基于SVD的相位相关方法在空间运动目标检测中的应用

12120071JournalofImageandGraphicsVol.12,No.1Jan.,2007:2005207215;:2005211203:(1977),2006,DSPE2mail:[e-mail]1)2)1)(,100083)2)(,130031),,,1,,(SVD),,3,,,,:TP391.41:A:100628961(2007)0120098206ApplicationofPhaseCorrelationintheSpacialObjectOrientationBasedonSVDZHAODan2pei1),WANGYan2jie2)1)(SchoolofAstronautics,BeijingUniversityofAeronauticsandAstronautics,Beijing100083)2)(ChangchunInstituteofOptics,FineMechanicsandPhysics,ChineseAcademyofSciences,Changchun130031)AbstractThephasecorrelationmethodprovidesstraightforwardestimationofrigidtranslationalmotionbetweentwosimilarimages.Itisoftenclaimedthattheoriginalmethodisbestsuitedtoidentifyintegerpixeldisplacement.Experimentalresultsshowthatthephasecorrelationmatrixisrankoneforanoise2freerigidtranslationmodel.Thepropertyleadstoanewlowcomplexitymethodfornon2integertranslationalmotion.Thismethodbasedonsingularvaluedecompositionestimatestheslopeofphasebyaleast2squaresfitandwell2knownFouriershiftpropertywhosespeedisnearlythreetimesasquicklyasoriginalmethod.Themethodisrobustinthepresenceofnoiseandshelterbecauseofusingphaseinformationinthefrequencydomain.Experimentsprovethatthismethodcaneffectivelyrestrainnoiseandaccuratelydetecttheshiftofobjectsheltered,whichresolvedtheproblemofobjectshiftdetectionforimagesseriouslypollutedbynoiseandcloudinthespace.Itprovidesastrongbasisforaccurateobjectorientation.Keywordsphasecorrelation,Fouriertransform,singularvaluedecomposition,subpixel1,,,1:SVD99,,,,,;,,,,,;KuglinHines[1],,,,,,,,,,,,,,,,1,,2,,2,,MNf(x,y)2:F(u,v)=1MNM-1x=0N-1y=0f(x,y)exp-j2uxM+vyNu=0,1,2,,M-1v=0,1,2,,N-12[2]:(1)2,1,F(x,v)=M1MNN-1y=0f(x,y)exp(-j2vy/N)F(u,v)=1MM-1x=0F(x,v)exp(-j2ux/M)(2)f(x,y)exp[j2(u0x/M+vy0/N)]ZF(u-u0,v-v0)(1)f(x-x0,y-y0)ZF(u,v)exp[-j2(u0x/M+vy0/N)](2)12,,(x0,y0),F(u,v)exp[-j2(u0x/M+vy0/N)],,(u0,v0),f(x,y)exp[-j2(u0x/M+vy0/N)]2,f(x,y),,(3)F(u,v)=F3(-u,-v)F(u,v)=F(-u,-v)(3),3SVD3.1,,,,,,[1,3]:(1),,x,y;(2),,,;(3),10012,,,;(4),,5,,3.2SVDAMN,R,A(singularvaluedecomposition,SVD)MN,A,U,V,:AV=UATU=V(4),,UVUnitary,,1,,AA=UVT,AA=RRi=1UiVTi,A,,R,,,1,SVD,,,3.3SVD1,SVD,,[4]:2AB,,A^A,B^B,:B^(k,l)=A^(k,l)exp{-j(ka+lb)},(k,l),(a,b)AB(a,b),A^B^,Q(k,l)B^(k,l)A^3(k,l)B^(k,l)A^3(k,l)=exp{-j(ka+lb)}Q,1,QQ(k,l)=exp(-jka)exp(-jlb),qa(k)=exp(-jka),qb(l)=exp(-jlb)Q=qaqHb,B^=(qaqHb)A^,Q()H,Q1,Q1,,,Q,MNQ,k=2x/M,l=2y/N,[5]:W[c]T=unwrap{},W[w1],w={0,1,2,,(s-1)},s,,cc=(WTW)-1WTunwrap{}=qa,,a=-(M/2);=qb,,b=-(N/2),,Q,R,,R016N/2,Nx,y1:SVD1012,,,,2,,Q,1,Q2SVD,,,3.4,,,,,;,,,,3.5,(1)1Fig.1Theexperimentofdetectingmovingobjectincludednoise1(a)256256pixels1(b)Q1(c)SVD,Q1,80pixels,,1(b),,1(c),1(d)1(e)SVDxySVDxy,,,x=-219797,y=310071,3pixels,3pixels,(2)2Fig.2Theexperimentofdetectingmovingobjectaddedseriousnoise2(a)128128pixels0,01072(b)Q,10212,Q2(c)SVD,Q,50pixels2(b),2(c)2(d)2(e)SVDxySVDxy,,,x=-419825,y=-510376,5pixels,5pixelsSVD,(3)3Fig.3Theexperimentofdetectingmovingobjectshelteredseriously3(a)3(b)128128pixels,3(b),35%,;3(c)SVD,Q,3(d)3(e)SVDxy,,,x=318282,y=-513918,4pixels,5pixels,35%,,SVD,,11SVDTab.1ThecomparisonofbasicperformancebetweenphasecorrelationmethodbasedonSVDandtraditionalphasecorrelationmethodSVDSVD3(0,0107),10%,,35%,,,,,,,4,,1:SVD103SVD;,4:(1),;(2),1,,;(3),,,;(4),,,(References)1KuglinCD,HinesDC.Thephasecorrelationimagealignmentmethod[A].In:ProceedingsofIEEEInternationalConferenceonCyberneticsandSociety[C],NewYork,1975:163165.2YeWu,WangJian2xin.ThemotiondetectionmethodsofTVsignalsbasedonFouriertransform[J].JournalofSouthChinaUniversityofTechnology(NaturalScience),1997,25(9):6266.[,.[J].(),1997,25(9):6266.]3ForooshH,ZerubiaJB,BerthodM.ExtensionofphasecorrelationtosubpixelRegistration[J].IEEETransactionsonImageProcessing,2002,11(3):188200.4HogeWS,MamataHatsuho,MaierStephanE.EfficientconstructionofhistologyslidemosaicsviaphasecorrelationRegistrationofhighresolutiontiles[A].In:IEEEInternationalConferenceonImageProcessing[C],Barcelona,Spain,2003:11171120.5HongWS.Subspaceidentificationextesiontothephasecorrelationmethod[J].IEEETransactionsonMedicalImaging,2003,22(2):277280.