FastSingleImageHazeRemovalUsingDarkChannelPriorandBilateralFilters
RachelYuen,ChadVanDeHey,andJakeTrotman
[email protected],[email protected],[email protected]
UW-MadisonComputerScience1210WDaytonStreetMadison,WI53706
http://dehazing.azurewebsites.net
ABSTRACTInthispaper,weproposeasimpleyeteffectiveimprovementtosingleimagehazeremovalusingdarkchannelprior(He,Sun,andXiaoou).Itisbasedontheobservationthathazeremovalusingdarkchannelprioraccuratelyremoveshazefromanimage;however,ithasarelativelyslowcomputationtime.Usingthedarkchannelpriorinadditiontoaseriesofbilateralfilterswecanefficientlycalculatetheamountofhazeinanimage.Ourmethodcomputes100timesfasterthanthedarkchannelpriormethod.Ourgoalwastoimproveperformanceofthedarkchannelprioralgorithm,whichultimatelycompromisestheoverallqualityoftheresultingdehazedimage.Resultsonavarietyofoutdoorhaze,smoke,andsteamimagesdemonstratethepoweroftheproposedprior.1.INTRODUCTIONLocationsarethemosttaggedandclassifiedphotographsintheworld[1].Itisassumedthatallofthosephotographsaretakenoutdoors,sincetheyarenotofobjects,artifacts,orpeople.Tosomedegreeeachoftheoutdoorimagesispollutedwithfog,smoke,haze,orsmog.Fogiscomposedofsmallwaterdropletssuspendedintheatmosphereatorneartheearth’ssurface.Duetothisproperty,fogscatterslightandmakesairmuchmorereflective,whichreducestheamountoflightreachingacamera.
Assubjectsbecomefartherfromacamera,bothcolorsaturationandcolorcontrastdropdramatically,whichproduceunclearandill-definedimagesasshownintheinputimageinFigure1.Theseunclearhazyimagesdegradetheperformanceofcomputervisiontaskssuchasfeaturedetection,accuratelycomputingtheenergyfunctionofanimageusedforseamcarving,etc.
Figure1:Smokeremovalusingasingleimage.Top:inputsmokeimage.Bottom:imageaftersmokeremovalbyourapproach.
Consequently,therehasbeenmucheffortforhazeremoval(i.e.dehazing).Totestatthesourceoftheproblem,photographershavetriedtomanuallyadjusttheircamera’sparameterssuchasadjustingexposuretoreducetheeffectsoffog.However,theresultsusingthistechniquehavebeenunsatisfactory,sincethereisatradeoffofeitherincreasingtheamountofreflectionormakingtheimagedimmerthanitoriginallyisbyincreasing/decreasingtheexposure.
Hazeremovalisamoreacomplexproblembecausehazeisdependentonanunknownparameter,depth.Computationalphotographytechniquesproducefarmorevisuallypleasingresults.Therefore,manyproposedcomputationalmethodsusingmultipleimages,additionalinformation,orthemodernapproach—singleimageinput.
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Earliercasesi.e.usingmultipleimagesand/oradditionalinformationsuccessfullyremovedhazefromanimage,butusingtheseapplicationsareundesirableduetotheadditionalinformationthatisnecessarytorunthem.Recentfindingsmostlyfocusonsingleimagehazeremoval,whichhasmadesignificantprogress.Thesemethodsowetheirsuccesstothestrongassumptionsorpriorsthataremadeonhazeandhaze-freeimages.
Forexample,themosthighlyusedmethod,andthemethodweuseinourresearch,isthedarkchannelpriortechnique[2].Thepriorassumesthatdarkpixelsinahazyimage(notwithintheskyregion)haveverylowintensitiesinatleastoneRGBcolorchannel.Thisinformationisusedtoestimatedepthbasedonthecomparisonbetweenthehazyandclearimages.Thedarkchannelpriormethodhasbeenprovedtobeaverypowerfulpriorinsingleimagedehazing.Nevertheless,itseemsthatdarkchannelpriorsystemstillhassomelimitationsinthatthedarkchannelpriorbecomesinvalidwhenthescenecolorhaslowcontrasttothehazecolor(e.g.,asnowsceneorawhitewall).Moreover,thedarkchannelpriormethodhasanextremelyslowsoftmattingtechniqueandtakesabout15minutestorunona400x400pixelimage.
