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- Copyright: © 2025 Guo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: All relevant data are within the manuscript and its Supporting information files. Funding: This study was funded by the National Nature Science Foundation of China (Grant No. 61903152) and the Jilin Province Science and Technology Development Plan, China (20210203102SF). The Funder is Jinghua Zhao. Jinghua Zhao‘s work clearly. Jinghua Zhao is mainly responsible for the data analysis and collection of objective parameters for our manuscript. Competing interests: The authors have declared that no competing interests exist.
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- 10.1371/journal.pone.0315176
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Abstract
We propose a Rayleigh Scattering and adaptive color compensation method. It capital- izes on the brightness and color differentials between the regions where DCP has failed within images for effective regional segmentation. First, we added B-channel compensa- OPEN ACCESS tion to the atmospheric illumination, made a simple evaluation of the B channel through Citation: GuoX, Sun Q, ZhaoJ, SunM, the atmospheric illumination of the R channel and the G channel. It repeatedly iterated ZhangY, ZhangY.etal.(2025)Single-image dehazing methodbasedonRayleighScattering to obtain and repaired the atmospheric illumination of the B channel, which eliminates andadaptivecolorcompensation.PLoS ONE the color dilution. Secondly, we obtained the dark channel image and the bright channel 20(3):e0315176.https://doi.org/10.1371/ image, and jointly evaluated the failure point of the dark channel prior method to select journal.pone.0315176 the area with inaccurate transmission. This can select the areas which need re-estimate Editor:YongjieLi,University ofElectronic the transmission. This step improves the image quality of the area and repairs the image ScienceandTechnologyofChina,CHINA details. Finally, we validated the effectiveness and resilience of the proposed method Received:March12,2024 through comprehensive experiments. It is conducted across diverse scenarios, involving Accepted:November19,2024 the adjustment of various parameters. Published:March20,2025 Copyright:©2025 Guoetal.Thisisanopen access articledistributedunderthetermsofthe CreativeCommonsAttributionLicense,which Introduction permitsunrestricteduse,distribution,and reproductioninanymedium,providedthe Airpollutionleadstoanincreaseinsuspendedparticlesintheatmosphere,whichresultsin originalauthorandsource arecredited. reducedvisibility.Itcreatesthenaturalatmosphericphenomenaknownasfogandhaze.Light raysundergomultipleinteractionswithairborneparticlesduetofogandhaze,whichleadsto Dataavailabilitystatement:Allrelevantdata arewithinthemanuscriptanditsSupporting adecreaseinlightintensity.Thisimpactsimagingdevicesandresultsinimagesandvideos informationfiles. withreducedbrightness,lowercontrastandcolordistortion.eTh developmentofdefogging techniquesiscrucialtomitigatethesechallengesintheimageprocessing. Funding:ThisstudywasfundedbytheNational NatureScienceFoundationofChina(GrantNo. Inrecentyears,imagedefoggingmethodsaremainlydividedintomulti-imagedefog- 61903152)andtheJilinProvinceScienceand gingmethods[1]andsingle-imagedefoggingmethods.Multi-imagedefoggingmethodsare TechnologyDevelopmentPlan,China limitedtoadefoggingscenariothatrequiresmulti-angleimages,whichgreatlyrestrictsthe (20210203102SF).TheFunderisJinghuaZhao. developmentofthisdirection.Incontrasttomulti-imagedehazingmethods,whichleverage JinghuaZhao’sworkclearly. JinghuaZhaois multipleimagesofthesamescenecapturedfromdifferentanglesandundervaryingweather mainlyresponsibleforthedataanalysisand conditions,single-imagedehazinglacksthisabundanceofdata.Varioustypesofhazyimages collectionofobjectiveparametersforour manuscript. PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 1/ 18 ID: pone.0315176 — 2025/3/20 — page 2 — #2 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation Competinginterests:Theauthorshave exist,eachwithcomplexandunpredictabledepthoffield.Single-imagedehazingmethods declaredthatnocompetinginterests exist. havemadesignificantadvancements,andtheirmainmethodscanbebroadlycategorized intothreetypes:imagedehazingmethodsbasedonimageenhancement[2–4],imagedehaz- ingmethodsbasedonimagefusion[5–7],andimagedehazingmethodsbasedonphysical models[8–11]. eTh lastcategoryofdehazingmethodsisbasedonphysicalmodels.Onenoteworthycon- tributiontothefieldistheDarkChannelPrior(DCP)[ 12]introducedbyHeetal.DCPis groundedintheatmosphericscatteringmodelandstemsfromextensiveobservationsofout- doorimages.eTh theorynotesatendencytowardzerovaluesinthethreecolorchannelsof pixelswithinnon-brightregionsofclearoutdoorimages.AndresearchersextendedtheDCP theory,introducingtheBrightChannelPrior(BCP)[13]theory.eir Th investigationscon- firmedthatfogconcentrationisdirectlylinkedtothedifferenceinbrightnessandsaturation. ThisledtotheamalgamationofBCPandDCP,resultingintheproposalofvariousimproved methods. Efficientimagedefoggingmethodsarestillatopicofresearchinthecomputervision.As described,comparedwithothermethods,theimagedehazingmethodbasedonthephysical modelreliesonapriortheory.Thisdeterminesthataccuratetransmissionandatmospheric illuminationsarekeytoobtainingclearimages.Weproposeasingleimagedefoggingmethod