fungsiemenscom Alan Katz St Francis Hospital 100 Port Washington Blvd Roslyn New York USA Abstract Coronary Heart Disease is the single leading cause of death worldwide with lack of early diagnosis being a key contributory factor This disease can be ID: 24712
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SparseclassiersforAutomatedHeartWallMotionAbnormalityDetectionGlennFung,MaleehaQazi,SriramKrishnan,JinboBi,BharatRaoSiemensMedicalSolutions51ValleyStreamParkwayMalvern,PA,USAglenn.fung@siemens.comAlanKatzSt.FrancisHospital100PortWashingtonBlvdRoslyn,NewYork,USAAbstractCoronaryHeartDiseaseisthesingleleadingcauseofdeathworld-wide,withlackofearlydiagnosisbeingakeycontributoryfactor.Thisdiseasecanbediagnosedbymea-suringandscoringregionalmotionoftheheartwallinechocardiographyimagesoftheleftventricle(LV)oftheheart.Wedescribeacompletelyautomatedandrobusttech-niquethatdetectsdiseasedheartsbasedonautomaticde-tectionandtrackingoftheendocardiumandepicardiumoftheLV.Wedescribeanovelfeatureselectiontechniquebasedonmathematicalprogrammingthatresultsinarobusthyperplane-basedclassier.Theclassierdependsonlyonasmallsubsetofnumericalfeatureextractedfromdual-contourstrackedthroughtime.Weverifytherobustnessofoursystemonechocardiogramscollectedinroutineclini-calpracticeatonehospital,bothwiththestandardcross-validationanalysis,andthenonaheld-outsetofcompletelyunseenechocardiographyimages.1.IntroductionCardiovascularDisease(CVD)isaglobalepidemicthatistheleadingcauseofdeathworldwide(17mil.deaths)[16].IntheUnitedStates,CVDaccountedfor38%ofalldeathsin2002[1]andwastheprimaryorcontributingcausein60%ofdeaths.CoronaryHeartDisease(CHD)accountsformorethanhalftheCVDdeaths(roughly7.2mil.deathsworldwideeveryyear,and1ofevery5deathsintheUS),andisthesinglelargestkillerintheworld.Itiswell-knownthatearlydetection(alongwithprevention)isanexcellentwayofcontrollingCHD.CHDcanbedetectedbymeasur-ingandscoringtheregionalandglobalmotionoftheleftventricle(LV)oftheheart;CHDtypicallyresultsinwall-motionabnormalities,i.e.,localsegmentsoftheLVwallmoveabnormally(moveweakly,notatall,oroutofsyncwiththerestoftheheart),andsometimesmotioninmulti-pleregions,orindeedtheentireheart,iscompromised.TheLVcanbeimagedinanumberofways.Themostcom-monmethodistheechocardiogramanultrasoundvideoofdifferent2-Dcross-sectionsoftheLV.Unfortunately,echocardiogramsarenotoriouslydifculttointerpret,evenforthebestofphysicians.Inter-observerstudieshaveshownthatevenworld-classexpertsagreeontheirdiagnosisonly80%ofthetime[10],andintra-observerstudieshaveshownasimilarvariationwhentheexpertreadsthesamecasetwiceatwidelydifferentpointsintime.Thereisatremendousneedforanautomatedsecond-readersystemthatcanprovideobjectivediagnos-ticassistance,particularlytotheless-experiencedcardiolo-gist.Inthispaper,weaddressthetaskofbuildingacomputer-aideddiagnosissystemthatcanautomaticallydetectwall-motionabnormalitiesfromechocardiograms.Thefollowingsectionprovidessomemedicalback-groundoncardiacultrasoundandthestandardmethodol-ogyusedbycardiologiststoscorewall-motionabnormali-ties.Wealsodescribeourreal-lifedataset,whichconsistsofechocardiogramsusedbycardiologistsatSt.FrancisHeartHospitaltodiagnosewall-motionabnormalities.Thenextsectionprovidesanoverviewofourproposedsystemwhichwebuiltontopofanalgorithmthatdetectsandtrackstheinnerandoutercardiacwalls[9,17,5,6].Itconsistsofaclassierthatclassiesthelocalregionoftheheartwall(andtheentireheart)asnormalorabnormalbasedonthewallmotion.Thenwedescribeourmethodologyforfeatureselectionandclassication,followedbyourexperimentalresults.Weconcludewithsomethoughtsaboutourplansforfutureresearch.2.MedicalBackgroundKnowledgeTherearemanyimagingmodalitiesthathavebeenusedtomeasuremyocardialperfusion,leftventricularfunction,andcoronaryanatomyforclinicalmanagementandre-search;forthisprojectweareusingechocardiography.TheCardiacImagingCommitteeoftheCouncilonClini- calCardiologyoftheAmericanHeartAssociationhascre-atedastandardizedrecommendationfortheorientationoftheheart,angleselectionandnamesforcardiacplanesandnumberofmyocardialsegments[4].Thisisthestandard-izationusedinthisproject.Accurateregionalwallmotionanalysisoftheleftven-tricleisanessentialcomponentofinterpretingechocardio-grams(echos).Theleftventricle(LV)isdividedinto17myocardialsegmentsasshowninFigure1(modiedfromreference[4]),whicharefedby3coronaryarteries:theleftanteriordescending(LAD)(feedssegments1,2,7,8,13,14,17),rightcoronaryartery(RCA)(feedssegments3,4,9,10,15),andtheleftcircumexcoronaryartery(LCX)(feedssegments5,6,11,12,16). Figure1.Display,onacircumferentialpolarplot,ofthe17myocardialsegmentsandtherecommendednomenclaturefortomographicimagingoftheheart.Modiedfromreference[4].TheechocardiogramsarerunthroughanalgorithmwhichautomaticallydetectsandtracksboththeendocardialandepicardialbordersoftheLV[5,6].Motioninterfer-ences(e.g.probemotion,patientmovement,respiration,etc.)arecompensatedforusingglobalmotionestimationbasedonrobuststatisticsoutsidetheLV.Numericalfeaturevectorsextractedfromthedual-contourstrackedthroughtimeformthebasisforregionalwallmotionclassication.3.DataThedataisbasedonstandardadulttransthoracicB-modeultrasoundimagescollectedfromthefourstandardviews:apical4chamber(A4C),apical2chamber(A2C),parasternallongaxis(PLAX)orapical3chamber(A3C), Figure2.Thethreebasicimageplanesusedintransthoracicechocardiography.Theventricleshavebeencutawaytoshowhowtheseimageplanesintersecttheleftandrightventricles.Dashedlinesindicatetheimageplanesatthegreatvesselandatriallevels.Fromreference[3]andparasternalshortaxis(PSAX)showninFigure2fromreference[3].Currentlyweareonlyutilizingtwoofthefourpossibleviews-A4CandA2C.Thesetwoviewsshow12ofthe16totalsegments,butthatisenoughtoachieveourgoalofclassifyinghearts.Eventhoughwehaveimagesatdifferentlevelsofstress(resting,low-dosestress,peak-dosestress,recovery)thisworkisbasedonimagestakenwhenthepatientwasrest-ing.Thegoalofthisworkistoautomaticallyprovideaninitialscoreorclassicationtodeterminewhetheraheartisnormalorabnormalgiventheultrasound.TheultrasounddatawascollectedfromSt.FrancisHeartHospital,Roslyn,NY,USA(abbrev:SF).TheSFdatacon-sistsof141casesthatwillbeusedfortraining,and59casesthatareear-markedasthenaltestset.Allthecaseshavebeenlabeledatthesegmentlevelbyagroupoftrainedcar-diologists.Theheartlevelclassicationlabelscanbeob-tainedfromthesegmentlevellabelsbyapplyingthefol-lowingdenition:Aheartisconsideredabnormaliftwoormoresegmentsareabnormal.4.MethodologyTheclassicationalgorithmusedinthesystemisbasedonanovelfeatureselectiontechnique,whichisinturnbasedonmathematicalprogramming.Asaresultweobtainahyperplane-basedclassierthatonlydependsonasub- Figure3.OneframefromanA4CimageclipwiththeyellowboxshowingthelocalizedLV,andtheyellowdotsrepresentingthecontrolpointsalongthedetectedcontour.setofnumericalfeaturesextractedfromthedual-contourstrackedthroughtime,andthesearethenusedtoprovideclassicationforeachsegmentandtheentireheart.4.1.ImageprocessingTherststeptowardclassicationoftheheartinvolvesautomaticcontourgenerationoftheLV[9].Ultrasoundisknowntobenoisierthanothercommonmedicalimag-ingmodalitiessuchasMRIorCT,andechocardiogramsareevenworseduetothefastmotionoftheheartmus-cleandrespiratoryinterferences.Theframeworkusedbythealgorithmweuseisidealfortrackingechosequencessinceitexploitsheteroscedastic(i.e.location-dependentandanisotropic)measurementuncertainties.Theprocesscanbedividedinto2steps:borderdetectionandbordertracking.BorderdetectioninvolveslocalizingtheLVonmultipleframesoftheimageclip(showninFigure3asaboxdrawnaroundtheLV),andthendetectingtheLV'sshapewithinthatbox.BordertrackinginvolvestrackingthisLVborderfromoneframetothenextthroughtheen-tiremovieclip.Motioninterferences(e.g.probemotion,patientmovement,respiration,etc.)arecompensatedforbyusingglobalmotionestimationbasedonrobuststatis-ticsoutsidetheLV.ThisglobalmotionestimationcanbeseeninFigure4asaverticalredlinenearthecenteroftheimage.Afterdetectionandtrackingnumericalfeaturesarecomputedfromthedual-contourstrackedthroughtime.Thefeaturesextractedarebothglobal(involvingthewholeLV)andlocal(involvingindividualsegmentsvisibleintheim-age),andarebasedonvelocity,thickening,timing,volumechanges,etc. Figure4.OneframefromanA4Cimageclipwiththeouterandinnercontourcontrolpointsshown.Theredverticallineshowsuseofglobalmotioncompensation,andthetwosquaresdenotethecentersoftheindividualcontours.4.2.ExtractedFeaturesAnumberoffeatureshavebeendevelopedtocharacter-izecardiacmotioninordertodetectcardiacwallmotionabnormalities,amongthem:globalandlocalejectionfrac-tion(EF)ratio,radialdisplacement,circumferentialstrain,velocity,thickness,thickening,timing,eigenmotion,curva-ture,andbendingenergy.Someofthesefeatures,includingtiming,eigenmotion,curvature,localEFratioandbendingenergy,arebasedontheendocardialcontour.Duetothepatientexaminationprotocol,onlythesystole(i.e.contractionphaseoftheheart)isrecordedforsomepatients.Inorderforthefeaturestobeconsistent,thesys-toleisextractedfromeachpatientbasedonthecavityareachange.Foreachframe,theLVcavityareacanbeestimatedaccuratelybasedontheendocardialcontourofthatframe.Theframecorrespondingtothemaximalcavityareathatisachievedattheendofdiastolicphase(expansionphaseoftheheart)istheframeconsideredtobethebeginningofsystole.Theframecorrespondingtotheminimalcavityarea(achievedattheendofsystolicphase)istheframeassumedtobetheendofsystole.Forthetimebeing,allfeaturesarecomputedbasedonlyonthesystolicphase.However,themethodsusedtocalculatethefeaturesaregenerallyappli-cableforthediastolicphaseaswell.Thefollowingisabasicdescriptionofsomeofthefea-tures:Timing-basedfeatures:examinethesynchronousness ofthecardiacmotion,i.e.whetherallthepointsalongtheLVmoveconsistentlyornot.Eigenmotion-basedfeatures:determinethemostsig-nicantmovingdirectionofapointandtheamountofit'smotioninthatdirection.Curvature-basedfeatures:Aremainlyaimedatdetect-ingabnormalitiesattheapex.Itisalsousefulinidenti-fyingmoregeneralabnormalitiesassociatedwithcar-diacshapes.Ifasegmentisdead,itmaystillmovebecauseitisconnectedtoothersegments,butwecanobservethatit'sshapewilllargelyremainunchangedduringthecardiaccycles.Curvaturecancapturethistypeofinformation.LocalEFratiofeatures:Areaimedatcapturinglocalcardiaccontractionabnormalities.Bendingenergyfeatures:Assumingthattheprovidedcontourismadeofelasticmaterialandmovingundertension,thenthebendingenergyassociatedwiththecontourmaybeusedtocapturethecardiaccontractionstrengthofasegmentorthewholeLV.Circumferentialstrainfeatures:alsocalledFractionalShortening,measureshowmuchthecontourbetweenanytwocontrolpointsshrinksinthesystolicphase.Ingeneral,theglobalversionofcertainfeatures(e.g.ra-dialdisplacement,radialvelocity,etc)canbecalculatedbytakingthemean,orstandarddeviation,ofthe6segment'srespectivefeaturevaluesfromanyoneview.Allinallwehad192localandglobalfeatures,allofwhichwerecontin-uous.4.3.ClassicationandFeatureSelectionOneofthedifcultiesinconstructingaclassierforthistaskistheproblemoffeatureselection.Itisawell-knownfactthatareductiononclassierfeaturedependenceim-provestheclassiergeneralizationcapability.However,theproblemofselectinganoptimalminimumsubsetoffea-turesfromalargepool(intheorderofhundreds)ofpo-tentialoriginalfeaturesisknowntobeNP-hard.Recently,Mikaetal,proposedanovelmathematicalprogrammingformulationforFisher'sLinearDiscriminantusingkernels[14,13],thisnewformulationsincludedaregularizationtermsimilartotheusedinthestandardSVMformulation[12].WewillmakeuseofMika'sformulationbutbyusingthe1-norminsteadofthe2-normwewillobtainedsolutionsthataremoiresparseandhencedependonasmallernum-beroffeatures.Thenextsectiondescribethedetailsoftheapproach.4.4.Fisher'sLinearDiscriminantLetAi2Rdlbeamatrixcontainingtheltrainingdatapointsond-dimensionalspaceandlithenumberoflabeledsamplesforclasswi,i2fg.FLD[7]istheprojection ,whichmaximizes,J( )= TSB TSW (1)whereSB=(m+ m )(m+ m )TSW=Xi2fg1 li Ai mieTli Ai mieTliTarethebetweenandwithinclassscattermatricesrespec-tivelyandmi=1 liAieliisthemeanofclasswiandeliisanlidimensionalvectorofones.Transformingtheaboveproblemintoaconvexquadraticprogrammingprob-lemprovidesussomealgorithmicadvantages.Firstnoticethatif isasolutionto(1),thensoisanyscalarmulti-pleofit.Thereforetoavoidmultiplicityofsolutions,weimposetheconstraint TSB =b2,whichisequivalentto T(m+ m )=bwherebissomearbitrarypositivescalar.Thentheoptimizationproblem(1)becomes,min 2Rd TSW s:t: T(m+ m )=b(2)Forbinaryclassicationproblemsthesolutionofthisproblemis =bS 1W(m+ m ) (m+ m )TS 1W(m+ m )(3)AccordingtothisexpansionsinceS 1Wispositivedeniteunlessthedifferenceoftheclassmeansalongagivenfea-tureiszeroallfeaturescontributestothenaldiscriminant.Ifagivenfeatureinthetrainingsetisredundant,itscon-tributiontothenaldiscriminantwouldbearticialandnotdesirable.AsalinearclassierFLDiswell-suitedtohan-dlefeaturesofthissortprovidedthattheydonotdominatethefeatureset,thatis,theratioofredundanttorelevantfea-turesisnotsignicant.Althoughthecontributionofasingleredundantfeaturetothenaldiscriminantwouldbenegligi-blewhenseveralofthesefeaturesareavailableatthesametime,theoverallimpactcouldbequitesignicantleadingtopoorpredictionaccuracy.Apartfromthisimpact,inthecontextofFLDtheseundesirablefeaturesalsoposenumer-icalconstraintsonthecomputationofS 1Wespeciallywhenthenumberoftrainingsamplesislimited.Indeed,whenthe