水下图像的校正

18　220083　　　　　　　　　　　JournalofHeilongjiangInstituteofScienceTechnology　　Vol.18No.2　　Mar.2008　　　　　　:1671-0118(2008)02-0133-04徐　杰1,　王宗义2,　刘　涛2(1.,150027;2.,150001)　:水具有与空气不同的折射率,在水下成像时,目标位于水介质的物空间,而成像平面位于空气介质的图像空间,这将使物镜畸变明显增大。文中研究了水下图像的畸变校正,给出了平面玻璃密封窗口的摄像机的水下图像转化为一般对应的空气中的图像的条件和转换算法,特别给出了密封窗应位于摄像机的焦距处的位置关系准则。此时,水下图像和空气中的图像存在一一对应的关系,凭借水下图像即可确定其对应的一般空气中的图像。在平面窗与外焦点距离和焦距与物距相比足够小时,该结果仍近似成立。:水下视觉;水下图像校正;水下三维测量　　:TB868:ACorrectionforunderwaterimageXUJie1,　WANGZongyi2,　LIUTao2(1.CollegeofElectricalandInformationEngineering,HeilongjiangInstituteofScienceandTechnology,Harbin150027,China;2.SchoolofAutomation,HarbinEngineeringUniversity,Harbin150001,China)Abstract:Theobjectlocatedinphysicalspacewithwatermediuminthecaseofimagingunderwaterandtheimagingplaneoperatinginimagespacewithairmediumresultingreateraberrationofviewinglens.Thispaperdiscussesthephysicaleffectsofimagedistortionandoffersanalgorithmtotransferun-derwaterimagetoimage-without-water,especiallytheprincipleofpositionrelatedtocameraandwater-proofhouse.Whentheboundaryisatthefocusoflens(outsidethecamera),thereexistsone-to-onecor-respondencebetweentheunderwaterimageandtheimage-without-water.Theimagetotheimage-without-watercanbetransferredonlywithoneunderwaterimage.Whenthedistancebetweenthefocuspointandwaterandthefocusoflensarebothsmallerthanthedistancefromthelenstotheobject,itisstillpossi-bletousetheresultaboveinagoodapproximation.Keywords:underwatervision;correctionforunderwaterimage;underwater3Dmeasurement　　:2008-03-03　　:　(1964-),,,,:、、、,E-mail:[e-mail]。0　引　言、、、、,、。(AUV、ROV),[1-3],CCD,,。,。。,。,,(CCD、)。、,,、、,[4-5]。,,[6]。,,。,。1　水下成像的投影关系,1。pw(xw,yw,zw)pi(xi,yi)2。1　Fig.1　Underwatercamerainwaterproofhouse,yi=0,yw=0。——,,,—。δ,Oc,f,nw、na,αwαa。:xi=f·tanαa,xw=δ·tanαa+(z-f-δ)tanαw,nw·sinαw=na·sinαa。(1)(1),,:xa=fxw/z,(2),。,(2)z,,xaxi。2　pw(xw,yw,zw)　Fig.2　Objectunderwateratpointpw(xw,yw,zw),pi(xi,yi)isitsimagepositioninimageplane2　图像转换关系2.1　αaαw,,(1)xi=f·αa,xw=δ·αa+(z-f-δ)·αw,nw·αw=na·αa,:xi=fδ+(z-f-δ)·nanwxw=fnanw·z+δ1-nanw-fnanwxw。(3)(3)(2):znanw·z+δ1-nanw-fnanw。zδ,zf,xi≈fnaz/nwxw=nwna·fzxw=nwna·xa,(),nw/na。:xa=na·xi/nw,na=1,nw=1.333,xa=0.75xi。134　　　　　　　　　　　　　　　　　　18　2.2　3。3　Fig.3　Boundaryatfocusoflensδ=0,(1)xi=f·tanαa,xw=(z-f)tanαw,nw·sinαw=na·sinαa,(4)xa=f·tanαw,(5):xaxi=tanαwtanαa=tan(arcsin(na·sinαa/nw))tanαa。(6)na=1,nw=1.333,αa,xaxi4。4　δ=0,xi/xaαaFig.4　Relationbetweenxi/xaandαaasδ=0(4)、(5):xa=f·tan(arcsin(nasin(arctan(xi/f))/nw)),(7)。(7)。(6)、(7)4,(),(),。,,,。2.3　5。(1)、(2),。5　(δ≥0)Fig.5　Boundarybetweenwaterandairisnotatfocusoflens(δ≥0)δ≥0、AP,pi(xi,0)。,pApB。pA=pi(xi,0),pB(xb,0),CD,CDCAC。pw(xw,yw,zw),pa(xa,0)pApB。pw(xw,0,z)CDxaxb,xaxb=xwxD=(z-f-δ)tanαw+δtanαa(z-f)tanαw=1+δz-ftanαatanαw-1。zδ,zf,xa/xb≈1,δf,pw(xw,0,z)CDpa(xa,0)pB(xb,0),pa(xa,0)pB(xb,0)。,z=1000mm,δ=10mm,f=25mm,αa=45°,na=1,nw=1.333,xaxb=1+δz-f·tanαatanαw-1=1+101000-25·tan45°tanαw-1=1.0061。1352　,:CDpB(xb,0)pw(xw,yw,zw)pi(xi,0),,(7)。δfz,pw(xw,yw,zw)pa(xa,0)。,δfz,δ=0。,(7)。,δfz。f≤δ≤0,(1),δ-δ:xi=f·tanαa,xw=-δ·tanαa+(z-f+δ)tanαw,nw·sinαw=na·sinαa。,xaxb=1-δz-f·tanαatanαw-1。,δfz,。3　结束语,。(),。,,。,,。:[1]　MCNEILGOMERT.Metricalfundamentalsofunderwaterlenssystem[J].Opt.Eng.,1997,16(2):128-139.[2]　THORNDIKEEM.Awide-angleunderwatercameralens[J].J.Opt.Soc.Am.,1950,40(12):823-824.[3]　CLINTON.Taleoftwounderwaterlenses[J].Proc.SPIE.,1991,1537:203-214.[4]　,　,,.[J].,1998,(10):5-11.[5]　SCHECHNERYY,NIRKARPEL.Clearunderwatervision[J].Proc.ComputerVisionPatternRecognition,2004,I:536-543.[6]　ATSUSHIYAMASHITA,HIROKAZUHIGUCHI,TORUKANE-KO,etal.Threedimensionalmeasurementofobject'ssurfaceinwaterusingthelightstripeprojectionmethod[C]//Proceedingsofthe2004IEEEInternationalConferenceonRoboticsandAutoma-tion(ICRA04),NewOrleans(U.S.A.),2004.2736-2741.(　吴维华)136　　　　　　　　　　　　　　　　　　18