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1Abstract—Theimportantcriteriausedinsubjectiveevaluationofdistortedimagesincludetheamountofdistortion,thetypeofdistortion,andthedistributionoferror.Anidealimagequalitymeasureshouldthereforebeabletomimicthehumanobserver.Wepresentanewgray-scaleimagequalitymeasurethatcanbeusedasagraphicalorascalarmeasuretopredictthedistortionintroducedbyawiderangeofnoisesources.BasedontheSingularValueDecomposition,itreliablymeasuresthedistortionnotonlywithinadistortiontypeatdifferentdistortionlevelsbutalsoacrossdifferentdistortiontypes.Themeasurewasappliedtofivetestimages(Airplane,Boat,Goldhill,Lena,andPeppers)usingsixtypesofdistortion(JPEG,JPEG2000,Gaussianblur,Gaussiannoise,sharpening,andDC-shifting),eachwithfivedistortionlevels.ItsperformanceiscomparedwithPSNRandtworecentmeasures.IndexTerms—imagequality,localerrormeasurement,objectivemeasures,PSNR,singularvaluedecomposition,subjectiveevaluation.I.INTRODUCTIONeasurementofimagequalityisachallengingprobleminmanyimageprocessingfieldsfromimagecompressiontoprinting.Inthepast30years,avastliteraturehasappearedwithmanyapproachesattemptingtoprovideasolution[1].Theimagequalitymeasuresintheliteraturecanbeclassifiedintotwogroups:Subjectiveandobjective[2].Subjectiveevaluationiscumbersomeasthehumanobserverscanbeinfluencedbyseveralcriticalfactorsincludingtheenvironmentalconditions,motivation,andmood.TheobjectivemeasuresincludebivariatemeasuressuchastheMeanSquaredError(MSE)orLp-norm[3,4,5,6],measuresmimickingthehumanvisualsystem(HVS)[4,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,2627,28,29,30,31,32,33,34,35],andgraphicalmeasures[33,36,37,38,39,40,41,42,43].Furthermore,severalpaperspresentcomparativeevaluationsofanumberofselectedManuscriptreceivedOctober1,2003.ThisworkwassupportedinpartbytheProfessionalStaffCongress(PSC)-CityUniversityofNewYork(CUNY)ResearchAward,2003-2004.A.ShnaydermanwaswiththeDepartmentofComputerandInformationScience,BrooklynCollegeoftheCityUniversityofNewYork,Brooklyn,NY11210,USA.A.GusevwaswiththeDepartmentofComputerandInformationScience,BrooklynCollegeoftheCityUniversityofNewYork,Brooklyn,NY11210,USA.A.M.EskiciogluiswiththeDepartmentofComputerandInformationScience,BrooklynCollegeoftheCityUniversityofNewYork,Brooklyn,NY11210,USA(correspondingauthorphone:718-758-8481,e-mail:[e-mail]).measuresforimagecompression[14,16,28,31,40,44],andfornoiseandblur[13,45].Themostcommonobjectiveevaluationtool,theMSE,isveryunreliable,resultinginpoorcorrelationwiththeHVS.Inspiteoftheircomplicatedalgorithms,theHVS-basedobjectivemeasuresdonotappeartobesuperiortothesimplepixel-basedmeasuresliketheMSE,PeakSignal-to-NoiseRatio(PSNR),orRootMeanSquaredError(RMSE).AnumberofresearcherspointtothedisadvantagesofthemeasuresthatincorporateanHVSmodel.Fuhrmannetal[44]discouragetheuseofmetricsbasedonthespatialfrequencypropertiesoftheHVSastheyrequirepreciseknowledgeoftheviewingconditions.Franti[30]arguesthatthedistortionmeasureshouldbeindependentofthefactorssuchasthecompressionmethodused,basicimageprocessingoperations,andtheviewingdistance.AccordingtoWangandBovik[34],althoughtheviewingconditionsplayanimportantroleinhumanperceptionofimagequality,theyarenotfixedinmostcases,andthespecificdataisgenerallyunavailabletotheimageanalysissystem.Anidealimagequalitymeasureshouldbeabletodescribe(1)theamountofdistortion,(2)thetypeofdistortion,and(2)thedistributionoferror.Suchameasureisexpectedtoprovideaccuratepredictionsofqualitynotonlyatdistortionrangesnearthevisualthresholdbutalsowhendistortionsaresignificantlyabovethevisualthreshold.Undoubtedly,thereisaneedforanobjectivemeasurethatprovidesmoreinformationthanasinglenumericalvalue.Assessmentofimagequalityisanopenproblemtoday.Intheir1982paper[11],LukasandBudrikistalkaboutapossibleimprovementinqualitypredictioniflocalratherthanglobalaveragingproceduresareused.Theybelievelocalerrormeasuresareparticularlypertinentinthecaseofcodingschemesthatintroducedistortionthatisverylocalizedinnature.Westenetal[24]presentaperceptualerrormeasure(PEM)basedonamultiplechannelHVSforuseindigitalimagecompression.PEMcombinestheresponsesindifferentfrequencybands,orientationsandpositions.Combinationoftheresponsesateachpositionresultsinanimagewithvaluesthatrepresentalocalvisibilityofdistortions.Incodingapplications,theauthorsbelieve,suchalocalmeasureofimagequalityisprobablymoreusefulthanaglobalone.EudeandMayache[31]comparefourmetricstoevaluatethequalityofJPEG-compressedimages.Theyconcludebystatingthatasthesemetricsdonottakeintoaccounttypicalartifactsofothercompressionmethods,amulti-dimensionalmeasure,witheachdimensionbeingrelatedtoanartifact,wouldbeanattractivesolution.AnSVD-BasedGray-ScaleImageQualityMeasureforLocalandGlobalAssessmentAleksandrShnayderman,AlexanderGusev,AhmetM.EskiciogluM2Arecentpaper[34]presentsanewnumericalmeasureforgrayscaleimages,calledtheuniversalimagequalityindex(UQI).ThedynamicrangeofUQIis[-1,1],withthebestvalueachievedwhenyi=xi,i=1,2,…,n.Asdescribedinthepaper,thisindexmodelsanydistortionasacombinationofthreedifferentfactors:lossofcorrelation