2.MOTIVATIONThedarkchannelpriormethodhasbecomeawell-adoptedalgorithmtoimprovehazyimages,andithasbeenusedasthebasisofnumerousresearchprojects.Forexample,thedarkchannelpriorisusedinavideoapplicationtorecognizefogbasedontrafficsceneinhazyweather[6].Therehavealsobeenextensionsofthedarkchannelpriortoimprovefilmandvideoqualityforunder
waterphotography[7,8].Therehavealsobeeneffortstoenhancethecurrentdarkchannelpriormethod.Forinstance,thedarkchannelpriormethodwasimprovedthroughtheuseofcontrastenhancementtoenhancecolorcontrastwithlesscolordistortion[9].
Still,therehasbeenlittleefforttoimprovethecomputationtimeofthedarkchannelpriormethod.Thesoftmattingfunctioninthedarkchannelprioralgorithmiscomputationallyexpensiveandcausesabottleneckinthecode.Forthisdehazingmethodtobeauser-friendlyapplication,webelievespeedmustbeimproved.Weusedaseriesofbilateralfilterstechniques[3].Specifically,wedesignanoptimizationalgorithmthatbalancesbetweenasystemofthreebilateralfiltersandthedarkchannelprior,sothatthetimetocleanuphazyimagesisimproved.
Experimentalresultsshowthattheproposedmethodaccuratelyfindsareasthathavelowcontrasttotheskyregiontodeterminewhatishazyandwhatisnotinanimage.Theproducedimageshaveundesirableartifacts;however,ourgoalwastoimprovetheperformanceofthedarkchannelpriormethodnotthequalityoftheproducedimage.Theresultsaresignificantlyfasterthantheconventionaldarkchannelpriormethod,withspeedsnowrunningatabout12secondsforan800x600pixelimage.Lastly,methodsbeforeclaimedthattheirmethodsworkedonimagesthatwerepollutedwithsmoke,fog,hazeetc.,butthosemethodsneverdemonstratedexperimentalresultsusingimagesotherthanhazyimages.Ourmethodusedimagesthatweretakenbothoffog/hazeaswellhasimagesthatwerepollutedwithsmokeandsteam.3.PROBLEMSTATEMENT
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ObjectivesThisprojectiscomprisedofseveralcomponentsandthushasanumberofkeyobjectives.
• Takeasinputanyuser-specifiedRGBsourceimagethatispollutedwithhaze.
• Accuratelydeterminewhichareasarepollutedwithhaze.
• Dehazetheimageusingthedarkchannelprior.
• Completeallcomputationinareasonableamountoftime(under30secondsforan800x600pixelimage,ifpossible).
Sub-problemsThesebroadobjectivesbreakdownnaturallyintoseveralsub-problems:
• Howcanthedehazingmethodbedoneasefficientlyaspossible?
• Whatkindofbilateralfiltersdoweneedtoachieveourgoaltime?
