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Measuring Material Appearance: BRDF, BSSRDF, BTFThanks to Steve Marschner, Shree Nayar, Ravi Ramamoorthi, Szymon Rusinkiewicz, Marc Levoy, Pat Hanrahan, Kristin Dana, Ken Perlin, Debevec, MatusikComputer Graphics, Fall 2009Mohit GuptaImages Courtest Ben-Ezra et alA variety of material appearancesMethods Relying on Surface ReflectanceShape from ShadingPhotometric StereoReflection SeparationTexture ModelingsourcesurfacereflectionsurfaceincidentdirectionbodyreflectionBody Reflection:Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etcSurface Reflection:Specular ReflectionGlossy AppearanceHighlightsDominant for MetalsImage Intensity = Body Reflection + Surface ReflectionMechanisms of ReflectionBody Reflection:Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etcSurface Reflection:Specular ReflectionGlossy AppearanceHighlightsDominant for MetalsMany materials exhibit both Reflections:Mechanisms of ReflectionImage intensities = f ( normal, surface reflectance, illumination )Surface Reflection depends on both the viewing and illumination directions.sourcesensorsurfaceelementnormalSurface Appearancexyzsourceviewingdirectionsurfaceelementnormalincidentdirection),(ii),(rr),(iisurfaceE),(rrsurfaceLIrradiance at Surface in direction ),(iiRadiance of Surface in direction ),(rrBRDF :),(),(),;,(iisurfacerrsurfacerriiELfBRDF: Bidirectional Reflectance Distribution FunctionDerivation of the Scene Radiance Equation),(iisrcL),(rrsurfaceL),;,(),(),(rriiiisurfacerrsurfacefELFrom the definition of BRDF:Important Properties of BRDFsxyzsourceviewingdirectionsurfaceelementnormalincidentdirection),(ii),(rrBRDF is only a function of 3 variables :),;,(),;,(iirrrriiff• Rotational Symmetry:BRDF does not change when surface is rotated about the normal. ),,(ririf• Helmholtz Reciprocity: (follows from 2ndLaw of Thermodynamics)BRDF does not change when source and viewing directions are swapped.Specular Reflection and Mirror BRDFsource intensity Iviewingdirectionsurfaceelementnormalincidentdirectionnvsrspecular/mirrordirection),(ii),(vv),(rr• Mirror BRDF is simply a double-delta function :• Very smooth surface.• All incident light energy reflected in a SINGLE direction. (only when = )• Surface Radiance :)()(vivisILvr)()(),;,(vivisvviifspecular albedoSpecular Reflections in NatureCompare sizes of objects and their reflections!The reflections when seen from a lower viewpoint are always longer than when viewedfrom a higher view point.It's surprising how long the reflections are when viewed sitting on the river bank.Specular Reflections in NatureDiffuse Reflection and Lambertian BRDFviewingdirectionsurfaceelementnormalincidentdirectioninvsdrriif ),;,(• Lambertian BRDF is simply a constant :albedo• Surface appears equally bright from ALL directions! (independent of )• Surface Radiance :v• Commonly used in Vision and Graphics!snIILdid.cossource intensitysource intensity IDiffuse Reflection and Lambertian BRDFWhite-out Conditions from an Overcast Sky CAN’T perceive the shape of the snow covered terrain!Modeling Rough Surfaces - Microfacets•Roughness simulated by Symmetric V-groves at Microscopic level.•Distribution on the slopes of the V-grove faces are modeled.•Each microfacet assumed to behave like a perfect lambertian surface.View Dependence of Matte Surfaces - Key Observation• Overall brightness increases as the angle between the source and viewing direction decreases. WHY?• Pixels have finite areas. As the viewing direction changes, different mixes between dark and bright are added up to give pixel brightness.Slope Distribution Model• Model the distribution of slopes as Gaussian.• Mean is Zero, Variance represents ROUGHNESS.Oren-Nayar Model – Different Factors (contd.)• Take into account two light bounces (reflections).• Hard to solve analytically, so they find a functional approximation.Oren-Nayar Model – Final ExpressionLambertian model is simply an extreme case with roughness equal to zero.Surface Roughness Causes Flat AppearanceActual Vase Lambertian VaseSurface Roughness Causes Flat Appearance Increasing surface roughnessLambertian modelValid for only SMOOTH MATTE surfaces.Bad for ROUGH MATTE surfaces.Rendered Sphere with Lambertian BRDF• Edges are dark (N.S = 0) when lit head-on• See shading effects clearly.Why does the Full Moon have a flat appearance? • The moon appears matte (or diffuse)• But still, edges of the moon look bright(not close to zero) when illuminated byearth’s radiance.Why does the Full Moon have a flat appearance? Lambertian Spheres and Moon Photos illuminated similarlyOren-Nayar Model – Main Points•Physically Based Model for Diffuse Reflection.•Explains view dependent appearance in Matte Surfaces•Lambertian model is simply an extreme case withroughness equal to zero.Comparison to Ground Truth• Delta Function too harsh a BRDF model (valid only for highly polished mirrors and metals).• Many glossy surfaces show broader highlights in addition to mirror reflection.• Surfaces are not perfectly smooth – they show micro-surface geometry (roughness).• Example Models : Phong modelTorrance Sparrow modelGlossy SurfacesBlurred Highlights and Surface RoughnessRoughnessPhong Model: An Empirical Approximation• How to model the angular falloff of highlights:Phong Model• Sort of works, easy to compute• But not physically based (no energy conservation and reciprocity).• Very commonly used in computer graphics.shinynsERIL ).(-SRVNPhong Examples• These spheres illustrate the Phong model as lighting direction and nshinyare varied:Those Were the Days• “In trying to improve the quality of the synthetic images, we do not expect to be able to display the object exactly as it would appear in reality, with texture, overcast shadows, etc. We hope only to display an image that approximates the real object closely enough to provide a certain degree of realism.”– Bui Tuong Phong, 1975Summary of Surfaces and BRDFsSmoothRoughDiffuseSpecularMirror BRDFTorrance-Sparrow BRDFLambertian BRDFOren-Nayar BRDFNo view dependenceModels view
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