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1、ISSN1000-9825,CODENRUXUEWE-mail:jos@iscas.ac.cnJournalofSoftware,Vol.18,No.9,September2007,pp.2100−2104http://www.jos.org.cnDOI:10.1360/jos182100Tel/Fax:+86-10-62562563©2007byJournalofSoftware.Allrightsreserved.∗P3P问题的多解现象的概率研究1,2+1,2张彩霞,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(
2、北方工业大学图像处理与模式识别研究所,北京100041)AProbabilisticStudyontheMultipleSolutionsoftheP3PProblem1,2+1,2ZHANGCai-Xia,HUZhan-Yi1(NationalLaboratoryofPatternRecognition,InstituteofAutomation,TheChineseAcademyofSciences,Beijing100080,China)2(InstituteofImageProcessingandPatternRecognition,Nor
3、thChinaUniversityofTechnology,Beijing100041,China)+Correspondingauthor:Phn:+86-10-88803183,E-mail:caixiazhang@gmail.com,http://www.ia.ac.cnZhangCX,HuZY.AprobabilisticstudyonthemultiplesolutionsoftheP3Pproblem.JournalofSoftware,2007,18(9):2100−2104.http://www.jos.org.cn/1000-98
4、25/18/2100.htmAbstract:Undersomespecialconditions,theP3Pproblemcanhave1,2,3and4solutions,andifthe3controlpointsandtheopticalcenterlieonacircle,theproblemisindeterminate.Inthispaper,bytheMonteCarloapproachofupto1millionsamples,itisshownthattheprobabilitiesoftheP3Pproblemwithone
5、solution,twosolutions,threesolutions,andfoursolutionsarerespectively0.9993,0.0007,0.0000,0.0000.Theresultconfirmsthewell-knownfactthatinthemostcases,theP3Phasauniquesolution.Keywords:P3Pproblem;multiplesolutions;MonteCarloapproach摘要:一般情况下,P3P问题可能出现1,2,3或4个解.但是,若3个控制点和摄像机光心这4点共
6、圆,则会出现无穷多组解.利用“蒙特卡洛”方法模拟出P3P问题分别出现1,2,3,4个解的概率为0.9993,0.0007,0.0000,0.0000.结果论证了如下的事实,即在大多数情况下,P3P问题有唯一解.关键词:P3P问题;多解现象;蒙特卡洛方法中图法分类号:TP309文献标识码:A1IntroductionTheperspective-n-pointproblem,orthePnPproblem,hasbeenextensivelystudiedoveryearsincomputervisionfieldduetoitsimportance
7、ofcameraorobjectposedetermination.AmongthePnPproblemfordifferent“n”,theP3Pproblemisthemostfundamentaloneduetoitswideapplicabilityaswellasitspivotalrole-playedforothers.OneofthemainresearchdirectionsfortheP3Pproblemisthestudyonitsmultiplesolutions.Itisshownthatthenecessaryandsu
8、fficientconditionfortheP3Pproblemtohaveaninfinitelylargenumbe