numberoffeatures,dishigherthanthenumberoftrainingsamples,l,SWbecomesill-conditionedanditsinversedoesnotexist.Henceeliminatingtheirrelevantandredundantfeaturesmayprovideatwo-foldboostontheperformance.InwhatfollowsweproposeasparseformulationofFLD.Theproposedapproachincorporatesaregularizationcon-straintontheconventionalalgorithmandseekstoeliminatethosefeatureswithlimitedimpactontheobjectivefunction.4.5.SparseFisher'sLinearDiscriminantvialinearprogrammingWeproposeaformulationsimilartotheoneusedfor1-normSVMclassiers[2]wherethe1-normisintroducedforbothmeasuringtheclassicationerrorandregulation.Theuseofthe1-norminsteadofthe2-normleadstolinearprogrammingformulationswhereverysparsesolutionscanbeobtained.Ourobjectiveistoformulateanalgorithmthatcanbeseenasanapproximationto(1)andthatprovidesasparseprojectionvector .Inorderachievethisweaddaregularizationtermtotheobjectivefunctionof(2):min 2Rd TSW +k k1s:t: T(m+ m )=b(4)Whereisthetrade-offbetweenJ( )maximizationandregularizationorsparsityoftheprojectionvector .Thepricetopayforsparsityofthesolutionisthatunlike(2),thereisnoaclosedformsolutionfortheconstrainedquadraticin(4),furthermoretheparameterintroducedin(4)hastobechosenbymeansofatuningsetwhichrequirestheproblemtobesolvedseveraltimesandthatcanbecom-putationallydemanding.Inordertoaddressthisissueweproposenext,alinearprogrammingformulationthatcanbeinterpretedasanapproximationto(4)andthatresultsinsparsersolutionsthan(4).Letsconsiderthefollowingma-trix:HT="1 p l+A+ m+eTl+T1 p l A m eTl #From(1)wehavethatSw=HTH,then: TSW = THTH =(H )T(H )=kH k22(5)Hence,quadraticprogrammingproblem(4)canberewrit-tenas:min 2RdkH k22+k k1s:t: T(m+ m )=b(6)Wecannowusethe1-norminsteadofthe2-normintheobjectivefunctionof(6)toobtainthefollowinglinearpro-grammingformulationthatcanbesolvedmoreefcientlyandgivessparsersolutions:min 2RdkH k1+k k1s:t: T(m+ m )=b(7)Thatthisproblemisindeedalinearprogram,canbeeasilyseenfromtheequivalentformulation:min 2Rde0s+e0ts:t: T(m+ m )=b sH s t t(8)Next,weproposeanalgorithmbasedonformulation(8)andequation(3)thatprovidesaccurateFLDclassiersdepend-ingonaminimalsetoffeatures.Algorithm1SparseLinearFisherDiscriminantGiventhetrainingdatasetfA ;A+gandasetofvaluesN=10 5;10 4;:::;105 fortheparameterdo:1.Foreach2Ncalculatecross-validationperfor-manceusingthelinearprogrammingformulation(8).2.Letthevalueforwhichformulation(8)givesthebestcross-validationperformance.Let'scall^ theob-tainedsparseprojection.3.Selectthesubset^FofthefeaturesetFdenedbyfi2^F,^ i=0,thisis,selectthefeaturescorrespondingtononzerocomponentsoftheprojection^ .4.Solveoriginalquadraticprogrammingproblem(1)withcloseformsolution(3)consideringonlythefea-turesubset^Ftoobtainanalprojection thatde-pendsononlythesmallfeaturesubset^F.5.NumericalExperimentsInordertoempiricallydemonstratetheeffectivenessoftheproposedapproach,wecomparedourfeatureselectionalgorithm,SparseLFD(SLFD)tothreeotherwell-knownclassicationalgorithms:Therstalgorithmisaverypop-ularpubliclyavailableimplementationofSVM,SVMlight[11].Thisformulationdoesnotincorporatefeatureselec-tionandproducesclassiersthatoftendependonalltheinputfeatures.Thepurposeofthecomparisonistoshowthatafeatureselectionmethodimprovesgeneralizationper-formanceonthisdataset.ThesecondmethodincludedinournumericalcomparisonsistheAutomaticRelevanceDetermination(ARD)algorithm[15]whichisoneofthe Table1.ResultsincludingAUCAreaundertheROCcurveforthetestingsetandnumberoffeaturesselectedforthefourmethods:SLFD,SVMlight,ARDandLFD.Bestresultsinbold AlgorithmAUC#offeatures SLFD89.6%3SVMlight87.4%79ARD85.8%13LFD87.4%79 