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Vbl_34.No.7ACTAAUTOMATICASINICAJuly,2008

    ;AnImprovedOpticalFlowMethodforImage

    ;RegistrationwithLarge?-scaleMovements

    ;XIONGJingYiLUOYuPinTANGGuang-Rong1

    ;AbstractInthispaper,animprovedopticalflowmethodforimageregistrationisproposed.Itisnovelinthewaythatitimproves

    ;theopticalflowmethodwithaninitialmotionestimator:extendedphasecorrelationtechnique(EPCT),usingmeritsofthelatterto

    ;compensatedeficienciesoftheformer.Inamoredetailedmanner.itcanbesaidthattheopticalflowmethodcanreachthesub-pixel

    ;accuracyandcalculatecomplexdistortionpatternslikechirpingandtiltingbutisweakwithlarge-scalemovements.BecauseEPCT

    ;coversmeasurementsoflargetranslationsandrotationswithpixellevelaccuracyandisefficientinthecalculatingload,itcanbe

    ;treatedasagoodinitialmotionestimatorforopticalflowmethod.Testshaveprovedthatthisimprovedmethodwillsignificantly

    ;enhancetheregistrationperformance,especially,forimageswithlargescalemovement

    sandrobustagainstrandomnoises.

    ;KeywordsImageregistration,improvedopticalflowmethod,motionestimator,extendedphasecorrelationtechnique(EPCT)

    ;Imageregistration.alundamentimageprocessmg

    ;problem,1stheProcessotoverlayingasequenceotimages

    ;ofthesamescenetakenatdifferenttimes,fromdifierent

    ;viewpoints,and/orbydifierentsensors.Duringthispro-

    ;cess.coordinatetransformationsarecalculatedsothatim

    ;agestakenfromthesamestaticscenearerelated.Image

    ;registrationhasbeenwidelyusedasanintermediatestep

    ;inmanyresearchfields,suchassuperresolution,panorama

    ;mosaics,medicalphotosanalysis,etc.

    ;Generallyspeaking,twocategoriesofregistrationalgo

    ;rithmsexist:feature.basedandnonfeaturebased.Inthe

    ;formercategory,therearealgorithmsusinglow-levelfea-

    ;tureslikeedgesandcorners,andhigh.1evelfeatures,such

    ;asidentifiedobjects.orrelationsbetweenfeaturest.While

    ;inthenonfeature-basedcategory.therearealgorithmsus

    ;ingfrequencydoraaininformation[2J.anddifferentialopti

    ;calflowequationmethodt.

    ;Fortheopticalflow.peoplefinditisonthebasisofthe

    ;Taylorexpansionsanddifferentiaitheory,andthus,itis

    ;weaktoestimatelarge-scalemovementsbetweenimages. ;ItwasproposedbyGibsoin1950,andthattheoptical ;flowmethodissensitivetonoisesbecauseitisontheba- ;sisofdifferentialtechnology.Somefilters(bothhighpass

    ;andlow-pass1areusedtoreducethisbadeffect.More

    ;over,Gaussianpyramidsareusedtoconstructdifierent ;levelsofresolutionandincrementallyaccumulatethetrack ;ofeachlevelusingthelawofcompositiont.Thisisuse- ;fulforenhancingtheabilitytoestimatelargescalemove

    ;ments.butitisstillnotenough.Someideashavebeen ;reportedtofurtherimprovetheregistrationbyusingan ;initiaimotionestimatorprovidingaroughinputforfol

    ;lowingcalculation[07I.Someworkshavebeendonebased

    ;onthis,likelog-polarmappingreliedonnonlinearleast ;squareiterativeoptimizationalgorithminl8I,however,this ;methodhasaheavycalculatingload.Andphasecorrela

    ;tionmethodreliedonnonrigidopticalflowestimationin ;91,whichisonlyspecifiedinindocyaninegreenangiogra- ;DllvfICGA)funduswithoutrotatioas.

