一种基于圆形标志点的摄像机标定方法-周艳青

35120141JournalofInnerMongoliaAgriculturalUniversityVol．35No．1Jan．2014*周艳青，薛河儒*，姜新华010018。。Zhang。0．3。TP391．4．1A1009－3575201401－0155－05ANCAMEＲACALIBＲATIONMETHODBASEONCIＲCULAＲFEATUＲEPOINTSZHOUYan－qingXUEHe－ru*JIANGXin－huaCollegeofComputerandInformationEngineeringInnerMongoliaAgriculturalUniversityHuhhot010018ChinaAbstractCameracalibrationistheestimationofparametersassociatedwithacamerabeingusedforimagingwhichdirectlyaffectstheaccuracyofthemeasurement．Accordingtothecharacteristicofcircularboardacameracalibrationbasedonthecircularfeaturepointswaspresented．Firstextractingthetargetoutlinesandobtainingthetargetpropertiesusedtothefunctioncancalculatethecoor-dinatesofcalibrationcircle．ThancalibrationcameraadoptedtheplanecalibrationmethodputforwardbyZhang．Theintrinsicparam-eterswereestimatedbymeansoflevenberg－marquardtandtheextrinsicparameterswerecomputedbyapplyingtotheleastsquaremethodandlevenberg－marquardt．Experimentalresultsshowthatthemeanerrorofcalibrationresidualislessthan0．3pixels．Sothecalibrationmethodisfeasibleandeffective．KeywordsCameracalibrationcircularfeaturepointscalibrationresidual。、、、12。3。。、4。*2013－08－20201203041“”Z2009－1－01062ZN2010101989－．*[e-mail]5。6。7。8ZhangZhang9。。。11．1。。10。1XNx=11YNy=99930mm520mm10mm5。zw=0xwywzw。1Fig．1calibrationboard1．21．2．1、、、、20～30。。、Ｒ、G、BOTSU。1．2．2Matlabbwboundaries2A。B。BBC。、、。2Fig．2lookingfortargetoutline38－Fig．38－freemanchaincode38。880、2、4、611、3、5、721/2L=N1+N2*21/2N10、2、4、6N21、3、5、7。4。fxyp+q6512014mpq=ΣNy=1ΣNx=1xpyqfxy1p+q=1m10m01xc=m10m00yc=m01m0021211。。99。10．9530300503000。499。AtheoriginalimageBbeforede－noisingimageCafterde－noisingimage4Fig．4theoriginalimageprocessing1．3Zhang55。8。PxwywzwPuvρ=uv1=fxscx0fycy001Ｒtxwywzw1=Ar1r2r3txwywzw1=Hxwywzw13ZhangH=Ar1r2tB=A－TA－1r1r2B=μA－TA－1。4。AH5cy=B12B13－B11B23/B11B22－B11B223μ=B33－B213+cyB12B13－B11B23/B11fx=μ/B槡11fy=μB11/B11B22－B212槡s=－B12f2xfy/μcx=scy/fx－B13f2x/μ4r1=λA－1h1r2=λA－1h2r3=r1×r2t=λA－1h2λ=1/‖A－1h1‖=1/‖A－1h2‖51．4Zhang6δxxy=k1x2+y2+p13x2+y2+2p2xy+s1x2+y2δyxy=k2x2+y2+p23x2+y2+2p1xy+s2x2+y267511δxδyk1、k2、p1、p2、s1、s2。Tsai。12。。u－cxx2u+y2uu－cxx2u+y2u2v－cyx2u+y2uv－cyx2u+y2u[]2k1k[]2u^－uv^[]－v7u^v^uv。k1、k2k3、k4。2MV－VD030SCCCD640*480100μs－30s。Ｒ2011bMatlabWin-dowsXP。565Fig．5thefirstgroupwiththeleftcameraimages6Fig．6thesecondgroupwiththerightcameraimages3A=1806．810．6375666．4501805．97453．40001k1=－0．0850k2=0．2126k3=0．0325k4=0．03773A=1821．500．4480680．5301821．54426．46001k1=－0．1024k2=0．3162k3=－0．0795k4=－0．3236。、3。。Pp’x’piy’pipxpiypipp’13。Ed=－Σni=1x＇pi－xpi2+y＇pi－ypi槡28。。0．20．40．60．6。11485120145。0．30．2。1Tab．1Averageresidualofimageserrorinpixels10．17165410．1182720．15546920．0336730．20867230．1183440．35420940．4593550．09659850．546400．197320．2552063Matlab。。。。1．J．199254279－286．2．3DJ．200822133－36．3．J．200922467－70．4．3DJ201132615－16．5．D．2007．6．J．2003291111－113．7．J．200225111150－1156．8ZhangZY．AFlexibleNewTechniqueforCameraCali-brationＲ．TechnicalＲeportMSＲ－TＲ－97－71Mi-crosoftＲesearchDecember1998．9．D．2010．10．J．201193398－3400．11．MATLABM．2009305－307．12．—M．2003．13．J．201010118－121．9511