basedonRayleighScatteringandadaptivecolorcompensation(RSA)forrepairingtransmis- sionandatmosphericilluminations.eTh RSAtakesafoggyimageasaninput,andadaptively adjusts.Ontheonehand,theatmosphericilluminationandtransmissionbyusingtheHis- togramCorrelationCoefficient(HCC)objectiveparameterasanadaptiveoperatorimproves thequalityoftherestoredimage.Thisprocessfixestheimagechromaticaberrationproblem andmakesthedehazedimageasclosetotheoriginalimageaspossible.eTh methodreduces theproblemofexcessivecolordeviationandcorrectsthecolordifferenceofimageobjects causedbythedehazingmethod.Itlaysasolidfoundationforthenextsteptoestimatethe accuratetransmission.Ontheotherhand,weuseDCPandBCPtogetthereferenceimageto filteroutareaswherethetransmissionestimationisinaccurateandimprovetheimage’sability toexpressdetails. Ourmaincontributionscanbesummarizedasfollows. • WeproposeanewadaptiveadjustmentframeworkbasedontheDCPtheory,whichadap- tivelyadjuststheatmosphericilluminationsforRayleighcompensation,addressingthe colordeviationissuesindehazedimages. • Weresearchanin-depthstudyoftheDCPtheory,extractareaswheretheDCPfails,and furtheroptimizeimagequality. • Weselectmultiplehazyimages,andhighlighttheeffectivenessofourmethodbasedonsix objectiveparameters,focusingontheadaptationtoatmosphericilluminations. Related work Todepicttheimageformationprocessinfoggyconditions,theatmosphericscatteringmodel servesasafundamentalreference.McCartneyetal.[14]introducedaprototypeatmospheric scatteringmodelin1976,anditislaterrefinedbyNarasimhanandNayar[ 15,16].Mostimage dehazingmethodsbasedonphysicalmodelsareproposedonthebasisoftheatmospheric scatteringmodel.Sincetheequationhastwounknownquantities,itisgreatuncertain. Tanetal.[17]believedthatclearimageshavehigherclarityandcontrastthanhazy images,andthechangesinatmosphericilluminationsaresoerft .eTh yusedwhitebalanceto improvehazyimages,andusedtheMaldivesRandomFields[18]toestimatetheatmospheric PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 2/ 18 ID: pone.0315176 — 2025/3/20 — page 3 — #3 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation illuminations.However,itmaximizesthecontrastoftheimageintheprocessofestimating theatmosphericilluminations,distortingthecolor,andduetotheblockoperation,which causesahalophenomenon. Heetal.[12]madeasignificantcontributionbyintroducingtheconceptofthedarkchan- nelimage(DCI)intheirresearch.eir Th meticulousexaminationofnumerousclearoutdoor imagesunveiledacompellingdiscovery.Inthemajorityofpixelswithintheseimages,oneof thethreeRGBchannelsconsistentlydisplayedremarkablylowpixelvalues,oenft approach- ing0.Yanetal.[13]providedacomprehensivesummaryoftheDCPtheory.eir Th analysis revealedaconsistentmaximumvalueinthethreechannelsofaclearimage,closelyapprox- imating255.Buildinguponthisobservation,theyproposedtheBCPtheory,markingthe beginningofphysically-basedimagedefoggingmethods.Chuetal.[19]introducedDBCP- IIIasanassessmenttoolforimagequalitypost-defogging,whichleveragestheDCPandBCP defoggingeffects.Furtherstridesinhazeremovalemerged,includingaversatilemethod effectivelyremovesfogfrombothdaytimeoutdoorimagesandnighttimefoggyscenes. Lietal.[20]addressedfoggyimagesthroughimagesegmentationtechniques,estimating atmosphericilluminationsandtransmissionforbrightregions,deployingenhancedBCPand DCPmethodologies.esTh eestimatesarefurtherrefinedusingGradientDomainGuidedFil- tering.Whiletheseinnovationsrepresentsignificantprogress,theydoexhibitcertainlimi- tations,particularlyinrestoringbrightnessinspecificimageregions,leadingtopotentially unsatisfactorydefoggingoutcomes.AlthoughDCPhashighprocessingefficiency,thethree pointvaluesmaynottendtozerowhenselectingpixelsinbrightareas.ItresultsinDCPbeing unabletoselectdarkchannelimagesinthisarea,causingthemethodtofail.Inaddition,due tothefailureofDCI,themethodalsohasdeviationswhenitselectsatmosphericillumination, whichaeff ctstheestimationoftransmissioninturn.Mostofthemethodsimprovedbasedon DCPcan’tgetridoftheconstraintsofthistheory,whichresultsinhighsaturationandpoor brightnessoftherepairedimage,halophenomenoninbrightareas,andintroductionofnoise. Zhuetal.[21]conductedathoroughexaminationofnumerousimages.eir Th findings indicatedthatatmosphericilluminationwasenhancedwhenanimagewascoveredbyfog. Thisenhancementmadeitchallengingtodiscerntheoriginalcolorofobjects.eTh yobserved thatasthefogconcentrationintheimageincreased,thisphenomenonbecamemorepro- nounced.Throughdetailedanalysisofareaswithvaryingfogconcentrations,theydiscovered thathigh-concentrationareasexhibitcharacteristicsofhighbrightnessandlowsaturation. eTh conclusiondrawnfromthisobservationisthattheconcentrationoffogisproportional tothedifferencebetweenbrightnessandsaturation.Thistheoryhasundergonewidespread refinementandapplication[ 22,23],whichshowcasesitsadaptabilityandrelevanceacrossvar- iousscenarios.eTh methodsbasedoncolorattenuationpriorobtaintheimagetransmission basedonthedifferencebetweenthebrightnessandsaturationoftheoutdoorimageandthe fogconcentration.Ithasagooddefoggingeffectonhazyimageswithclearbackgrounds,but theimagesprocessedbythismethodarepronetoadditionalnoisepoints,andtheenhance- menteffectaroundthefoggroupispoor.ItisworthnotingthatSahuetal.