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1、InternationalJournalofComputerVision,13,3,331-356(1994)©1994KluwerAcademicPublishers.ManufacturedinTheNetherlands.SystemsandReplicationReviewandAnalysisofSolutionsoftheThreePointPerspectivePoseEstimationProblemROBERTM.HARALICKIntelligentSystemsLaboratory,Departmen
2、tofElectricalEngineeringFT-IO,UniversityofWashington,Seattle,WA98195,USACHUNG-NANLEEInstituteofInformationEngineering,NationalSunYat-SenUniversity,Kaohsiung,Taiwan80424,ROCKARSTENOTTENBERGPhilips-Forschungslabor,Vogt-KfllnStrafle30,D-2000Hamburg54,GermanyMICHAELNO
3、LLETechnischeUniversitiitHamburg-Harburg,TechnischeInformatik1,HarburgerSchloflstrafle20,D-2100Hamburg90,GermanyReceivedOctober30,1990;revisedMarch27,1992andOctober29,1993Abstract.Inthispaper,themajordirectsolutionstothethreepointperspectiveposeestimationproblemsa
4、rereviewedfromaunifiedperspectivebeginningwiththefirstsolutionwhichwaspublishedin1841byaGermanmathematician,continuingthroughthesolutionspublishedintheGermanandthenAmericanphotogrammetryliterature,andmostrecentlyinthecurrentcomputervisionliterature.Thenumericalsta
5、bilityofthesethreepointperspectivesolutionsarealsodiscussed.Weshowthatevenincasewherethesolutionisnotnearthegeometricunstableregion,considerablecaremustbeexercisedinthecalculation.Dependingontheorderofthesubstitutionsutilized,therelativeerrorcanchangeoverathousand
6、toone.Thisdifferenceisdueentirelytothewaythecalculationsareperformedandnotduetoanygeometricstructuralinstabilityofanyprobleminstance.Wepresentananalysismethodwhichproducesanumericallystablecalculation.1Introductionaswellasincomputervision,becauseithasava-rietyofap
7、plications,suchascameracalibrationGiventheperspectiveprojectionofthreepoints(Tsai1987),objectrecognition,robotpicking,constitutingtheverticesofaknowntriangleandrobotnavigation(Linnainmaaetal.1988;in3Dspace,itispossibletodeterminetheHoraud1987;Lowe1987;Dhome1988)in
8、com-positionofeachofthevertices.Theremayputervisionandthedeterminationoftheloca-beasmanyasfourpossiblesolutionsforpointtioninspacefromasetoflandmarksapp
