Vessel Linear

8/8/2019 Vessel Linear

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Vessel-basedregistrationwithapplicationtonoduledetection

inthoracicCTscans

ChanghuaWuaandGady

Agamb

aDepartmentofScienceandMathematics,KetteringUniversity,Flint,MI

48504bDepartmentofComputerScience,IllinoisInstituteofTechnology,Chicago,IL

60616

ABSTRACT

Volumeregistrationisfundamentaltomultiplemedical

imagingalgorithms.Speci


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cally,non-rigidregistrationofthoracicCTscans

takenatdierenttimeinstancescanbeusedtodetectnewnodules

morereliablyandassessthegrowthrateofexistingnodules.Voxel-basedregistrationtechniques

aregenerallysensitivetointensityvariationandstructuraldierences,whicharecommoninCTscansduetopartialvolumeeectsandnaturallyoccurringmotionand

deformations.Theapproach


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eldusingthinplatesplines.Theproposed

approachisevaluatedonbothrealandsyntheticallydeformedvolumes.Theobtained

resultsarecomparedtoseveralstandardregistrationtechniques.Itisshownthatby

usingvesselstructure,theproposedapproachresultsinimprovedperformance.

1.INTRODUCTIONSuccessfulregistrationisfundamentaltothefusionofmedicalimagesand

thediagnosisof


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abnormalstructuresfromtemporalimages.Computerizedvolumetric

warpingandregistrationof3Dlungimagescanprovideobjective,accurate,

andreproduciblemeasurestotheunderstandingofthelungstructureandfunction.It

isalsoinvaluabletotheassessmentofthepresenceofdiseasesandtheirresponsetotherapies.Intheautomatedcomputerdiagnosisofnodules,thedierence

betweentemporalCT


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scansafterregistrationcanbeusedto

trackthedevelopmentofexistingnodulesanddetectnewones.1,2The

changeinsizeandintensitycanbeusedtotellwhetheranodule

ismalignantorbenign.3Registrationcanbeusedtoestimateregionallungexpansion,4breathingmotion,5,6andstructure-functionrelationships.7,8Itcanalsobeused

toreducethe


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falsepositiveinnoduledetection.9,10

Howeveronlylimitedworkthattargetstheaccurateregistrationoflung

volumeshasbeendone.Somework2usedtheiterativeclosestpoint(ICP)to

registerthecontoursoflungvolumes.ZhangLi11developeda3Dsurface-basedregistrationtechniquetoregisterpulmonaryCTvolumes.Theregistrationincludesaglobal

transformationanda


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localelastictransformationbysubdividingtheimage

andatlasvolumeintosub-imagescalledcubes.Thedisplacementvectorsofeach

cubeareprocessedusingBurr'sdynamicmodeltogiveasmootheddeformationvector

foreachvoxelintheimage.However,thisapproachisentirelydependentontheintensityinformationandmakesnouseofaprioriknowledgeof

thelungstructure


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suchasthevesselnetwork.Someresearchers

trytoestimatethetransformation


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eldby


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ndingmatchesofthejunctionsofvessels

andairwaysinthelungvolume.FanLi12,13proposedaninterpolation

methodforobtainingdensetransformation


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eldfromsparsedisplacementvectorsobtainedby

trackingthebronchialpointsofairways.Thedensetransformation


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eldisobtainedbyminimizinganobject

functionbasedonamodelofcontinuummechanicsandanisotropicsmoothnessconstraints.

Thisapproachassumesthattheintensityofapointinthelungdoes

notchangeinallscans.Howeverthisisnotalwaystrue,especiallyinthickCTscansduetothepartialvolumeeect.Prado14proposeda

sequentialpolynomialregistration


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schemetointeractivelyregisterlungvolumes.The

coecientsofthepolynomialfunctionareupdatedbyaddingcontrolpointsmanually.