[ 24]proposeda uniqueattention-basedend-to-enddehazingnetworkforrestoringclearimagesfromtheir counterpartswithoutusingatmosphericscatteringmodels. However,thesemethodsoenft deviatefromrealityinestimatingthetheatmospheric illuminationsandtransmissionprocess.eTh gapbetweenactualvalueandestimatedvalue leadstoproblemssuchascolordeviationandpoorbrightnessintheimages.Forexample, theDCPoenft includeshighpixelvaluesinnon-skyregionsintheestimationoftheatmo- sphericilluminations,whichcausesadeviationbetweentheestimatedandactualvalues. eTh image’stransmissionrateiscalculatedbasedontheatmosphericilluminations.Itleads tocorrespondingdeviationsandthisultimatelyresultsinagloballylowerbrightnessofthe PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 3/ 18 ID: pone.0315176 — 2025/3/20 — page 4 — #4 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation dehazedimage,withhalophenomenainthesky,significantlyreducingtheoverallimage quality.Toaddresstheseissues,improveimagequality,andfixcolordeviation,weadaptthe atmosphericilluminationsbasedonRayleighScattering,performcolorcompensation,and optimizecolordeviationissues.BycombiningDCIandBCI,weidentifytheareaswhereDCP fails,repairthetransmissionrateinthoseregions,enhanceimagequality,andimprovethe unsatisfactoryrestorationintheskyregion. Methods Inthispart,wepresentasingle-imagedehazingmethodbasedonRayleighScatteringand adaptivecolorcompensation(RSA).eTh RSAadaptivelycompensatestheatmosphericillu- minationoftheB-channelwiththeHCCoperatorandderivesthereferenceimageusing theBCPandDCP.eTh methodidentifiestheregionswhereDCPtheoryfailsintheimage throughadaptivesegmentationthresholdadjustmentsoftheHCCoperator.Moreover,it optimizesthetransmissionoftheseregionsusingatoleranceparameterandfinallycomputes theclearimageusingtheatmosphericscattering.Comparedwithothermethods,ourshas madegreatchangesinimagecolorrestoration.Bycontinuouslyiteratingandselectingthe optimalsolutionforatmosphericilluminations,italsoreducestheerrorintransmissionand furtheroptimizestheimagequality.Sincemostofthecurrentphysicalmodel-baseddehazing methodsarebasedontheDCP,andtheycannotgetridofthelimitationofregionalfailurein extremelybrightareas.WecombineDCIwiththebrightchannelimage(BCI),adjustthepix- elswhereDCPfails,andoptimizethetransmissionofthearea.eTh processisshowninthe Fig1. Atmosphericillumination Weemployasmoothingfunctionontheoriginalimagebyapplyingtheguidedfilter[ 25].eTh guidefilterisalinearfilterthatmaintainsthegradientvalueoftheimagewhileensuringthat thesmoothedimageretainsthecharacteristicsofboththeoriginalandsmoothedimages.This approachguaranteesthatthequalityofthesmoothedimage,denotedasS,closelyresembles thatofthefilteredimage.Italsoreducestherelativedifferencesinpixelvaluesbetweenthe imagesandeliminatestheinfluenceofspecklenoiseontheselectionofatmosphericillumi- nations.eTh processisshownin Eq(1). S =GUIDEFILTER(I,q,r,𝛿 ), (1) whereSrepresentsthesmoothedimage,GUIDEFILTER()denotesguidedfiltering, I repre- sentsthehazeimage,qstandsfortheguideimage,r isthewindowsize,and𝛿 istheregular- izationparameter.ToobtaintheatmosphericilluminationAfromthesmoothedimage[26], thefirst0.1%ofpixelpointsareselected.However,it’sessentialtonotethat,accordingto RayleighScatteringtheory,bluelightintheimagingspectrumismoresusceptibletodisper- sioneffectsinfoggyconditions.Deviationsintheatmosphericilluminationcansignificantly impactimagecolor,brightness,andotherqualityattributes. Inanyimage,thereexistsanatmosphericilluminationthreshold,wheretheobjective parameterthatdescribesimagecolor,brightness,andotherqualitiesreachesanextreme value.Whentheestimatedatmosphericilluminationfallsbeloworexceedsthisthreshold, theobjectiveparameterdeviatesfromitsextremevalue.eTh HCC[ 27]isanobjectiveparam- eterusedtogaugeimagesimilarity,withhighervaluesindicatingahigherdegreeofcolor similaritybetweentwoimages. PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 4/ 18 ID: pone.0315176 — 2025/3/20 — page 5 — #5 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation Fig1.Methodflowimage. Thisimagedepictstheactualflowofthemethod. https://doi.org/10.1371/journal.pone.0315176.g001 Toenhancetheaccuracyoftheestimatedatmosphericillumination,theB-colorchannel shouldundergoadaptivecompensation.eTh HCCobjectiveparameterisemployedtoadjust theB-colorchannelcontinuously,alteringitsvaluebasedonHCCasacriterion.Thisprocess aimstoselecttheB-colorchannelvaluethatresultsinthehighestHCCobjectiveparameter. eTh following Eq(2)demonstratesthisprocess. A =A r R A ⎨A =A , (2) g G ⎪A =APT(A ) b B whereArepresentstheadjustedatmosphericillumination,A ,A ,andA representthe R G B atmosphericilluminationsofthethreecolorchannelsofA beforeadjustment,andA ,A ,and i r g A representtheatmosphericilluminationsofthethreecolorchannelsofA aerft optimiza- b i tion.APT()istheadaptivetuningfunctionthatiterativelyreplacestheoldvaluewiththenew oneuntiltheHCCreachesitsextreme. Optimizationoftransmissionusingthereferenceimagesegmentation method erTh ewillalwaysbeachannelwitharelativelyloworhighpixelvalueformostpixelsin thethreechannelsofclearoutdoorimages,approaching0or255respectively,throughthe PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 5/ 18 ID: pone.0315176 — 2025/3/20 — page 6 — #6 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation analysisoftheDCPtheoryandtheBCPtheory.However,somepixelshavehighvaluesinall threechannels,whichcausestheDCPtheorytofail.Itresultsininaccurateestimatesofthe transmissionratethroughthistheory.Toaccuratelyfindtheregionsthatneedoptimization