A Zernike Moment Phase-Based Descriptor for Local

IEEETRANSACTIONSONIMAGEPROCESSING,VOL.19,NO.1,JANUARY2010205AZernikeMomentPhase-BasedDescriptorforLocalImageRepresentationandMatchingZenChenandShu-KuoSunAbstract—Alocalimagedescriptorrobusttothecommonphotometrictransformations(blur,illumination,noise,andJPEGcompression)andgeometrictransformations(rotation,scaling,translation,andviewpoint)iscrucialtomanyimageunder-standingandcomputervisionapplications.Inthispaper,therepresentationandmatchingpowerofregiondescriptorsaretobeevaluated.Acommonsetofellipticalinterestregionsisusedtoevaluatetheperformance.Theellipticalregionsarefurthernormalizedtobecircularwithafixedsize.Thenormalizedcircularregionswillbecomeaffineinvariantuptoarotationalambiguity.Here,anewdistinctiveimagedescriptortorepresentthenormalizedregionisproposed,whichprimarilycomprisestheZernikemoment(ZM)phaseinformation.Anaccurateandrobustestimationoftherotationanglebetweenapairofnormalizedregionsisthendescribedandusedtomeasurethesimilaritybetweentwomatchingregions.ThediscriminativepowerofthenewZMphasedescriptoriscomparedwithfivemajorexistingregiondescriptors(SIFT,GLOH,PCA-SIFT,complexmoments,andsteerablefilters)basedontheprecision-recallcriterion.Theexperimentalresults,involvingmorethan15millionregionpairs,indicatetheproposedZMphasedescriptorhas,generallyspeaking,thebestperformanceunderthecommonphotometricandgeometrictransformations.Bothquantitativeandqualitativeanalysesonthedescriptorperformancesaregiventoaccountfortheperformancediscrepancy.First,thekeyfactorforitsstrikingperformanceisduetothefactthattheZMphasehasaccurateestimationaccuracyoftherotationanglebetweentwomatchingregions.Second,thefeaturedimensionalityandfeatureorthogonalityalsoaffectthedescriptorperformance.Third,theZMphaseismorerobustunderthenonuniformimageintensityfluctuation.Finally,atimecomplexityanalysisisprovided.IndexTerms—Geometricandphotometrictransformations,imagerepresentationandmatching,performanceevaluation,phaseandmagnitudecomponents,precisionandrecall,regiondescriptors,Zernikemoments(ZM).I.INTRODUCTIONLOCALfeaturesrobusttocommonphotometrictrans-formations(blur,illumination,noise,andJPEGcom-pression)andgeometrictransformations(rotation,scale,translation,andviewpoint)arecrucialtomostimageunder-standingandcomputervisionapplicationsincludingimageManuscriptreceivedOctober16,2008;revisedAugust12,2009.Firstpub-lishedSeptember22,2009;currentversionpublishedDecember16,2009.TheassociateeditorcoordinatingthereviewofthismanuscriptandapprovingitforpublicationwasProf.SabineSusstrunk.TheauthorsarewiththeDepartmentofComputerScience,NationalChiaoTungUniversity,1001UniversityRoad,Hsinchu,Taiwan,R.O.C.(e-mail:[e-mail];[e-mail]).Colorversionsofoneormoreofthefiguresinthispaperareavailableonlineatfication,andimageretrieval,etc.[1]–[5].Theprocessingoflocalfeaturesinvolvesthreetasks:featuredetection,featuredescription,andfeaturematching.Thelocalfeaturesbelongtoaninterestpoint(key-point)oraninterestregion.Sinceasingleimagepointcarrieslittleinformation,aninterestpointmustbeassociatedwithitssurroundingimagepatch.Fromthisimagepatch,asecondmomentmatrixofimageintensitiesrevealsthecharacteristicstructureofthelocalimageregion.ThekeypointdetectorssuchasHarriscornerdetector[6]andtheSIFTdetector[7],whichisbasedonthedifferenceofGaussians(DOG),utilizeacircularwindowtosearchforapossiblelocationofakeypoint.However,theimagecontentinthecircularwindowisnotrobusttoaffinedeformations.Recently,anumberoflocalfeaturede-tectorsusingalocalellipticalwindowhavebeeninvestigated.Matasetal.[5]presentedamaximallystableextremalregion(MSER)detector.TuytelaarsandVanGool[8]developedanedge-basedregion(EBR)detectoraswellasanimage-based(IBR)regiondetector.MikolajczykandSchmid[9]proposedHarris-AffineandHessian-Affinedetectors.Theperformancesoftheexistingregiondetectorswereevaluated[11],indicatingMSERdetectorandHessian-Affinedetectorarethetwobest.Aftertheregionsofinterestaredetected,aregiondescriptorisneededforregionrepresentation.Inthedescriptorconstruc-tion,thedetectedellipse-shapedregionisfirstnormalizedtoacircularpatchofafixedsize(typically,4141pixels).Thenormalizedcircularpatchcanbeshowntobeaffineinvariantuptoarotationalambiguity[10],[33].Agoodfeaturedescriptorshouldhaveagreatdiscriminativepower.Fivemajortypesofexistingdescriptorsaretobebrieflyreviewedinthenextsec-tiontoexploretheircapabilityforimagerepresentation.Aftertheregiondescriptorisdetermined,amatchingfunctionisdefinedtomeasurethesimilaritybetweenregionsextractedfromdifferentimagesofthesamescene.Themeritsofvariousregiondetectors,coupledwiththeirownregiondescriptors,areoftenjudgedbasedontheROC(receiveroperatingcharacter-istic)curveorthePR(precision-recall)curve.Inthispaper,anewdescriptor,calledtheZernikemomentphase-baseddescriptor(orZMphaseinshort),isproposed.Thephaseinformationofasignalismoreinformativethanthemagnitudeinformationduringsignalreconstruction,asdemon-stratedbyOppenheim[34].Therobustnessoflocal