matlab相机定标工具箱程序的算法原理

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1、CameraCalibrationToolboxforMatlabDescriptionofthecalibrationparametersAftercalibration,thelistofparametersmaybestoredinthematabfileCalib_ResultsbyclickingonSave.Thelistofvariablesmaybeseparatedintotwocategories:Intrinsicparametersandextrinsicparameters.Intrinsicparame

2、ters(cameramodel):TheinternalcameramodelisverysimilartothatusedbyHeikkil伯a>andSilvenattheUniversityofOuluinFinland.Visittheironlinecalibrationpage,andtheirpublicationpage.WespecificallyrecommendtheirCVPR'97paper:AFour-stepCameraCalibrationProcedurewithImplicitImageCor

3、rection.Thelistofinternalparameters:·Focallength:Thefocallengthinpixelsisstoredinthe2x1vectorfc.·Principalpoint:Theprincipalpointcoordinatesarestoredinthe2x1vectorcc.·Skewcoefficient:Theskewcoefficientdefiningtheanglebetweenthexandypixelaxesisstoredinthescalaralpha_c.

4、·Distortions:Theimagedistortioncoefficients(radialandtangentialdistortions)arestoredinthe5x1vectorkc四个内参，包括焦距fc，原点坐标cc，相机坐标系中x和y轴夹角alpha_c（接近90°），几何畸变系数kc.Definitionoftheintrinsicparameters:LetPbeapointinspaceofcoordinatevectorXXc=[Xc;Yc;Zc]inthecamerareferenceframe.L

5、etusprojectnowthatpointontheimageplaneaccordingtotheintrinsicparameters(fc,cc,alpha_c,kc).Letxnbethenormalized(pinhole)imageprojection: Letr2=x2+y2.Afterincludinglensdistortion,thenewnormalizedpointcoordinatexdisdefinedasfollows:wheredxisthetangentialdistortionvector:

6、 Matlab中计算几何畸变还考虑了切向畸变Therefore,the5-vectorkccontainsbothradialandtangentialdistortioncoefficients(observethatthecoefficientof6thorderradialdistortiontermisthefifthentryofthevectorkc).ItisworthnoticingthatthisdistortionmodelwasfirstintroducedbyBrownin1966andcalled"Plu

7、mbBob"model(radialpolynomial+"thinprism").Thetangentialdistortionisdueto"decentering",orimperfectcenteringofthelenscomponentsandothermanufacturingdefectsinacompoundlens.Formoredetails,refertoBrown'soriginalpublicationslistedinthereferencepage.Oncedistortionisapplied,t

8、hefinalpixelcoordinatesx_pixel=[xp;yp]oftheprojectionofPontheimageplaneis: Therefore,thepixelcoordinatevectorx_pixelandtheno