PDF-基于时间变化的鲁棒各向异性扩散模型

359Vol.35,No.920099ACTAAUTOMATICASINICASeptember,20091112.,:.,.,,.,,.,Pinecone.,,.,,,TP751TimeDependentRobustAnisotropicDi®usionProcessesWANGYi1NIURui-Qing1YUXin1SHENHuan-Feng2AbstractThekeypointofresearchonanisotropicdi®usionistobuildtheadaptiveandstabledi®usionmodel.However,therearestilltwoproblemsintheexistinganisotropicdi®usionmod-els|thedeterminationofthegradientthresholdandtheitera-tivestoppingtime.Inthispaper,weproposeatime-dependentrobustanisotropicdi®usionmethod.Inthemethod,theGaus-sianscaleandthegradientthresholdaresettothemonoton-icallydecreasingfunctionofthetime,whichisveryusefultoaccuratelyextractedgeandboundaryfeatures.Meanwhile,aniterativeSNRmeasureisde¯nedtoe®ectivelydeterminethestoppingtime,soastolessenover-smoothregions.Inordertoshowthevalidityoftheproposeddi®usionscheme,weuseonegrayimage\Pineconeinourexperiments.Experimentalresultshaveshownthatthetime-dependentrobustanisotropicdi®usionmethodshavesuperiorityovertheexistingmethodsandtheycane®ectivelysmoothoutnoisewhilepreservingedgefeatures.KeywordsAnisotropicdi®usion,timedependent,di®usioncoe±cient,robust,(Partialdi®erentialequation,PDE)[1¡2].,PeronaMalik[3]2008-07-082009-05-14ReceivedJuly8,2008;inrevisedformMay14,2009(863)(2007AA12Z160),(40672205),(200809),(09R02)SupportedbyNationalHighTechnologyResearchandDevelopmentProgramofChina(863Program)(2007AA12Z160),NationalNatu-ralScienceFoundationofChina(40672205),ProjectSupportedbyKeyLaboratoryofMappingfromSpaceofStateBureauofSurvey-ingandMapping(200809),andOpenResearchFundofStateKeyLaboratoryofInformationEngineeringinSurveying,MappingandRemoteSensing(09R02)1.()4300742.4300791.InstituteofGeophysicsandGeomatics,ChinaUniversityofGeo-sciences,Wuhan4300742.SchoolofResourceandEnvironmentalScience,WuhanUniversity,Wuhan430079DOI:10.3724/SP.J.1004.2009.01253125435(P-M),.:1),;2);3),;4).,,[4¡14]..,:1);2).,|k¾T,k¾,,,.11.1P-MPeronaMalik,(P-M).8:@I(x;y;t)@t=r¢(c(jrI(x;y;t)j)rI(x;y;t))I(x;y;0)=I0(x;y)(1),c(jrIj),r¢(),r.c(jrIj),.PeronaMalik[3]:c(jrI(x;y;t)j)=11+µjrI(x;y;t)jk¶2(2)c(jrI(x;y;t)j)=exp¡µjrI(x;y;t)jk¶2#(3)P-M,:1);2),.1.2Catte,Catte[4](Catte):8:@I(x;y;t)@t=r¢(c(jr(G¾¤I(x;y;t))j)rI(x;y;t))I(x;y;0)=I0(x;y)(4),G¾¾.jrG¾¤I(x;y;t)j¾.Catte,P-M,.,Catte.1.3RADPeronaMalik,,.,Black[12](RAD(Robustanisotropicdi®usinon)):c(x;y;t)=8:12·1¡(jrI(x;y;t)j¾e)2¸2;jI(x;y;t)j·¾e0;(5),¾e.,(5)Tukey.P-M,Tukey\,\.(5),P-M,.1.4,Gilboa[13](Forwardandbackward),c(x;y;t)=11+µjI(x;y;t)jkf¶n¡®1+µjI(x;y;t)j¡kbw¶2m(6),.,.1.5Gilboa[14]:RMP(Ramppreserving).8:@I(x;y;t)@t=r¢(c(Im(I(x;y;t)))rI(x;y;t))I(x;y;0)=I0(x;y)(7)(7),c(s)=ejµ=(1+(s=(kµ))2),Laplacian,.