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Movement

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    Movement

    InternationalJournalofAutomationandComputing7(4),November2010,543549

    DOI:10.1007/sl1633010-05380

    MovementInvariants--basedAlgorithmforMedicalImage

    TiltCorrection

    MeiSenPan,Jing-TianTangXiaoLiYang

    InstituteofBiomedicalEngineering,Schoolofhfo

    physicsaridGeomaticsEngineering,CentralSouthUniversity,Changsha410083,PRC DepartmentofComputerScienceandTechnology,HunanUniversityofArtsandScience,Changcle415000,PRC

    Abstract:Inthispaper,theedgedetectionforamedicalimageisperformedbasedonSobeloperator,andtheboundingboxis

    obtained,bywhichtheeffectivemedicalsub

    imageisextracted.Then,thecentroidandthenormalizedcentralmomentsofthemedical sub

    imagearecalculated.andtherotationangle0isobtainedbyminimizingthesecond.ordercentralmomentbasedonitsrotation

    invariance.Finally.thewholemedica1imageisrotatedaroundthecentroidby

    Qtocorrectthetiltedimage.F51rthermore.inspired

    bytheuniformitydegreeoftheimage,therotationangle0isrevised,whichachievesabettercorrectioneffectandperformance.The

    experimentalresultsshowthattheproposedalgorithmsarefairlyreliableandaccurateforthedeterminationoftiltangles,andare

    practicalandeffectivetiltcorrectiontechniques.

    Keywords:Tiltcorrection,centralmoment,medicalimage,imageuniformity,Sobeloperator

    1Introduction

Inthecourseofcomputerizedtomography(CT)ormag

    neticresonance(MR)imaging,theCTandMRimages frequentlyhavesomeobviousandserioustilt,whichhas costlynegativeeffectonthefollowingimageregistration, fusionandsegmentation,andevenmisdiagnosesofthedis

    eases.Therefore,correctingthetiltisverynecessary,which iscommonlyalsocalledrotationtransformationinthefield ofimageregistrationl.Correctingthetilti.e..rota

    tiontransformation),inessence,rotatestheoriginalimage aroundtheoppositedirectiontothetiltanglepreciselyac

    quired.Inl6l,analignmentmethodbymaximizationof mutualinformationwasproposedtoobtaintheparameters forthetranslationandrotationneededtoregister.Dueto theexistenceofamutualinformationfunctioncontaining manylocalmaxima.iteasilygetsintothelocaloptimum. Therefore.therotationangleisnottheglobaloptimumone. In[79byusingmultiparameteropt,imizationsofPowe]l andsimplexmethods,theparametersforthetranslation androtationareobtained.However,theyarestronglyde

    pendentoninitialvaluesselected.Inthefieldofmedicalim

    agesegmentation,correctingthetiltshouldbethefirstand crucialpreproeessasitdirectlyinfluencesthesegmentation resultssuchasextractingthecontourandfoCUSofadis

    ease.Butunfortunately,wefindthatnopublishedsources or1iteraturesespeciallygearedtowardthetiltproblemin thecontextofmedicalimagesegmentationthathavebeen mentionedandintroduced.

    Inotherapplicationfields,however,suchasinatiltdec

    umentimageandatiltvehiclelicenseplateimage,many ingeniousandpracticaltiltcorrectionmethodshavebeen

    proposed.Amongwhichthemosttypicalandprevalent arethefollowingthreekindsofmethods:projectionpro

    file(PP),Houghtransformation(HT))componentnear

    ManuscriptreceivedMarch6,2009;revisedOctober12,2009 ThisworkwassupportedbyFoundationof1ithFiveyearPlanfor

    KeyConstructionAcademicSubject(Optics)ofHunanProvince, PRCandScientificResearchFundofH1lnallProvinciaEducation

    Department.PitC(No06C581)

    estneighborclusteringfCNNC1.ppt"J."J,whichisbuilt ontheanalysisoftheprojectionshape,hasanextremely heavycomputationalloadbecauseitneedstocalculatethe projectionshapeofeachangle.HT[..asthemost

    widelyemployedone.calculatesthepossibletrackinpa

    rameterspaceaccordingtotargetpixe1coordinatesinthe imagespace.Itisverywelladaptedtolineargraphic,but withalotofcomputational1oadandlackofrobustness. CNNCl"1.bydiscoveringKnearestneighborsofthe centralpointofallconnectedcomponents,computesthe vectordirectionofeachcouplenearestneighborandgets thestatistica1histogramwherethepeakvaluedenotesthe entireimagetiltangle.Sincethereexistsomeconnected componentsinthe~mage.1tsprocessingtimeisalsoaquite prodigiousload.Inaddition,in181,anewmethodforcor

    rectingvehiclelicenseplatetiltwaspresented.According toKarhunenLoeve(KL)transformation,thecoordinates ofcharactersinthevehiclelicenseplateimagearearranged intoatwo-dimensionalcovariancematrix.oi1thebasisof whichthecenteredprocessiscarriedout.Then.theeigen

    vectorandtherotationanglearecomputedinturn.The experimentalresultsverifythatthisproposedmethodcan

    beeasilyimplemented,andcanquicklyandaccuratelyget thetiltangle.Theabovemethodsareverysuitablefor correctingtheuniformgrayimages,suchasdocumenttilt imagesandvehiclelicenseplatetiltimages.butnotforthe nonuniformgrayimage.especiallyforCTandMRimages. Forallthosereasons,wehavetodevelopanewmethodto correctthetiltCTandMRimages.

