Marr 关于视觉的计算理论(来自网络)

162.12.1.12.1.22.22.2.12.2.1.12.2.1.2Marr2.2.1.32.2.1.4scalingtheoremsforzero-crossing2.2.2fullprimalsketch2.32.52.3.12.3.22.52.42.52.6Roberts[Rob65][Wa72][Huf77]60HubelWiesl[Hub,Wie62,68]CampellRobesn[Cam68]Fourier17MITD.MarrNewellSimon[new81]MarrMarrMarrMarrFourierFourierFourierFourierFourierFourier18MarrMarrrepresentating0,1,2,,8,9nn103101+710037101001012Marrprimalsketch2.52.5dimensionalsketch3Dmodel(1)(2)(3)(4)highlight2.52.52.12.22.4192.1Marredgesegmentsbarblobterminationstokens2.22.5202.2AI.App.p.212.fig8-3(a)(b)(c)(d)(e)(f)21+1-12.3(a)2.3(b)2.32.4(a)(b)(c)(a)I(b)I(b)(a)+1+1-1-122(c)I(d)I2.4(a)(b)(c)(d)2.4(b)IiiAii311+-++=iiiiIIIAAi+1-AiAi-Ai-1Ai+1Ai-1Fi()()FAAAAAAiiiiiii=-+-=-+-+-1111222.5(a)(b)(a)(c)(b)(d)(c)Si()()SFFFFFFiiiiiii=-+-=-+-+-111122232.5(b)2.5(c)S2.5(d)SIjOioPIijijj=×-∑P2.6(a)2.6(b)2.6(c)2.6(a)(b)(a)(c)ScaleCampbellRobson[cam68](a)(b)(c)24ΔwConstraintofspatiallocalization(1)(2)(3)Δx[Bra65],160-175ΔΔxwp≥14Gaussian()()[]()Gxx=-1221222/expspssGaussian()Grxy=-⎛⎝⎜⎞⎠⎟=[phone]psgsgexp,GaussianI(x,y)Gaussians2G*I(x,y)zerocrossingf(x,y)=D2[G(r)*I(x,y)]I(x,y)*f(x,y)=D2G*I(x,y)D2GI(x,y)G(r)I(x,y)D2G2.7D2GLaplacian∇2Marr[Mar80]∇2D2(G*I)()∇*2GIxy,()[]()∇=---2142212222Ggpwgsgsexp4/,,42222222sg¶¶¶¶=+=+=∇wyxyx25s2.7w2Dws222D=sw2DwwdD≥362.2.7()∇2Gg2.8∇2GGaussian262.8∇2G(a)∇2G(b)Fourier(a)272.9∇2G(a)2.8(a)(b)Fourier28sideblobss∇2G∇2G∇2GDOGDifferenceofGaussianDOGGaussianGaussianGaussian1.62.10DOG2.10GaussianGaussianMarr2.112.122.12(a)2.12(b)2.12(c)XXXX2.12(c)292.12(b)2.12(c)GaussianGaussianGaussianGaussian2.12(d)(1)(2)(3)GaussianMarr2.11302.12(a)(b)(c)(d)Haralik[Har80]Binford[Bin81]Mayhew[May81]FrisbyMarrspatialcoincidenceassumption∇2G312.13∇2G2.132.14322.14Marr&Hildrechp.204Fig82.14(a)(b)ω=918∇2Gω=2s(a)(c)(d)(e)(a)(c)(d)(e)1462110423118134105120)12076-25)-251625)25642.142.2.1.4ScalingTheoremsforZeroCrossing33∇2GMarr∇2GTerzopoulos[Terz82]Witkin[Wit83]Gaussianx-sxsGaussianWitkinBabaud[Bab83]GaussianYuillePoggio[Yui86]2.2.2fullprimalsketch43151656Gestaltplacetokens2.15primitive34leastcommitmentrelaxationprocess[Dav81]MarrMarrMarr2.152.152.1435Marr2.52.162.162.12.1dgg,ΔsΔggdgg,,ΔsgsΔgΔgΔsg36ΔgsdsΔsgdggΔggsdssΔss2.16MarrMarr1.2.3.374.Marr2.52.172.5p,q2.172.52.52.5[Marr82]BarrowTemenbaum[Bar78,81]intrinsicimageMarr2.52.172.5visualinformtion,D.MarrP53.Fig.12(a)(b)2.5382.4Marr2.5Marr2.182.18generalizedcones392.192.202.19402.202.52.541regularitycoherenceContinuity[86]Marrholistic2.5Marr[Kan87]MarrMarr2.5Marrperceptualorganiztion[Hoc81]MarrMarr42regularities[Pen86]PantlandSurperquadricsConnectionistModelsofVision[Fel83,85][Bal86]MarrHoughHoughactivevision[Swa91][Bab83]Babaud,J.,Wintkin,A.andDuda,R.,UniquenessoftheGaussiankernalforscale-spacefiltering,FairchildTech.Rep.645,Flair22,1983.