Characterization of Signals from Multiscale Edges - CMAP PDF e8d64e6f
Characterization of Signals from Multiscale Edges - CMAP
710IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCEVOL14NO7JULY1992CharacterizationofSignalsfromMultiscaleEdgesStephaneMallatandSifenZhongAbstractAmultiscaleCannyedgedetectionisequivalenttofindingthelocalmaximaofawavelettransformWestudythepropertiesofmultiscaleedgesthroughthewavelettheoryForpatternrecognitiononeoftenneedstodiscriminatedifferenttypesofedgesWeshowthattheevolutionofwaveletlocalmaximaacrossscalescharacterizethelocalshapeofirregularstructuresNumericaldescriptorsofedgetypesarederivedThecompletenessofamultiscaleedgerepresentationisalsostudiedWedescribeanalgorithmthatreconstructsacloseapproximationof1Dand2DsignalsfromtheirmultiscaleedgesForimagesthereconstructionerrorsarebelowourvisualsensitivityAsanapplicationweimplementacompactimagecodingalgorithmthatselectsimportantedgesandcompressestheimagedatabyfactorsover30IndexTermsEdgedetectionfeatureextractionlevelcrossingsmultiscalewaveletsIINTRODUCTIONOINTSOFSHARPvariationsareoftenamongthemostimportantfeaturesforanalyzingthepropertiesoftransientsignalsorimagesInimagestheyaregenerallylocatedattheboundariesofimportantimagestructuresInordertodetectthecontoursofsmallstructuresaswellastheboundariesoflargerobjectsseveralresearchersincomputervisionhaveintroducedtheconceptofmultiscaleedgedetection182325ThescaledefinesthesizeoftheneighborhoodwherethesignalchangesarecomputedThewavelettransformiscloselyrelatedtomultiscaleedgedetectionandcanprovideadeeperunderstandingofthesealgorithmsWeconcentrateontheCannyedgedetector2whichisequivalenttofindingthelocalmaximaofawavelettransformmodulusTherearemanydifferenttypesofsharpvariationpointsinimagesEdgescreatedbyocclusionsshadowshighlightsroofstexturesetchaveverydifferentlocalintensityprofilesTolabelmorepreciselyanedgethathasbeendetecteditisnecessarytoanalyzeitslocalpropertiesInmathematicssingularitiesaregenerallycharacterizedbytheirLipschitzexponentsThewavelettheoryprovesthattheseLipschitzexponentscanbecomputedfromtheevolutionacrossscalesofthewavelettransformmodulusmaximaWederiveanumericalproceduretomeasuretheseexponentsIfanedgeissmoothwecanalsoestimatehowsmoothitisfromthedecayoftheManuscriptreceivedJanuary101990revisedJanuary291992ThisworkwassupportedbytheNSFgrantIRI890331AFOSRgrantAFOSR900040andONRgrantN0001491J1967RecommendedforacceptancebyAssociateEditorRWoodhamSMallatiswiththeCourantInstituteNewYorkUniversityNewYorkNY10012SZhongwaswiththeCourantInstituteNewYork
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