    Inordertoaddresstheissueofcorrectingthetilt medicalimage,onthebasisofacomprehensiveand thoroughinvestigatioI1intotherotationinvarianceof imagemoment,weproposeamovementinvariants

    basedalgorithmfMIA1forcorrectingthetiltmedical image.Moreover,basedonMIA,sortieimprovedille3- surementsareadopted,andtwomodifiedalgorithms, amovementinvariantsanduniformitybasedalgo

    rithmfMIUA)forcorrectingthetiltmedicalimageanda 544InternationalJournalofAutomationandComputingz(4),November2010

    movementinvariantsbasedanglecoordinationalgorithm (MIAA)forcorrectingthetiltmedicaIimage,areintro- duced.Therestofthispaperisorganizedasfollows.Sec- tion2expoundsthetiltmodelsofmedicalimages.The procedureofMIAisbrieflydescribedinSection3.Section 4introducesthecourseofMIUAindetail.andSection5 explainstheprocessofMIAA.Someexperimentalresults andcomparisonaregiveninSection6explicitly.Finally.a briefconclusionandfutureworkareoutlinedinSection7. 2Thetiltmodelsofmedicalimages

    Accordingtothetiltdirectionofamedicalimageregion, themedicalimagehastwopossibletiIts:positivetiltfsee Fig.1(a))andnegativetilt(seeFig.1(b)).Thepositive

    tiltdenotesthattheimageisrotatedcounterclockwiseby aroundaxisX,andthenegativetiltindicatesthatthe imageisrotatedclockwisebyaaroundaxisX.InFig.1. theessenceofimagetiltisthat,thereisatiltangleQbe- tweenthetiltregionprincipalaxisXandtheverticalaxis X.Figs.2(a)and(b)are,respectively,theactualpositive tiItandnegativetiltmedicalimages.

    LXJ

    Fig2Tiltmedicalimages

    Accordingtotheabovetiltmodels,thekeytasksoftilt correctionfocusonfindingthecentroidandobtainingthe tiltangleo/.

    3MIA

    3.1Edgedetection

    Inordertogetamoreaccuratetiltangle.itisnecessary toeliminatetheinterferenceofimagenoiseandgettheac- tualsizeofthetiltimageasmuchaspossible.Therefore, weperformthefollowingprocessessequentially:detecting theedge,gettingthebinarizationimage,computingthe boundingbox,andextractingthesubimage.

    SupposethatimageFisofM×Npixelswithitsupper

    leftpixelbeing(1,1),andf(x,Y)isthegrayvalueatpoint (x,Y).Becauseofbeingsimpleandprovidingamoreexcel

    lentnoisereductioncapability,Sobeloperatorisselectedas theedgedetectionmethod.Afterhavingdetectedtheedge inimageFbyusingSobeloperatorandbinarizing,thebi

    narizationimageBisobtainedasshowninFig.3,withits gra_yvaluesbeing0and1.

    (b)Negativetilt

    Fig.3Medicalimageedges

    Acquiringtheeffectivesizeoftheoriginalimage,in essence,isthattheboundingboxofthebinarizationimage Bisextracted.Thus,weneedtogetthe4boundariesof theboundingbox:top,bottom,left,andrightones.After havingprocuredtheboundingbox,thesubimageF_Sub

    isderivedfromtheoriginaltiltimage.Fig.4isthebound- ingboxthatresultsfromFig.3,andFig.5isthesubimage

    thatisextractedfromFig.2accordingtotheboundingbox inFig.4.

    (b)Negativetilt

    Fig.5Sub-images

    3.2Tiltcorrectionofthemedicalimage

    Sincesomemomentsofanimageregionareinvariantto geometrictransformationsuchastranslation,rotation,and scalechange,theyarewidelyappliedtoobjectclassification andidentification.

    M.S.Paneta1./MovementInvariants-basedAlgorithmforMedicalImageTiltCorrection

    Definition1.Fora2Dcontinuousfunctionf(x,),the momentoforder(P+q)isdefinedas

    ,十?roo

    ,

    q=

    //xPy.,(z,y)dxdy,p,q=0,1,2J一?Jo.