[Bar78]Barrow,H.G.AndTenenbaum,J.M.,Recoveringscenecharacteristicsfromimages,InA.R.HansonandE.M.Riseman(Eds),ComputerVisionSystems,NewYork,AcademicPress,3-26,1978.[Bar81]Barrow,H.G.andTenenbaum,J.M.,ComputationalVision,ProceedingsofIEEE,Vol.69,no.5,1981.[Bin81]Binford,T.O.Inferringsurfacesfromimages,SpicialIssueonVision,ArtificilaIntelligence17,205-244,1981.[Bra65]Bracewell,R.,TheFouriertransformanditsapplications,NewYork,MacGraw-Hill,1965.[Cam68]Campbell,F.W.C.andRobson,J.,ApplicationofFourieranalysistothevisibilityofgratings,J.Physiol.(Land)197,551-566,1968.[Fel83]Feldman,J.A.AndBallard,D.H.,Computingwithconnections,InJ.Beck,B.HoopeandA.Rosenfeld(Eds.),HumanandMachineVision,AcademicPress,107,1983.43[Fel85]Feldman,J.A.,Fourframessuffice:AProvisionalmodelofvisionandspace,BehavioralandBrainSciences8,1985,265-284.[Har84]Haraick,M.,Digitaledgesfromzerocrossingofseconddirectionalderivative,IEEETrans.PatternAnal.Mach.Intell.,PAMI-6,1984,58-68.[Hoc81]Hochberg,J.,Levelsofperceptualorganization,InM.KubovyandJ.R.Pomerantz(Eds.),PereptualOrganization,255,1981.[Hub,Wie62]Hubel,D.H.andWiesel,T.N.,Receptivefields,Binocularinteractionandfunctionalarchitecture,InCat'svisualcortex,J.Physiol.(Land),166,106-154,1962.[Hub68]Hubel,O.H.AndWiesel,T.N.,Receptivefieldsandfunctionalarchitectureofmonkeystriatecortex,J.Physiol.(Land)195,215-243,1968.[Huf77]Huffman,D.A.,Relizableconfigurationsoflinesinituresofpolyhedre,InE.W.ElcockandD.Mikhail(Eds),MachneIntelligence8,EdiburghUniversityPress,493-509,1977.[Kan87]Kanal,L.AndTsao,T.,ArtificialIntelligenceandnaturalperception,InIntelligenceAutonomousSystems,60-70,1987.[Mar80]Marr,D.AndHildreth,E.,Theoryofedgedetection,Proc.R.Soc.LandB207,187-217,1980.[Mar82]Marr,D.,Vision,W.H.FreemanandCompany,1982.[May81]Mayhew,J.E.W.andFrisby,J.P.,Psychophysicalandcomputationalstudiestowardsatheoryofhumanstereopisis,ArtificialIntelligence17,347-386,1981.[New72]Newell,A.AndSimon,H.A.,Humanproblemsolving,Englewood,Cliffs,N.J.,Prentice-Hall,1972.[Pen86]Pentlad,A.P.,Partmodels,InProc.ofInt.Conf.PatternRecognitionandComputerVision,MiamiBeach,Florida,June22-26,1986,242-249.[Rob85]Roberts,L.,Machineperceptionofthree-dimensionalsolids,InJ.TippetlEds.OpticalandElectro-opticalinformationprocessing,Cambridge,Mass,MITPress,159-197,1965.[Swa