Duetothelimiteddegree,thepolynomialfunctionmaynotbecapableof

accuratelydescribingthenon-rigiddeformationbetweenlungvolumes.Moreover,themanual

E-mail:[email protected],[email protected]


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interactionmayintroduceerrorinthe

positionofcontrolpointsandalsoreducestheeciency.Shikata15proposeda

lungregistrationmethodbymatchingbifurcationpointsfromareconstructedvessel-tree.However,it

onlyestimatedarigidtransformation


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eldwhiletherealtransformationbetweenlung

volumesisnon-rigid.Finally,BaojunLi7proposedamethodtocombinethe

junctionsofairwaywithintensityconsistency.Inhismethod,thesimilaritybetweenjunctions

andvoxelsaremeasuredbyasetofcostfunctions,whichareminimizedtogetthe


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naltransformation


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eld.However,thematchingbetweenjunctionsis

manuallyestablished,whichreducesitseciencyandmakesitunsuitableforautomated

lungregistration.Furthermore,itishardtoavoidlocalminimuminthe

minimizationofthecostfunctions.

Inthispaper,anautomaticregistrationmethodbasedonthestructureofvesselsisproposed.Thispaperis

organizedasfollows.


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eld,incorporationofsmoothnessandvessel-basedconstraints

arediscussedinthissection.Section3discussestheevaluationofthe

proposedmethod.Section4presentstheconclusionandoutlinesthefuturework.

2.THEPROPOSEDAPPROACHBloodvesselsareprominentfeaturesinthoracicCTscans.Thenetworkofvesselscoversmostofthevolume,whichmakes

vesselsgoodlandmarks


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intheregistrationoflungvolumes.In

thissection,ageneralregistrationalgorithmthatusesvessel-basedlandmarkstoregister

CTvolumesisproposed.Theproposedregistrationalgorithmusesbothjunctionsandvessels

toestimatethenon-rigidtransformationbetweenvolumes.Falsematchingofjunctionsareremovedbysmoothnessconstraintusingthecurvaturesofthetransformation


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eld.Thentheregistrationisfurtherimproved

byincorporatingthelinearvesselsegmentswhosematchesarefoundbyactively

deformingtheircenterlinestotheirmatches.Thissectionisorganizedasfollows.

Section2.1discussestheinitialalignment.Junctiondetectionisdiscussedinsection2.2.Section2.3introducesthin-platesplines(TPSs),whichareusedintheinterpolation

ofthetransformation


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eld.Section2.4discussestheenforcementof

smoothnessconstraintsonthetransformation


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eld.Section2.5discussestheincorporationof

vesselconstraints.

2.1.InitialalignmentAtthebeginning,thesource

andthetargetvolumesareinitiallyalignedthroughananetransformation.Thisinitial

alignmentreducesthesearchingspacein


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centersofboththesourceand

xyz

targetvolumestotheiroriginsrespectivelyaregivenby:

..

I..cI..c.

T=

;T.=(1)

0101

whereIisan33identitymatrix.

Therotationandscalingcomponents

areestimatedfrom


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nedbyPandP.are

givenby

..1..1

p1p2p30

ppp0

R.123

R=,=(3)

0001

0001


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LetE=f1;2;3gTandE.

=f.1;2.;.3gTbetheeigenvaluescorrespondingtothe

eigenvectorsinPandP..ThescalingmatricesSandS.

thattransformboththesourceandtargetvolumestoaunitvolumearegivenby:

23..1..3..1

10

0010


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00.7...02

00000

6.S..27

S=

,=(4)

.00305.00.3

0.00010001

UsingthematricesabovetonormalizethesourcevolumeIsandthetargetvolumeIt,wegetSRTIs

=S0R0T0It.


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SotheanetransformationmatrixMathat

alignsIstoItis:

..1

Ma=(S.R0T

0)SRT(5)

2.2.LandmarkselectionTherearetwogeneralapproachesin

imageregistration,voxel-basedapproachesandlandmark-basedapproaches.Thevoxel-basedapproachesusetheintensityofallvoxelsintheoverlappingarea.Similaritymeasuressuchasmutual

informationandintensity


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landmarksaremanuallyselected.Voxel-basedapproachestreat

voxelsoftissueandstructuresinthesamewaywhilelandmark-basedapproaches

givehigherweighttostructures.Voxel-basedapproachesarealsomoresensitivetonoise

andintensityvariation.

