One of the essential problems in computer vision is to recover the distance information of an object from captured images. Its application areas range from industrial inspection and reverse engineering to autonomous robot navigation

“character”image .Thecameramotionspeedis230mm/s.

Aperture0.8mm

Distance mm 500750100012501500

x10974564537

z1545805

z2549807

e1

e2

x

Aperture1.8mmz1547803

z2551805

e1

e2

Acknowledgment

ThesupportofthisworkinpartbytheNationalScienceCouncilofTaiwanundergrantNSC-93-2218-E-194-024isgratefullyacknowledged.

8.99.81097.47.6

74564436

9.410.27.15.47.5

7.35.88.7

106610716.67.1131113234.95.9160116276.78.5

1054105813441358

References

1.E.TruccoandA.Verri,IntroductoryTechniquesfor3-DComputerVision,PrenticeHall,EnglewoodCliffs,NJ 1998 .

2.M.SubbaraoandG.Surya,“Depthfromdefocus:Aspatialdomain

approach,”put.Vis.13,271–294 Dec.1994 .

3.A.N.RajagopalanandS.Chaudhuri,“Simultaneousdepthrecoveryandimagerestorationfromdefocusedimages,”IEEEComputerVi-sionPatt.Recog.1,348–353 1999 .

4.P.FavaroandS.Soatto,“Ageometricapproachtoshapefromdefo-cus,”IEEETrans.PatternAnal.Mach.Intell.27 3 ,406–417 2005 .5.F.Deschênes,D.Ziou,andP.Fuchs,“Anuni edapproachfora

simultaneousandcooperativeestimationofdefocusblurandspatialshifts,”put.22 1 ,35–57 2004 .

6.A.N.Rajagopalan,S.Chaudhuri,andU.Mudenagudi,“Depthesti-mationandimagerestorationusingdefocusedstereopairs,”IEEETrans.PatternAnal.Mach.Intell.26 11 ,1521–1525 2004 .

7.M.BanhamandA.Katsaggelos,“Digitalimagerestoration,”IEEE

SignalProcess.Mag.14,24–41 Mar.1997 .

8.S.Kang,J.Min,andJ.Paik,“Segmentation-basedspatiallyadaptive

motionblurremovalanditsapplicationtosurveillancesystems,”Intl.Conf.ImageProcess.,pp.245–248 2001 .

9.G.BrostowandI.Essa,“Image-basedmotionblurforstopmotionanimation,”SIGGRAPH01Conf.Proc.,pp.561–566 Aug.2001 .10.M.Ben-EzraandS.Nayar,“Motion-basedmotiondeblurring,”IEEE

Trans.PatternAnal.Mach.Intell.26,689–698 June2004 .

11.H.Y.Lin,“Vehiclespeeddetectionandidenti cationfromasingle

motionblurredimage,”IEEEWACV/MOTION,pp.461–467 2005 .12.D.Slepian,“Restorationofphotographsblurredbyimagemotion,”

BellSyst.Tech.J.46,2353–2362 Dec.1967 .

13.M.Sondhi,“Imagerestoration:Theremovalofspatiallyinvariant

degradations,”Proc.IEEE60,842–853 July1972 .

14.Y.Yitzhaky,I.Mor,ntzman,andN.Kopeika,“Directmethod

forrestorationofmotionblurredimages,”J.Opt.Soc.Am.A15,1512–1519 June1998 .

15.Z.MylesandN.daVitoriaLobo,“Recoveringaf nemotionand

defocusblursimultaneously,”IEEETrans.PatternAnal.Mach.In-tell.20,652–658 June1998 .

16.J.Fox,“Rangefromtranslationalmotionblurring,”IEEEComputer

VisionPatt.Recog.1,360–365 1988 .

17.P.Favaro,M.Burger,andS.Soatto,“Sceneandmotionreconstruc-tionfromdefocusedandmotion-blurredimagesviaanisotropicdif-fusion,”inLect.NotesComput.Sci.3021,257–269 2004 .

i,C.W.Fu,andS.Chang,“Ageneralizeddepthestimation

algorithmwithasingleimage,”IEEETrans.PatternAnal.Mach.Intell.14 4 ,405–411 1992 .

19.N.Asada,H.Fujiwara,andT.Matsuyama,“Edgeanddepthfrom

focus,”put.Vis.26,153–163 Feb.1998 .

wrence,“Aninvestigationofmethodsfordetermin-ingdepthfromfocus,”IEEETrans.PatternAnal.Mach.Intell.15 2 ,97–108 1993 .

21.M.BornandE.Wolf,PrinciplesofOptics,6thed.,PergamonPress,

Oxford,England 1980 .

22.E.Hecht,Optics,4thed.,PearsonEducation,ISBN0805385665

2001 .

23.M.SubbaraoandN.Gurumoorthy,“Depthrecoveryfromblurred

edges,”IEEEComputerVisionPatt.Recog.1,498–503 1988 .24.M.Subbarao,T.Choi,andA.Nikzad,“Focusingtechniques,”Opt.

Eng.32 11 ,2824–2836 Nov.1993 .

25.S.NayarandY.Nakagawa,“Shapefromfocus,”IEEETrans.Pattern

Anal.Mach.Intell.16,824–831 Aug.1994 .

26.A.Pentland,“Anewsensefordepthof eld,”IEEETrans.Pattern

1651168010.112.0

scenedistanceperpendiculartotheimageplaneisnotaconstantfordifferentimageacquisitionpositions.Thus,themotionblurredimageiscapturedwhenthecamerareachesthedepthmeasurementposition i.e.,theplacerightinfrontoftheobject’scenter .

Tables6and7showtheexperimentalresultsusingthe“edge”image,withcameramotionspeedsof115and230mm/s,respectively.Theresultsofthe“character”im-agearetabulatedinTables8and9withtwodifferentcam-eramotionspeeds.Equations 20 and 27 areusedfordepthcomputationwiththeangle =15deg.

FromtheexperimentalresultsshowninTables2–9,mostoftherelativeerrorsarelessthan10%.Theresultssuggestthatthereisalinearrelationbetweenthetruedis-tanceandtherecovereddepth.Basedontheproposedcam-eramodel,theparametersgivenbythedepthrecoveryfor-mulasaretheerrorsources.Inadditiontothepossibleerrorcausedbytheincorrectnessofthecameraparameters,theaccuracyofthemotionspeed controlledbythesteppingmotor andblurextentestimationwillalsoaffectthecor-rectnessofthedepthmeasurement.

5ConclusionandFutureWork

Findingthedistanceofanobjectinasceneisanessentialprobleminmanyapplications.Severalapproachesbasedondifferentvisualcuesobservedfromimageshavebeenpro-posedinthepastfewdecades.Inthiswork,wepresentanovelapproachfordepthrecoveryfromasinglemotionanddefocusblurredimage.Differentfrompreviousdepthfromdefocusapproaches,whichusedatleasttwoblurredimages,ourmethodrequiresonlyasingledefocusedimagetorecoverthedepthofascene.Furthermore,thecalibrationstageforourdepthrecoveryalgorithmismuchsimplercomparedtothegeneraldepthfromfocusapproaches.Itisshownthat,inmostcases,defocusblurcanbeignoredinthepresenceofmotionblur.Infuturework,robustblurparameterestimationformorecomplexsceneswillbede-veloped.Depthmeasurementofoutdoorsceneswillbecar-riedoutbycapturingtheblurredimagesfrommovingob-