Our method is conceptually simple computationally ef64257cient robust and easy to use We manipulate the gradient 64257eld of the luminance image by attenuating the mag nitudes of large gradients A new low dynamic range image is then obtained by solv ID: 23514
Download Pdf The PPT/PDF document "Gradient Domain High Dynamic Range Compr..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
GradientDomainHighDynamicRangeCompressionRaananFattalDaniLischinskiMichaelWermanSchoolofComputerScienceandEngineeringTheHebrewUniversityofJerusalemWepresentanewmethodforrenderinghighdynamicrangeim-agesonconventionaldisplays.Ourmethodisconceptuallysimple,computationallyefÞcient,robust,andeasytouse.WemanipulatethegradientÞeldoftheluminanceimagebyattenuatingthemag-nitudesoflargegradients.Anew,lowdynamicrangeimageisthenobtainedbysolvingaPoissonequationonthemodiÞedgra-dientÞeld.Ourresultsdemonstratethatthemethodiscapableofdrasticdynamicrangecompression,whilepreservingÞnedetails devices,whilepreservingasmuchoftheirvisualcontentaspossi-ble?Thisispreciselytheproblemaddressedinthispaper.TheproblemthatwearefacedwithisvividlyillustratedbytheseriesofimagesinFigure1.Thesephotographsweretakenusingadigitalcamerawithexposuretimesrangingfrom11000to1ofasecond(atf/8)frominsidealobbyofabuildingfacingglassdoorsleadingintoasunlitinnercourtyard.Notethateachexposure AlloftheimagesinthispaperareprovidedatfullresolutionontheproceedingsCD-ROM(andalsoathttp://www.cs.huji.ac.il/÷danix/hdrc),assomeoftheÞnedetailsmaybedifÞculttoseeintheprintedproceedings. Figure1:AseriesofÞvephotographs.Theexposureisincreasingfromleft(1/1000ofasecond)toright(1/4ofasecond).playdevices.Inthissectionweprovideabriefreviewofpreviouswork.Moredetailedandin-depthsurveysarepresentedbyDiCarloandWandell[2001]andTumblinetal.al.MostHDRcompressionmethodsoperateontheluminancechannelorperformessentiallythesameprocessingindependentlyineachoftheRGBchannels,sothroughoutmostofthispaperwewilltreatHDRmapsas(scalar)luminancefunctions.PreviousapproachescanbeclassiÞedintotwobroadgroups:(1)global(spatiallyinvariant)mappings,and(2)spatiallyvariantop-erators.DiCarloandWandell[2001]refertotheformerasTRCs(tonereproductioncurves)andtothelatterasTROs(tonerepro-ductionoperators);weadopttheseacronymsfortheremainderofthispaper.ThemostnaiveTRClinearlyscalestheHDRvaluessuchthattheyÞtintoacanonicrange,suchasas0,1].Suchscalingpreservesrelativecontrastsperfectly,butthedisplayedimagemaysufferse-verelossofvisibilitywheneverthedynamicrangeofthedisplayissmallerthantheoriginaldynamicrangeoftheimage,andduetoquantization.OthercommonTRCsaregammacorrectionandhistogramequalization.Inapioneeringwork,TumblinandRushmeier[1993]describeamoresophisticatednon-linearTRCdesignedtopreservetheappar-entbrightnessofanimagebasedontheactualluminancespresentintheimageandthetargetdisplaycharacteristics.Ward[1994]sug-gestedasimplerlinearscalefactorautomaticallydeterminedfromimageluminancessoastopreserveapparentcontrastandvisibil-ityaroundaparticularadaptationlevel.Themostrecentandmostsophisticated,toourknowledge,TRCisdescribedbyWardLarsonetal.