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

LinandChang:Depthfrommotionanddefocusblur

Fig.11Motionblurredimage.

opticalaxis.Boththecameramotiondirectionsparallelandnonparalleltothetestpatternarecarriedoutintheexperiments.

4.2.1Parallelcameramotion

Inthiscase,thecameramotionisparalleltothetestobject.Thelenspositionofthecameraisadjustedsuchthatthefocusingrangeis900mm.Ablackandwhitepatternisplacedat500,750,1000,1250,and1500mmfromthecamerafordepthrecovery.Foursetsofexperimentswithtwodifferentcameramotionspeeds 115and230mm/s andtwodifferentaperturediameters 0.8and1.8mm areperformed.Thecameraexposuretimeis xedas1/5stoobservedifferentscalesofblurextentsfordifferentcameramotionspeeds.Therestofthecameraparametersaregivenasfollows:focallengthf=9mmandCCDpixelsizes=6.8 m.

Figure11showsanexampleofablurimagecapturedwiththecameramotionspeedof115mm/s,exposuretimeof1/5s,andaperturesizeof0.8mm.Thecorrespondingimageintensitypro leisillustratedinFig.12.Theblurextentsoftheimages,recovereddepths,andabsoluteerrorsrelativetothemeasureddistancesareshowninTables2and3.Thecolumnswithx,z1,z2,e1,ande2representtheblurextent inpixel ,recovereddistance inmillimeter ,andabsoluteerrors inpercent ofdifferentdistancescal-culatedusingEqs. 20 and 27 ,respectively.Oneinterest-ingobservationisthattheresultsgivenbyEq. 20 arevery

Fig.13Experimentalsetupfornonparallelcameramotion.

closetothosegivenbyEq. 27 inmostcases.Thissug-geststhatmotionblurmightdominatetheblurextentintheexperiments.

Anotherfoursetsofexperimentsarecarriedoutusingthe“character”image asshowninFig.7 .Onlytheimagescanlineswithverticaledgesareusedforblurextentesti-mation.Thecameraparametersettingsarethesameasthosedescribedinthepreviousexperiments.TheresultsofdifferentobjectdistancesaretabulatedinTables4and5.Fromtheexperimentalresults,nosigni cantdifferencescanbefoundbetweenthesetwotypesoftestimagepat-terns.Withthe xedcameraexposuretime,theblurextentisapproximatelyproportionaltotherelativemotionspeedasexpected.

4.2.2Nonparallelcameramotion

TheexperimentalsetupforthecameramotiondirectionnonparalleltothetestobjectisshowninFig.13.Theanglebetweentheobjectpatternandthelinearrailis15deg.FoursetsofexperimentswiththesameparametersettingsasdescribedinSec.4.2.1areperformedfordifferentimagepatterns.Thecenteroftheobjectis xedat500,750,1000,1250,and1500mmfordepthrecovery.Duetothenonpar-allelrelativemotionbetweentheobjectandthecamera,the

Table2Depthrecoveryfrommotionanddefocusblur withthe“edge”image .Thecameramotionspeedis115mm/s.

Aperture0.8mm

Distance

mm 50075010001250

x583932

z1527788963

z

2530790964

e1

e2

x

Aperture1.8mmz1491769

z2500773

e1

e2

5.36.1635.05.340

1.70.02.53.1

3.73.630103610423.64.2

27113911448.98.526116311767.05.9