SincevesselsintheCTscanscanbeeasilyobtainedafterenhancement16,17andwecaremoreabouttheaccurate

registrationofvessels


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edandmatched.Second,theyshouldbe

spatiallydistributedasuniformlyaspossibletoprovideadequateinformationthroughoutthe

volume.Accordingtothesecriteria,junctionsofvesselsareidealcandidates.Theyhave

beenwidelyusedinimageregistration.15,18Afterenhancement,vesselscanbesegmentedbyasimplethresholding.Linearvesselsegmentscanbeobtainedbytracing

alongvesseldirections


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untiljunctionsaremet.Intheproposed

approach,junctionsaredetectedbycheckingtheeigenvaluesofthegradientcorrelation

matrix.Let1.2betheeigenvaluesofthematrix.Itis

assumedthatforlinearvesselsegments,2isneartozeroand

1ismuchbiggerthan2,therefore2=1isverysmall.Soto

detectjunctions,we


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onlyneedtocheckthevalueof

2=1.Ifitislargerthanathreshold,thenajunctionis

detected.Toensurethattheselectedjunctionsareuniformlydistributedinthevolume,

apost-processisappliedtoremovejunctionsthataretooclosetoeachothersothatthedistancebetweenanytwojunctionsisabovea

minimumdistance(30


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ndamatch.Thesimilaritybetweenjunctions

ismeasuredbyintensitycorrelationina1010window.To

improvetheaccuracyofregistration,onlythosejunctionpairswithhighcorrelation(top

50%amongallmatchingpairsofjunctions)arekept.Theremainingjunctionpairsarethenusedtogenerateasmoothtransformation


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eldthroughthin-platesplineinterpolation.

2.3.Interpolationofthetransformation


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eldIntheproposedapproach,thetransformation


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eldisinterpolatedusingthin-platesplines(TPSs),

whichbelongtoafamilyofsplinesbasedonradialbasisfunctions.

TPShasbeenformulatedbyDuchon19andMeinguet20forsurfaceinterpolationofscattered

data.TPSmodelsthedeformationofathinmetalplateunderexternalforces.ThesurfaceinterpolatedbyTPSpassesthroughthecontrolpoints.Eachcontrol

pointhasglobal


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inuenceontheshapeoftheinterpolated

surface.InrecentyearsTPShasbeenwidelyusedinimageregistration.21{23

Thede


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nitionofTPSisalinearcombination

ofnradialbasisfunctions(s):

n

t(x,

y,z)=a1+a2x+a3y+a4z+bj(jj-(x,

y,z)j)(6)j=1


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De


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ningthetransformationasthreeseparatethin-plate

splinefunctionsT=(t1;t2;t3)Tyieldsamappingbetweenimagesinwhichthe

coecientsa1,a2,a3anda4characterizetheanepartofthetransformation

whilethecoecientsfbjgj=1:::ncharacterizethenon-anepartofthetransformation.Thencontrolpointsformasetof3nlinearequations.Todeterminethe

3(n+4)


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coecientsuniquely,twelveadditionalequationsarerequired.

Thesetwelveequationsguaranteethatthenon-anecoecientsfbjgj=1:::nsumtozero

andthattheircrossproductswiththex,yandzcoordinatesofthe

controlpointsarelikewisezero.Inmatrixformthiscanbeexpressedas

.

.

.

.

.

.

.

.b.

=(7)T


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0a0

Herea

isa43matrixoftheanecoecientsa1,a2,a3

anda4,bisan3matrixofthenon-anecoecientsfbjgj=1:::n,

and.isthekernelmatrixwithij=(ji-jj).Solvingforaandbusingstandardalgebrayieldsathin-platespline

transformationthatwill


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interpolatethetranslationatthecontrolpoints.

Theradialbasisfunctionofthin-platesplinesisde


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eldEventhoughstrictcriteriaisused

inselectingmatchingjunctions,therecanstillbefalsematchingdueto

variousreasons,suchasnoiseandthepartialvolumeeect.Thereareseveral

commonwaystoremovefalsematching.Oneway24isto


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ndmultiplematchesforeachcontrolpoint

inthesourcevolumeandthentryallthepossiblecombinationsof

thematchingrelationsto


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ndthetransformationthatminimizesthedierence

betweenthesourceandtargetvolumes.Thismethodisapplicabletoboth

rigidandnon-rigidregistration.Theshortcomingisthatitiscomputationallyexpensive.A

secondmethodistoestimateatransformation


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eld,i.e.arigidtransformation,andthen

checktheregistrationerrorateachjunction.Iftheerroristoo

big,thenitisafalsematch.HoweverthesurfaceinterpolatedbyTPS

passesthroughthecontrolpoints,whichmakesthismethodnotsuitable.Athirdwayistocheckthelocalfeaturesoftheestimatedtransformation


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eldateachjunction,andremovethose

withlocalfeaturesdeviatingtoomuchfromtheaverage.Intheproposed

approach,thethirdmethodisusedandthelocalfeatureischosento

bethecurvaturesofthetransformation


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eld.Thecurvaturesofthetransformation


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eldinbothhorizontalandverticaldirections

arecomputedusingLaplacianoperator,seeEquation9-10.