[1997].TheyÞrstdescribeacleverimprovementtohistogramequalization,andthenshowhowtoextendthisideatoincorporatemodelsofhumancontrastsensitivity,glare,spatialacuity,andcolorsensitivityeffects.Thistechniqueworksverywellonawidevarietyofimages.ThemainadvantageofTRCsliesintheirsimplicityandcompu-tationalefÞciency:onceamappinghasbeendetermined,theimagemaybemappedveryquickly,e.g.,usinglookuptables.However,suchglobalmappingsmustbeone-to-oneandmonotonicinordertoavoidreversalsoflocaledgecontrasts.Assuch,theyhaveafunda-mentaldifÞcultypreservinglocalcontrastsinimageswherethein-tensitiesoftheregionsofinterestpopulatetheentiredynamicrangeinamoreorlessuniformfashion.ThisshortcomingisillustratedinthemiddleimageofFigure2.Inthisexample,thedistributionofluminancesisalmostuniform,andWardLarsonÕstechniqueresultsinamapping,whichisrathersimilartoasimplegammacorrection.Asaresult,localcontrastisdrasticallyreduced.SpatiallyvarianttonereproductionoperatorsaremoreßexiblethanTRCs,sincetheytakelocalspatialcontextintoaccountwhendecidinghowtomapaparticularpixel.Inparticular,suchoperatorscantransformtwopixelswiththesameluminancevaluetodifferentdisplayluminances,ortwodifferentluminancestothesamedisplayintensity.Thisaddedßexibilityinthemappingshouldmakeitpos-sibletoachieveimprovedlocalcontrast.Theproblemofhigh-dynamicrangecompressionisintimatelyrelatedtotheproblemofrecoveringreßectancesfromanimage[Horn1974].Animageisregardedasaproductisthereßectanceandistheilluminanceateach.Thefunctioniscommonlyreferredtoastheintrinsicimageofascene.ThelargestluminancevariationsinanHDRimagecomefromtheilluminancefunction,sincereal-worldreßectancesareunlikelytocreatecontrastsgreaterthan100:1Thus,dynamicrangecompressioncan,inprinciple,beachievedbyseparatinganimagetoitscomponents,scalingdowncomponenttoobtainanewilluminancefunction,andre-Intuitively,thisreducesthecontrastbetweenbrightlyilluminatedareasandthoseindeepshadow,whileleavingthecontrastsduetotextureandreßectanceundistorted.Tumblinetal.[1999]usethisapproachfordisplayinghigh-contrastsyntheticimages,wherethematerialpropertiesofthesurfacesandtheilluminanceareknownateachpointintheimage,makingitpossibletocomputeaper-fectseparationofanimagetovariouslayersoflightingandsurfaceUnfortunately,computingsuchaseparationforrealimagesisillposedproblem[RamamoorthiandHanrahan2001].Conse-quently,anyattempttosolveitmustmakesomesimplifyingas-sumptionsregarding,orboth.Forexample,[Stockham1972],anearlyimageenhancementtechnique,makestheassumptionthatvariesslowlyacrosstheimage,incon-trasttothatvariesabruptly.Thismeansthatcanbeextractedbyapplyingahigh-passÞltertothelogarithmoftheimage.Exponenti-atingtheresultachievessimultaneousdynamicrangecompressionandlocalcontrastenhancement.Similarly,Horn[1974]assumesissmooth,whileispiecewise-constant,introducinginÞ-niteimpulseedgesintheLaplacianoftheimageÕslogarithm.Thus,mayberecoveredbythresholdingtheLaplacian.Ofcourse,inmostnaturalimagestheassumptionsaboveareviolated:forex-ample,insunlitscenesilluminancevariesabruptlyacrossshadowboundaries.Thismeansthatalsohashighfrequenciesandintro-ducesstrongimpulsesintotheLaplacian.Asaresult,attenuatingonlythelowfrequenciesinhomomorphicÞlteringmaygiverisetostrongÒhaloÓartifactsaroundstrongabruptchangesinillumi-nance,whileHornÕsmethodincorrectlyinterpretssharpshadowsaschangesinreßectance.Morerecently,Jobsonetal.[1997]presentedadynamicrangecompressionmethodbasedonamultiscaleversionofLandÕsÒretinexÓtheoryofcolorvision[LandandMcCann1971].Retinexestimatesthereßectancesastheratiooftoitslow-passÞlteredversion.AsimilaroperatorwasexploredbyChiuetal.