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1、AGenericCameraCalibrationMethodforFish-EyeLensesJuhoKannalaandSamiBrandtHelsinkiUniversityofTechnologyLaboratoryofComputationalEngineeringP.O.Box9203,02015HUT,Finlandjkannala@lce.hut.fi,Sami.Brandt@hut.fiAbstractjdla[1]insteadaimatcalibratingfish-eyelensesg
2、enerally.However,theirmethodsareslightlycumbersomeinprac-Fish-eyelensesareconvenientinsuchcomputervisiontisebecausealaserbeamoracylindricalcalibrationobjectapplicationswhereaverywideangleofviewisneeded.isrequired.However,theiruseformeasurementpurposesisl
3、imitedbyInthispaper,weproposeanewgeneralcalibrationthelackofanaccurate,generic,andeasy-to-usecalibra-methodthatrequiresthatthecameraobservesaplanarcal-tionprocedure.Wehenceproposeagenericcameramodelibrationpattern.Moreprecisely,inSection2,wedescribeforca
4、merasequippedwithfish-eyelensesandamethodforthecameramodelthatwehaveusedforfish-eyelenscam-calibrationofsuchcameras.Thecalibrationispossiblebyeras.InSection3,weproposeaprocedureforestimatingusingonlyoneviewofaplanarcalibrationobjectbutmoretheparametersofth
5、emodel,andtheresultsarepresentedviewsshouldbeusedforbetterresults.Theproposedcali-anddiscussedinSections4and5.brationmethodwasevaluatedwithrealimagesandtheob-tainedresultsarepromising.Thecalibrationsoftwarewill2.Cameramodelbecomecommonlyavailableattheaut
6、hor’sWebpage.2.1Genericmodelforafish-eyelenscameraTheperspectiveprojectionofapinholecameracanbede-1.IntroductionscribedbythefollowingformulaCameraswithanarrow-anglelenscanbemodelledwiththe (perspectiveprojection)(1)pinholecameramodelwhichisjustaper
7、spectiveprojec-tionfollowedbyanaffinetransformationintheimageplanewhereistheanglebetweentheopticalaxisandthein-[5].Thefish-eyelensinsteadisdesignedtocoverthewholecomingray, isthedistancebetweentheimagepointandhemisphericalfieldinfrontofthecamera,hence,thea
8、ngletheprincipalpointandisthefocallength.Fish-eyelensesofviewisverylarge,aboutÆ.Becauseitisimpossibleinsteadareusuallydesignedtoobeyoneofthefollowing projections:toprojectthehemisphericalfieldofviewonafiniteimageplanebyap
