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Computer Vision. Spring 2010 15-385,-685 Instructor: S. Narasimhan PH A18B T-R 10:30am 11:50am Lecture #13. Mechanisms of Reflection. source. incident direction. surface reflection. body reflection. surface. Surface Reflection: Specular Reflection Glossy Appearance - PowerPoint PPT Presentation

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<ul><li><p>Computer VisionSpring 2010 15-385,-685</p><p>Instructor: S. Narasimhan</p><p>PH A18BT-R 10:30am 11:50am</p><p>Lecture #13</p></li><li><p>Mechanisms of Reflectionsourcesurfacereflectionsurfaceincidentdirection bodyreflection Body Reflection:</p><p>Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etc Surface Reflection:</p><p>Specular ReflectionGlossy AppearanceHighlightsDominant for MetalsImage Intensity = Body Reflection + Surface Reflection</p></li><li><p>Example SurfacesBody Reflection:</p><p>Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etcSurface Reflection:</p><p>Specular ReflectionGlossy AppearanceHighlightsDominant for MetalsMany materials exhibitboth Reflections:</p></li><li><p>Diffuse Reflection and Lambertian BRDF</p></li><li><p>Diffuse Reflection and Lambertian BRDFviewingdirectionsurfaceelementnormalincidentdirection Lambertian BRDF is simply a constant :albedo Surface appears equally bright from ALL directions! (independent of ) Surface Radiance : Commonly used in Vision and Graphics!source intensitysource intensity I</p></li><li><p>White-out: Snow and Overcast SkiesCANT perceive the shape of the snow covered terrain!CAN perceive shape in regions lit by the street lamp!!</p><p> WHY?</p></li><li><p>Diffuse Reflection from Uniform Sky Assume Lambertian Surface with Albedo = 1 (no absorption)</p><p> Assume Sky radiance is constant</p><p> Substituting in above Equation:Radiance of any patch is the same as Sky radiance !! (white-out condition)</p></li><li><p>Specular Reflection and Mirror BRDFsource intensity Iviewingdirectionsurfaceelementnormalincidentdirectionspecular/mirror direction Mirror BRDF is simply a double-delta function : Valid for very smooth surfaces.</p><p> All incident light energy reflected in a SINGLE direction (only when = ). Surface Radiance :specular albedo</p></li><li><p>Combing Specular and Diffuse: Dichromatic ReflectionObserved 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 reflection</p></li><li><p>Diffuse and Specular Reflectiondiffusespeculardiffuse+specular</p></li><li><p>Photometric Stereo</p><p>Lecture #9</p></li><li><p>Image Intensity and 3D Geometry</p><p>Shading as a cue for shape reconstructionWhat is the relation between intensity and shape?Reflectance Map</p></li><li><p>Surface Normalsurface normal</p></li><li><p>Surface Normal</p></li><li><p>Gradient Space</p></li><li><p>Reflectance MapRelates image irradiance I(x,y) to surface orientation (p,q) for given source direction and surface reflectanceLambertian case:</p></li><li><p>Lambertian caseReflectance Map</p></li><li><p>Lambertian caseiso-brightnesscontourNote: is maximum whenReflectance Map</p></li><li><p>Glossy surfaces (Torrance-Sparrow reflectance model)diffuse termspecular termReflectance Map</p></li><li><p>Shape 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 surface reflectance) can we determine (p,q) uniquely for each image point?NO</p></li><li><p>SolutionTake more imagesPhotometric stereo</p><p>Add more constraintsShape-from-shading (next class)</p></li><li><p>Photometric Stereo</p></li><li><p>We can write this in matrix form:Image irradiance:Lambertian case:Photometric Stereo</p></li><li><p>Solving the Equations</p></li><li><p>More than Three Light SourcesGet better results by using more lights</p></li><li><p>Color ImagesThe case of RGB imagesget three sets of equations, one per color channel:</p><p>Simple solution: first solve for using one channelThen substitute known into above equations to get</p><p>Or combine three channels and solve for </p></li><li><p>Computing light source directionsTrick: place a chrome sphere in the scene</p><p>the location of the highlight tells you the source direction</p></li><li><p>For a perfect mirror, light is reflected about NSpecular Reflection - RecapWe see a highlight when Then is given as follows:</p></li><li><p>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 3D</p></li><li><p>LimitationsBig problemsDoesnt work for shiny things, semi-translucent thingsShadows, inter-reflections</p><p>Smaller problemsCamera and lights have to be distantCalibration requirementsmeasure light source directions, intensitiescamera response function</p></li><li><p>Trick for Handling ShadowsWeight each equation by the pixel brightness:Gives weighted least-squares matrix equation:Solve for as before</p></li><li><p>Results: Lambertian SphereInput ImagesEstimated AlbedoEstimated Surface NormalsNeedles are projectionsof surface normals on image plane</p></li><li><p>Lambertain Mask</p></li><li><p>Results Albedo and Surface Normal</p></li><li><p>Results: Lambertian ToyInput ImagesEstimated Surface NormalsEstimated AlbedoI.2</p></li><li><p>Depth from NormalsGet a similar equation for V2Each normal gives us two linear constraints on zcompute z values by solving a matrix equation</p></li><li><p>Results Shape of Mask</p></li><li><p>ResultsEstimate light source directionsCompute surface normalsCompute albedo valuesEstimate depth from surface normalsRelight the object (with original texture and uniform albedo)</p></li><li><p>Original Images</p></li><li><p>Results - AlbedoNo Shading Information</p></li><li><p>Results - ShapeShallow reconstruction (effect of interreflections)Accurate reconstruction (after removing interreflections)</p></li><li><p>Next ClassShape from ShadingReading: Horn, Chapter 11.</p><p>******************************************</p></li></ul>