O2Tx(x,y,

z)=Tx(x+1,y,z)+Tx(x-1,y,z)+Tx(x,y+1;z)+(9)

Tx(x,y-1;z)-4Tx(x,y,z)

O2Ty(x,y,z)=Ty(x+1,y,z)+Ty(x-1,y,z)+Ty(x,y+1;z)+(10)

Ty(x,y-


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1;z)-4Ty(x,y,z)

whereTx(x,y,z)isthehorizontalcomponentofthedisplacementvector

at(x,y,z)andTy(x,y,z)istheverticalcomponent.Due

totheanisotropicnatureofthickCTscansonwhichtheexperimentsarecarriedout,thedisplacementvectorsintheneighboringslicesarenotused.

Thecurvaturein


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thezdirectionisnotcomputedeither.

Itisassumedthattherealtransformation


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isremoved.Thisprocessisrepeatediteratively

untilnojunctionsareremoved.

2.5.Enforcementofvesselconstraints

Inlandmark-basedregistration,itisdesirabletohaveaslessfalsematchesas

possible,whichoftenleadstoastrictcriteriainselectingthematchingpairsoflandmarks.Ontheotherhand,itisalsoimportanttohave

enoughmatchinglandmarks


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togetanaccurateestimateofthe

transformation.Thismeansthecriteriashould


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segmentB.doesnotshowup.The

vesselsegmentABismatchedtoA.B.,resultinginan

inaccuratetransformationvectorAA..Howeverthetranslationcomponentinthedirectionof

AA0.isaccurate.(b)Adjustmenttothetransformation


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eld.visavesselandl

isthenormaldirectionofv.pisthemiddlelocationof

vesselv.Whenj(t-t.)lj,shownasjabj,is

largerthan0.5,anadditional

pairofcontrolpointsisaddedtotheTPSinterpolationsuchthatvectortwillbemovedtot.

Theprojectionof


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morereliablethanthatbetweenjunctions.In

theexperiments,thetop50%ofvesselsareselectedaccordingtothe

intensitycorrelation.Howeverthereisanapertureproblemwhenusingthematchingbetween

vesselstoestimatethedisplacementvectorsduetothelinearnatureofthevesselsegmentsandthepartialvolumeeect.Itissimilartothe

apertureproblemin


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opticalow.Intheproposedapproach,we

onlytracethelinearvesselsegmentswithinasingleplane.Howevera

realvesselmayshowupintwoormoresliceswitheachslice

showingapartofit.Thissituationmayleadtoinaccuracyinmatching,seeFigure1-(a).ABisavesselsegmentinthesourcevolume.

A.B.is


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thevesselsegmentshowninthetarget

volume.ThematchingsegmentB0B0.doesnotshowup,thereforevesselsegment

ABismatchedtoA.B0,resultinginaninaccuratedisplacementvectorAA.

.HoweverthetranslationcomponentinthedirectionofAA0.isaccurate,whichcanbeusedtoimprovetheregistration.

Toimprovethe

robustnessofvessel


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matching,onlythosevesselsthatsatisfythe

constraintsinwidth,lengthandintensityareselected.Intheexperiments,those

segmentswithwidthlargerthanonevoxel,lengthlongerthan20voxels,and

meanintensityhigherthan40areselected.Comparedwithjunctions,vesselsegmentsareeasiertodetect(theycanbeeasilytracedalongvesseldirections16).By

usinglinearvessel


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segments,thematchingrelationisnotbased

onasmalllocalregionasthecaseofjunctions,butbased

onthematchingofthewholevesselsthusimprovingtherobustnessofthe

matching.Toimprovethespeedandrobustnessofthesearchformatchingvessels,pyramidsofboththesourceandtargetvolumesarecreated.Thesearch

startsonthe


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topandgoesdowntothebottom

ofthepyramids.

