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1、700IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.PAMI-9,NO.5,SEPTEMBER1987TABLEIcussesanextensionofthemethodtocoverbothtranslationalandro-VAX11/780CPUTIMEPERRUNINmstationalmovements.MethodUsedIndexTerms-Digitalimageprocessing,fastFouriertransform,im
2、-NumberofPointageregistration,imagesequenceanalysis,motionestimation.CorrespondencesSVDQuaternionIterative354.626.6126.8(25)I.INTRODUCTION741.632.4108.2(12)Letusconsideraplaneimageperformingrigidmovementsof1137.041.0105.2(8)translationandrotationwithinarectangula
3、rdomainCrepresenting1639.445.694.2(5)theobservedfield.Lettheimagebedefinedbyadensityfunction2040.445.2135.0(6)vanishingoutsidearegionA,whosepositionvarieswithtimet,but3044.248.3111.0(6)isalwaysfullycontainedinsideC.Thelimitationswhicharisewhenpartsoftheimageleave
4、theobservedfieldwillbementionedlateron.usedinfindingtheSVD(subroutineLSVDF)andindoingtheei-Letso(x,y)representtheimageatareferencetime,t=0,andgenanalysis(subroutineEIGRS)forthequaternionmethod.Forst(x,y)bethepresentimage,whichisbutareplicaofso(x,y)theiterativemet
5、hod,theinitialguesssolutionwaszeroinallcases.translatedby(xo,yo)androtatedby00:WeobservethatthecomputertimerequirementsoftheSVDandst(x,y)=SO(u,v),(1)thequatemionalgorithmsarecomparable,whilethetimefortheiterativemethodismuchlonger.However,intheiterativemethod,whe
6、rethesolutionswerecalculatedto7-digitaccuracy.Ifwecanacceptx-xo=ucos00-vsin0010percentaccuracy,thenthenumberofiterationsarereducedbyy(2)-yo=usin0O+vcos00.afactorof2to3.Furthermore,therateofconvergencecanbeincreasedbyoverrelaxation.Inordertorealignimagessoandst,it
7、isfirstnecessarytodeter-minethetranslationvector(xo,yo)andtherotation00fromtheinformationprovidedbyso(x,y)andst(x,y).Severalimagereg-REFERENCESistrationalgorithmsareknown:forexcellentreviewpaperssee[1][1]S.D.BlosteinandT.S.Huang,"Estimating3-Dmotionifromrange[6].
8、data,"inProc.1stConf.ArtificialIntelligenceApplications,Denver,ThepresentcorrespondenceismeantasacontributionintheCO,Dec.1984,pp.246-250.contextofthephasecorre