classierusesallthefeatures.mostsuccessfulBayesianmethodsforfeatureselectionandsparselearning.Itndstherelevanceoffeaturesbyopti-mizingthemodelmarginallikelihood,alsoknownastheevidence.Thethirdapproachconsistsofapplyingthestan-dardLFDalgorithm[7]withoutfeatureselection.Alltheclassiersweretrainedusing141cases,andweretestedon59cases.Forthemethodsthatneededparameterstobetuned,i.e.ouralgorithmandSVMlight,themodelpa-rametersweretunedbythemeansofleave-one-patient-out(LOPO)[8]crossvalidationonthetrainingset.Wehavegottenmanydifferentanswersfromdoctorsastowhattheyfeelthecostofafalsepositive(FP,i.e.wronglylabelingtheheartabnormal)orfalsenegative(FN,i.e.wronglylabelingtheheartnormal)happenstobe.IfthissystemisusedasaninitialreaderthentoomanyFPsorFNswillcausethedoctorstoshutoffthesystembecauseitistoounreliable.ButasavalidationsystemthemainfocusistokeeptheFNratelow.Ingeneral,ifyouhaveahighFPratethenyouaresendingtoomanypatientsforadditional,moreexpensivetests,whichwouldleadtohighercostsforhealthinsurance.AhighFNratecouldmeanthatapatientmightgoundiagnosedifthedoctorusingthesystemisnotwelltrainedandalsomissespotentialabnormalities.Forus,thecostofaFNisthushigherthanaFP.ByfocusingonkeepingtheFNratelow,welowertheriskofmissingabnor-malitiesandleavethenaldiagnosistotheexpertiseofthedoctor.Takingthisintoaccount,wedecidedthatthebestwaytoevaluatetheclassierperformanceistomeasuretheareaundertheROCcurve(AUC).Foreachalgorithm,Table(1)showstheAUCforthetest-ingsetandthenumberoffeaturesthatthecorrespondingclassierdependson.Asitcanbeseenfromtheresults,ourmethodobtainedtheROCwiththelargestareaandonlyde-pendedonthreefeatures.Thisverylowfeaturedependenceisveryimportantinourapplicationsincethefeaturesusedforclassicationhavetobecalculatedinrealtime.6.FinalResultsThethreefeaturesselectedbySLFDwere:1.Afeaturethatmeasuresthemotionalongthesigni-cantdirectionsofmovementofthewallofhearts2.Afeaturethatmeasuresthecorrelationbetweenthees-timatedareaoftheheartcavityandthedistancebe-tweenthewallsofthehearttothecenterofmassoftheheart.3.Theestimatedejectionfractionoftheheart.TheReceiverOperatingCharacteristic(ROC)curveonthetestingsetforthenalclassierisshowningure5.TheareaundertheROCcurveforthetestingsetwas0.896.TheLOPOcross-validationperformanceforthenalmodelwas7falsepositivesand17falsenegativesoutof81pos-itives(abnormals)and60negatives(normals),i.e.,88.3%ofthenormalheartsand79.0%oftheabnormalheartswerecorrectlyclassied.Onthetestingsetwegot3falseposi-tivesand6falsenegativesoutof39positives(abnormals)and20negatives(normals),i.e.,85.0%ofthenormalheartsand84.6%oftheabnormalheartswerecorrectlyclassied.A3DplotdepictingthenalclassierandthetestingsetisshowninFigure6.TheclinicalresultswerepresentedandpublishedattheAmericanCollegeofCardiologymeet-inginMarch2005underthetitle:ClinicalEvaluationofaNovelAutomaticReal-TimeMyocardialTrackingandWallMotionScoringAlgorithmforEchocardiographyIntroduc-tion. Figure5.ROCcurveforthetestingset -0.4 -0.2 0 0.2 0.4 0 0.5 1 -1 -0.5 0 0.5 1 1.5 EF feature Distance feature Timing feature Normal Hearts Abnormal Hearts Figure6.Finalhyperplaneclassierinthreedimensions,circlesrepresentnormalheartsandstarsrepresentabnormalheartsinthetestingset7.FutureworkInthefutureweplanonexpandingourclassicationtoidentifydifferentlevelsofCHDseverity(Levels1-5:1=normal,2=hypo-kinetic,3=a-kinetic,4=dys-kinetic,5=aneurysm),incorporatingtheuseofotherstan-dardechocardiographyviews(forexample:apical3cham-ber(A3C),parasternalshortaxis(PSAX),parasternallongaxis(PLAX)),andincludingimagesfromotherlevelsofstress.ComparisonsofourproposedSLFDalgorithmonotherpubliclyavailabledatasetsandmedicalapplicationsarealsoplannedtofurtherexplorethepotentialofthealgo-rithm.References[1]AmericanHeartAssociation.Heartdiseaseandstrokestatistics2005update.2005.URL:http://www.americanheart.org/downloadable/heart.