fortransmissionrates,RSAselectstheregionsoptimizedforbrightnessintheDCIandBCI. However,duetotheinclusionofawindowduringtheselectionofchannelimages,theDCI andtheBCIbecomeblocky.eTh windowmakesitchallengingtoaccuratelyselectthepre- ciseregionsneededimproving.AsshowninFig2Cand2Drepresentconventionalchannel images,theBCIandDCIhavebeenblurredbythewindow,whichcausestheimagedetailsto becomeblocky.Itisdifficulttojudgewhethertheimagedetailsneedoptimization. erTh efore,whenselectingtheDCIandBCI,weremovedtheselectionwindowtoallow theselectionofimprovedchannelimages.AsshowninFig2Eand2F,thesearetheimproved channelimages.Byobserving,wecanseethattheimprovedBCIandDCIhaveundergone significantchangesindetail.Thisrevealsthecontoursofobjectsandpreservingdetailswell. Aerft subtractingtheimprovedBCIfromtheDCI,theresultingimageisnamedthereference imageR(x,y),asshowninFig2G. MostpixelvaluesintheBCIarecloseto255,whiletheyarecloseto0intheDCI.How- ever,theDCPdoesnotholdinareasthatneedoptimization,andthepixelvaluesarerelatively large.erTh efore,theareaswithverysmallvaluescorrespondtotheregionsthatneedopti- mizationfortransmissionratesofthehazeimageinthereferenceimageR(x,y).Tocomplete thisstep,asegmentationthreshold𝜑 established.eTh thresholdisadaptivelyadjustedusing HCCobjectiveparametertogetFig2Hand2I. AccordingtoFig2Hand2I,weobtainedthesetofpixelsthatrequiretransmissionopti- mizationduetothefailureoftheDCP.Weoptimizedthemthroughthetolerancevalueand obtainedFig2K.BycomparingFig2Jand2K,wecanfindthatthetransmissioninareassuch astheskyandunderthebridgeiseffectivelyoptimized.Aerft obtainingtheaboveparameters, Fig2.Methodimage.(A)istheimagethatneedtobedefogged.(B)istheguideimageforcalculatingatmosphericilluminations.(C)and(D)areconventional channelimages.(E)and(F)areimprovedchannelimages.(G)istheimageusedtofindfailedareas(H)and(I)selectthepixelstobeoptimizedfrom(J)basedonthe segmentationthreshold.(J),(K)arethetransmissionbeforeandaerft optimizationrespectively.(L)istheclearimagerecovered. https://doi.org/10.1371/journal.pone.0315176.g002 PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 6/ 18 ID: pone.0315176 — 2025/3/20 — page 7 — #7 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation wecancalculatetheclearimageJ(x,y)throughEq(3). ⎧ I(x,y)–A +A,R(m,n) ≥𝜑 ⎪ ⋅max(t(x,y),t ) ⎪ 0 I(x,y) J(x,y) ⎨ , (3) ⎪ I(x,y)–A +A,R(x,y) <𝜑 ⎩max(t(x,y),t ) whereI(x,y)representsthehazyimage,J(x,y)representstheclearimage,K isthetolerance value[28],R(x,y)isthereferenceimage,Adenotestheatmosphericillumination,𝜑 isaseg- mentationthreshold,andt(x,y)standsfortransmission.Aconstantt isintroducedtoprevent thetransmissionfrombeingzero,whichwouldrendertheformulameaningless.Additionally, xandyrepresentthehorizontalandverticalcoordinatesofthepixelpoints,respectively. Experiments and result Inthissection,weaimtodemonstratethevalidityoftheexperimentbyassessingbothsub- jectivevisualeffectsandobjectiveparameters.eTh imagesinourmethodareallfromfreeand opensourcedatabasesprovidedbymethod[29],method[30],method[31],andmethod[32]. eTh datasetcontainshazefreeimages,syntheticdistancemapsandcorrespondingsimu- latedhazeimages[31].eTh goalistoillustratethemethod’seffectivenessandversatility.We selectedanimagethatencompassesatownandnaturallandscapeforthispurpose.Further- more,westartedacomparativeanalysisbyevaluatingobjectiveparametersobtainedfromthe processedimage. Experimentalenvironmentandobjectiveparameters OurexperimentsareproposedonanordinaryPCcomputerwitha64-bitoperatingsys- tem.eTh detailedconfigurationisthattheprocessorisIntel(R)Core(TM)i7-6700CPU@ 3.40GHz3.40GHz,thesystemmemoryis8GB,theenvironmentisMatlab2016.Inorderto furtherillustratetheeffectivenessofRSA,weevaluateobjectivelyfromsixparameters:SSIM (StructuralSIMilarity),UQI(UniversalQualityIndex),PSNR(PeakSignal-To-NoiseRatio), AVE(Average),HCCandMS-SSIMillustrate. SSIMobjectiveparametersevaluatethequalityoftherestoredimagefromthreelevels: brightness,contrastandimagestructureoftheimage.eTh brightness L(x,y),contrastC(x,y) andimagestructureS(x,y)ofexpressionareEqs(4)–(6). 2𝜇 𝜇 +C I J 1 L(x,y) = , (4) 2 2 U +U +C J I 1 2𝜎 𝜎 +C I J 2 C(x,y) = , (5) 2 2 𝜎 +𝜎 +C J I 2 𝜎 +C IJ 3 S(x,y) = , (6) 𝜎 𝜎 +C I J 3 Aerft obtainingtheaboveparameters,theSSIMcanbeshown: C = (0.01T ) 1 t ⎨ , (7) C = (0.03T ) 2 t C =C /2 3 2 SSIM(m,n) =L(m,n)∗C(m,n)∗S(m,n), (8) PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 7/ 18 ID: pone.0315176 — 2025/3/20 — page 8 — #8 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation whereI andJ arethehazyimageandclearimagerespectively.𝜇 and𝜇 aretheaverageofthe I J twoimages,and𝜎 ,𝜎 arethevariancesofthetwoimages.eTh 𝜎 isthecovarianceofI andJ I J IJ oftheimage,andT istherangeofimagepixelvalues.eTh x,yarethehorizontalandvertical coordinatesofthepixelrespectively. eTh expressionsofPSNRareasshownin Eqs(9)and(10): M N MSE = ∑∑ (I(x,y)–J(x,y)) , (9) M∗N x=1 y=1 max 1 I ( ) MSE PSNR = 10log , (10) M∗N whereMSE(MeanSquareError)representsthemeansquareerrorofthehazyimageI and theclearimageJ,M andN aretheimagesizes,andx,yarethehorizontalandverticalcoor- dinatesoftheimage.eTh max isgenerallytakenas255.eTh expressionofUQIisshownin Eq(11),assumingthatthesizeoftheimageisM∗N,xandyarethehorizontalandvertical coordinatesoftheimage: 4𝜎 xy xy UQI = , (11) 2 2 2 2 (𝜎 +𝜎 )[(x) + (y) ] x y M N 1 1 xandyaretheaverageofxandy,whichcanbeexpressedasx = ∑x andy = ∑y. i j M N i=1 j=1 𝜎 and𝜎 