2024年2月22日发(作者：魅族mx5g手机)

ImageandVisionComputing21(2003)205–/locate/imavisOverallviewregardingfundamentalmatrixestimationq´,JoaquimSalvi*XavierArmangue´sSantalo´,s/n,E-17071Girona,SpainComputerVisionandRoboticsGroup,InstituteofInformaticsandApplications,UniversityofGirona,ıReceived26September2002;accepted24October2002AbstractEpipolargeometryisakeypointincomputeticleisafreshlookinthesubjectthatoverviewclassicandlatestpresentedmethodsoffundamentalmatrixestimationwhichhavebeenclassifiedintolinearmethods,hesemethodshavryincludingexperimentalresultsads:Epipolargeometry;Fundamentalmatrix;uctionTheestimationofthree-dimensional(3D)ent,fi,theimagingsensormodelthatughsurveyoncameramodellingandcalibrationwaspresentedbyItoin1991[1]ly,basicmethodsmodeltheimagingsensorthroughasingletransformationmatrix[2,3].Othermethodsfixgeometricalconstraintsinsuchmatrixintroducingasetofintrinsicandextrinsiccameraparameters[4].Moreover,lensdistortionintroducestwonon-linearequations,thorshaveconsideredonlyradiallensdistortion[5],whileothersconsideredtangentialdistortion[6],dependingbasicallyonthefocaldistanceandlenscurvature(seethiscameracalibrationsurvey[7]).Finally,oncethesystemiscalibrated,thecameramodelcanbeusedeithertoestimatethe2Dprojectionofanobjectpointortocomputethe3Dopticalraypassingthroughagiven2DWorkfundedbySpanishprojectCICYTTAP99-0443-C05-01.*.:þ34-972-41-8483;fax:þ34-972-41-8098.E-mailaddresses:qsalvi@(),armangue@´).(ore,atleasttwoopticalraysareneeationcannotbeusedinactivesystemsduetoitslackofflatinactivesystems,theopticalandgeometricalcharacteristicsofthecamerasondapproachthenisbasedoncomputingeithertheepipolargeometrybetweenbothimagingsensors[8]oranEuclideanreconstruction[9].Euclideanrecon-structionisachievedthroughpreviousknowledgeofthescene[10]r,thisassumptionisdifficulttointegrateintomanycomputervisionapplications,icationofscenereconstructionusingEpipolargeometrywasfirstpublishedbyLonguet-Higginsin1981[11].Sincethattime,agreatdealofefforthasbeendoneincreasingtheknowledge[8,12].Manyarticleshavebeenpresentedonsetance,in1992Faugeraspublishedabriefsurveyonself-calibrationandthederivedKruppaequationswhichareusedtoestimatethecameraparametersfromtheepipolargeometry[13].Basically,intrinsicparametersofbothcamerasandthepositionandorientationofonecamerarelatedtotheothercanbeextractedbyusingKruppaequations[14].Inthesameyear,Faugerasalsogaveananswertothequestion“Whatcanbeseeninthreedimensionswithanuncalibrated0262-8856/03/$-:S0262-8856(02)00154-3

206´,/ImageandVisionComputing21(2003)205–uestereorig?”[15].Hartleyalsodidalotofworkwithgeometryandhowitiscontainedintheessentialandthefundamentalmatrix[16]aswellastheestimationofthecamerapose[17].Twoyearslater,tedarobustmethodforrecoveringepipolargeometrybasedonamatchingbycorrelationanddetectingtheoutliers[18].Asaresult,Hartleystudiedthegeometryinvolvedinarotatingcamera[19]whileListudiedthegeometryofahead-eyesystem[20]ucedacanonicrepresentation[21].Also,in1994,LuongandFaugeraspublishedaninterestingarticleonanalyzingthestabilityofthefundamentalmatrixduetouncertaintyintheepipolecomputation,noiseintheimagepointlocalization,cameramotion,andsoon[22].Someapplicationsofepipolargeometryarethesimplifi-cationoftheimagematchinginstereoscopicsystems[23],theestimationofcameramotion[24]andscenereconstruc-tion[25].Itisimportant,therefore,clinearmethodsaremainlybasedonleast-squaresminimization[26]andeigenvaluesminimization[27].Othermethodsarebasedonoptimizinglinearmethodsbymeansofiteration[28].Robustmethodsarebasedoncomputingamoreaccurategeometrydetectionandremovingfalsematchings[26,29].Robustcomputationisstillasubjectforwideresearchfocusingmainlyonproposingnewestimatorstoimprovetheaccuracyofthefundamentalmatrixandonreducingcomputationexpenses[30–32].Thisarticlesurveysupto19ofthemostwidelyusedtechniquesincomputingthefundamentalmatrixsuchastheseven-point,least-squaresandeigenanalysislineartech-niquesamongothersandrobusttechniquessuchasM-Estimators,LMedS,setechniqueshavebe,,allthesurveyedmethodsaredescribedinSection4analyzingtheiradvantagesanddrawbackswithrespecttothepreviousmethods,presentinganoven5dealswiththeexperimentalresultsobtainedwity,argeometryGivena3DobjectpointM¼ðWX;WY;WZ;1ÞTexpressedwithrespecttoaworldcoordinatesystem{W};andIits2Dprojectionontheimageplaneinpixelsm¼ðIX;Y;1ÞT;bothpointsarerelatedtoaprojectivetransformationmatrixasshowninEq.(1),sm¼IPWMð1ÞinwhichsisascalefactorandIPWisa3£4matrix,whichcanbedecomposedasIPW¼IACCKWð2ÞinwhichIACisa3£4matrixrelatingthemetriccameracoordinatesystemlocatedatthefocalpointOCtotheimagecoordinatesystemlocatedatthetop-leftcorneroftheimageplaneinpixels,er,CKWisa4£4matrixwhichrelatesthecameracoordinatesystem{C}totheworldcoordinatesystem{W};thatisthepositionandorientationofthecamerainthescene.C

CK¼RWCtW!W01ð3ÞThen,epipolargeometrydefinesthegeometrybetweenthetwocamerascreatingastereoscnobjectpointMandits2Dprojectionsmandm0onbothimageplanes,thethreepointsdefineaplaneP;whichintersectsbothimageplanesattheepipolarlineslm0andl0m;respectively,atthesameplanePcanbecomputedusingbothfocalpointsOCandOC0andasingle2Dprojection,whichistheprincipletoreduer,theintersectionofalltheepipolarlinesdefinesanepipoleonbothimageplanes,whichcanalsobeobtainedbyintersectingthelinedefiepipolargeometryiscontainedinthesocalledfundamentalmatrixasshowninEq.(4).mTFm0¼0ð4ÞThefundamentalmatrixFcontainstheintrinsicparametersofbothcamerasandtherigidtransformationofonecamerarelatedtotheother,whichdependsonwh.(5),theoriginoftheworldcoordinatesystemcoincideswiththecoordinatesystemofthesecondcamera,locatedatOC0:F¼IA20CT½CtC0