4.RELATEDWORKThemodelwidelyusedtodescribetheformationofahazeimageisasimplesetofequationsthatcalculatestheintensityIofanimage,
(1)
whereJisthesceneradiance,Aistheglobalatmosphericlight,andtisthemediumtransmissiondescribingtheportionofthelightthatisnotscatteredandreachesthecamera.ThegoalofhazeremovalistorecoverJ,A,andtfromI[4].InouralgorithmweusethedarkchannelpriortoestimateJ(x)t(x)andbilateralfilteringtoestimateA(1-t(x)).4.1DarkChannelPriorThedarkchannelpriorusestheassumptionthatwithinmostlocalnon-
skyregionstherearedarkpixels,whichhaveverylowintensityinatleastoneRGBchannel[2].ThedarkchannelforanarbitraryimageJisgivenby
(2)where,JdarkisthedarkchannelofimageJ,JcisacolorchannelofJ,andΩ(x)isthepatchcenteredatx.Thedarkchannelistheoutcomeofthetwominimumoperators:minc€(R,G,B)isperformedoneachpixelandminy€Ω(x)isaminimumfilter.ThedarkchannelpriorobservationisthatifanimageJishaze-free,thentheintensityofJ’sdarkchannelisequaltozero. He,SunandTang[2]improvedatmosphericlightestimationusingthedarkchannelprior.Theypickedthetop0.1%brightestpixelsinthedarkchannelbecausethesepixelsarethemosthazeopaque.ThenpixelswiththehighestintensityintheinputimageIwithinthisgroupofhazeopaquepixelsarechosenastheatmosphericlight. Thelasttwostepsofthedarkchannelpriormethod,beforeproducingthefinalimage,areestimatingthetransmissionandasoftmattingtechnique.Wechosetoomitthesoftmattingmethodduetoisslowcomputationtime,andreplaceitwithaseriesofbilateralfilters.Estimatingtransmission,asaresult,neededtobeestimatedusingthenewvalueforA.4.2GuidedBilateralFiltersandRegularBilateralFiltersAseriesofbilateralfilterswereusedtocompleteouralgorithm.Specifically,athree-filtersystemwasused:medianfilter,bilateralfilterandjointbilateralfilter.Thefollowingalgorithmwasused
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from[3]toimplementthisthree-stepprocess.
(1) CalculatethemincomponentsW(x)ofI(x)andestimatetheatmosphericlightA;
(2) YieldinginitialatmosphericmaskV(x)usingmedianfiltering(Eq.5);
(3) FilteringW(x)usingbilateralfiltertogetthereferenceimageR(x)(Eq.6);
(4) FilteringV(x)takingR(x)asthereferenceimagetoreceivecorrectedatmosphericscatteringlightVR(X)(Eq.7);
(5) Calculatethetransmissiont(x)(Eq.3)(sameasdarkchannelpriorstep3);
(6) GettherecoveredimageJ(x).(3)
Severalequationswereusedtocreatethisalgorithm,whicharelistedbelow.Thekeyresultoftakingaseriesofbilateralfiltersistoquicklycomputeanaccurateatmospheremaskthatissmoother.4.2.1MediumFilter:
(4)
ThegoalhereistocalculatetheatmosphericscatteringlightV(x)whereΩisasquarewindowofmedianfilter.FirstfilterW(x)usingamedianfiltertoreceiveB(x).Next,toalleviatetheaffectofcontrastedtextureforthehazeremoval,applythedifferenceofthelocalmeanB(x)andlocalstandarddeviationofW(x).Finally,multiplyC(x)byascalefactorp∈[0,1]tocontrolthestrengthofvisibilityrestoration.4.2.2BilateralFilter:
(5)
ThefilterisappliedtoW(x)tofilteroutsometexturedetails,whiletheedgefeaturescanbewellpreserved.4.2.3Guidedjointfilter:
(6)
kisthenormalizingfactor,therangefilterkernelg(∥R(y)∥)=e−(R(x)−R(y))2/2σr2.Thetermg(R(x)−R(y))andh(V(y)−R(y))worktogethertopreservetheedgeinformationandremovetheuselesstextureinformationoftheimageR(x),whichproducesamoreaccurateatmosphericmaskVR(x).4.2.4EstimatingTransmissionFinally,toestimatethetransmission,theportionofthelightthatisnotscatterandreachesthecamera,XiaoandGan[3]assumedthattheatmosphericlightAisgivenandthetransmissioninalocalpatchωisconstant.Thetransmissiontisestimatedthroughthefollowing:
t(x)=1 −ωV(x)/A (7)
where,ω∈(0,1]isusedtopreservelittlehazeinthedistantsceneandmakestherecoveredimagemorenatural.Moreover,itprovidestheestimationofthetransmission.