arethevarianceoftheimageinthexandydirections,𝜎 isthecovarianceof x y IJ M N 2 2 2 1 2 1 2 theimage.eTh ycanbeexpressedas 𝜎 = ∑(x –x) ,𝜎 = ∑(y –y) ,𝜎 = x i y j xy M–1 N–1 i=1 j=1 M N 2 2 1 1 [ ∑(x –x) ] ⋅ [ ∑(y –y) ].Hereiandjrespectivelyplaytheroleofcounting.In i j M–1 N–1 i=1 j=1 ordertobetterdescribethecharacteristicsofthethreefactorsofcomprehensivecorrelation loss,brightnessdistortionandcontrastdistortionofUQIparameters,UQIcanberewrittenas Eq(12): 𝜎 2xy 2𝜎 𝜎 xy x y UQI = ⋅ ⋅ , (12) 2 2 2 2 𝜎 𝜎 𝜎 +𝜎 x y (x) + (y) x y AVErepresentstheaverageofimagepixelvalues.Inthesameimage,theimagesthatare restoredbydifferentdefoggingmethodscontaindifferentimageinformation.Itsinternal brightness,colorsaturationandotherimageelementswillinterferewiththelevelofpixel values.eTh lowerthepixelvalue,theloweritsrecoveryquality,anditsexpressioncanbe expressedasEq(13). M N AVE = ∑∑E(x,y), (13) M∗N x=1 y=1 wherex,yarethehorizontalandverticalcoordinatesoftheimagepixel,M,N arethelength andwidthdimensionsoftheimage,andE(x,y)isthepixelvalueofthepixel. eTh HCCobjectiveevaluationparameteristocomparethehistogramsoftwoimages anddeterminethesimilarityofthetwohistogramsthroughthecorrelationcoefficientofthe PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 8/ 18 ID: pone.0315176 — 2025/3/20 — page 9 — #9 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation histogramdistribution.eTh higherthevalue,thehigherthematchingdegree,whichmeans thelowertheimagedistortionrateandchromaticaberration. eTh MS-SSIMisanalgorithmusedtocomparethesimilaritybetweentwoimages[ 33].It isdesignedbasedontheperceptionprincipleofthehumanvisualsystemonimagesandcan effectivelyreflectthestructuralsimilarityofimages[ 34,35].eTh algorithmcanbedescribedas Eq(14) 𝜎 j 𝛾 Z j MS-SSIM = [L (x,y)] ⋅∏ [C (x,y)] [S (x,y)] (14) Z j j j=1 Amongthem, [L (x,y)],C (x,y)andS (x,y)havethesamemeaningastheparameter Z j j SSIMinEqs(5)–(7),Zisthethreedimensionsoftheimage,𝜎 ,𝛽 and𝛾 areusedtoadjust Z j j therelativeimportanceofdifferentcomponents. Adaptiveselectionofatmosphericillumination Tovalidatetheeffectivenessofadaptiveatmosphericillumination,weselecttwoimages fromseparateexperimentsandmanuallyadjustedtheatmosphericilluminationsintheB channel.Subsequently,wecomparetheseadjustmentswiththeHCCobjectiveparame- ters.Uponinspectingtheimages,itiseasilyobservedthattheimagetakesonabluishover- allhue,whentheatmosphericilluminationoftheBchannelistoosmall.Althoughthesky mayseesomeimprovement,theordinaryareasexhibitanoticeablebluebias.Conversely, whentheatmosphericilluminationintheB-colorchannelisexcessivelylarge,thenon- brightareasoftheimageexperiencesignificantenhancement.eTh brightskyareamayappear yellowish. UponevaluatingtheimagesandcorrespondingHCCobjectiveparameters,wefoundthat theB-channelatmosphericilluminationtendstoalignwiththeaveragevalueoftheRandG colorchannels,withadeviationofapproximately+0.04.Thisleadstoyellowingoftheimage andcolordistortion.esTh edeviationsgenerallymanifestasquadraticfunctionsandtypically occurwithinarangeof±0.04aroundtheaveragevaluesoftheRandGcolorchannels’atmo- sphericilluminations.IntheRSA,theatmosphericilluminationisselectedthroughadap- tiveoptimizationconsistentlyyieldedimageswithobjectiveparametersthatreachedextreme values,confirmingtheefficacyofours. AccordingtoFig3,itisevidentthatastheatmosphericilluminationintheB-colorchan- nelincreases,theimagegraduallyturnsyellow.Whentheatmosphericilluminationsofthe Snowmountainimagereaches0.8,theimageexhibitsanoticeabledeviationincolor,andfor theTownImage.Andwhentheatmosphericilluminationreaches0.9,theimagetakesona yellowishhue.Fromthis,wecanpreliminarilyinferthattheatmosphericilluminationsforthe twoimagesarelessthan0.8and0.9,respectively.Furthermore,intheSnowmountainImage, theatmosphericilluminationisbelow0.6,andintheTownimage,theatmosphericillumina- tionis0.8,bothresultinginadistinctbluishtint.Weroughlydepictalinegraphillustrating thevariationoftheHCCwithchangesintheatmosphericilluminationintheB-colorchan- nel.AndtheHCCreachesextremevaluesatthesametime.Italignswiththespeculatedrange fromsubjectiveobservation. Superioritytest ToevaluatetheeffectivenessofRSA,TestExperiment1isdesigned.eTh sectionkeepsall othervariablesconstantandreplacestheimprovedtransmissionsuggestedinourmethod PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 9/ 18 ID: pone.0315176 — 2025/3/20 — page 10 — #10 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation Fig3.AtmosphericilluminationvariationimageandtheirHCC-atmosphereofBchannellinechart.(A)–(J)showstheSnowMountainimage A graduallyincreasing,(K)–(T)showstheCityimageA graduallyincreasing,(U)istheHCC-AtmosphereofB-colorchannelLineChartof b b Mountain,(V)istheHCC-AtmosphereofB-colorchannelLineChartofMountain. https://doi.org/10.1371/journal.pone.0315176.g003 withthetransmissionproposedbyDCPbeforeperformingdefogging,namedTestExperi- ment1.Combinethehazyimage,DCPprocessedimage,TestExperiment1processedimage, andtheimageprocessedthoughtourstoformFig4.Moreovercompareitusingthesixobjec- tiveparametersofPSNR,SSIM,AVE,UQI,HHCandMS-SSIMasshowninTable1. UponFig4Band4C,wecandrawthefollowingpoints. • eTh brightnessof Fig4Chasbeenimproved.Itscolorsaturationisclosertotheoriginal image. • ItisevidentthattheimagedetailshaveimprovedinTestExperiment1uponcloserinspec- tionoftheareanearthebridgeinbothimages,includingthewindowdetails. • Whenenlargingthetowerpartoftheimages,thedetailsofthetowerpartoftheimagepro- cessedbyTestExperiment1areclearerthantheimagerepairedbyDCP,andthecoloris morenatural. • ComparetheobjectiveparametersinTable1.eTh parametersinExperiment1arehigher thanthoseinDCP. esTh ecomparisondemonstratestheeffectivenessandrobustnessofthemodifiedatmo- sphericilluminationproposedinRSA.eTh analysisabovefurtherprovesthatplaysakey roleinrepairingimagecolorandimprovingimagebrightnesstoacertainextentinourRSA. However,therearestillsomeproblemsintheprocessedimagesinTestExperiment1. PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 10/ 18 ID: pone.0315176 — 2025/3/20 — page 11 — #11 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation Fig4. Experimentalcomparisonchart.