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1、第24卷第11期计算机学报Vol.24No.112001年11月CHINESEJ1COMPUTERSNov.2001摄像机自标定的线性理论与算法1),2)1)吴福朝胡占义1)(中国科学院自动化研究所模式识别国家重点实验室北京100080)2)(安徽大学人工智能研究所合肥230039)摘要文中提出一种新的摄像机线性自标定的算法和理论.与文献中已有的方法相比,该文方法的主要优点是对摄像机的运动要求不苛刻,如不要求摄像机的运动为正交运动.该方法的关键步骤是确定无穷远平面的单应性矩阵(Homography).1112文中从理论上严格证明了下述结论:摄像机作两组运动参数未
2、知的运动M1={(R1,t),(R1,t)},21),(2211122122M2={(R2,tR2,t)},若下述两个条件满足:(1)T1={t,t},T2={t,t}是两个线性无关组(即本组内的两个平移向量线性无关);(2)R1,R2的旋转轴不同,则可线性地唯一确定摄像机的内参数矩阵和运动参数.另外,在四参数摄像机模型下,严格证明了一组运动可线性地唯一确定摄像机的内参数矩阵和运动参数.模拟实验和实际图像实验验证了本文方法的正确性和可行性.关键词摄像机自标定,无穷远平面,单应性矩阵中图法分类号:TP391ANewTheoryandAlgorithmofLinea
3、rCameraSelfCalibration1),2)1)WUFu2ChaoHUZhan2Yi1)(NationalLaboratoryofPatternRecognition,InstituteofAutomation,ChineseAcademyofSciences,Beijing100080)2)(InstituteofArtificialIntelligence,AnhuiUniversity,Hefei230039)AbstractActivevisionbasedcameracalibrationisoneofthemajorresearchdire
4、ctionsin3Dcomputervision.Anewtheoryandalgorithmoflinearcameracalibrationisproposedinthispa2per.Comparedwiththerelatedtechniquesreportedintheliterature,themainadvantageofourmethodisthatitislessstringenttothecamera'smotion,forexample,itdoesnotrequirethecameratoundertakeorthogonalmotion
5、swhicharedifficulttobedonewithoutspecialhardwaresupport.Ourmethodcanbeeasilydonewithahand2heldcamera.Thekeystepinournewmethodistodeterminelinearlythehomographyoftheplaneatinfinity.Inthispaper,weproverigorouslythefollowingconclusion:Assumethecameraundertakestwosuchsetsofmotions1112212
6、2withunknownparametersM1={(R1,t),(R1,t)}andM2={(R2,t),(R2,t)},andifthefol2lowingtwoconditionsaresatisfied,thenthecamera's5intrinsicparameters,tworotationsma-tricesR1,R2,aswellasthedirectionsofthefourtranslationvectorscanbelinearlyanduniquely11122122determined:(1)tandtarelinearlyindep
7、endent,andtandtarelinearlyindependent;(2)ThetworotationaxesofthetwomatricesR1,R2arenotparallel.Inaddition,supposethecamera'sskewparameteriszero,weproveadditionallythatthecameramatrixandtherotationmatrixcanbeuniquelyfactorizedfromthehomographyoftheplaneatinfinity.Simulationsandexperim
8、entsvalidate
