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1、COMPUTERVISION,GRAPHICS,ANDIMAGEPROCESSING29,273-285(1985)ANewMethodforGray-LevelPictureThresholdingUsingtheEntropyoftheHistogramJ.N.KAPURDepurtmentofMathematics,IndianInstituteofTechnology,Kanpur,India208016P.K.SAHOODepartmentofAppliedMathematics,Unive
2、rsityofWaterloo,Waterloo,Ontario,Canado,N2L3GIANDA.K.C.WONGDepartmentofSystemsDesign,UniversityofWaterloo,Waterloo,Ontario,Canada,N2LX1ReceivedAugust27,1982;revisedApril30.1984andOctober16,1984TwomethodsofentropicthresholdingproposedbyPun(SignalProcess.
3、2,1980.223-237;Comput.GraphicsImageProcess.16,1981,210-239)havebeencarefullyandcriticallyexamined.Anewmethodwithasoundtheoreticalfoundationisproposed.Examplesaregivenonanumberofrealandartificallygeneratedhistograms.“.1985AcademicPress.Inc.1.INTRODUCTION
4、Inpictureprocessing,themostcommonlyusedmethodinextractingobjectsfromapictureis“thresholding.”Iftheobjectisclearlydistinguishablefromtheback-ground,thegray-levelhistogramwillbebimodalandthethresholdforsegmentationcanbechosenatthebottomofthevalley.However
5、,gray-levelhistogramsarenotalwaysbimodal.Methodsotherthanvalley-seekingare,thus,requiredtosolvethisproblem.Overtheyearsseveraltechniqueshavebeenproposedtoovercomethisdifficulty.Mostofthemattempttoreducetheproblemtothebimodalcase.Weszkaetal.[l]andWeszkaa
6、ndRosenfeld[2]presentmethodstoovercomethethresholdselectionproblemwhenthepeaksvarysignificantlyinsizeandthevalleyisrelativelywide.Otherstrytoimprovehistogramsbyusingsecond-ordergray-levelstatisticsasdescribedin[3].Stillothersattempttomakethresholdselect
7、ioneasiertodefineanimprovedimagehistogram[4].Amethodwhichusesthestatisticalrelationofpointsanditsneighbourhoodisproposedin[5].Besidesthese,thereareanumberofothermethodssuchasOstu’smethod[6],theiterativemethod[7],thequadtreemethod[8],andtherelaxationmeth
8、od[9].Asurveyofsomeofthesemethodsmaybefoundin[lo,111.Recently,Pun[12,131hasproposedtwointerestingalgorithmsbasedonentropyconsiderationsforpicturethresholding.But,whilederivingalowerboundfortheaposteriorientropyofthegray-levelhist