(A)eTh foggyimageoftheimage.(B)eTh dehazedimageaerft darkchan- nelimageprocessing.(C)AnexperimentaldehazingimageforreplacingthealgorithminthispaperwithDCP transmission,whichisTestExperiment1.(D)RSA. https://doi.org/10.1371/journal.pone.0315176.g004 Table1.Objectiveparametersofexperimentalcomparisonchart. Objectiveparameters DCP[12] TestExperiment1 RSA PSNR 63.3504 64.6734 69.1043 SSIM 0.7513 0.8480 0.9902 AVE 0.2761 0.3301 0.3863 UQI 0.6624 0.8141 0.8702 HCC –0.0471 0.2560 0.5680 https://doi.org/10.1371/journal.pone.0315176.t001 • eTh colorsaturationoftherepairedimageisstilltoohigh.Thisseriouslyinterfereswiththe expressionofinformationinimagedetails.eTh overallimageisunnatural. • erTh eisstillhalophenomenonintheskyoftheimage.Whenobservingtheriver,itisnot difficulttofindthatnoiseisintroduced. • Awhitehalophenomenonappearsaroundthetower. eTh rootcauseoftheaboveproblemsisthatthetransmissionisnotaccurateenough.Due toanerrorinimagetransmission,thedehazingprocessisnotfullyeffective.Itresultsina slightlyfoggyimagewithlightercolors.eTh outlineofthetowerclockinthetowerisaeff cted byinaccuratetransmissionofDCPandTestExperiment1,whichresultsinawhiteaperture. OurRSAhassuccessfullycorrectedtheseissues.ExaminingTable1,itisevidentthatsev- eralobjectiveparametershaveimprovedsignificantly.However,despitethesefactors,the AVEvalueoftheimageprocessedbyoursisstillhigherthanthatofTestExperiment1.This demonstratestheaccuracyofthetransmissionestimatedandfurthervalidatesitseffective- ness. Wepreviouslyintroducedsixobjectiveparameters.Table1showsthatthemethodspro- posedhavehigherobjectiveparametermeasurements.eTh reasonforthissituationmaybe thatsomeareashaveablackouterframeintheimageofTestExperiment1.Itindicatesthat theatmosphericilluminationselectedbythemethodsdeviatesfromtheactualvalue.This causestheestimatedtransmissiontoalsodeviate,resultinginerrorsindepthoffieldestima- tion,inaccuratecolorrestoration,lossofdetails,anddeviationsfromtheoriginalimage.eTh PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 11/ 18 ID: pone.0315176 — 2025/3/20 — page 12 — #12 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation lossofdetailscausesadecreaseintheobjectiveparametersofPSNR,SSIM,UQIandMS- SSIM.Halosappearintheskyandalargeamountofnoiseisintroducedduetotheinaccuracy oftransmission,greatlyaeff ctingtheevaluationofparameters.Asaresult,Wecanfindthat theimprovedtransmissioneffectivelyimprovesthequalityoftheimage. Previously,weproposeddarkchannelimagedehazingbasedontheimprovedbinaryimage segmentation(IBS)[36].Inthiswork,wefocusonimprovingtheDCPmethodthroughacol- lectionofmethodstoimproveimagequality.However,asexplainedabove,theimagerepaired bytheIBSwillproduceobviousboundariesattheedgeoftheimagesegmentation.This causestheobservertofeeluncomfortablewhenobservingtheimage,andthesaltandpep- pernoiseisscatteredatthejunctionofthebrightareaandtheordinaryarea.Now,ourwork focusesonimprovingtheDCPmethoditself,byfindingandimprovingtheDCPfailurepart, andrepairingthetransmittanceofthisparttofurtherimprovetheimage.Fig5isanimage producedbytherepairedimagesofthetwomethodsweproposedandtheircorresponding objectiveparameters.Fortheconvenienceofobservation,wenormalizedthedata.Wecansee thatthisworkhaswellavoidedthenoiseproblemattheboundaryandfurtherimprovedthe image.Byobservingthebargraph,wecanfindthatalthoughtheSSIMandUQIofIBSare slightlyhigherthanRSA,thePSNR,AVE,HCC,andMS-SSIMarealllowerthanRSA.RSA isproposedtofixthecolordifferenceproblemoftheimageandbetterensuretheauthen- ticityandreliabilityoftheimagecolor.eTh improvementoftheobjectiveparameterHCCis enoughtoillustratetheeffectivenessofRSA.Inaddition,RSAhasalsomadecorresponding improvementsinalgorithmoperationefficiency. Qualitativeresultsonreal-worldimages Indefoggingmethods,improvingthefogprocessingeffectintheskyregionhasoenft proven challenging.Thisisattributedtothepresenceofbrightareasornoiseinthefoggyimages, whichaeff ctstheaccuracyofatmosphericilluminationselection.Furthermore,theskyareas Fig5.Ourworkcomparison.(A)isIBS[36].(B)isRSA.