[2]P.S.BradleyandO.L.Mangasarian.Featureselectionviaconcaveminimizationandsupportvectormachines.InJ.Shavlik,editor,MachineLearningProceedingsoftheFif-teenthInternationalConference(ICML'98),pages8290,SanFrancisco,California,1998.MorganKaufmann.[3]M.CatherineM.Otto.TextbookofClinicalEchocardiog-raphy,2ndedition.W.B.SaundersCompany,Philadelphia,PA,2000.ISBN0-7216-7669-3.[4]M.Cerqueira,N.Weissman,V.Dilsizian,A.Jacobs,S.Kaul,W.Laskey,D.Pennell,J.Rumberger,T.Ryan,andM.Verani.Standardizedmyocardialsegmentationandnomenclaturefortomographicimagingoftheheart.Ameri-canHeartAssociationCirculation,105:539542,Jan2002.URL:http://circ.ahajournals.org/cgi/content/full/105/4/539.[5]D.Comaniciu.Nonparametricinformationfusionformo-tionestimation.Proc.IEEEConf.ComputerVisionandPat-ternRecognition,I:5966,2003.[6]D.Comaniciu,X.S.Zhou,andS.Krishnan.Robustreal-timetrackingofmyocardialborder:Aninformationfusionapproach.IEEETrans.MedicalImaging,23,NO.7:849860,2004.[7]R.Duda,P.Hart,andD.Stork.PatternClassication.JohnWiley&Sons,NewYork,2001.[8]M.Dundar,G.Fung,L.Bogoni,M.Macari,A.Megibow,andB.Rao.Amethodologyfortrainingandvalidatingacadsystemandpotentialpitfalls.InCARS2004,ComputerAs-sistedRadiologyandSurgery,Proceedings,Chicago,USA,2004.Elsevier.[9]B.Georgescu,X.S.Zhou,D.Comaniciu,andA.Gupta.Database-guidedsegmentationofanatomicalstructureswithcomplexappearance.IEEEConf.ComputerVisionandPat-ternRecognition(CVPR'05),SanDiego,CA,2005.[10]R.Hoffmann,T.Marwick,D.Poldermans,H.Lethen,R.Ciani,P.vanderMeer,H.-P.Tries,P.Gianfagna,P.Fioretti,J.Bax,M.Katz,R.Erbel,andP.Hanrath.Re-nementsinstressechocardiographictechniquesimproveinter-institutionalagreementininterpretationofdobutaminestressechocardiograms.EuropeanHeartJournal,23,is-sue10:821829,May2002.doi:10.1053/euhj.2001.2968,availableonlineathttp://www.idealibrary.com.[11]T.Joachims.SVMlight,2002.http://svmlight.joachims.org.[12]O.L.Mangasarian.Generalizedsupportvectorma-chines.InA.Smola,P.Bartlett,B.Sch¨olkopf,andD.Schuurmans,editors,AdvancesinLargeMarginClas-siers,pages135146,Cambridge,MA,2000.MITPress.ftp://ftp.cs.wisc.edu/math-prog/tech-reports/98-14.ps.[13]S.Mika,G.R¨atsch,andK.-R.M¨uller.Amathematicalpro-grammingapproachtothekernelsheralgorithm.InNIPS,pages591597,2000.[14]S.Mika,G.R¨atsch,J.Weston,B.Sch¨olkopf,andK.-R.M¨uller.Fisherdiscriminantanalysiswithkernels.InY.-H.Hu,J.Larsen,E.Wilson,andS.Douglas,editors,Neu-ralNetworksforSignalProcessingIX,pages4148.IEEE,1999.[15]Y.Qi,T.P.Minka,R.W.Picard,andZ.Ghahramani.Predic-tiveautomaticrelevancedeterminationbyexpectationprop-agation.InProceedingsofTwenty-rstInternationalCon-ferenceonMachineLearning,2004.[16]WorldHealthOrganization.Theatlasofglobalheartdis-easeandstroke.2004.URL:http://www.who.int/cardiovas-cular diseases/resources/atlas/.[17]X.S.Zhou,D.Comaniciu,andA.Gupta.Aninformationfusionframeworkforrobustshapetracking.IEEETrans.onPatternAnal.andMachineIntell.,27,NO.1:115129,January2005.