Asdiscussedearlier,thetranslationinthe

normaldirectionofvesselscanbeusedtoimprovetheregistration.Thisis

donebyaddingadditionalcontrolpointstotheTPSinterpolationifthereisabigdierenceintheprojectionontothenormaldirectionofvessels

betweenthedisplacement


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fromjunctions.Whenj(t.-t)

lj,seeFigure1-(b),islarger

than0.5,apair

ofcontrolpoints(p,p0)isaddedintothesetofjunctionpairs.

pisde


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nedas

p=p

+t.+((t-t0)l)l(11)

where

tisthetranslationvectorestimatedfromvesselmatching.Afteraddingadditionalcontrol

points,asimilariterativeprocessasdiscussedinsection2.4isappliedtofurtherremovethefalsematching.


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(a)(b)Figure2.Theleft


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gureshowstheirmatchesinatarget

slice.Duetothefactthatthesourcevesselsandtheirmatches

arenotnecessarilyonthesameslice,thematchofsomevesselsin

(a)isnotshownin(b),viceversa.

3.RESULTSTheregistrationschemewastriedon6pairsoftemporalCTscans.We

usethenormalized


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sumofabsolutedistance(NSAD)betweenthe

transformedsourcevolumeandthetargetvolumetomeasuretheregistrationerror.

TheNSADisde


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nedbythefollowingequation:

1

NSAD=j(I.(x,y,z)-1)-

(It(x,y,z)-2)(12)

s

N

(x;y;z)2W

whereWisalocalwindowcenteredat(x,y,z),NisthenumberofvoxelsinW,1and2

arethemean


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intensityofI.andItinW

.I.andItarethetransformedsourcevolumeandthetarget

volumerespectively.Sincethe

ss

intensityofthesame

structuremaybeondierentlevelsinthesourceandtargetvolumes,byusingthisdistancemeasure,theinuenceofthemeanintensityiseliminated.

Toevaluatethe


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performance,theproposedalgorithmiscomparedwith

threeotherregistrationalgorithms.Thethreealgorithmsare3Dsurface-basedregistration,253D

voxel-basedregistration,263Dnon-rigidregistrationbasedonnormalizedmutualinformation.27,28

Inordertoevaluatehowwelltheproposedregistrationalgorithmrecoversthetransformation


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eldusedintheexperimentshouldbe

closetothetransformation


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eldthathappensintherealsituation

tomaketheexperimentvalid,thesynthetictransformation


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eldisestimatedbyregisteringthesix

pairsofrealtemporalCTscans.Table1showsthequantitativeevaluation

oftheproposedalgorithm.Itcanbeseenfromthe


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rstpartofTable1thatNSAD

measurebetweenthesourceandtargetvolumesafterregistrationbytheproposed

algorithmiswithinrangeof[0:932:87],whichismuchsmallerthanthe

distanceobtainedusingthethreeotherregistrationmethods.ThesecondpartofTable1showsthedierencebetweentheestimatedtransformation


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eldandtheknownone.Itshows

themeanlengthdierence(measuredinvoxels),thedeviationofthelength

dierence,therelativedierencewhichisthedierenceinlengthdividedbythe

lengthofvectorsintheknowntransformation


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eld,thedeviationoftherelativedierence,

orientationdierenceinradian,andthedeviationoforientationdierencerespectively.We

canseethemeanlengthdierenceislessthanhalfvoxel,themean

relativedierenceislessthan6percents,andthemeanorientationdierenceislessthan0.16radiansor10degrees.Therefore,theresultsdemonstratethe

accuracyofthe


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proposedapproach.Figure3showsboththe

synthetictransformation


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elds(rigidandradial)andtheestimated

ones.Wecanseethattheestimatedtransformation


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eldsarealmostidenticaltotheknown

ones.Inordertoevaluatetherobustnessoftheregistrationmethodagainst

noisemore


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NormalizedSumofAbsoluteDistancecase

1case2case3case4case5case6Initial

alignment12.93593410.1846024.0380314.59260610.81813012.540091Ourmethod2.8742461.7595470.9330381.105014

