偏微分方程在图像处理中的应用

[]2007-02-10[],1,2(1.,230061,2.,230027)[],,,:,,(PDE),PDE,[];;;[]TP317.4[]A[]1001-5116(2007)03-0062-041[1],,,,,;,,60,,,,,,,:,,,,,:,,(PDE),,,:,,:PDE,;,;PDE,1990,,PDE,,(:IEEETrans.onPAMIIEEETrans.onImageProcessingInternationalJournalofComputerVision,JournalofVisualCommunicationandImageRepresentation)PDE,CVPR,IC2CV,ICIPSophiaAntipolis,:PDE,PDE,PDE,PDE2PDE[2]PDE2620075253JournalofAnhuiInstituteofEducationMay.2007Vol.25No.3GaborJainKoenderinkWitkin,PDEPeronaMalikOsherRu2din,Rudin,Price-,PDEPDE,OsherSethian,PDE,MumfordShahM-S,KasssnakePDE3PDERn,x=(x1,x2,,xn),u(x)=u(x1,x2,,xn),:Fx1,L,xn,u,5u5x1,L,5u5xn,L,5mu5x1m15x2m2L5xnmn(1)PDEm=m1+m2+L+mn:1);2),PDE,PDE3.1PDE[3],(x,y),PDE,:a11uxx+2a12uxy+a22uyy+F(x,y,u,ux,uy)=0(2)(x,y)=a212-a11a22,x0:1):(2)x0(x,y)052u55=A5u5+B5u5+Cu,52u5s2-52u5t2=A15u5s+B15u5t+C1u2):(2)x0(x,y)052u52+52u52=A5u5+B5u5+Cu3):(2)x0(x,y)=052u52=A5u5+B5u5+Cu3.2,1):,,,,-uxx-uyy=f-ui,j-1-ui-1,j+4ui,j-ui+1,j-ui,j+1=h2fi,j2):(),,,,P(x,y),-uxx-uyy=fux(u)x+uy(u)y=fu+5unu3):,,4PDE,,,,,,PDE[4]4.1,,,,,,36,,:u0=Ru+(3)u:R2R,u0(u),,R(3),u0u,u:infu|u0-Ru|2dx(4)||(4)u,:R3u0-R3Ru=0(5)R3R,(5),,Tikhonov(4),:F(u)=|u0-Ru|2dx+|ýu|2dx(6),,,()u,Tikhonov,4.2,Tikhonov:infu|ýu|2d(7)(7)u=0PDE,u0:5u/5t=u(ut=0=u0(8),,(8)tu0G(=2t),,,,4.3Perona2malikPeronamalik,(8)5u/5t=u=div(ýu),g(s):[0,+[[0,1]:5u/5t=div(g(ýu)ýu)(9)g(ýu)(ýu)1,(9)(8);(ýu),,,Per2ona2malikg(ýu)=exp(-ýu2/K2),K,4.4,,infu(|ýu|)d,div(ýu)ýuýu=0,PDE:5u5t=div(ýu)ýuýu(ut=0=u0)(10),(s)=s2Tikhonov;(s)=1-exp(-s2/K2)Pe2rona2malik,(10)=ýu/ýu=1Duu:5u/5t=cucu,c=(ýu),c=(ýu)ýu:1):cc0,,PDE,,:(ýu)0(ýu)02):,,:limýu+c=0limýu+c/c=03):,,:limýu0c=limýu0c=0(s)=1+s2,465,PDE:(1)PDE,,,,,,,(2),,,PDE,PDE,,(3)PDE,,PDE(4)PDE,[][1]GillesAubert,PierreKornprobst.MathematicalProb2lemsinImageProcessing[M].NewYork:SpringerVer2lag,2002.[2]GuillermoSapiro.GeometricPartialDifferentialEqua2tionsandImageAnalysis[M].Cambridge:CambridgeUniversityPress,2001.[3].[M].:,2002.[4]D.Tschumperl,PDEsBasedRegularizationofMulti2valuedImagesandApplications,PhDthesis,UniversitdeNice2SophiaAntipolis,Dec.2002.ATentativeDiscussionaboutApplicationofPDEinImageProcessingZHOUXiao1,ZHUCai2zhi2(11DepartmentofEducation,AnhuiInstituteofEducation,Hefei230061;2.DepartmentofElectricEngineeringandInformationScience,theUniversityofScienceandTechnologyofChina,Hefei230027,China)Abstract:Thelow2levelimageprocessingisalwaysanimportantfactorcontainingvisiondevelopmentofcomputer.TherecentstudyshowsPDEtheoryprovidesthetheoreticalframeworkforimageprocessing,hasproducedincomparableeffectsinseveralimageprocessingfields.ThispaperintroducesthedevelopmenthistoryandrelatedtheoreticalbackgroundbasedonPEDimageprocessing,chieflyfocusingontheapplica2tionofPEDinimagerestoration.KeyWords:partialdifferentialequation;imagerestoration;anisotropicdiffusion(55)[][1].[M].:.1985.[2]D.P.Ausubel/F.G.Robinson,SchoolLearningAnIntroductiontoEducationalPsychology.1969,455.[3].[M].:.1990.368.[4].[J]..1992,(1).26.[5].[J]..2002,(6).66AnAnalysisontheEffectofPhysicsMajorsAcademicAchievementsinNormalUniversitiesonTheirTeachingAbilityMEIZhong2yi,ZHANGYun2li(SchoolofScience,HefeiUniversityofTechnology,Hefei230009,China)Abstract:Statisticsofnormaluniversityphysicsmajorgraduatesrevealthat,theirteachingabilityissignifi2cantlyrelatedtoacademicachievementsofsuchcoursesasexperimentandphysicspedagogy,butlessrele2vanttoacademicachievementsofsomespecializedcoursesoftraditionalimportance.Thisanalysistellsusacademicachievementsarerelatedtoteachingabilitytosomeextent,buttherestillexistslackintrainingofsomebasicteachingskills,suchasexperimentalskill.KeyWords:physicsmajorinnormaluniversities;academicachievements;teachingabilities56