一种基于三焦点张量的度量重建方法

30620096ChineseJournalofScientificInstrumentVol130No16Jun.2009:2008208ReceivedDate:20082081,2,1,1(1110016;2100039):,,,,:;;;:TP391.4:A:520.60ApproachtometricreconstructionbasedontrifocaltensorHuangYijun1,2,LiuWeijun1,ZhaoJibin1(1KeyLabofAdvancedManufactureTechnology,ShenyangInstituteofAutomation,ChineseAcademyofSciences,Shenyang110016,China;2GraduateSchoolofChineseAcademyofSciences,Beijing100039,China)Abstract:Reconstructingthestructureofascenefrom2Dviewshasbeenanimportantresearchfieldincomputervi2sion.Byinvestigatingtheepipolargeometrybetweenthreeviews,thispaperdevelopsanovelmethodformetricre2constructionofascenebasedonthetrilinearrelations.Ouralgorithmdoesnotputanyrestrictiononthecameramovementorthescenestructure;thealgorithmadoptsdirectreconstructionmethodandappliesthetrifocaltensortometricreconstruction.Experimentswithbothsimulationdataandrealimagedatashowthattheproposedmethodofmetricreconstructionisveryaccurateandpractical.Keywords:metricreconstruction;trilinearrelation;trifocaltensor;computervision1[122],,,[325],2090[629],,278,,,,[10][11][12],,,,,;,13083022.1[13]():P=K[R|T](1):K;RT,,,[14]:xn=[R|T]Xxd=kr(xn)xp=Kxd(2):X;xnX();xdxn;xp;kr;Xxnxdxp2.2,;,;,(1),P=[I|0],P=[A|a4],P=[B|b4];A=[a1,a2,a3],B=[b1,b2,b3];aibiPPi,i=1,2,3,433{1,2,3},:i=aibT4-a4bTi(3)1Fig.1Threeviews[4,6],:1)1,e21e31uivii,uTii=0T,ivi=0,:eT21[u1,u2,u3]=0TeT31[v1,v2,v3]=0T(4)2):F21=[e21][1,2,3]e31F31=[e31][T1,T2,T3]e21(5),a=(a1,a2,a3)T,:[a]=0a3a2a30a1a2a103),:P=[I|0]P=[[1,2,3]e31|e21]P=[(e31eT31-I)[T1,T2,T3]e21|e31](6)2.31,X,PPP,{x,x,x}x=(x1,x2,x3)T,x=(x1,x2,x3)T,x=(x1,x2,x3)T,[4,5]:xixjxkilmiqukrvqri=0uv(7):qri,27,18,,det(F)=0,8,Faugeras[7]:[6],,Hartley[9]3,,(6){P,P,P,X},{P,P,P,X}{PM,PM,PM,XM}H:{PM,PM,PM,XM}={PH,PH,PH,H-1X}(8),,H,(2):{xd,xd,xd}{xn,xn,xn},;6:1309Hartley[9],{xn,xn,xn},(5),E21E31,():Pn=[I|0]Pn=[R|T]Pn=[R|T](9)[13],(9)RRttE21E31,(9):Pn=[I|0]Pn=[R|kt]Pn=[R|kt](10):k=Tk=Tkk,(10)PnPn,3.1k/k:ŽX,(10):xn=[I|0]ŽX1xn=[R|t]ŽXk=[R|t]1kŽX1xn=[R|t]ŽXk=[R|t]1kŽX1(11)ŽX1=1kŽX,ŽX2=1kŽX,ŽX1ŽX2ŽX,{Pn,Pn}{Pn,Pn},N,Dij,:Dij1=ŽXi1-ŽXj1Dij2=ŽXi2-ŽXj2(12),kk:kk=N-1i=1Nj=i+1Dij1N-1i=1Nj=i+1Dij2(13)3.2k/k,(11):xn=[I|0]ŽXkxn=[R|t]ŽXkxn=[R|kkt]ŽXk(14)Pn=[I|0],Pn=[R|t],Pn=[R|kkt]ŽXn=ŽXk,,{Pn,Pn,Pn},ŽXnŽX,ŽXk:ŽXn=12ŽX1+kkŽX2=1kŽX(15),,,(LM)[15],(ML)423,4.1(2):K=65703020657242001,[-0.25520.1260],[-0.00030.00003];32025020050,50,,2Fig.2Simulationscene1310303,:res=Ni=1(d(xi-^xi)+d(xi-^xi)+d(xi-^xi))6N1/2(16):xixixi;^xi^xi^xi3Fig.3Residualerrorsofmetricreconstructionwithdifferentnoiselevels,ŽXMŽXE,:k=N-1i=1Nj=i+1DijN-1i=1Nj=i+1DijM(17):DijMDij,(ij),‰XE=k‰XM,‰XE=(x,y,z)T‰X=(€x,€y,€z)Td=(x-€x)2+(y-€y)2+(z-€z)2,,454Fig.4Themeansofreconstructionerrorswithdifferentnoiselevels5Fig.5Thestandarddeviationsofreconstructionerrorswithdifferentnoiselevels,,4.5,,;4.26,K=4119.41501943.17904091.2331346.464001,[-0.0940.082],0,38722592,7,,0.7,6Fig.6Realimageandpoint6:1311103Fig.10Theback2projectionerrorsinimage35,,,[1]LONGUET2HIGGINSHC.Acomputeralgorithmforre2constructingascenefromtwoprojections[J].Nature,1981,293(10):1332135.[2]ZHANDZ.Determiningtheepipolargeometryanditsun2certainty:Areview[J].InternationalJournalofComput2erVision,1998,27(2):1612195.[3]LIUL,MANNERR.Anefficientandaccuratemethodfor3D2pointreconstructionfrommultipleviews[J].In2ternationalJournalofComputerVision,2005,65(3):1752188.[4]GERARDOSR,MIGUELAE.3Drecoverywithfreehandcameramotion[C].Proceedingsofthe6thMexi2canInternationalConferenceonComputerScience,2005:1452151.[5],.[J].,2001,22(2):2192220.TANYG,WUZHP.ANewThree2dimensionalrecon2structionmethodusingtwocameras[J].ChineseJournalofScientificInstrument,2001,22(Suppl.2):2192220.[6]HARTLEYR.Linesandpointsinthreeviewsandthetrifocaltensor[J].InternationalJournalofComputerVi2sion,1997,22(2):1252140.[7]FAUGERASO,PAPADOPOULOT.Grassmann2Cayleyalgebraformodelingsystemsofcamerasandthealgebraic131230equationsofthemanifoldoftrifocaltensors[C].Pro2ceedingsoftheIEEEWorkshopofRepresentationofVis2ualScenes,1995.[8]TORRPHS,ZISSERMANA.Robustparameterizationandcomputationofthetrifocaltensor[J].ImageandVi2sionComputing,1997,15(8):5912650.[9]HARTLEYR.Minimizingalgebraicerroringeometrices2timationproblems[C].Proceedingsofthe6thInterna2tionalConferenceonComputerVision,1998:4692476.[10]SUGIMRUAY,SATOJ.Cameracalibrationandrecon2structionfromthechainconnectionofmutualcamerapro2jections[C].Proceedingsofthe17thInternationalCon2ferenceonPatternRecognition,2004,1:1002103.[11]ZHANGJ,SHIFH,LIUYC.Motionsegmentationbymultibodytrifocaltensorusinglinecorrespondence[C].Proceedingsofthe18thInternationalConferenceonPat2ternRecognition,HongKong,China,2006,1:5992602.[12]YUYK,ORSH,WONGKH,etal.Accurate32Dmotiontrackingwithanapplicationtosuper2resolution[C].Proceedingsofthe18thInternationalConferenceonPatternRecognition,2006,3:7302733.[13]HARTLEYR.Multipleviewgeometryincomputervision[M].Cambridge:CambridgeUniversityPress,2000.[14]HEIKKILAJ,SILVENO.Afour2stepcameracalibrationprocedurewithimplicitimagecorrection[C].Proceed2ingsofComputerVisionandPatternRecognition,1997:110621112.[15]TRIGGSB,MCLAUCHLANP,HA