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Figure2:Fromtoptobottominleftcolumn:inputsmokeimage,minimumcolorchannel,custommedianfilter,andcustombilateralfilter.Fromtoptobottominrightcolumn:guidedjointbilateralfilter,Jdark,transmission,andradiance(imageaftersmokeremovalbyourapproach).
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5.METHODANDTHEORYToconductourexperimentsweenhancedadarkchannelpriorMatlabcodebuiltbyMicrosoftResearchgroupinAsia[2].WealsousedMatlabcodefrom[4]toapplytheguidedjointfilterinthebilateralfilteringalgorithm.WedecidedtocontinuerunningthecodeinMatlabbecauseittendstobearobustapplicationforcomputationalphotography.
Weusedequation(1)fromsection4.1toexecutethedehazingmethodasawhole,andalgorithm(3)tocompletethethree-stepbilateralfilteringprocess.Thefollowingbreaksdownthestepswiththeircorrespondingfunctionsthatwerenecessarytodevelophazefreeimages.
Thetestimagesweusedinourexperimentswereimageswetookinthefieldpriortotheproject.Imagesareeitherpollutedwithhaze,steam,orsmoke.Theinputimageusedinthissectionwaspollutedwithsmoke;however,theresultswouldbesimilarforahazyorsteamyimage.WeranourresultsonaMacI54GBRAMusingtheMatlablauncher.5.1BilateralFilteringFunctionsFirst,weappliedaseriesofbilateralfiltersandregularbilateralfilters[3].
5.1.0MinimumColorChannelW(x)wascalculatedusingMatlab’sminimumChannelfunction,anditisdisplayedinFigure2.Thefunctioncalculateswhatisscenecontentandwhathashighintensityi.e.smoke.Theoutputisablackandwhitemappedimagethathighlightsareasoflowintensityinwhiteandhighintensityinblack,asseeninFigure2.
Thedarkareasshowregionsoftheoriginalimagethatwereeitherhighlysaturated,colorful,orhaddarkshadows.Thisisespeciallyprominentforthetree
andtheshadowsonthemountainlandscape.Thelightareasshowwherethemostsmokeisfound,whichislocatedmainlyintheskyregionandinthemountainpeaks.Peaksthatarefartherinthebackgroundaremorepollutedwithsmokecomparedtomountainsintheforegroundbecausethereismoresmokepollutedairthatlightmusttravelthroughbeforereachingthecamera.(Note:thissamecolorconventionofdarkandlightpixelswillbeusedfortheremainingportionofsection5.1)5.1.1CustomMedianFilteringWeusedsteps2-4inequation(4)tocalculateaninitialatmospherescatteringlightmodel,whichisobtainedthroughmedianfiltering.Thisstepofthefilteringprocesshelpswithpreservingtextureofthebackground.InputtothefunctionistheminimumcolorchannelW(x).Theassumptionthatwasmadewasa3x3medianfilterusingwasusedtocalculatethefinalresult.Outputtothefunctionisablackandwhiteimage.