(7).,.2:k¾T..,,.2.1,,:8:c(x;y;t)=121¡µjrG¾(t)¤I(x;y;t)jk(t)¶2#2;jrG¾(t)¤Ij·k(t)0;(8)9:1255,k(t),[15]k(t)=1+®1t(9),,®1.k,,.¾(t),,,.,,[16].2.2((8)(9)),:1)G¾(t).,,.2)k(t).(8),t!0,jrIj1=,c(x;y;t!0)!1,(8),,k(t),,;t!1,c(x;y;t!1)=0,,.,256,k(t)1,.k(t)®1.®1,,.3)T.,,.,,(),T.T,.,G¾(t)k(t),.,.,.3:1..t¤h¾(t)¢t,®1.2.jrG¾(t)¤Inj.n,I=In.[4]8-jrG¾(t)¤Ij.,M£N,,,.3.c(rI).jrG¾(t)¤Ij®1(8),.4.,.,I(x;y;t)I(ih;jh;n¢t),¢t,h,i,j.[3].(a)(a)Originalimage(b)(b)Noisyimage(i)(i)IterativeSNR1Fig.1Smoothingresultsfora\Pineconeimage1256355..,T=t¤,,In+1;,2.4,.1(a)Pinecone(256£256),¾2=400,1(b).P-MCatteRADFABRMP.1(c)»(h)6,26T.200,P-MCatteRAD,.FAB,,,,,FAB,.RMP.,,.,1(i)\{,.1(c)»(h)2,,.1(i),60,,5.,(),.,,.5,.,:1),,;2),.,,,..References1GuichardF,MoisanL,MorelJM.AreviewofPDEmodelsinimageprocessingandimageanalysis.JournaldePhysiqueIV,2002,92(12):137¡1542SapiroG.GeometricPartialDi®erentialEquationsandIm-ageAnalysis.England:CambridgeUniversityPress,20013PeronaP,MalikJ.Scale-spaceandedgedetectionusinganisotropicdi®usion.IEEETransactionsonPatternAnal-ysisandMachineIntelligence,1990,12(7):629¡6394CatteF,LionsPL,MorelJM,CollT.Imageselectivesmoothingandedgedetectionbynonlineardi®usion.SIAMJournalonNumericalAnalysis,1992,29(1):182¡1935WangY,ZhangLP,LiPX.Localvarianced-controlledforward-and-backwarddi®usionforimageenhancementandnoisereduction.IEEETransactionsonImageProcessing,2007,16(7):1854¡18646Aja-FernandezS,Alberola-LopezC.Ontheestimationofthecoe±cientofvariationforanisotropicdi®usionspeckle¯lter-ing.IEEETransactionsonImageProcessing,2006,15(9):2694¡27017LuoHG,ZhuLM,DingH.Coupledanisotropicdi®usionforimageselectivesmoothing.SignalProcessing,2006,86(7):1728¡17368YuHC,ChuaCS.GVF-basedanisotropicdi®usionmod-els.IEEETransactionsonImageProcessing,2006,15(6):1517¡15249Martin-HerreroJ.Anisotropicdi®usioninthehypercube.IEEETransactionsonGeoscienceandRemoteSensing,2007,45(5):1386¡139810RifkahE,AmerA.Fastautomatedstopping-timeandedge-strengthestimationforanisotropicdi®usion.In:ProceedingsofIEEEInternationalConferenceonAcoustics,Speech,andSignalProcessing.LasVegas,USA:IEEE,2008.933¡93611KrissianK,WestinCF,KikinisR,VosburghKG.Orientedspecklereducinganisotropicdi®usion.IEEETransactionsonImageProcessing,2007,16(5):1412¡142412BlackMJ,SapiroG,MarimontDH,HeegerD.Robustanisotropicdi®usion.IEEETransactionsonImageProcess-ing,1998,7(3):421¡43213GilboaG,SochenN,ZeeviYY.Forward-and-backwarddif-fusionprocessesforadaptiveimageenhancementandden