    Iff(x,Y)isa2Ddiscretefunction,then(1)becomes whereparameter(P+q)istheorderofthemoment. Definition2.Thezerothmomentisexpressedas o=

    (2)

    (3)

    Iff(x,Y)isa2Ddiscretefunction,then(3)isrewritten

(4)

    AllthefirstandhigherordermomentsdividedbyM0,

    0

    areindependentofthesizeofanobject.

    Definition3.WhenP=1andq=0,and,P=0and q=1,

    i:

    M1,0

    ,

    

    :

    (5)M

    0

    

    .

    0,YM

    0.0

    J

    where,)iscalledthecentroidcoordinatesoftheobject. Inordertogetthemomentinvariants,thecentralandthe normalizedcentralmomentsareadoptedinthispaper. Definition4.Supposethat,)istheobjectcentroid, thenthecentralmomentisdefinedas

    )(一可)/(x,).(6)

    Whenthecentralmomentiscomputed.thecentroidis regardedastheoriginofcoordinates.

    Theorem1.Themomentoftheobjecthavingrotated by.orcomputedwithreferencetoaxesand.isin

    varianttorotationtransformation.TherotationangleoLis asfollows:

tan2~--

    545

    Step4.ThetiltangleofthesubimageF_Subisgot

    andthenthearctanfunctionissolvedaccordingto(7): =an()×180(8)

    Step5.ThewholeimageFisrotatedarounditscen- troidby.andthetiltcorrectionisperformed. InFig.6,asthefinalresultfromrotatingtheimagesin Fig.2,alltwotiltimagesarecorrectedwell,whichlaysthe firmfoundationofimageregistration,fusion,andsegmen

    tation.

    (b)Negativetilt

    Fig.6ThecorrectionresultsofFigs.2(a)and(b) 3.3TheprocedureofMIA

    Insummary.MIAisdescribed58follows:

    Algorithm1.MIA

    Step1.TheedgeoftheimageFisdetectedbyusing Sobeloperator,andthebinarizationedgeimageBisob

    talned.

    Step2.Theboundingboxoftheimageisidentified. namely,the4boundariesoftheboundingboxarerespec

    tivelyfoundout.

    Step3.Accordingtothesizeoftheboundingbox,the sub-imageSubisderivedfromthetiltimageF. Step4.Accordingto(5)and(6),thecentroidandthe normalizedcentralmomentsofthesubimageF_Subare

    calculated.andthentherotationangleQisobtained. Step5.ThetiltimageFisrotatedarounditscentroid by.andthefinalcorrectedimageisprocured. 4MIUA(

7)

    InFig.1,axesandarerespectivelyrotatedbyoL andbecomeaxes)candY'.whicharetheso-calledprinci

    palaxes.

    Accordingtotheabovedefinitionsandtheorem,weas

    sumethatthetiltofthemedicalimageistheresultthat theimageprincipalaxesarerotatedarounditscentroidby withreferencetoaxesXandConversely,thetilteor- rectionofthemedicalimageistheresultthattheimageis rotatedarounditscentroidby.Therefore.thecourse

    ofcorrectingtheimageisshownasfollows:

    Step1.ThezerothmomentM0,o,firstmomentsM1.0 andMo.

    1,ofthesubimageSt'barecomputed.

    Step2.Thecentroidcoordinatesarecalculated. Step3.Thecentralmoments.

    1,,0,and.

    2,of

    thesubimageSubareobtained.

    ?,eapplyMIAt0thetiltCTandMRimages.anddis- coverthatthevisualacceptabledegree(VAD1ofthecor

    rectedimagesneedstobefurtherimproved.Thefactors thatmaketheVADtobelowarevaried.amongwhich. themostcrucialarethefollowingtwofactors.Thefirstis that,inthesubimage,therestillexistsomerandomnoises, whichonthewholehasaweakinfluenceonDThesec- ondisthatthegrayvaluedistributionsintheimagearenot uniform,whichgeneratessomeerrorintherotationangle computedbyf81.Asfortheformer,wecanusemeanfilter ormedianfiltertoeliminatethenoises.Inthispaper,since

    therearemanymorethingstobediscussedthefirstisnot touched.Thelatterisourpointofinterest.forwhichsome pertinentimprovedmeasurementsaredeveloped. Inordertoaddressthesecond,weusetheuniformityde

    gree(uD)ofamedicalimagetorevisetherotationangle. ,

    ??

    M?一

    Z

    ,

    ??

    M?

    0

    

    

    ??

    M?

    =

    ,pM

    546InternationalJournalofAutomationandComputing7(4J,November2010

    LetthemedicalimageIbeofMxNpixels;UDisdefined as

    Uniformity((r91

    Mean(~

    whereStd(J1,asthestandarddeviationoftheimage

    reflectsthedispersiondegreeoftheimagegrayvalues; Meanfdenotesthemeanvalueofthegrayvaluesinthe imageFrom(9),thegreaterthevalueUniformity(1) is,themorenonuniformtheimageis;conversely,witha smallervalue,theimageismoreuniform.Therefore,f8)is

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