Figure2showstheoutputimageoftheatmosphericvial.Again,thedarkestpartsoftheimageareintheforeground,becausethereislessatmospherebetweentheobjectandthecamera.Theskyhasthemosthaze.Theoutputofthemedianfilterfunctionisdoingbesttopreservetextureinthebackground.Youcanseethisfeatureasthemountainbackgroundhasmaintainedfinedetails,versesthetreeintheforegroundappearsblurry.5.1.2CustomBilateralFilteringNext,weusedequation(5)tofilterW(x)usingabilateralfiltertogetthereferenceimageR(x).TheminimumcolorchannelW(x)isalsotheinputforthisstep.Itisrefinedtogenerateanewatmospheremask,whichpreservestextureinthe
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foreground.Assumptionusedwasapredefined3x3patchwithdistanceandintensityfilters.Again,theoutputimagetothefunctionisablackandwhiteimageillustratingtheintensity. Thesameconventionsapplyasfaraswhatisblackandwhiteintheimageastheywereinthemedianfilteringoutputimage.Whatisdifferentforthisfilteringtechniqueisthattheforegroundtextureispreservedinsteadofthebackground.TheimageinFigure2presentsthatboththebackgroundandforegroundareblurry,buttheforegroundhasmoredetailcomparedtothebackground.Thetreeandthewhitelineontheroadaremuchclearerthantheveryblurredmountainbackdrop.5.3.3GuidedJointBilateralFilterFinally,weusedaDeSilva’sMatlabfunctionjbfilter2[4]tosolveforthecorrectatmosphericscatteringlight,VR(X).Inputtothefunctionistheoutputimagesfromboththemedianfilteringfunctionandthebilateralfilteringfunction.Theassumptionsthatwereusedwasthehalf-sizeoftheGaussianbilateralfilterwindowissize6,andthestandarddeviationofthebilateralfilteraregivenbySIGMA=1000.Detailsforbothinputimagesareusedtoproducethefinalimage,whichisanotherblackandwhiteimagedemonstratingintensity.
Blackandwhiteareasaresimilartobothinputfilteringimages.Whatthisfunctiondoesispreservessomedetailofboththebilateralandmedianfilter.ThiscanbeseeninFigure2whereboththebackgroundandforegroundhavevisibletexture.5.2JdarkFunctionTheJdarkequation(2)wasrunafterthefilteringinouralgorithm.Theinputtothefunctionisminimumcolorchannel
W(x).ThemaingoaloftheJdarkfunctionistouseitsoutputforestimatingtheatmosphericlightA.A30x30pixelpatchsizewasusedintheequationforan800x600pixelimage.Theoutputisablackandwhitemappedimagethathighlightsareasofhighintensityinwhiteandlowintensityinblack,asseeninFigure2.
Likeinthebilateralfilteringimages,thedarkareasshowregionsoftheoriginalimagethatwereeitherhighlysaturated,colorful,orhaddarkshadows.Oncemore,thetreeandtheprairielandscapeintheforegroundarethedarkest.Thelightareasarelocatedmainlyintheskyregionandinthemountainpeaks.Theimageisverypixilatedduetothe30x30pixelpatchsizeweused.
5.3AtmosphereEstimationFunctionNext,weestimatetheatmosphericlightusingJdarkasaheuristic.TheuseofJdarkhelpsbecauseitmeasuresthelevelsofwhitenessduetosmokeandwhatareasareactuallywhitei.e.awhitelineontheroadorsnow.Weselectedthetop0.1%-0.2%ofthebrightestpixelsinthedarkchannel.Thiswasdonetoreduceerrorsforwhiteobjects.InputtotheatmosphericfunctionistheoutputimagefromtheJdarkfunctionandtherawinputimage.Theatmosphericfunctionreturns1x3pixelimagewiththeaverageatmosphereateachRGBchannel.5.4TransmissionEstimationFunctionFourth,weestimatedthetransmissionoftheimageusingequation(3).Inputtothetransmissionfunctionisthefollowingparameters:theguidedjointbilateraloutputimageandthehighestvalueofAfromthe1x3averageatmospherepixelimage.AconstantvalueΩ(x)=.95,whichrepresentsthepercentofhazekeptwas
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inputintothefunctiontosolveforthetransmission.OutputtothefunctionisatransmissionimageandcanbeseeninFigure2.