[1993],andwasalsofoundtosufferfromhaloartifactsanddarkbandsaroundsmallbrightvisiblelightsources.Jobsonetal.computethelogarithmoftheretinexresponsesforseverallow-passÞltersofdifferentsizes,andlinearlycombinetheresults.Thelin-earcombinationhelpsreducehalos,butdoesnoteliminatethementirely.Schlick[1994]andTanakaandOhnishi[1997]alsoexper-imentedwithspatiallyvariantoperatorsandfoundthemtoproducehaloartifacts.Pattanaikandco-workers[1998]describeanimpressivelycom-prehensivecomputationalmodelofhumanvisualsystemadaptation Forexample,thereßectanceofblackvelvetisabout0.01,whilethatofsnowisroughly0.93. Figure2:BelgiumHouse:AnHDRradiancemapofalobbycom-pressedfordisplaybyourmethod(top),themethodofWardLarsonetal.(middle)andtheLCISmethod(bottom).andspatialvisionforrealistictonereproduction.Theirmodelen-ablesdisplayofHDRscenesonconventionaldisplaydevices,butthedynamicrangecompressionisperformedbyapplyingdifferentgain-controlfactorstoeachbandpass,whichalsoresultsinhalosaroundstrongedges.Infact,DiCarloandWandell[2001],aswellasTumblinandTurk[1999]demonstratethatthisisafundamentalproblemwithanymulti-resolutionoperatorthatcompresseseachresolutionbanddifferently.InordertoeradicatethenotorioushaloartifactsTumblinandTurk[1999]introducethelowcurvatureimagesimpliÞer(LCIS)hi-erarchicaldecompositionofanimage.Eachlevelinthishierarchyisgeneratedbysolvingapartialdifferentialequationinspiredbyanisotropicdiffusion[PeronaandMalik1990]withadifferentdif-fusioncoefÞcient.Thehierarchylevelsareprogressivelysmootherversionsoftheoriginalimage,butthesmooth(low-curvature)re-gionsareseparatedfromeachotherbysharpboundaries.Dynamicrangecompressionisachievedbyscalingdownthesmoothestver-sion,andthenaddingbackthedifferencesbetweensuccessivelev-elsinthehierarchy,whichcontaindetailsremovedbythesimpli-Þcationprocess.Thistechniqueisabletodrasticallycompressthedynamicrange,whilepreservingtheÞnedetailsintheimage.How-ever,theresultsarenotentirelyfreeofartifacts.TumblinandTurknotethatweakhaloartifactsmaystillremainaroundcertainedgesinstronglycompressedimages.Inourexperience,thistechniquesometimestendstooveremphasizeÞnedetails.Forexample,inthebottomimageofFigure2,generatedusingthistechnique,certainfeatures(door,plantleaves)aresurroundedbythinbrightoutlines.Inaddition,themethodiscontrolledbynolessthan8parameters,soachievinganoptimalresultoccasionallyrequiresquiteabitoftrial-and-error.Finally,theLCIShierarchyconstructioniscompu-tationallyintensive,socompressingahigh-resolutionimagetakesasubstantialamountoftime.3GradientdomainHDRcompressionInformally,ourapproachreliesonthewidelyacceptedassumptions[DiCarloandWandell2001]thatthehumanvisualsystemisnotverysensitivetoabsoluteluminancesreachingtheretina,butratherrespondstolocalintensityratiochangesandreducestheeffectoflargeglobaldifferences,whichmaybeassociatedwithilluminationdifferences.Ouralgorithmisbasedontherathersimpleobservationthatanydrasticchangeintheluminanceacrossahighdynamicrangeim-giverisetolargemagnitudeluminancegradientsatsomescale.Finedetails,suchastexture,ontheotherhand,correspondtogradientsofmuchsmallermagnitude.Ourideaisthentoiden-tifylargegradientsatvariousscales,andattenuatetheirmagnitudeswhilekeepingtheirdirectionunaltered.Theattenuationmustbeprogressive,penalizinglargergradientsmoreheavilythansmallerones,thuscompressingdrasticluminancechanges,whilepreserv-ingÞnedetails.Areducedhighdynamicrangeimageisthenre-constructedfromtheattenuatedgradientÞeld.Itshouldbenotedthatallofourcomputationsaredoneonthelogarithmoftheluminances,ratherthanontheluminancesthem-selves