数字图像处理-光度立体视觉.ppt

信息视觉处理 光度立体视觉PhotometricStereo Materialsfrom http www cs cmu edu afs cs academic class 15385 s06 lectures ppts DC CVLab CSIENTU 双向反射分布函数 BRDF Thebidirectionalreflectancedistributionfunctionisthefractionofincidentlightemittedinonedirectionwhenthesurfaceisilluminatedfromanotherdirection ratioofthesceneradiancetothesceneirradiance Bi directionalReflectanceFunction Polarangle Azimuthangle 双向反射分布函数 BRDF polaranglebetweensurfacenormalandlenscenter azimuthangleofthesensor emittingfrom incidentto irradianceoftheincidentlightattheilluminatedsurface radianceofthereflectedlight ratioofthesceneradiancetothesceneirradiance Differentialreflectancemodel 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 source surfacereflection surface incidentdirection bodyreflection BodyReflection DiffuseReflectionMatteAppearanceNon HomogeneousMediumClay paper etc SurfaceReflection SpecularReflectionGlossyAppearanceHighlightsDominantforMetals ImageIntensity BodyReflection SurfaceReflection MechanismsofReflection BodyReflection DiffuseReflectionMatteAppearanceNon HomogeneousMediumClay paper etc SurfaceReflection SpecularReflectionGlossyAppearanceHighlightsDominantforMetals ManymaterialsexhibitbothReflections ExampleSurfaces viewingdirection surfaceelement normal incidentdirection LambertianBRDFissimplyaconstant albedo SurfaceappearsequallybrightfromALLdirections independentof SurfaceRadiance CommonlyusedinVisionandGraphics sourceintensity sourceintensityI DiffuseReflectionandLambertianBRDF DiffuseReflectionandLambertianBRDF CAN Tperceivetheshapeofthesnowcoveredterrain CANperceiveshapeinregionslitbythestreetlamp WHY White out SnowandOvercastSkies AssumeLambertianSurfacewithAlbedo 1 noabsorption AssumeSkyradianceisconstantSubstitutinginaboveEquation RadianceofanypatchisthesameasSkyradiance white outcondition DiffuseReflectionfromUniformSky sourceintensityI surfaceelement normal incidentdirection viewingdirection specular mirrordirection MirrorBRDFissimplyadouble deltafunction Validforverysmoothsurfaces AllincidentlightenergyreflectedinaSINGLEdirection onlywhen SurfaceRadiance specularalbedo SpecularReflectionandMirrorBRDF ObservedImageColor axBodyColor bxSpecularReflectionColor R G B Klinker Shafer Kanade1988 ColorofSource Specularreflection ColorofSurface Diffuse BodyReflection DoesnotspecifyanyspecificmodelforDiffuse specularreflection CombingSpecularandDiffuse DichromaticReflection DiffuseandSpecularReflection diffuse specular diffuse specular PhotometricStereo ImageIntensityand3DGeometry ShadingasacueforshapereconstructionWhatistherelationbetweenintensityandshape ReflectanceMap SurfaceNormal surfacenormal SurfaceNormal GradientSpace ReflectanceMap RelatesimageirradianceI x y tosurfaceorientation p q forgivensourcedirectionandsurfacereflectanceLambertiancase Imageirradiance Lambertiancase ReflectanceMap Lambertiancase iso brightnesscontour Note ismaximumwhen ReflectanceMap Glossysurfaces Torrance Sparrowreflectancemodel diffuseterm specularterm ReflectanceMap ShapefromaSingleImage Givenasingleimageofanobjectwithknownsurfacereflectancetakenunderaknownlightsource canwerecovertheshapeoftheobject GivenR p q pS qS andsurfacereflectance canwedetermine p q uniquelyforeachimagepoint NO Solution TakemoreimagesPhotometricstereoAddmoreconstraintsShape from shading PhotometricStereo Wecanwritethisinmatrixform Imageirradiance Lambertiancase PhotometricStereo SolvingtheEquations MorethanThreeLightSources Getbetterresultsbyusingmorelights Leastsquaressolution Solveforasbefore ColorImages ThecaseofRGBimagesgetthreesetsofequations onepercolorchannel Simplesolution firstsolvefornusingonechannelThensubstituteknownnintoaboveequationstogetOrcombinethreechannelsandsolveforn Computinglightsourcedirections Trick placeachromesphereinthescenethelocationofthehighlighttellsyouthesourcedirection Foraperfectmirror lightisreflectedaboutN SpecularReflection Recap WeseeahighlightwhenThensisgivenasfollows ComputingtheLightSourceDirection CancomputeNbystudyingthisfigureHints usethisequation canmeasurec h andrintheimage N rN C H c h Chromespherethathasahighlightatpositionhintheimage imageplane spherein3D DepthfromNormals GetasimilarequationforV2Eachnormalgivesustwolinearconstraintsonzcomputezvaluesbysolvingamatrixequation 积分方法 积分的方法可以分为局部方法 localapproach 和全局方法 globalapproach 两类 局部方法比较容易操作 计算效率也比较高 可是它会传递误差 因此对光度立体得到的法向数据要求很精确 局部和全局积分方法 局部方法 Coleman和Jain提出了一种扫描算法 是从点P相邻两点的法向矢量来计算P点的深度 Healey和Jain是从P点的相邻8个点的法向来恢复P点的深度的 Wu和Li用格林理论和多路径积分去恢复相对高度 最简单的局部积分方法就是利用梯度从不同路径积分 然后去平均全局方法 把表面积分当作一个优化问题 因为他把梯度数据当成全局数据 所以这种算法比较抗噪声 Ikeuchi用最小二乘法从针图来估计表面深度 Horn FrankotandChellappa Simchony等也提出了一些相应的全局算法 积分方法的比较 真实形状 不同方法积分结果 Possion方程优化方法对尺度的保持比较好 FrankotChellapp频域优化的方法对形态保持的比较好 不同方法积分结果 仿射变换方法 加权能量方程 Limitations BigproblemsDoesn tworkforshinythings semi translucentthingsShadows inter reflectionsSmallerproblemsCameraandlightshavetobedistantCalibrationrequirementsmeasurelightsourcedirections intensitiescameraresponsefunction TrickforHandlingShadows Weighteachequationbythepixelbrightness Givesweightedleast squaresmatrixequation Solveforasbefore 由多个视图获取表面法线与发射率 一个球面组成的5幅图像 是使用正交投影从一个视角得到的 由多个视图获取表面法线与发射率 表面的反射系数 由多个视图获取表面法线与发射率 法线向量场 由法线获取表面形状 通过积分求形状 实际例子 乒乓球图像 a b c d e f g h 实际例子 恢复结果 OriginalImages Results Shape Shallowreconstruction effectofinterreflections Accuratereconstruction afterremovinginterreflections Results Albedo NoShadingInformation OriginalImag