Optical Engineering 4512, 127201 December 2006 Depth from mo(4)

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

correspondingdepthof eldissmallerforgeneralopticalsystems.Thedepthcorrespondingtothemaximumblurextentisalsoshorterinthiscase,whichgivesmoreaccu-rateblurparameterestimationforthein nitedistance.Givena xedfocusposition,theblurparameterscorc correspondingtothein nitedistancecanbeobtainedbyeitherdirectcomputationusingEq. 7 withknownfocallengthandaperturediameter,orblurextentestimationbyplacingacalibrationpatternatin nity.IftheGaussianmodelisconsidered,theparameterc hastobederivedusingthesecondmethod.Forthe rstmethod,assuggestedbyEq. 7 ,theprecisionofccanbeincreasedbysettingalargeraperturediameterDandasmallerdistancep.3.2MotionBlurEstimation

ToestimatetheblurextentduetotherelativemotionandopticaldefocususedinEqs. 19 , 23 ,and 27 fordepthmeasurements,atwo-stepalgorithmisproposed.Withoutlossofgenerality,weassumethedirectionofmotionblurisparalleltotheimagescanlines.Forthegeneralcasethattherelativemotionisnotparalleltotheimagescanlines,themotiondirectioncanbeidenti ed rstandthenusedtorectifytheimage.14

Itiswellknownthattheresponseofasharpedgetoanedgedetectorisathincurve,whereastheresponseofabluredgetothesameedgedetectorspreadsawiderregion.Thissuggeststhattheresultofedgedetectioncanbeusedasinitialestimationofthemotionblurextent.Intheimple-mentation,averticalSobelmaskisusedtoidentifythehorizontalblurextentforeachverticaledgealongtheim-agescanlines.Duetonoiseandtextureoftheobject,thederivedblurextentsareusuallynotallidentical.Thus,themodeoftheblurextentsisusedtoderiveanoverallhori-zontalblurextentoftheimage,andthenusedasaninitialestimateforthenextstep.

Atthesecondstep,theinitialblurextentisusedasaparametertocreateasequenceofdeblurredimagesbyaWiener lter.Amodi edLaplacianfocusmeasure25isthenusedtoselectthebestdeblurredimageandthecorrespond-ingblurextent.Ifopticaldefocusismodeledaswell,thedefocusblurextentdgivenbyEq. 25 isalsoconsideredforimagedeblurring.Fromx =x+dandEq. 25 ,thede-focusblurextentcanbewrittenasd=

Fig.6Theedgeimageusedinthe

experiments.

placedonastagemountedonalinearrailtoobtainedthemotionblurredimages.ThemovementofthestageisdrivenbyaPC-controlledsteppingmotor.

4.1OpticalDefocus

Toobtainthemaximumblurextent correspondingtotheobjectatin nity ,focuscalibrationfortwodifferentfocus-ingrangesisperformedwithtwodifferentaperturesizes.Inthe rstexperiment,thefocusingrangeissetas265mmfromthecamera.Theblurextentsestimatedfromdifferentobjectdistanceswithfocallengthsof36mmareshowninFig.8.Solidanddottedlinesrepresenttheresultswithaperturediametersof7.2and15mm,respectively.Theplotshowsthat,astheobjectdistancegoestoin nity,theblurextentsapproach79and163pixelsforthesetwoaperturesizes.Theresultsalsoverifythatthemaximumblurispro-portionaltotheaperturediameterasderivedinEqs. 7 and 38 .DirectcomputationsoftheblurextentcusingEq. 7 aregivenby166.5and346.8pixelsfortheaperturediam-etersof7.2and15mm,respectively.Thus,theconstantkgivenbyEq. 36 isabout0.47forbothcases.

Inthesecondexperiment,thefocusingrangeissetas1000mmfromthecamera.Thefocallengthissetas36mm.Figure9showstheblurextentsobtainedfrom

dif-

fx sD .p fss kD

39

Sincethefocusmeasurehighlydependsonlocalintensityvariation,thedefocusblurextentdcanbeusedtodeter-minethenumberofdeblurredimagestobecreated.How-ever,motionblurdominatestheblurextentinmostcases,andtypicallynineimagesarecreatedformotiondeblurringintheimplementation.

4ImplementationandExperimentalResults

Theproposeddepthrecoverymethodhasbeentestedinthelaboratoryenvironment.Aschematicdiagramfortheex-perimentalsetupisshowninFig.5Twotypesofplanarpatterns,onewithastepedgeandtheotherwithafewcharacters asshowninFigs.6and7,respectively ,are