Otsu多阈值算法推广实现

346200911ScienceofSurveyingandMappingVol134No16Nov1:(19782),,,,,E2mail:liuli052560@yahoo1com1cn:2008206226::CCD(:2007143)Otsu,,(,066004)Otsu,Otsu,Nelder2MeadOtsuOtsu,,,;;;Otsu;Nelder2MeadTP391;TP751A100922307(2009)06202402031(Imagesegmentation)[1],,,,Otsu(),Otsu,,Otsu,,,ReddiOtsu[2],Ridder[3]OtsuOtsu,[4],,,256;n,n256n,Sezan[5]Tsai[6],[7],Nelder2MeadOtsu,,,,2Otsu211Otsu1L,ini,N=Li=1ni,,pi=ni/N,:=Li=1ipi,=Li=1(i-)2piT,:C1={1T},C2={T+1L},C1,C21,2;1,221,221=Ti=1pi,2=Li=T+1pi(1)1=Ti=0ipi1,2=Li=T+1ipi2(2)21=11Ti=1(i-1)2pi,22=12Li=T+1(i-2)2pi(3),:2B=1(1-)2+2(2-)2(4)Otsu2B,T,,,212OtsuOtsu,n,Ti(i=1,2,3111n),(1)i(5)i=ni=1p(Ti+1:Ti+1)(5)(2)ii(6),i=ni=1(Ti+1:Ti+1)p(Ti+1:Ti+1)/i(6)(7)2B=ni=1i(i-)2(7)Otsu,n,n256n,Nelder-Mead,,2B,:y=-2B,y,6Otsu213Nelder-MeadOtsuNelder-Mead[8],,()NelderMead:;n+1xi(i=1,2,n,n+1)f(xi)f(x1)111f(xn)f(xn+1)(8)f(xn+1)-f(x1)(9)(9),,:xr=(1+)€x-xn+1,,1€xxi(8)x1,xn,xn+1,1)f(x1)f(xr)f(xn),xrxn+1,f(xi),(8)2)f(xn)f(xr)f(xn+1),xc=xn+1+(1-)€x,=015,,f(xc)f(xr),xcxn+1,f(xi),(8)xi=(x1+xi)/2,f(xi)(:i=2,3n,n+1),(9),3)f(xr)f(x1),xe=xr+(1-)€x,=2f(xe)f(xr),xexn+1,f(xi),(8);xi=(x1+xi)/2f(xi),(9)4)f(xr)f(xn+1),x^c=xr+(1-)€x,f(x^c)f(xr),x^cxn+1f(xi),(8);xi=(x1+xi)/2f(xi)(9),f(xn+1)-f(x1)0,f(xn+1)-f(x1)x3,,n,f(x)n-1,n-1,,4,,016mQuickbird,9006891a,,,,,1b,,,1c1f,,,;1d,,,,;1e,,;1f,1OtsuOtsu11Otsu297249110ms380,1262492360ms465,108,140249343min568,98,132,180249459min29624998ms379,1273069221ms470,105,14810749367ms568,101,134,17728809405ms,,OtsuNelder2Mead,,5Melder2MeadOtsu,Otsu,OtsuOtsu,[1]MadhubantiMaitra,AmitavaChatterjee1Ahybridcoop2erative2comprehensivelearningbasedPSOalgorithmf2orimagesegmentationusingmultilevelthresholding[J]1ExpertSystemswithApplications2008,34(2)1[2]ReddiSS,RudinSF,KeshavanHR1Anopticalmulti2plethresholdschemeforimagesegmentation1[J]IEEETrans1SystemManCybernet,1984,141[3]RidlerTW,Calward,S1Picturethresholdingusinganiterativeselectionmethod[J]1IEEETrans1SystemsManCybernet11978,8:6306321[4]SArora,JAcharya,A1Vermaetc1Multilevelthreshol2dingf2orimagesegmentationthroughafaststatisticalre2cursivealgorithm[J]1PatternRecognitionLetters,2008,29(2)1[5]MISezan,Apeakdetectionalgorithmanditsapplicationtohistogram2basedimagedatareduction,Comput[J]1VisionGraphicsImageProcess,1990,49:362511[6]d2m,TsaiandY2h1Cheng1Afasthistogram2clusteringapproachformulti2levelthresholding,PatternRecognitionLett11992,13:24522521(230)14234,,,,,;,,,,[2]4,,,:1),,,,,,,,,,,2),20,10,(1815km,11km)(10),()(),,,,5,,,,,,3),1,,50001,12,5000,,[1],,1[M]1:,1997:1232124,1971[2],1[J]1(),2005,41(1)1[3],1[J]1,1998,13(1)1[4],,1[J]1,2001,17(2)1[5],,,1[J]1,1997,17(1)1[6],1[J]1,2007,32(1)1AnurbansystemstudyofBinzhouareabasedonfractaltheoryAbstract:Usingfractaltheory,ananalysisofthehierarchicalscalestructureandthespatialdistributionofBinzhoucityareawereperformed1TheprimatecityindexofBinzhoucityandthetownsizefractaldimensionwerecalculatedaccordingtothetownprimacyruleofM1Jefferson1Inaddition,spatialcorrelationdimensionofthetownsizedistributionwasputforwardtoanalyzethespatialstruc2tureofurbansystem1AccordingtoalltheseanalysisitconcludessomeadvisestodevelopetheurbansystemofBinzhoucity,suchasenlargingthescaleoftheprimecity,cultivatingasecondarycentrecityinWudi,YangxinandHuimincounties,anddevelopingtownsofcountiesadministrativeareasactively1Keywords:urbansystem;fractaltheory;BinzhoucityDONGLi2feng,YUANHui2li,SONGFu2rong,CHENShu2qing(BinzhouUniversity,Geographyandtourismdepartment,Binzhou256603,China)(241)[7]KamalHammouche,MoussaDiaf,PatrickSiarry1Amultilevelautomaticthresholdingmethodbasedonag2eneticalgorithmforafastimagesegmentation[J]1Com2puterVisionandImageUnderstanding2008,109(2)1[8],1[J]1,2008,33(1)1[9]MarineBaulac,Jero^meDefrance,PhilippeJean1Opti2mizationofmultipleedgebarrierswithgeneticalgorith2mscoupledwithaNelderMeadlocalsearch[J]1Journ2alofSoundandVibration12007,300(122)1Otsumulti2thresholdpromotionandrealizationofOtsumulti2thresholdsegmentationmethodAbstract:Landscapesegmentationisnecessaryforanalyzingandinterpretingtheremotesensingimages1Asthedevelopmentofremotesensingtechnology,remotesensingimageshavehigherresolutionandmorerichgrayvalue1Onewaythatweadequatelyusetheinformationinthehighresolutionimagesisdoingmulti2thresholdsegmentation1Aneffectivemethodforimagesegmentation,Otsualgo2rithm,basedonthresholdwasanalyzedinthispaper1WhiletheOtsualgorithmisveryslowinprocessingthemulti2thresholdsegmenta2tion1SoweoptimizedtheOtsualgorithmwithNelder2Meadmethod1Wecomparedtheimprovedmethodwiththetraditionalone1ThemethodinthispapercanspeedupthesegmentationofthebigsizeremotesensingimagesKeywords:imagessegmentation;multi2threshold;remotesensingimages;Otsualgorithm;Nelder2MeadLIULi,JIAOBin2liang,LIUQin2long(InformationandEngineeringAcademy,YanshanUniversity,Qinhuangdao066004,Chi2na)032