Thetransmissionimageisaminimaloperationonachannelbasis,andgivesbetterresultsfortheskyregion.ItisessentiallyaninverseoftheminimumchannelimageW(x).Highintensityisinwhite,whicharepixelswewanttokeep.Therefore,wewanttokeepthetree,baseofthemountain,andtheprairieflatland.Lowintensityisseeninblack,whichareareasofhazeandwhatwewanttoremove.Theskyisthedarkest,whichhasthemosthaze,whichwasdeterminedintheprecedingimages.Wealsowanttoridhazeonthemountainpeaks.Theoutputofthisfunctionisusedintherecoveredradiancestep,whichfinallyremovesthehaze.5.5RadiancewithoutRefinementThelaststepofouralgorithmistoproducetheradianceimage,whichisthefinalresultimageofthedehazingmethod.Inputtothefunctionistheatmosphericestimationoutput,therawinputimage,andfinallyoutputfromthetransmissionfunction.Asyoucanseetheimagesuccessfullyremoveshaze.Theskyshowsthebestdemonstrationofhazeremoval,withbeautifulcolorrestorationandcolorsaturation.Therestoftheimage;however,isoverlysaturatedintheshadowedareasandalreadysaturatedareasoftheoriginalimage.6.EXPERIMENTALRESULTSFigure3showsourhazeremovalresults.Theimagerecoversdepthintheimageandaccuratelyremoveshaze.However,colorisoversaturatedandcolorcontrastishigh.Likewise,thereareartifactsintheskyregion.Ourfocusforthispaperwasonreducingthetimeittooktorunthe
Figure3.Hazeremovalusingasingleimage.Top:inputhazeimage.Bottom:imageafterhazeremovalbyourapproach.experiment.Therefore,wewerehappywiththeresultsbecausetherewassuccessfulhazeremovalwithafastcomputationtime.
Figures1andFigure4alsodemonstratesuccessfulsmokeandsteamremoval.Smokeproducesmoreofagrayhazyappearanceversesthewhiteinfogorhaze.Thisisbecausesmokeispollutedwithdarkashparticles.Eventhoughthereisadifferenceintheairpollutioncolor,ourresultsprovethatthemethodworksforanytypeofairquality. Next,Figure5showsacomparisonofourresultstothoseofthedarkchannelpriormethod[2].Advantagesthatourcodehasoverthedarkchannelprioristhatitcouldrunonlargerimages,andproducedresultsmoreefficiently,seediscussionbelowformoredetail.Also,therearenotasmanyartifactsintheoutputimage.Finally,theblendingbetweentheskyandmountainisimproved.Adisadvantageofourmethod
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comparedtothedarkchannelpriormethodisthatourmethoddoesnotremoveasmuchhazeastheothermethod.Second,therearestillsomeartifactsinthehaze-regionthatislikelyduetothelargelevelofhazepresentintheimage.Afinaldisadvantageseenbetweenthetwoimagesisthatthereisthecolorrestorationisoff.Theentireimageappearsdarkerthanitactuallyisandmoresaturated. He,Sun,andTang’s[2]methodhasarelativelyhighcomputationtime.Ittakesroughly10-15minutestoprocessa400x400pixelimageonaMacI54GBRAMusingtheMatlablauncher.Thehighesttimecostisfromthesoft-mattingfunction.Thecomputationaltimeofourmethodissignificantlyshorterwithonly12secondstoprocessalarger800x600pixelimage.Therefore,ourmethodcomputes100timesfasterthantheleadinghazeremovalmethod.
Figure4.Steamremovalusingasingleimage.Top:inputsteamimage.Bottom:imageafterhazeremovalbyourapproach.
Figure5.Hazeremovalusingasingleimage.Top:inputhazeimage.Center:imageafterhazeremovalbydarkchannelpriorapproach.Bottom:imageafterhazeremovalbyourapproach.7.CONCLUSIONInthispaperwehaveproposedasimpleenhancementtothedarkchannelprior,aseriesofbilateralfilters,forsingleimagehazeremoval.Thealgorithmweproposedprimarilyconsidersefficiencywhendehazinghazyorsmokyimages.Thiswasdonebyreplacingthesoftmattingcodewiththemoreeffectivethree-filtersystemcode,resultinginquicklydeterminingtheatmospherevial.Combiningthebilateralfilteringmethodwiththedarkchannelpriormethod,
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singleimagehazeremovalbecomesfaster.
