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1、Featuredetectionandestimation:DifferentialgeometricstructuresinImagesDaviGeigerIntroductiontoFeatureDetectionWehaveobtainedimagemeasurementssuchas(orsimply),and.Wenowwishtomakedetectionsandestimations,whicharedecisionsbaseduponourmodels.Decisionsaretheresultofsomeco
2、mparisonfollowedbyachoice.Examples(i)ifameasurementisaboveathresholdweaccept,nototherwise;(ii)ifameasurementisthelargestcomparedtoothers,weselectit.Inparticularwewilldiscussedgedetection,orientation,curvature,andjunctiondetectionandclassification.1.Edgels:edgedetect
3、ion,edgeorientation(tangent)Inordertodetectanintensityedgewerequirethatthereisavalueinthesetabovesomethresholdvalue,say.Inordertodetecttheorientationofadetectededgeelement,atagivenscale,welookfortheangleqthatsimultaneouslymaximizesthevalueinmagnitudeandminimizesthev
4、alueinmagnitude.Thisisessenceourmodelofextracting/detectingtheorientationofahypothesizedcontourpresentatapixel(x,y).Itrequiresadecision,andonepossiblecriteriaistoextracttheorientation,atagivenscale,viawhereall(16)directionsareconsidered,q=0,p/6,...,5p/6,andforlocati
5、onswherethereisanangleqsuchthatFigure1(right).EdgelsResultsofdetectingandestimating.Darklevelsrepresent0degreesorientation,whilethebrightestvaluesrepresent11p/67Figure2.Showsastepedgeatq=0.Thevalueis(equally)largeforbothq=0andq=p/4asshown(inred)forscales=3pixels.Iti
6、salsolargeforvaluesq=p/6,p/3notshown.However,thequantityissignificantlylargerforq=0.Figure3.Showsastepedgeatq=p/6.Thevalueat“edge”locationsis(equally)largeforbothq=p/6andq=p/4asshown(inred)forscales=3pixels.Itisalso(equally)largeforvaluesq=0,p/3(notshown).However,th
7、equantityissignificantlylargerforq=p/6.Figure4.Showsastepedgeatq=0.Asthemeasurementsaremadeawayfromthelocationoftheedge,Thequantitydecreases,andalsospuriousresponseareobtained,asinthiscasetheresponseisequalforbothq=0andq=p/6.Ahomogeneitymeasurewilldetecttheselocatio
8、ns.7Wecanfurtherfilteroutspuriousdetectionsbyremovinglocationswhereandisathresholdtobeestimated.WecandefinearoutinecalledEdgel(x,y,s)which