(C)isimageobjectiveparameterhistogram. https://doi.org/10.1371/journal.pone.0315176.g005 PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 12/ 18 ID: pone.0315176 — 2025/3/20 — page 13 — #13 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation sharevisualcharacteristicswithfog,whichmakestransmissionestimationlessprecise.From theFig6,itisclearthefollow. • DuetotheintroductionofDCI,theDCPhasaninaccurateevaluationoftransmissionin theprocessofimageprocessing.Itoverestimatesthetransmission,causingthedehazed imagetohavetoolargedepthoffieldandlossofdetails,andcannothandleareaswithtoo manybrightareaswell.Inaddition,whentherearetoomanybrightareas,theatmospheric illuminationismistakenlyselectedtothebrightarea.Itmakestheatmosphericillumina- tionsislargerthanactualvalue.Becauseoftheatmosphericilluminations’issues,thetrans- missionisfurtherdeviated.eTh DCPprocessedimageexhibitsanoticeablehaloeffectin theskyandoverallreducedbrightness,accompaniedbyexcessivesaturation.Although DCPhasmanyshortcomingsinimageprocessing,itfundamentallyprovidesanewideafor thetraditionaldehazedimagemethodandhasextremelyfastprocessing. • eTh MAMFinputimageisdecomposedintointensityandLaplacianmodules,whichare enhancedatthepixelandgradientlevelsrespectively.Sincethedetaillayerguaranteesthe gradientinformation,theoutputimagecanproduceresultsthatguaranteedetailseven undersmoothtransmission.AlthoughtheMAMF’salgorithmspeedhasbeenimproved, theimageisover-superimposedinthedetails.Itresultsinseriousdetaillossandexcessive saturationduetotheadditionoflayers. • eTh HRPusesnonlinearcompressiontooptimizetransmissionandimproveaccuracy.At thesametime,ituseslogarithmiccompressiontosimulateDCIofhaze-freeimageand receiveapolishingtransmission.However,thereisalotofnoiseintheskyarea,andalotof noiseisrevealedaerft processing,resultinginhalophenomenon. • AlthoughthePDEproposesthemethodbasedonfindingdarkpixels,whicheffectively improvedtheoverallbrightnessproblemoftheimageandenrichedtheimagedetails.Butit Fig6.Qualitativecomparisonofdifferentmethodsonreal-worldimages. (A)arefoggyimages,(B)areimages processedbyDCP[12].(C)areimagesoptimizedbyMAMF[30].(D)areimagesprocessedbyTDD[37],(E)are imagesprocessedbyPDE[38],and(F)areimagesprocessedbyJCE[39].(G)areRSA. https://doi.org/10.1371/journal.pone.0315176.g006 PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 13/ 18 ID: pone.0315176 — 2025/3/20 — page 14 — #14 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation hasnotfundamentallygottenridoftheconstraintsoftheDCP.eTh imageexhibitexcessive saturation,darkenedbrightness,anddetailsthatarelostinseveralparts. • eTh JCEcombinesthreebasicpreprocessingtechniquestocreateintermediateimagesto enhancecontrastanduseadaptabilitytohandlecomplexandchangingenvironments. Inthefusionstage,itusesanadaptivekernelsizebasedonfaststructuralblockdecom- positiontofuseimagesprocessedbythreebasicpreprocessingtechniques.eTh method greatlyimprovesthecalculationtime,butintermsofimagequality.eTh threetechniques areallbasedonimageenhancementpreprocessingtechniques,whichdonottakeinto accountthefactthatfogexistsandenhancethecontrastoftheimage.Althoughthecon- trastoftheeffectiveinformationoftheimageisenhanced,theimagequalityisnoteffec- tivelyimproved.Duetothefusionofmultipleimages,thedetailsoftheimagearerepeat- edlysuperimposed,whichcausesthedetailstodeepen,becomesblurredandisdifficultto observe.Secondly,theprocessingoftheimagecausestheimagesaturationtoincrease,the depthoffieldtodeepen,andchromaticaberrationtooccurinsomedetailsoftheimage. eTh yresultsinpoorimagequality. Table2.Objectiveevaluationparameters. Objective Figure DCP[12] MAMF[30] TDD[37] PDE[38] JCE[39] RSA parameters PSNR Town 63.3504 65.0244 63.9385 65.2371 60.2194 69.1043 Mountain 61.9267 64.5344 65.4546 63.9213 62.4864 68.3010 Snowmountain 60.9663 67.0110 63.9949 67.2597 62.9520 69.8626 Forest 62.1010 65.3265 67.3813 63.6416 62.6516 70.3602 City 60.0309 65.4584 67.6920 63.9520 60.2866 69.6575 Pampkin 64.1027 65.6477 64.2120 63.6034 61.7083 69.1640 SSIM Town 0.7513 0.7152 0.8524 0.8180 0.5189 0.9002 Mountain 0.7408 0.6847 0.8466 0.7861 0.6883 0.8665 Snowmountain 0.4888 0.6084 0.7229 0.7683 0.6428 0.8911 Forest 0.7673 0.6897 0.9010 0.8072 0.6731 0.9260 City 0.6411 0.7200 0.8592 0.7978 0.6546 0.9260 Pampkin 0.8002 0.7089 0.8079 0.7772 0.6775 0.8848 AVE Town 0.2761 0.3411 0.3319 0.3225 0.1915 0.3863 Mountain 0.2781 0.3484 0.3620 0.3082 0.2724 0.3981 Snowmountain 0.2703 0.3785 0.3897 0.3313 0.2950 0.4037 Forest 0.2538 0.3400 0.3695 0.2826 0.2574 0.3892 City 0.2108 0.3630 0.4029 0.2849 0.2970 0.4282 Pampkin 0.2876 0.3424 0.3182 0.2800 0.2534 0.3864 UQI Town 0.6624 0.7759 0.8483 0.7412 0.3475 0.8702 Mountain 0.6885 0.8137 0.8510 0.7800 0.6989 0.9030 Snowmountain 0.4963 0.7780 0.8389 0.7607 0.7069 0.8498 Forest 0.7368 0.8619 0.9207 0.7819 0.7174 0.9508 City 0.5206 0.7974 0.9288 0.7456 0.5502 0.9396 Pampkin 0.7835 0.8483 0.8524 0.6814 0.6670 0.9217 HCC Town –0.0471 0.0899 0.4502 0.0707 –0.1372 0.5680 Mountain 0.1487 0.1455 0.2441 0.2394 0.0388 0.5896 Snowmountain –0.1143 0.2510 0.1984 –0.0072 0.0481 0.5399 Forest 0.0324 0.2536 0.5893 0.2048 0.0222 0.6633 City –0.1470 0.0402 0.4256 0.1011 –0.0637 0.5587 Pampkin 0.1476 0.2578 0.4423 0.0294 -0.0159 0.5848 MS-SSIM Town 0.8279 0.9076 0.8705 0.9140 0.6960 0.9669 Mountain 0.8567 0.8916 0.8967 0.8672 0.8249 0.9559 Snowmountain 0.8569 0.9491 0.9027 0.9437 0.6457 0.9744 Forest 0.8582 0.8983 0.9241 0.8315 0.7909 0.9499 City 0.8476 0.8795 0.8879 0.8802 0.7924 0.9009 Pampkin 0.8268 0.9042 0.8475 0.8615 0.7763 0.9529 https://doi.org/10.1371/journal.pone.0315176.t002 PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 14/ 18 ID: pone.0315176 — 2025/3/20 — page 15 — #15 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation • eTh RSAoptimizestheatmosphericilluminationbasedontheRayleighScattertheory.It enrichestheeffectiveinformationintheimage,greatlyimprovestheimagequality,ensures theimagedetails,andoptimizesthecolorproblembetweenthedefoggingimageandthe