    ;0nthebasisofthepreviouswork,anewseparatemo- ;tionpreestimator,EPCT(Extendphasecorrelationtech

    ;nique1.isregardedasamoresuitablechoiceinthispaper. ;Theproposedapproachtakesgreatadvantageoftheprop

    ;ertiesofEPCT.measurementsoflargetranslationsandto- ;tations,andcalculatingefficiency,sothattheincreaseof ;workloadisalineargrowthoftheimagesize.Although ;EPCTonlyreachespixellevelaccuracyandcannotdeal ;ReceivedMaly14,2007;inr~visedformAugust9,2007 ;1.DepartmentofAutomation,TsinghuaUniversity,Beijing ;100084.P.R.China

    ;DOI:l0.3724/SP.J.1004.2008.00760

    ;withmorecomplexdistortionslikekeystoningorchirping, ;thesedeficiencieswillberefinedbytheopticalflowmethod ;later.

    ;Anotherworkdoneisdefiningawaytogaugetheregis- ;trationaccuracyandtorevisethelooptimeinopticaiflow ;fromfixedtoself-adaptiveaccordingtoaccuracy.Thus,it ;willsavetimeandeffortincalculation.

    ;Thispaperisorganizedasfollows.Section1outlinesthe ;principlesoftheprojectivemodel,opticalflowmethod,as ;wellasEPCT.then.describeshowtoimproveopticalflow ;methodbyusingEPCTasaprocessortoestimateaninitial ;input.Section2presentssomeregistrationresultsusingthe ;improvedopticalflowmethodandcomparestheresultsof

    ;EPCTwiththatoftheoriginalopticalflowmethod.In ;Section3,conclusionsandsomeresearchperspectivesare ;given.

    ;1Principles

    ;1.1Projectivemodel

    ;Theprojectivemodelischosentodescribemovements

    parameterequationpair ;betweentwoimages.Itisaneight

    ;dealingwithrotation,translation,scaling,chirping,and ;tilting.

    ;z,=

    ;?n6x?77,7Y,=?n

    ;6x()十十lr71

    ;Itcanberewrittenasamari)(

    ;m2

    ;(2)

    ;wherex/,Y=v/w.

    ;Inthismodel,m2and?77,5standfortranslationsinhori

    ;zontalandverticaldirectionsseparately,?77,0,777,1,?77,3,and

    ;m4forscalingandrotation,and?77,6and?77,7areincharge ;ofchirpingandkeystoningeffects.Anexampleislistedin ;Fig.1(seenextpage)fordetailsofeveryparameter. ;1.2Opticalflowmethod

    ;Intheopticalflowassumption,foreachpoint(x,Y)in ;flamet,therewillbeacorrespondingpointiname+?,

    ;whjchmeans

    ;E(z,,t)=E+?z,+?,t+?t)(3)

    ;Applyraylorexpansionstotherightsideof(3),?regetthe

    ;t?dimensionalopticalfl0wconstraint:

    ;++=0c4d.d.d.,

    ;

    ;No.7XIONGJing-Yieta1.:AnImprovedOpticalFlowMethodforImagesRegistration’?’

    761

    ;?

    ;??(e)(f)

    ;Fig

    ;,

    ;.1Relationshipbetweenparametersandimagemotions ;(caThe.rname,m=f;;(b)Horizontal

    ;;(d)Chirpingeffect,m=

    ;,m=

    ;

    ;m=00780Rotation001,=1.1:f.

    ;II

    ;m=.

;)

    ;Definecostfunctiona8

    ;.=

    ;?(ue+e+et)(5)

    ,=YY,e=,e=,and ;whereu=

    ;et=.

    ;Minimizethecostfunctionsothatitsatisfiestheoptical ;flowconstraintasmuchaspossible.Thesmallerthevalue ;of0w,thebettertheregistration.Moredetailscanbe ;foundin[5].

