁcity, Sensitivityand AccuracyofTraingdxandthe proposed training function1 withmomentum0.3andlearningrate0.7areshowninFig.6.

TheclassiﬁcationaccuracyandmeansquareerrorofTraingdx,

75 80 85 90 95 100

Hebb Madaline

Classiﬁcaon Percentage

Adaline Perceptron

propagaon back

Fig.5–Classiﬁcationaccuracyoffeedforwardnetworks andbackpropagationnetwork.

80 85 90 95 100 105

Percentage of Classiﬁcaon

Speciﬁcity

Traingdx versus proposed training funcon 1

Sensivity Accuracy

Traingdx

Proposed training funcon

Fig.6–Traingdxversusproposedtrainingfunction1.

Fig.7–Classiﬁcationaccuracyandmeansquareerrorof Traindx,trainingalgorithm1andtrainingalgorithm2.

0 10 20 30 40 50 60 70 80 90 100

-5 0 5 10 15 20 25 30 35

Sensivity

FPs/Scan

FROC curve

Proposed method

Fig.8–FROCcurve.

trainingfunction1andtrainingfunction2withmomentum 0.3andlearningrate0.7areshowninFig.7.Theperformance ofthesystemisanalyzedbytheFROC(Free-responseReceiver OperatingCharacteristic)curveshowninFig.8.Thesensitivity ismeasuredasthepercentageofsegmentedslicescontain- ingcancerousnoduleiscorrectlyclassiﬁedascancerous.The FROCcurveshowsthatthesensitivityis82%with2FPs/scan andthesensitivityincreasedto90%with15FPs/scanandto 91.4%with30FPs/scan.

6. Conclusion

Acomputeraidedsegmentationandclassiﬁcationmethodis proposed.Morphologicaloperationsare usedforsegmenta- tionandclassiﬁcationisdonebydifferentneuralnetworks.

Theregionofinterestisthesegmentedsingleslicescontain- ing 2lungs. Thestatisticalparametersare usedasfeatures forclassification.Comparedtothestatisticalparameterslike mean,standarddeviation,kurtosis,fifthcentralmomentand sixth centralmoment, skewness givesthe maximum classification accuracy. There is5–8% increase inclassification accuracyforskewness.Amongthealreadyavailablethirteen training functions, the traingdx training functiongives the maximum classification accuracyof 91.11%. The proposed trainingfunction1givesclassificationaccuracyof93.3%with aspecificityof100%andsensitivityof91.4%.Theproposed

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trainingfunction2givesclassificationaccuracyof93.3%and meansquareerrorof0.0942.Theperformanceoftheproposed CADsystemisgoodwithasensitivityof82%with2FPs/scan, whichisincreasedto91.4%with30FPs/scan.Thesensitivity ismeasuredasthepercentageofsegmentedslicescontaining cancerousnoduleiscorrectlyclassifiedascancerous.Themis- classificationoccurredintheimageswherethecancernodule islocatednearthepleuralsideofthelungs.

Conﬂict of interest

Theauthorsdonothaveanyconflictsofinterest,anddisclose anyfinancialandpersonalrelationshipswithotherpeopleor organizationsthatcouldinappropriatelyinfluence(bias)the presentedwork.

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