originalfoggyimage.Asthealgorithmcomplexityincreases,thetimecomplexityofoursis relativelyhigh. Incontrast,weoptimizetransmissioninbrightregions,whichsignificantlyimprovesthe visualqualityoftheskyarea.Itcloselyresemblestheoriginalimageintermsofcolor,which avoidscolordistortionanddetailloss.Todemonstratethealgorithm’seffectivenessfurther, weprovideacomparisonofvfi eobjectiveparameters:PSNR,SSIM,AVE,UQI,HCCand MS-SSIM. eTh orderinthetablecorrespondstotheorderinthefigure.Inthe Table2,thesixobjec- tiveparameterswereintroducedpreviously.ByobservingTable2,wecanseethatthe objectiveparametersmeasuredbyourmethodishigherthanthoseofothermethods.eTh rea- sonsforthisphenomenonareanalyzedasfollows.WecanseefromFig6thatthebrightness oftheimageprocessedbymethodsotherthantheRSAisdarker,andtheDCP,MAMF,PDE andJCEprocesscolorlossindetails.Asaresult,theouterframeofsomeareasappearsblack, whichindicatesthattheatmosphericilluminationsselectedbythesealgorithmsdeviatesfrom theactualatmosphericilluminations.Itcausesthetransmissionestimatedbyusinginaccu- rateatmosphericilluminationstoalsodeviateandimagesofdepthoffieldestimationerrors. esTh eparametersresultininaccuratecolorrestoration,lossofdetails,anddeviationsfromthe originalimage.eTh lossofdetailscausestheobjectiveparametersofPSNR,SSIMandUQIto decrease.Duetotheinaccuracyoftransmission,halosappearintheskyandalargeamountof noiseisintroduced,whichgreatlyaeff ctstheevaluationofparameters.Weproposeamethod formodifyingatmosphericilluminationsandtransmission,whichgreatlyimprovestheabove problems,restoresimages,enrichesimagedetails,andimprovesimagequality. Fig7.Performancecomparisonchartofeachmethod.eTh barchartrepresentstheaveragerunningtimeofeach methodonsomedata,andthelinechartrepresentsthemeanoftheobjectiveparametersofeachmethod. https://doi.org/10.1371/journal.pone.0315176.g007 PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 15/ 18 ID: pone.0315176 — 2025/3/20 — page 16 — #16 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation Inordertoconductobjectiveandmulti-anglecomparativeexperiments.Weselectssome imagesfromthedatasetfortimetestingandcalculatestheiraveragevalues.Asshownin Fig7. Bycomparison,itcanbefoundthattherunningtimeofDCP,MAMFandJCEmethods isshorter,buttheimagequalityrestoredbythesethreemethodsisrelativelylow,thecolor isgenerallybiased,andthebrightnessanddepthoffieldaretoohigh,makingitdifficultto observethedetails. eTh runningtimeofTDD,PDEandoursislonger,buttheimagequalityrestoredbythese threemethodsisrelativelyhigh.Amongthem,ourshasashorteraveragerunningtimeanda higherqualityofrestoredimages,whichismoreadvantageous. Fromtheabovecomparativeexperiments,itcanbeseenthatthequalityoftheimageis proportionaltothetimecomplexityofthemethod.Reducingthecomplexityofmethodwhile improvingtheimagequalityisatopicforfutureresearchinthisdirection. Conclusion WeintroduceacolorcompensationdehazingmethodbasedonRayleighScattering.eTh rea- sonsforthelowbrightness,largecolordifference,uncleardetails,haloandotherproblems oftheimageprocessedbythetraditionalimprovedmethodsareanalyzed.ByanalyzingBCP andDCPtheory,thereasonsfortheinaccurateestimationofatmosphericilluminationand transmissionaresummarized.AccordingtoBCPandDCPtheory,RSAfindstheareaswith low-lightimageandoptimizesrestorationquality.Ontheonehand,accordingtoRayleigh scattering,whenatmosphericlightpassesthroughtheatmosphere,itwillscatterduetothe shortwavelengthofbluelight,anditsabilitywillbedamagedtoalargeextent,whichresults inthedifferencebetweenthecoloroftheobjectanditstruecolor.Sincethetransmissionis estimatedbasedontheatmosphericillumination,thedeviationofatmosphericillumination willalsocauseerrorsinthetransmissionoftheimage.Ontheotherhand,DCPfailsinhigh- brightnessareas,whichresultsininaccuratetransmissionestimation,unclearexpressionof processedimagedetails,andaperturephenomenonaroundindividualobjects.Byoptimiz- ingatmosphericilluminationandtransmission,wereducetheimpactoftheaboveproblems ontheimageandimprovetheoverallimagequality.However,itshouldbenotedthatthis methodisnotnecessarilysuitableforallhazeimages,whichisalsoadirectionforourfuture research.AndRSAwilltakealittlelongertoprocesswhenencounteringtoolargeimages.It issignificantlyimportantforourfutureresearchtooptimizethemethodcomplexity,improve themethodprocessingspeedandrobustness. Author contributions Conceptualization:XinGuo. Datacuration:QilongSun. Formalanalysis:XinGuo. Fundingacquisition:JinghuaZhao. Investigation:JinghuaZhao. Methodology:XinGuo. Projectadministration:XinGuo. Resources:YiyangQiao. PLOS ONE https://doi.org/10.1371/journal.pone.0315176 March 20, 2025 16/ 18 ID: pone.0315176 — 2025/3/20 — page 17 — #17 PLOS ONE Single-image dehazing method based on Rayleigh Scattering and adaptive color compensation Sowa ft re: YingyingZhang. Supervision:QilongSun. Validation:XinGuo,YanZhou. Writing–originaldraft: XinGuo. Writing–review&editing:XinGuo,QilongSun,MingchenSun. References 1. Kopf J, Neubert B, Chen B, et al. Deep photo: model-based photograph enhancement and viewing. ACM. 2008. https://doi.org/10.1145/1409060.1409069 2. Sahu G, Seal A, Krejcar O, et al. Single image dehazing using a new color channel. J Visual Commun Image Representation. 2020;74(5):103008. https://doi.org/10.1016/j.jvcir.2020.103008 3. Zhou C, Yang X, Zhang B, et al. 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Published: Mar 20, 2025