搜索
X(100083),,,4,,,,,ApproachforCalibrationofLensDistortionBasedonCrossRatioInvariabilityHeJunjiZhangGuangjunYangXianming(BeijingUniversityofAeronauticsandAstronautics,Beijing100083,China)AbstractAnewapproachforlensdistortioncalibrationispresented,whichutilizesthecrossratioinvariabilityofperspectiveprojection.Itovercomesthedisadvantagesofexistingdistortioncalibrationapproaches.Assumedonlywithoneorderradialdistortion,imagecoordinatesofonly4specialcollinearpointsareneededaswellasthecrossratioofthem.Anmonadictwoorderequationisbuiltwiththeseinfo,whichwillgivethesolutionofdis2tortioncoefficient.Digitalimitationexperimentandrealdistortedimagecorrectionprovedthisapproachissim2ple,accurateandtimesaving.KeywordsCameralensDistortioncorrectionDistortioncoefficientsCalibrationCrossratioinvariability1,,,,[16],:;,,;,;,,[79]:,(),(10),,,:,,;,,,,,255200410X200211,21,lABC,AB,C(C),,:SR(A,B,C)=ACöBClABCD:CR(A,B,C,D)=SR(A,B,C)SR(A,B,D)=ACBCBDAD(1):AB,CD[10]:CR(A,B,C,D)=CR(A1,B1,C1,D1)(2)13A(xa,ya,za),B(xb,yb,zb),C(xc,yc,zc),D(xd,yd,zd),:(xa-xc)(xb-xd)(xb-xc)(xa-xd)=CR(ya-yc)(yb-yd)(yb-yc)(ya-yd)=CR(za-zc)(zb-zd)(zb-zc)(za-zd)=CR(3),:xif=xzyif=yz(4)ABCD(xia,yia),(xib,yib),(xic,yic),(xid,yid):(xia-xic)(xib-xid)(xib-xic)(xia-xid)=CR(yia-yic)(yib-yid)(yib-yic)(yia-yid)=CR(5),,(x,y,z)(xi,yi),(xq,yl),,:xi=xq(1+k1r2)yi=yl(1+k2r2):r2=xq2+yl2(6):xia=xqa(1+k1r2a)yia=yla(1+k2r2a)xib=xqb(1+k1r2b)yib=ylb(1+k2r2b)xic=xqc(1+k1r2c)yic=ylc(1+k2r2c)xid=xqd(1+k1r2d)yid=yld(1+k2r2d)r2a=xqa2+yla2r2b=xqb2+ylb2r2c=xqc2+ylc2r2d=xqd2+yld2(7)(7)(5),k1,k24,411:(1)k1=k2=3100010-4,f=16mm(2),,[2]:adac-FD(ad,D)ac-FD(ac-FD(ad,D),D)ac-FD(ac-FD(ac-FD(ad,D),D),D):ac=[xi,yi]T,ad=[xq,yl]TFD(ad,D)=[xqk1r2,ylk2r2]T(3),:k1=3100010-4,k2=2199910-43133310-2%89525412,12mm,CCD780582,,220mm2(a),()4,(1)4:k1=3116910-3,k2=3127710-3k1,k2(6),2(b),(a)(b)25,,,,,4,,10,4,210,,4,,1RogerY.Tsai.Aversatilecameracalibrationtechniqueforhigh2accuracy3Dmachinevisionmetrologyusingoff2the2shelfTVcamerasandlenses.IEEE.JournalofRoboticsandAutomation,1987,RA23(4):323344.2JanneH.Geometriccameracalibrationusingcircularcontrolpoints.IEEETransactionsonPatternAnalysisandMachineIntelligence,2000,22(10):10661077.3,11:,199815271.4ZhengyouZhang.Aflexiblenewtechniqueforcameracalibration.IEEETransactionsonPatternAnalysisandMachineIntelligence,2000,22(11):13301334.5AlanM.Mclvor.Nonlinearcalibrationofalaserstripeprofiler.OpticalEngineering,2002,41(1):205212.6JuyangWeng.Cameracalibrationwithdistortionmod2elsandaccuracyevaluation.IEEETransactionsonPat2ternAnalysisandMachineIntelligence,1992,14(10):965980.7K.VijayanAsari.Anewapproachfornonlineardistor2tioncorrectioninendoscopicimagesbasedonleastsquaresestimation.IEEETransactionsonMedicalImaging,1999,18(4):345354.8WarrenE.Smith.Correctionofdistottioninendoscopeimages.IEEETransactionsonMedicalImaging,1992,11(1):117122.9HideakiHaneishi.Anewmethodfordistortioncorrec2tionofelectronicendoscopeimages.IEEETransactionsonMedicalImaging,1995,14(3):548555.101.:,1992.34.9955