.Thisisalsothecasewithmostofthepreviousmethodsreviewedintheprevioussection.Thereasonforworkinginthelogdomainistwofold:(a)thelogarithmoftheluminanceisa(crude)approximationtotheperceivedbrightness,and(b)gradientsinthelogdomaincorrespondtoratios(localcontrasts)intheluminanceWebeginbyexplainingtheideain1D.Considerahighdynamicrange1Dfunction.Wedenotethelogarithmofthisfunctionby.Asexplainedabove,ourgoalistocompresslargemagnitudechangesin,whilepreservinglocalchangesofsmallmagnitude,asmuchaspossible.Thisgoalisachievedbyapplyinganappro-priatespatiallyvariantattenuatingmappingtothemagnitudesofthederivatives.MorespeciÞcally,wecompute:Notethathasthesamesignastheoriginalderivativeevery-where,butthemagnitudeoftheoriginalderivativeshasbeenal-teredbyafactordeterminedby,whichisdesignedtoattenuatelargederivativesmorethansmallerones.Actually,asexplainedinSection4,accountsforthemagnitudesofderivativesatdifferent (a) Figure3:(a)AnHDRscanlinewithdynamicrangeof2415:1.(b).(c)Thederivatives.(d)Attenuatedderivatives;(e)Reconstructedsignal(asdeÞnedineq.1);(f)AnLDRscanlineexp:thenewdynamicrangeis7.5:1.Notethateachplotusesadifferentscaleforitsverticalaxisinordertoshowdetails,except(c)and(d)thatusethesameverticalaxisscalinginordertoshowtheamountofattenuationappliedonthederivatives.Wecannowreconstructareduceddynamicrangefunctiontoanadditiveconstant)byintegratingthecompressedderivatives:Finally,weexponentiateinordertoreturntoluminances.TheentireprocessisillustratedinFigure3.Inordertoextendtheaboveapproachto2DHDRfunctionswemanipulatethegradients,insteadofthederivatives.Again,inordertoavoidintroducingspatialdistortionsintotheim-age,wechangeonlythemagnitudesofthegradients,whilekeepingtheirdirectionsunchanged.Thus,similarlytothe1Dcase,wecom-Unlikethe1Dcasewecannotsimplyobtainacompresseddynamicrangeimagebyintegrating,sinceitisnotnecessarilyintegrable.Inotherwords,theremightnotexistanimagesuchthatInfact,thegradientofapotentialfunction(suchasa2Dimage)mustbeaconservativeÞeld[HarrisandStocker1998].Inotherwords,thegradientmustsatisfy xy=2I whichisrarelythecaseforourOnepossiblesolutiontothisproblemistoorthogonallyprojectontoaÞnitesetoforthonormalbasisfunctionsspanningthesetofintegrablevectorÞelds,suchastheFourierbasisfunctions[FrankotandChellappa1988].InourmethodweemployamoredirectandmoreefÞcientapproach:searchthespaceofall2Dpotentialfunc-tionsforafunctionwhosegradientistheclosesttointheleast-squaressense.Inotherwords,shouldminimizetheintegraldxdy xGx2+I AccordingtotheVariationalPrinciple,afunctionthatmini-mizestheintegralin(2)mustsatisfytheEuler-Lagrangeequation Id F Ixd F whichisapartialdifferentialequationin.Substitutingweobtainthefollowingequation: x2Gx x+22I y2Gy Dividingby2andrearrangingterms,weobtainthewell-knownPoissonequationdiv Figure4:GradientattenuationfactorsusedtocompresstheBel-giumHouseHDRradiancemap(Figure2).Darkershadesindicatesmallerscalefactors(strongerattenuation).istheLaplacianoperator x2+2I anddivisthedivergenceofthevectorÞeld,deÞnedasdiv x+Gy .Thisisalinearpartialdifferentialequation,whosenumericalsolutionisdescribedinSection5.4GradientattenuationfunctionAsexplainedintheprevioussection,ourmethodachievesHDRcompressionbyattenuatingthemagnitudesoftheHDRimagegra-dientsbyafactorofateachpixel.Wewouldliketheat-tenuationtobeprogressive,shrinkinggradientsoflargemagnitudemorethansmallones.Real-worldimagescontainedgesatmultiplescales.Conse-quently,inordertoreliablydetectallofthesigniÞcantinten-sitytransitionswemustemployamulti-resolutionedgedetectionscheme.However,wecannotsimplyattenuateeachgradientattheresolutionwhereitwasdetected.Thiscouldresultinhaloartifactsaroundstrongedges,asmentionedinSection2.Oursolutionistopropagatethedesiredattenuationfromthelevelitwasdetectedattothefullresolutionimage.Thus,allgradientmanipulationsoccuratasingleresolutionlevel,andnohaloartifactsarise.WebeginbyconstructingaGaussianpyramidisthefullresolutionHDRimageandisthecoarsestlevelinthepyramid.ischosensuchthatthewidthandtheheightareatleast32.Ateachlevelwecomputethegradientsusingcentraldifferences: 2k+1,Hk(x,y+1)Hk(x,y1) Ateachlevelascalingfactorisdeterminedforeachpixel basedonthemagnitudeofthegradientthere: Hk(x,y)Hk(x,y) Thisisatwo-parameterfamilyoffunctions.TheÞrstparameterdetermineswhichgradientmagnitudesremainunchanged(mul-tipliedbyascalefactorof1).Gradientsoflargermagnitudeareattenuated(assuming1),whilegradientsofmagnitudesmallerareslightlymagniÞed.Inalltheresultsshowninthispa-perwesetto0.1timestheaveragegradientmagnitude,andbetween0.8and0.9.Thefullresolutiongradientattenuationfunctioniscom-putedinatop-downfashion,bypropagatingthescalingfactorsfromeachleveltothenextusinglinearinterpolationandaccumulatingthemusingpointwisemultiplication.Moreformally,theprocessisgivenbytheequations:isthecoarsestlevel,denotestheaccumulatedattenua-tionfunctionatlevel,andisanupsamplingoperatorwithlinearinterpolation.Asaresult,thegradientattenuationateachpixeloftheÞnestlevelisdeterminedbythestrengthsofalltheedges(fromdifferentscales)passingthroughthatlocationintheimage.Figure4showsattenuationcoefÞcientscomputedfortheBelgiumHouseHDRradiancemap.Itisimportanttonotethatalthoughthecomputationofthegra-dientattenuationfunctionisdoneinamulti-resolutionfashion,ul-timatelyonlythegradientsattheÞnestresolutionaremanipulated,thusavoidinghaloartifactsthattypicallyarisewhendifferentreso-lutionlevelsaremanipulatedseparately.5ImplementationInordertosolveadifferentialequationsuchas(3)onemustÞrstspecifytheboundaryconditions.Inourcase,themostnaturalchoiceappearstobetheNeumannboundaryconditions(thederivativeinthedirectionnormaltotheboundaryiszero).WiththeseboundaryconditionsthesolutionisnowdeÞneduptoasingleadditiveterm,whichhasnorealmeaningsinceweshiftandscalethesolutioninordertoÞtitintothedisplaydevicelimits.SinceboththeLaplaciananddivarelinearoperators,approx-imatingthemusingstandardÞnitedifferencesyieldsalinearsystemofequations.MorespeciÞcally,weapproximate:takingthepixelgridspacingtobe1atthefullresolutionoftheim-age.ThegradientisapproximatedusingtheforwarddifferencewhilefordivweusebackwarddifferenceapproximationsdivThiscombinationofforwardandbackwarddifferencesensuresthattheapproximationofdivisconsistentwiththecentraldifferenceschemeusedfortheLaplacian.AttheboundariesweusethesamedeÞnitions,butassumethatthederivativesaroundtheoriginalimagegridare0.Forexample,foreachpixelontheleftimageboundarywehavetheequationTheÞnitedifferenceschemeyieldsalargesystemoflinearequa-tionsÑoneforeachpixelintheimage,butthecorrespondingma-trixhasonlyÞvenonzeroelementsineachrow,sinceeachpixeliscoupledonlywithitsfourneighbors.WesolvethissystemusingFullMultigridAlgorithm[Pressetal.1992],withGauss-Seidelsmoothingiterations.Thisleadstooperationstoreachanap-proximatesolution,whereisthenumberofpixelsintheimage.AnotheralternativeistouseaÒrapidPoissonsolverÓ,whichusesthefastFouriertransformtoinverttheLaplacianoperator.How-ever,thecomplexitywiththisapproachwouldbeAsmentionedearlier,ourmethodoperatesontheluminancesofanHDRradiancemap.InordertoassigncolorstothepixelsofthecompresseddynamicrangeimageweuseanapproachsimilartothoseofTumblinandTurk[1999]andSchlick[1994].MorespeciÞcally,thecolorchannelsofapixelinthecompresseddy-namicrangeimagearecomputedasfollows: