10-数字图像处理-光度立体视觉

Image&VisionLab信息视觉处理光度立体视觉PhotometricStereoImage&VisionLabMaterialsfrom:双向反射分布函数（BRDF）Thebidirectionalreflectancedistributionfunctionisthefractionofincidentlightemittedinonedirectionwhenthesurfaceisilluminatedfromanotherdirection.ratioofthesceneradiancetothesceneirradiancerfBi-directionalReflectanceFunctionImage&VisionLabΘ:Polarangleφ:AzimuthangleImage&VisionLab双向反射分布函数（BRDF）:polaranglebetweensurfacenormalandlenscenter:azimuthangleofthesensor:emittingfrom:incidentto:irradianceoftheincidentlightattheilluminatedsurface:radianceofthereflectedlight:ratioofthesceneradiancetothesceneirradiance),,,(),(),,,(eeiiriiiiieerfdLdLeiiLrLrfDifferentialreflectancemodel:Image&VisionLab双向反射分布函数（BRDF）定义：输出方向的辐射度与输入方向的辐照度的比率；BRDF可以从零（在该方向没有反射光）变化至无穷大（输出方向的单位辐射度来自于输入方向任意小的辐射度）；BRDF在输入和输出方向是对称的。（著名的Helmholtz互易原理）；尽管对于某些输入与输出的角度，BDRF可以较大，但对大多数来说它不能大。事实上平均值必须相当小。Image&VisionLabsourcesurfacereflectionsurfaceincidentdirectionbodyreflection•BodyReflection:DiffuseReflectionMatteAppearanceNon-HomogeneousMediumClay,paper,etc•SurfaceReflection:SpecularReflectionGlossyAppearanceHighlightsDominantforMetalsImageIntensity=BodyReflection+SurfaceReflectionMechanismsofReflectionImage&VisionLabBodyReflection:DiffuseReflectionMatteAppearanceNon-HomogeneousMediumClay,paper,etcSurfaceReflection:SpecularReflectionGlossyAppearanceHighlightsDominantforMetalsManymaterialsexhibitbothReflections:ExampleSurfacesImage&VisionLabviewingdirectionsurfaceelementnormalincidentdirectioninvsdrriif),;,(•LambertianBRDFissimplyaconstant:albedo•SurfaceappearsequallybrightfromALLdirections!(independentof)•SurfaceRadiance:v•CommonlyusedinVisionandGraphics!snIILdid.cossourceintensitysourceintensityIDiffuseReflectionandLambertianBRDFImage&VisionLabDiffuseReflectionandLambertianBRDFImage&VisionLabCAN’Tperceivetheshapeofthesnowcoveredterrain!CANperceiveshapeinregionslitbythestreetlamp!!WHY?White-out:SnowandOvercastSkiesImage&VisionLab•AssumeLambertianSurfacewithAlbedo=1(noabsorption)•AssumeSkyradianceisconstant•SubstitutinginaboveEquation:RadianceofanypatchisthesameasSkyradiance!!(white-outcondition)2/0sincos),;,(),(),(iiiirriiiisrcrrsurfaceddfLLskyiisrcLL),(1),;,(rriifskyrrsurfaceLL),(DiffuseReflectionfromUniformSkyImage&VisionLabsourceintensityIsurfaceelementnormalnincidentdirections),(iiviewingdirectionv),(vvrspecular/mirrordirection),(rr•MirrorBRDFissimplyadouble-deltafunction:•Validforverysmoothsurfaces.•AllincidentlightenergyreflectedinaSINGLEdirection(onlywhen=).•SurfaceRadiance:)()(vivisILvr)()(),;,(vivisvviifspecularalbedoSpecularReflectionandMirrorBRDFImage&VisionLabObservedImageColor=axBodyColor+bxSpecularReflectionColorRGBKlinker-Shafer-Kanade1988ColorofSource(Specularreflection)ColorofSurface(Diffuse/BodyReflection)DoesnotspecifyanyspecificmodelforDiffuse/specularreflectionCombingSpecularandDiffuse:DichromaticReflectionImage&VisionLabDiffuseandSpecularReflectiondiffusespeculardiffuse+specularImage&VisionLabPhotometricStereoImage&VisionLabImageIntensityand3DGeometryShadingasacueforshapereconstructionWhatistherelationbetweenintensityandshape?ReflectanceMapImage&VisionLabSurfaceNormalNsurfacenormalyzxEquationofplane0DCzByAx0CDzyCBxCAorLetpCAxzqCByz1,,1,,qpCBCANSurfacenormalImage&VisionLabGradientSpaceyzx1zqp1snN11,,22qpqpNNn11,,22SSSSqpqpSSsNormalvectorSourcevectori111cos2222SSSSiqpqpqqppsn1zplaneiscalledtheGradientSpace(pqplane)•EverypointonitcorrespondstoaparticularsurfaceorientationSImage&VisionLabReflectanceMapRelatesimageirradianceI(x,y)tosurfaceorientation(p,q)forgivensourcedirectionandsurfacereflectanceLambertiancase:yxI,svni:sourcebrightness:surfacealbedo(reflectance):constant(opticalsystem)kcImageirradiance:snkckcIicosLet1kcthensniIcosImage&VisionLabLambertiancaseqpRqpqpqqppISSssi,111cos2222snReflectanceMap(Lambertian)coneofconstantiIso-brightnesscontourReflectanceMapImage&VisionLabLambertiancase0.13.00.09.08.07.0,qpRpq90i01SSqqppSSqp,iso-brightnesscontourNote:ismaximumwhenqpR,SSqpqp,,ReflectanceMapImage&VisionLabGlossysurfaces(Torrance-Sparrowreflectancemodel)qpRGpkckcIrsid,coscosdiffusetermspeculartermpq5.0,qpRSSqp,DiffusepeakSpecularpeakReflectanceMapImage&VisionLabShapefromaSingleImage?Givenasingleimageofanobjectwithknownsurfacereflectancetakenunderaknownlightsource,canwerecovertheshapeoftheobject?GivenR(p,q)((pS,qS)andsurfacereflectance)canwedetermine(p,q)uniquelyforeachimagepoint?NOpqImage&VisionLabSolutionTakemoreimagesPhotometricstereoAddmoreconstraintsShape-from-shadingImage&VisionLabPhotometricStereopq11,SSqp22,SSqp33,SSqpImage&VisionLabWecanwritethisinmatrixform:Imageirradiance:1kc11snI1snv2s22snI3s33snInsssTTTIII322211Lambertiancase:snikcIcosPhotometricSte