Asseenintheexperimentalresults,ourproposedapproachsuccessfullyremoveshazethatis100timesfasterthanthedarkchannelprior.Thetimetorunthesoftmattingmethodisexponentialtothesizeoftheimage.Now,withbilateralfilteringtimeincreaseslinearlyasimagesizeincreases,whichisideal.Ourtestimagesincludeavarietyofweatherconditionsincludinghaze/fog,smoke,andsteam.Priormethodsusedonlyhazyimagesyetclaimedthattheirmethodswouldworkforotheratmosphericconditions,andourresultsactuallyprovesthatthealgorithmworksforthoseatmosphericconditionssuchassmokeandsteam.
Ourwork,however,doeshavesomelimitations.Replacingsoftmattingwithaseriesofbilateralfilteringcauses,insomerespects,failuretorestoretheoriginalsceneradianceandcolor.Thereareundesirableartifactsespeciallyintheskyregion,whichwereproducedfromthebilateralfilteringmethod.Also,colorcontrastandsaturationwerehighincomparisontotheoriginalimage.Infutureworks,abetterestimationoftheatmosphericcontentcouldbemadetoimprovethisquality.Tofocusonperfection,wewouldneedtoreferbacktoincreasingthesoftmattingspeedandimproveouratmosphericparticledetection.
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CodeUsedandWorkBreakdownWeusedcodefromHe,Sun,Tang[2]toimplementtheJdarkmethodandatmosphericestimationinordertocompleteJ(x)t(x)intheequation
(1)
WealsousedcodefromDeSilva[4]toreplaceruntheguidedjointbilateralfilteringportionofthebilateralfilteringalgorithmtocompleteA(1-t(x)).Bothsetsofcodewereranasiswithafewchangestotheirparameters.Forexample,JdarkissameexceptexperimentpatchsizetodecidehowdetailedwewantedJdarktobewasadjusted.Atmospherefunctionstayedsame,butweexperimentedwithareaoftesting.Wealsotriedownfunctioncallatm1D,whichproducedsameresultssowasn’teffective.
Theremainingpartsofthecodee.g.medianfiltering,bilateralfiltering,andtransmissionfunctionwerecodedbyourgroupmembers.WeutilizedMatlabfunctionstocompletethemedianfilteringfunction.Thetransmissionfunctionandthebilateralfunctionwerecalculatedusingthefunctionsin[2]and[3]andwerealloriginalcode.Wewroteabout150-200linesofcodeinMATLAB.Othercodethatisincludedinoursubmissioniscodethatwefoundonlineandusesstrictlyforperformancecomparisonstoourcode.Itisincludedtoprovidereferencesonrelativeimageprocessingamountsoftime,andhowwereabletodecreasetotalcomputationtimegreatly.
Webroketheworkbetweentheteammembersevenly.Chad,Jake,andRacheleachwrotepartsofthecode,withmostoftheworkbeingdonetogether.Chadwrotethemedianfilteringfunctionandatmosphericfunction.Jakewrotethe
bilateralfilteringmethodandfoundtheDeSilva[4].RachelwrotethecolortransmissionfunctionandtheJdarkfunction.Simultaneouslywhilecodingwewrotethefinalreport.RachelYuenwrotetheintroduction,motivation,problemstatement,andrelatedworkssections.BothJakeandChadcontributedtowritingthetheory,method,experimentalresults,andconclusion.Rachelalsowrotetheabstract,Chadwrotethemidpointreviewcheck,andeveryonecontributedtothepowerpointpresentation.Finally,Jakecreatedthewebpageforourprojecttobehostedon.Ourgroupwasverycooperativeandproductive,andweenjoyedworkingontheprojectasateam.