2.1995411.6177453Dsurface12.2641078.2869623.6247273.9547608.64555710.4357953Dvoxel10.8507078.8791893.4118764.1106118.32550611.2126773DNMI10.9701947.5256862.9425833.6689758.144775

8.570295


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DierenceofTransformationVectorscase1case

2case3case4case5case6Lengthdierence(mean)

0.3753670.4286000.3498460.3254190.3832610.250679Lengthdierence(dev)0.5332790.4612560.4737730.344143

0.4033070.225654Ralativedierence(mean)0.0495370.0566070.0543910.0496500.0568970.045490Ralativedi

erence

(dev)0.0648170.0847360.0986900.0695910.0744860.066269Orientationdierence(mean)0.0792090.075370

0.0834420.0714920.087357


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0.060312Orientationdierence(dev)0.1085360.1177590.143446

0.1597500.1209570.105408

Table1.Resultsofevaluatingtheproposed

approachinrecoveringknowntransformation


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eld.Itcanbeseenfromthe


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rstpartthatdistancebetweenthesource

andtargetvolumesafterregistrationbyouralgorithmsiswithinrangeof

[0:932:87],whichismuchsmallerthanthedistanceobtainedusing

theotherthreeregistrationmethods.Fromthesecondpartofthistable,Wecanseethemeandierenceinlengthislessthanhalfvoxel,

themeanrelative


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errorinlengthislessthan6

percents,andthemeanorientationerrorislessthan0.16radiansor

10degrees.(a)(b)Figure3.Theresultofregistrationonimagedeformed

bysynthetictransformation


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eld.(a)knownnon-rigidtransformation


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eld.(b)estimatednon-rigid


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eld.

comprehensively,additivezero-meanGaussian

noiseatmultiplelevelsisaddedtothesyntheticdeformedvolumes.Figure

4showsthemeananddeviationofthemagnitudedierenceofthedisplacement

vectors.Itcanbeseenthattheregistrationalgorithmisquiterobustupto10dB(signaltonoiseratio).

4.CONCLUSIONIn

thispaper,a


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generalregistrationframeworkthatusesbothjunctions

andvesselsareproposed.Thelandmarks(junctionsandlinearvesselsegments)are

obtainedfromthevesselnetworkafterenhancement.Weusethevesselenhancement


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lterproposedinourpreviouswork,16which

candistinguishbetweenjunctionsandnodules,thus


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2

1.61.81.41.6

1.20 5 10 15 20

0 5 10 15 20

Mean normal of difference vector

1.41.21

Angle of difference vector

1

0.80.80.60.60.40.40.20.2Signal to noise ratio (SNR)Signal to noise ratio (SNR)(a)

(b)Figure4.Evaluationoftheregistrationalgorithmwithrespecttonoise.(a)meanmagnitudeofdierencevectorbetweenthetransformation


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elds.(d)thestandarddeviationofthe

magnitudeofthedierencevectorsbetweenthetransformation


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elds.Itcanbeseenthatthe

registrationalgorithmisquiterobustupto10dB.

the

negativeimpactofnewnodulesaresuppressed.Inthesegmentedvesselnetwork,junctions

areselectedbycheckingtheratioofeigenvaluesofthegradientcorrelationmatrix.Thematchingbetweenjunctionsisbuiltbysearchinginthetargetvolume

withinalocal


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windowafterinitialalignmentofthesource

andtargetvolumes.Thefalsematchingofjunctionsareiterativelyremovedusing

thelocalfeatureofthetransformation


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eld.Besidesjunctions,additionalconstraintsfromvessels

areincorporatedtoimprovetheregistration.Thematchingbetweenvesselsareobtained

bydeformingthecontourofvesselstotheirmatchesundertheguidanceof

anenergyfunction.Thetransformation


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eldisinterpolatedusingthinplatesplines.

Variousexperimentsshowthetheproposedalgorithmisaccurateinestimatingthe

non-rigidtransformation


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eldbetweentemporalCTscansandalso

robustagainstnoise.Theexperimentwithsyntheticnodulesdemonstratestherobustnessof

theproposedmethodagainstnewnodules.Futureworkwouldbetoevaluatethe

registrationonhigh-resolutionCTscansandcheckitsapplicationinthediagnosisoflungdiseasesuchasdetectionofnewnodulesandotherbloodvessel

relateddiseases.


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Documents

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