Edge-Based-Color-Constancy

IEEETRANSACTIONSONIMAGEPROCESSING,VOL.XX,NO.Y,DATE100Edge-BasedColorConstancyJ.vandeWeijer,Th.Gevers,A.GijsenijAbstractColorconstancyistheabilitytomeasurecolorsofobjectsindependentofthecolorofthelightsource.Awell-knowncolorconstancymethodisbasedontheGrey-Worldassumptionwhichassumesthattheaveragereflectanceofsurfacesintheworldisachromatic.Inthisarticle,weproposeanewhypothesisforcolorconstancynamelytheGrey-Edgehypothesis,whichassumesthattheaverageedgedifferenceinasceneisachromatic.Basedonthishypothesis,weproposeanalgorithmforcolorconstancy.Contrarytoexistingcolorconstancyalgorithms,whicharecomputedfromthezero-orderstructureofimages,ourmethodisbasedonthederivativestructureofimages.Furthermore,weproposeaframeworkwhichunifiesavarietyofknown(Grey-World,max-RGB,Minkowskinorm)andthenewlyproposedGrey-Edgeandhigher-orderGrey-Edgealgorithms.Thequalityofthevariousinstantiationsoftheframeworkistestedandcomparedtothestate-of-the-artcolorconstancymethodsontwolargedatasetsofimagesrecordingobjectsunderalargenumberofdifferentlightsources.Theexperimentsshowthattheproposedcolorconstancyalgorithmsobtaincomparableresultsasthestate-of-the-artcolorconstancymethodswiththemeritofbeingcomputationallymoreefficient.June14,2007DRAFTIEEETRANSACTIONSONIMAGEPROCESSING,VOL.XX,NO.Y,DATE101I.INTRODUCTIONColorconstancyistheabilitytorecognizecolorsofobjectsindependentofthecolorofthelightsource[1].Obtainingcolorconstancyisofimportanceformanycomputervisionapplications,suchasimageretrieval,imageclassification,colorobjectrecognitionandobjecttracking[2],[3],[4].Approachestothisproblemcanbedividedintotwogroups.Forthefirstgroup,theaimistorepresentimagesbyfeatureswhichareinvariantwithrespecttothelightsource,forexamplewithinthecontextofimageretrieval.SuchinvariantrepresentationhavebeenproposedbyFuntandFinlayson[5],GeversandSmeulders[2],Geusebroeketal.[6],andVandeWeijerandSchmid[7].Forthesemethodstheactualestimationofthelightsourceisnotnecessary.Forthesecondgroupofapproaches,theaimistocorrectimagesfordeviationsfromacanonicallightsource.Contrarytomethodsinthefirstgroup,solutionstothisproblemdoestimatethecolorofthelightsource,beitexplicitlyorimplicitly.Methods,eitherproposealightsourceestimation,afterwhichtheimageiscorrected[8],[9],[10][11],ortheydirectlyestimatethecolorcorrectedimage[1],[12],afterwhichthelightsourcecanbederived.Ifdesired,illuminantinvariantfeaturescansubsequentlybederivedfromthecorrectedimage.Inthispaperwelookatcolorconstancyapproachesofthesecondgroup,i.e.methodsfromwhichalightsourcecorrectedimagecanbecomputed.OneofthemostsuccessfulcolorconstancymethodsisgamutmappingproposedbyForsyth[1].ThemethodisbasedontheobservationthatonlyalimitedsetofRGBvaluescanbeobservedunderagivenilluminant.ThesetofallpossibleRGBvaluesforthecanonicalilluminant,typicallyawhiteilluminant,iscalledthecanonicalgamut.ThiscanonicalgamutisproventobeaconvexhullinRGBspace.Thealgorithmcomputeswhattransformationsmapanobservedgamutintothecanonicalgamut.Fromthesetransformations,theilluminantcolorisderived.Thegamutmappingalgorithmprovidesamongthebestresultsincolorconstancyexperiments[3].Finlaysonetal.[12]improvethegamutmappingalgorithmbyrestrictingthetransformationstobeplau-sible,meaningthatonlyilluminantsareallowedwhichcorrespondtoexistingilluminants.Thisadaptationofthegamutalgorithm,calledGCIEforgamutconstrainedilluminationestimation,wasshowntooutperformthestandardgamutalgorithm.Furtherapproachestocolorconstancyincludeprobabilisticapproaches[10],andlearning-basedmethods[11].AframeworkwhichJune14,2007DRAFTIEEETRANSACTIONSONIMAGEPROCESSING,VOL.XX,NO.Y,DATE102unifiesmultiplecolorconstancyalgorithmstogetherispresentedbyFinlaysonandHordley[9].Theyproposetoestimatetheilluminantfromthecorrelationoftheimagedata,andthepriorknowledgeaboutwhichcolorsappearunderacertainlight.Althoughtheabovedescribedalgorithmsarriveatreasonablecolorconstancyaccuracy,adrawbackisthattheyarebasedoncomplexalgorithmsandallrequireanimagedatasetwithknownlightsourcesforcalibration.Inthispaper,wewillfocusoncolorconstancybasedonlesscomplexcolorconstancyalgorithms.Tothisend,fastalgorithmsareconsideredwhicharebasedonlow-levelimagefeatures,suchasmax-RGBandGrey-World.Max-RGBisasimpleandfastcolorconstancyalgorithmwhichestimatesthelightsourcecolorfromthemaximumresponseofthedifferentcolorchannels[13].Anotherwell-knownsimplecolorconstancymethodisbasedontheGrey-Worldhypothesis[8],whichassumesthattheaveragereflectanceinthesceneisachromatic.Iftheimagesunderevaluationarepartofacoherentimagedatabase,Gershonetal.[14]showedthatassumingtheaverageofascenetobeequaltotheaveragereflectanceofthedatabase,improvestheresultsoverthestandardgrey-worldmethod.Asanexample,theymentionforestpicturesfullofgreencolors.Inthiscase,mostcolorconstancymethodswillpredictlightsourcesbiasedtowardsthegreencolor.Thedatabase-compensatedgrey-worldalgorithmresolvesthisproblem.Theselow-levelmethodsarewidelyinuse,evenindigitalconsumercameras,duetotheirverylowcomputationalcosts,i.e.takingthemaximum(max-RGB)oraveragepixelvalues(Grey-World).Low-levelapproachesregainedfurthe