Optical Engineering 4512, 127201 December 2006 Depth from mo(2)

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

blursimultaneouslyfromanimagepair.Amodelwaspro-posedandusedtoobtaintherelationshipbetweentheaf netransformationandthelevelofblur.Thederivedequationwasthensolvedusinganiterativeapproach.Althoughtheexperimentalresultswerepresentedwithseveralrealandcomplicatedimages,onlythechangesindefocusduetothemotionalongtheopticalaxiswereconsidered.Motionblurcausedbytherelativemotionbetweenthecameraandthesceneduringnonzerocameraexposuretimewasnotexplic-itlytakenintoaccount.Furthermore,theirformulationbasedonanaf nemodelrequirestwoimagesforbothde-focusblurandaf nemotionrecovery.Inthecurrentre-search,wearemoreinterestedindepthrecoveryfromasingleblurredimage.Theimageblurismodeledasopticaldefocusand/ortheimagedegradationcausedbytheobjectmotionduringnonzeroimageacquisitiontime.Thus,somepracticalissuesrelatedtotheproblem,suchastheimageformationandmotionblur,arenotcompletelyaddressedRef.15.

InFox’searlywork,16theconceptofrangefromablur-acutestereopairwasintroduced.Aspecialhardwarewasdesignedtocaptureboththeblurredandunblurredimagesfordepthmeasurements.Itwasbasicallyaconventionalstereomethodincorporatedwithtranslationmotionblurin-formation.Moreover,theauthormainlydescribedthethe-oreticalaspectoftheproposedideawithoutexperimentalresults.Recentworkrelatedto3-DreconstructionfromblurimagecueswasgivenbyFavaro,Burger,andSoatto.17Theyproposedavariationalapproachtorecoverthedepthmapandradianceofasceneusingadefocusedandmotion-blurredimagesequence.Theblurinformationwasusedtominimizethediscrepancybetweenthemeasureddefocusedimagesandtheoutputsynthesizedbythediffusionprocess.Althoughanoff-the-shelfcameracanbeused,multipleim-agesarestillrequiredforanisotropicdiffusion.Further-more,theirapproachisonlyvalidundertheassumptionofLambertiansurfacewithuniformillumination.

Incontrasttothepreviouswork,weuseonlyasinglemotionanddefocusblurredimagefordepthrecovery.Depthcalculationisaccomplishedbyidentifyingtheblurextentcausedbylateralcameramotionanddistance-varyingdefocus.Inthisresearch,animageblurmodelforuniformlinearmotionandopticaldefocusisformulatedbasedongeometricoptics.Theblurextentoftheimageisthenestimatedandusedfordepthmeasurement.

Theworkorganizedasfollows.Section2introducesthetheoryofimageformationwithdefocusandmotionblur.InSec.3,wepresentthemethodsforblurparameterestima-tionandcamerafocuscalibration.Section4providestheimplementationdetailsandexperimentalresults.Severaltypesofrealimageswithdifferentexperimentalsetupsareusedtovalidatetheproposedtechnique.Finally,Sec.5concludestheworkandpointstopossibledirectionsoffu-tureresearch.

2TheoreticalFormulation

Asimplecameramodelconsistingofathinlensandanimageplaneisusedtoderivesomefundamentalcharacter-isticsoffocusingbasedongeometricoptics.TheexistingalgorithmsfordeterminingobjectdepthfromimagefocusordefocususuallyformulatetheopticalblurduetotheFig.1Cameramodelfordefocusblur.

thiswork,boththeimageblurcausedbythecameramotionandopticaldefocusaretakenintoaccount.We rstmodelthemotionbluronly,i.e.,theobjectisinfocusifthereisnorelativemotionbetweenthecameraandthescene,andthenconsiderthedefocusbluraswell.

2.1GeometricCameraModel

Inthissectionwebrie ydescribethecameramodelforthegeometricimageformationprocess.InterestedreaderscouldrefertoRefs.21and22formoredetailedinforma-tiononthistopic.AsillustratedinFig.1,acamerasystemconsistingofasingleconvexlenswithfocallengthfisconsidered.TherelationshipbetweenthepositionofapointPinthesceneandthecorrespondingfocusedpositionP intheimageisgivenbythewellknownlensformula111+=,pqf

1

wherepisthedistanceoftheobjectfromthelensononeside,andqisthedistanceoftheimageplanefromthelensontheotherside.

IfweconsideranobjectpointQwithadistancezfromthelens withoutlossofgenerality,weassumezisgreaterthanp ,thenEq. 1 canberewrittenas111+=,zz f

2

wherez isthedistanceofthevirtualfocuspositionfromthelens.Furthermore,thecorrespondingimagepointofQismodeledasablurcirclecenteredatCaccordingtogeo-metricoptics.FromEq. 2 andtherelationdq z =,Dz

thediameterdoftheblurcircleisgivenbyd=Dq

3

111

,fzq

4

whereDisthediameterofthelensandqisthedistancefromthelenstotheimageplane.23Sincethedistanceqis

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

d=

Dpf11

.

p fpz

5

Thatis,thesizeoftheblurcircleforanyscenepointlo-catedatadistancezfromthelenscanbecalculatedbyEq. 5 .

SimilarderivationsofEq. 5 canbefound,forexample,inRefs.20and24.Itisclearthattheblurcirclediameterddependsonlyonthedepthzif xedcamerasettingsofD,f,andparegiven.Inthiswork,wemakeseveralfurtherobservationsontheimagingmodel.First,Eq. 5 canberewrittenasd=c wherec=

Df

.p f

7

s =s cos +sin tan .

10

cp,z

6

Fig.2Cameramodelforpuremotionblur.

FromEq. 6 ,thesizeoftheblurcircleislinearlyrelatedtotheinversedistanceoftheobject.Moreover,theblurcirclediameterd→0asthedistancez→p,andconverselyd→casz→ .Inthelattercase,theconstantcgivenbyEq. 7 representsthemaximumdiameteroftheblurcirclewhentheobjectapproachesin nity.

IfwerewriteEq. 6 asafunctionofd,thenthedepthzoftheobjectisgivenbyz=cp

.c d

8

SubstituteEq. 9 withEqs. 10 and 1 ,andthedistancepisgivenby

s

p=1+ cos +sin tan f,

x

11

whichisindependentofthedistanceqbetweenthelensandtheimageplane.

Sincetheangle isusuallysmallifonlythecentralpartoftheimageisconsidered,especiallyfo …… 此处隐藏：11389字，全部文档内容请下载后查看。喜欢就下载吧 ……