denotetheluminancebeforeandafterHDRcompression,respectively,andtheexponentcontrolsthecolorsaturationoftheresultingimage.Wefoundvaluesbetween4and06toproducesatisfactoryresults.6ResultsMultipleexposureHDRs.WehaveexperimentedwithourmethodonavarietyofHDRradiancemapsofrealscenes.Inallcases,ourmethodproducedsatisfactoryresultswithoutmuchpa-rametertweaking.Incertaincaseswefoundthatthesubjectivequalityoftheresultingimageisslightlyenhancedbyrunningastandardsharpeningoperation.Thecomputationtimesrangefrom1.1secondsforan512by384imageto4.5secondsforan1024by768imageona1800MHzPentium4.ThetoprowinFigure5showsthreedifferentrenderingsofaÒstreetlightonafoggynightÓradiancemap.Thedynamicrangeinthissceneexceeds100,000:1.Theleftimagewasproducedus-ingthemethodofWardLarsonetal.[1997],andtherightimagewasproducedbyTumblinandTurkÕs[1999]LCISmethod.Themiddleimagewasgeneratedbyourmethod.Theleftimagelosesvisibilityinawideareaaroundthebrightlight,detailsarelostintheshadowedregions,andthetextureonthegroundiswashedout.TheLCISimage(right)exhibitsagrainytextureinsmoothareas,andappearstoslightlyoveremphasizeedges,resultinginanÒembossedÓ,non-photorealisticappearance.Inourimage(middle)smoothnessispreservedinthefoggysky,yetatthesametimeÞnedetailsarewellpreserved(treeleaves,groundtexture,caroutlines).Ourmethodtook5secondstocomputethis751by1130image,whiletheLCISmethodtookaround8.5minutes.ThesecondrowofimagesinFigure5showsasimilarcompari-sonusinganHDRradiancemapoftheStanfordMemorialchurchThedynamicrangeinthismapexceeds250,000:1.Overall,thesameobservationsasbeforeholdforthisexampleaswell.IntheleftimagethedetailsinthedarkregionsaredifÞculttosee,whiletheskylightandthestainedglasswindowsappearover-exposed.IntheLCISimage(right)theßoorappearsslightlybumpy,whileourimage(middle)showsmoredetailsandconveysamorerealisticThelastrowofimagesinFigure5andtheÞrstrowinFig-ure6showseveraladditionalexamplesofHDRcompressionby RadiancemapcourtesyofJackTumblin,NorthwesternUniversity.Imagereprintedbypermission,1999JackTumblin[1999].RadiancemapcourtesyofPaulDebevec.SourceexposurescourtesyofShreeNayar. Figure5:Thetoptworowscompareresultsproducedbyourmethod(middlecolumn)tothoseofWardLarsonetal.(leftcolumn)andthoseofTumblinandTurk(rightcolumn).ThedifferencesarediscussedinSection6.Thebottomrowshowsthreemoreexamplesofresultsproducedbyourmethod(thethumbnailsnexttoeachimageshowsomeoftheLDRimagesfromwhichtheHDRradiancemapwasconstructed). Figure6:Toprow:moreexamplesofHDRradiancemapcompression.Ourmethodsuccessfullycombinesfeaturesthatcanonlybecapturedusingverydifferentexposuresintoasingleimage.Secondrow:anHDRpanoramicvideomosaic.Theremainingimagesdemonstratethatourmethodcanalsobeusedforordinaryimageenhancement.SeeSection6formoredetailedexplanations. ourmethod.Nexttoeachimagetherearethumbnailimagesshow-ingsomeoftheexposuresusedtoconstructtheHDRmap.Notethatourmethodmanagestocombineinarealisticmannerdetailsthatcanonlybecapturedwithverydifferentexposures.ThetoprightimageinFigure6(astainedglasswindowintheNationalCathedralinWashington,DC)wasmadeusingonlythetwoex-posuresshownonitsleft.Thesetwoexposuresareroughlyfourstopsapart;theyweretakenbyaprofessionalphotographer,whomanuallyblendedthesetwoimagestogetherinordertodisplayboththebrightwindowandthedarkstonesurfacessimultaneously(http://users.erols.com/maxlyons).Ourmethodachievesasimilareffectautomatically,whilerevealingmoredetailinthedarkregions.HDRpanoramicvideomosaics.Apopularwaytoacquireapanoramicimageistoscanasceneusingavideocameraandthenconstructamosaicfromthevideoframes.IfweletthecameraÕsauto-exposurecontrolsetthecorrectexposureforeachframe,eachsceneelementisimagedatmultipleaperturesettingsandwecanconstructanHDRasin[DebevecandMalik1997].Usingspecial-izedhardware[SchechnerandNayar2001;AggarwalandAhuja2001a]alsoproducedHDRpanoramicvideomosaics.ThesecondrowinFigure6showsanHDRpanoramacom-pressedbyourmethod.Thetopleftimagesimulateswhatthepanoramawouldhavelookedlikewithanexposuresuitablefortheleftpartofthepanorama,whiletheonebelowitsimulatesanex-posuresuitablefortherightpartofthepanorama.Clearly,noneofthesetwoexposuresettingsyieldsatisfactoryresults.WithourHDRcompressionmethodwewereabletoobtainthepanoramaontheright,inwhichdetailisvisibleacrosstheentireÞeldofview.LDRimageenhancement.Ourmethodcanalsobeusedtoenhanceordinary(LDR)images.Byattenuatingstronggradientsandrescalingthereconstructedimagebacktotheoriginal0..255range,smallcontrastsindarkregionsbecomeeasiertosee.TheÞveimagesoftheNotreDamedeParis(Figure6)demon-strateimageenhancementusingourmethod.Thetopleftimageistheoriginal;thetoprightimageistheresultproducedbyourmethod.Thebottomrowshowsthebestresultswecouldobtainwithgammacorrection(left),histogramequalization(middle),andcontrastlimitedadaptivehistogramequalization[Pizeretal.1987](right).Noticethatourresultbringsoutmoredetailsfromtheshad-owedareas,whilemaintaininggoodcontrastselsewhere(brickwallintheforeground,Þnedetailsonthebuilding).Adaptivehistogramequalizationisalmostasgood,butitintroduceshaloartifactsintheskyalongtheroofsandthetreetopontheright.ThebottomrowofFigure6showstwomoreexamples.Theexampleontheleftisatypicalexampleofanimagecontainingsunlightandshadows.Again,ourmethod(onitsright)succeedsinbringingoutthedetailsfromtheshadowedareas.Thepairontherightshowsadark,lowcontrastßuoroscopicfe-murimage.Afterenhancementusingourmethodthebonestructureisvisiblemuchmoreclearly(notethatthefemurcanalbecomesclearlyvisible).7ConclusionsandFutureWorkWehavedescribedanew,simple,computationallyefÞcient,androbustmethodforhighdynamicrangecompression,whichmakesitpossibletodisplayHDRimagesonconventionaldisplays.Ourmethodattenuateslargegradientsandthenconstructsalowdy-namicrangeimagebysolvingaPoissonequationonthemodiÞedgradientÞeld.Futureworkwillconcentrateonthemanydifferentexcitingpos-sibleapplicationsoftheconstructionofanimagefrommodiÞedgradientÞelds.Preliminaryresultsshowpromiseindenoising,edgemanipulationandnon-photorealisticrenderingfromrealim-ages.Inaddition,wewouldliketoextendourworksoastoin- ExposurescourtesyofMaxLyons,2001MaxLyons.corporatevariouspsychophysicalpropertiesofhumanvisualper-ceptioninordertomakeourtechniquemoreusefulforapplicationssuchaslightingdesignorvisibilityanalysis.AcknowledgmentsWewouldliketothankPaulDebevec,MaxLyons,ShreeNayar,JackTumblin,andGregWardformakingtheircodeandimagesavailable.ThanksalsogotoSiggraphÕsanonymousreviewersfortheircomments.ThisworkwassupportedinpartbytheIsraelSci-enceFoundationfoundedbytheIsraelAcademyofSciencesandReferencesGGARWAL,M.,HUJA,N.2001.Highdynamicrangepanoramicimaging.InProc.IEEEICCV,vol.I,2Ð9.GGARWAL,M.,HUJA,N.2001.Splitapertureimagingforhighdynamicrange.InProc.IEEEICCV,vol.II,10Ð17.,K.,H,M.,S,P.,SWAMY,S.,W,C.,K.1993.Spatiallynonuniformscalingfunctionsforhighcontrastimages.InProc.GraphicsInterfaceÕ93,MorganKaufmann,245Ð253.,J.,T,C.,HAWKINS,T.,,P.2001.Real-timehigh-dynamicrangetexturemapping.InRenderingTechniques2001,S.J.GortlerandK.Myszkowski,Eds.Springer-Verlag,313Ð320.,P.E.,,J.1997.Recoveringhighdynamicrangeradiancemapsfromphotographs.InProc.ACMSIGGRAPH97,T.Whitted,Ed.,369Ð378.,P.1998.Renderingsyntheticobjectsintorealscenes:Bridgingtradi-tionalandimage-basedgraphicswithglobalilluminationandhighdynamicrangephotography.InProc.ACMSIGGRAPH98,M.Cohen,Ed.,189Ð198.,J.M.,,B.A.2001.Renderinghighdynamicrangeimages.InProceedingsoftheSPIE:ImageSensors,vol.3965,392Ð401.RANKOT,R.T.,HELLAPPA,R.1988.Amethodforenforcingintegrabilityinshapefromshadingalgorithms.IEEETransactionsonPatternAnalysisandMachineIntelligence10,4(July),439Ð451.,J.W.,TOCKER,H.1998.HandbookofMathematicsandComputa-tionalScience.Springer-Verlag.,B.K.P.1974.Determininglightnessfromanimage.ComputerGraphicsandImageProcessing3,1(Dec.),277Ð299.,D.J.,R,Z.,,G.A.1997.Amulti-scaleRetinexforbridgingthegapbetweencolorimagesandthehumanobservationofscenes.IEEETransactionsonImageProcessing6,7(July),965Ð976.,E.H.,,J.J.1971.LightnessandRetinextheory.JournaloftheOpticalSocietyofAmerica61,1(Jan.),1Ð11.AYAR,S.K.,ITSUNAGA,T.2000.Highdynamicrangeimaging:Spatiallyvaryingpixelexposures.InProc.IEEECVPRATTANAIK,S.N.,FERWERDA,J.A.,F,M.D.,,D.P.1998.Amultiscalemodelofadaptationandspatialvisionforrealisticimagedis-play.InProc.ACMSIGGRAPH98,M.Cohen,Ed.,287Ð298.ERONA,P.,,J.1990.Scale-spaceandedgedetectionusinganisotropicdiffusion.IEEETransactionsonPatternAnalysisandMachineIntelligence12(July),629Ð639.,S.M.,AMBURN,E.P.,A,J.D.,CROMARTIE,R.,GESELOWITZ,A.,,T.,,B.,Z,J.B.,UIDERVELDK.1987.Adaptivehistogramequalizationanditsvariations.ComputerVision,Graphics,andImageProcessing39,3(Sept.),355Ð368.,W.H.,TEUKOLSKY,S.A.,V,W.T.,LANNERY,B.P.NumericalRecipesinC:TheArtofScientiÞcComputing,2nded.CambridgeUniversityPress.AMAMOORTHI,R.,,P.2001.Asignal-processingframeworkforinverserendering.InProc.ACMSIGGRAPH2001,E.Fiume,Ed.,117Ð128.,Y.Y.,AYAR,S.K.2001.Generalizedmosaicing.InProc.IEEE,vol.I,17Ð24.,C.1994.Quantizationtechniquesforvisualizationofhighdynamicrangepictures.InPhotorealisticRenderingTechniques,Springer-Verlag,P.Shirley,G.Sakas,andS.Muller,Eds.,7Ð20.TOCKHAM,J.T.G.1972.Imageprocessinginthecontextofavisualmodel.InProceedingsoftheIEEE,vol.60,828Ð842.ANAKA,T.,,N.1997.Painting-likeimageemphasisbasedonhumanvisionsystems.ComputerGraphicsForum16,3,253Ð260.,J.,,H.E.1993.Tonereproductionforrealisticimages.IEEEComputerGraphicsandApplications13,6(Nov.),42Ð48.,J.,,G.1999.LCIS:Aboundaryhierarchyfordetail-preservingcontrastreduction.InProc.ACMSIGGRAPH99,A.Rockwood,Ed.,83Ð90.,J.,H,J.K.,,B.K.1999.Twomethodsfordisplayofhighcontrastimages.ACMTransactionsonGraphics18,1(Jan.),56Ð,G.,R,H.,IATKO,C.1997.Avisibilitymatchingtonereproductionoperatorforhighdynamicrangescenes.IEEETransactionsonVisualizationandComputerGraphics3,4,291Ð306.,G.J.1994.Acontrast-basedscalefactorforluminancedisplay.InGraphicsGemsIV,P.S.Heckbert,Ed.AcademicPressProfessional,415Ð421.