    ;BecauseopticalflowmethodisonthebasisofTaylor ;expansions,anddxandaresubstitutedby,_and

    ;

    ;incalculation,itisweakinestimatinglarge-scale ;movements.Insomecircumstance,itmightevenleadto ;failures.Ifthereisamotionestimationfortheopticalflow ;methodasaninitialinputtoturnthelarger-scalemove- ;mentsintosmaller-scalemovements,itwillbebeneficialfor ;registrationeffect.Thisinitialestimationdoesnotneedto ;beprecisebecauseopticalflowisgoodataccuracyandwill ;refineitsresults,andthelesscosttheprrocessor,the

    ;betterthealgorithm.Agoodchoiceforthispreprocessor ;isEPCTaccordingtoourpreviousanalysisintheintro

    ;ductionsection.

    ;1.3EPCT

    ;Assumethat,2,Y)isatranslatedandrotatedreplica ;of,1,Y),suchthat

    ;,2,)=fl

    ;

    ;(xc

    ;s

    ;o

    ;in

    ;s

    ;6l0

    ;g0

    ;+

    ;+y

    ;co

    ;sin

    ;s

    ;g

    ;6l0

    ;0--

;

    ;x

    ;

    ;0

    ;),(6)

    ;sin0+cos0一珈)

    ;AccordingtothepropertiesofFouriertransform,(6)can ;betransferredfromspacedomaintothefrequencydomain ;as

    ;?,cos.9+0sin90,一?sin90+sin90)(7)R+,一?+)

    ;LetM1andM2bethemagnitudesofEland.From

    ;(7),becausethemagnitudeofe-J(?0+nYo)is1,wehave

    ;(,)M1COS90+sin90,--~sin90+COS90)(8)

    ;MappingthemagnitudefromCartesiancoordinatesto ;polarcoordinates,wehave

    ;M1(P,)=M2(P,90)(9)

    ;whereP,//+,=tan().

    ;Aftertheoperationsmentionedabove,thisproblemhas ;becomeatypicaloneforPCTinpolarcoordinatesbywhich ;90iscalculated.Byrotatingoneoftheframesaccording ;to90,therewillbeonlytranslationsbetweenimages.PCT ;shouldbeappliedagaininCartesiancoordinatessothat ;translationsinverticalandhorizontaldirectionscallbecal- ;culated.

    ;1.4Theimprovedopticalflowalgorithm

    ;SinceEPCTandopticalflowmethodhavebeendis

    ;cussedinprevioussubsections,nowletuscometotheim

    ;provedversionofopticalflowmethod.First.EPCTisused ;togettherotationandtranslationbetweenimages.from ;which90andx0,y0areestimated.Becausethematching ;imagesareofthesamesize,noscalingeffectissupposed. ;Chirpingandkeystoningeffectsarealsounknownatthe ;momentsom6and;7arebothsettobe0.Then.an

    ;

    ;72ACTAAUToMATICASINICAVl01.34

    ;initialpixel--accuratevalueoftheprojectivemodelmatrix ;is

    ;.iCOS00sin00x0l

    ;m=I’sin00cos00y0f(10)

    ;001J

    ;Itiscoarsebutgoodenoughfortheopticalflowmethod ;asaninitialinput,asc.mparedwithm=[],whichmeansthematchingimagesareidentica1.Fr

    omexperi-

    ;mentstheopticalflowmethodissensitivetotheinitialm,

    ;andabetterestimationwillgreatlyimprovetheultimate ;result.SousingtheresultofEPCTinsteadofaniden- ;titymatrixwillsignificantlyenhancetheregistration.An ;overviewofthisimprovedalgorithmisshowninFig.2. ;IEPCTf

    ;,0

    ;.

    ;_

    ;r

    ;ICalculateIitjalm0

    ;|

    ;m0

    ;IOpticalfl.wmeth.dI

    ;ultimate