10数字图像处理光度立体视觉

1、10数字图像处理光度立体视觉Materials from: /afs/cs/academic/class/15385-s06/lectures/ppts/DC & CV Lab.CSIE NTU双向反射分布函数（BRDF）The bidirectional reflectance distribution function is the fraction of incident light emitted in one direction when the surface is illuminated from another direction.ratio of the scene radi

2、ance to the scene irradianceBi-directional Reflectance Function:Polar angle :Azimuth angle双向反射分布函数（BRDF） : polar angle between surface normal and lens center : azimuth angle of the sensor : emitting from : incident to : irradiance of the incident light at the illuminated surface : radiance of the re

3、flected light : ratio of the scene radiance to the scene irradianceDifferential reflectance model: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。sourcesurfacereflectionsurfa

4、ceincidentdirection bodyreflection Body Reflection:Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etc Surface Reflection:Specular ReflectionGlossy AppearanceHighlightsDominant for MetalsImage Intensity = Body Reflection + Surface ReflectionMechanisms of ReflectionBody Reflectio

5、n:Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etcSurface Reflection:Specular ReflectionGlossy AppearanceHighlightsDominant for MetalsMany materials exhibitboth Reflections:Example Surfacesviewingdirectionsurfaceelementnormalincidentdirection Lambertian BRDF is simply a const

6、ant :albedo Surface appears equally bright from ALL directions! (independent of ) Surface Radiance : Commonly used in Vision and Graphics!source intensitysource intensity IDiffuse Reflection and Lambertian BRDFDiffuse Reflection and Lambertian BRDFCANT perceive the shape of the snow covered terrain!

7、 CAN perceive shape in regions lit by the street lamp! WHY?White-out: Snow and Overcast Skies Assume Lambertian Surface with Albedo = 1 (no absorption) Assume Sky radiance is constant Substituting in above Equation:Radiance of any patch is the same as Sky radiance ! (white-out condition)Diffuse Refl

8、ection from Uniform Skysource intensity Isurfaceelementnormalincidentdirectionviewingdirectionspecular/mirror direction Mirror BRDF is simply a double-delta function : Valid for very smooth surfaces. All incident light energy reflected in a SINGLE direction (only when = ). Surface Radiance :specular

9、 albedoSpecular Reflection and Mirror BRDFObserved Image Color = a x Body Color + b x Specular Reflection ColorRGBKlinker-Shafer-Kanade 1988Color of Source(Specular reflection)Color of Surface(Diffuse/Body Reflection)Does not specify any specific model forDiffuse/specular reflectionCombing Specular

10、and Diffuse: Dichromatic ReflectionDiffuse and Specular Reflectiondiffusespeculardiffuse+specularPhotometric StereoImage Intensity and 3D GeometryShading as a cue for shape reconstructionWhat is the relation between intensity and shape?Reflectance MapSurface Normalsurface normalEquation of planeorLe

11、tSurface normalSurface NormalGradient SpaceNormal vectorSource vectorplane is called the Gradient Space (pq plane) Every point on it corresponds to a particular surface orientationReflectance MapRelates image irradiance I(x,y) to surface orientation (p,q) for given source direction and surface refle

12、ctanceLambertian case: source brightness: surface albedo (reflectance): constant (optical system)Image irradiance:Let then Lambertian caseReflectance Map(Lambertian)cone of constantIso-brightness contourReflectance MapLambertian caseiso-brightnesscontourNote: is maximum whenReflectance MapGlossy sur

13、faces (Torrance-Sparrow reflectance model)diffuse termspecular termDiffuse peakSpecular peakReflectance MapShape from a Single Image?Given a single image of an object with known surface reflectance taken under a known light source, can we recover the shape of the object?Given R(p,q) ( (pS,qS) and su

14、rface reflectance) can we determine (p,q) uniquely for each image point?NOSolutionTake more imagesPhotometric stereoAdd more constraintsShape-from-shadingPhotometric StereoWe can write this in matrix form:Image irradiance:Lambertian case:Photometric StereoSolving the EquationsinverseMore than Three

15、Light SourcesGet better results by using more lightsLeast squares solution:Solve for as beforeMoore-Penrose pseudo inverseColor ImagesThe case of RGB imagesget three sets of equations, one per color channel:Simple solution: first solve for n using one channelThen substitute known n into above equati

16、ons to getOr combine three channels and solve for nComputing light source directionsTrick: place a chrome sphere in the scenethe location of the highlight tells you the source directionFor a perfect mirror, light is reflected about NSpecular Reflection - RecapWe see a highlight when Then s is given

17、as follows:Computing the Light Source DirectionCan compute N by studying this figureHints:use this equation:can measure c, h, and r in the imageNrNCHchChrome sphere that has a highlight at position h in the imageimage planesphere in 3DDepth from NormalsGet a similar equation for V2Each normal gives

18、us two linear constraints on zcompute z values by solving a matrix equationV1V2N积分方法积分的方法可以分为局部方法(local approach)和全局方法(global approach) 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

19、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、Frankot and Chellappa、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Frankot Chellapp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LimitationsBig problemsDoesnt work for shiny

20、things, semi-translucent thingsShadows, inter-reflectionsSmaller problemsCamera and lights have to be distantCalibration requirementsmeasure light source directions, intensitiescamera response functionTrick for Handling ShadowsWeight each equation by the pixel brightness:Gives weighted least-squares matrix equation:Solve for as before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