Computational VisionU. Minn. Psy 5036Daniel KerstenLecture 20: Surface MaterialInitialize‡Spell check offIn[1]:=Off@General::spell1D;<< VectorFieldPlots`In[3]:=SetOptions@ArrayPlot, ColorFunction Ø "GrayTones", DataReversed Ø True,Frame Ø False, AspectRatio Ø Automatic, Mesh Ø False,PixelConstrained Ø True, ImageSize Ø SmallD;SetOptions@ListPlot, ImageSize Ø SmallD;SetOptions@Plot, ImageSize Ø SmallD;SetOptions@DensityPlot, ImageSize Ø Small, ColorFunction Ø GrayLevelD;nbinfo = NotebookInformation@EvaluationNotebook@DD;dir =H"FileName" ê. nbinfo ê. FrontEnd`FileName@d_List, nam_, ___D ßToFileName@dDL;OutlineLast time‡Local measurementsRepresenting motion, Orientation in space-timeFourier representation and samplingOptic flow, the gradient constraint, aperture problemNeural systems solutions to the problem of motion measurement.Space-time oriented receptive fields‡Global integrationSketched a Bayesian formulation--the integrating uncertain local measurements with the right priors can be used to model a variety of human motion results. TodayLater, we'll pick up on motion again--namely structure from motion in the context of determining layout and computing headingToday, surface material:Surface properties, color, transparency, etc..Reflectance & lightness constancyTransparencyCooperative computation2 20.SurfaceMaterial.nbIntroduction to material perceptionMaterial & Texture modelingGeneral categories of the "stuff" we see: surfaces (opaque and transparent), particle clouds (e.g. smoke, mist,..), liquids, hair, fur,...Connection with count vs. mass nouns.Reseearch in computer graphics has provided major progress in the characterization of real surfaces, but realism is still a challenge.Uniform materialsSurfaces with material properties or attributes:reflectance ("paint" or pigment or albedo)matte and shinymirrorstransparencymultiplicative, additive20.SurfaceMaterial.nb 3‡Physics-based generative modeling: Bidirectional reflectance distribution functionsFigure from: Image-Based BRDF Measurement Including Human Skin Stephen R. Marschner* Stephen H. Westin Eric P. F. Lafortune, Kenneth E. Torrance Donald P. GreenbergThe Bidirectional Reflectance Distribution Function (BRDF) describes direc-tional dependence of the reflected light energy. The BRDF represents, for each incoming angle, the amount of light that is scattered in each outgoing angle. For a given wavelength, it is the ratio of the reflected radiance in a particular direction to the incident irradiance:r(qi,fi,qe,fe)=dLeH,qe,feLdEiHqi,fiLwhere E is the irradiance, that is the incident flux per unit area (w-m-2), and L is the reflected radiance, or the reflected flux per unit area per unit solid angle (w-m-2-sr-1). The units of BRDF are inverse steradians. Respects the physics: Reciprocity, energy conservation.We've assumed isotropy, i.e. the BRDF is the same for all directions at a point, and spatially uniform material. For a Lambertian (perfectly diffuse) surface, for example, the BRDF is con-stant. The Phong model described earlier can approximate only a subset of surfaces characterized by BRDFs.4 20.SurfaceMaterial.nbwhere E is the irradiance, that is the incident flux per unit area (w-m-2), and L is the reflected radiance, or the reflected flux per unit area per unit solid angle (w-m-2-sr-1). The units of BRDF are inverse steradians. Respects the physics: Reciprocity, energy conservation.We've assumed isotropy, i.e. the BRDF is the same for all directions at a point, and spatially uniform material. For a Lambertian (perfectly diffuse) surface, for example, the BRDF is con-stant. The Phong model described earlier can approximate only a subset of surfaces characterized by BRDFs.Figure from: http://graphics.stanford.EDU/~smr/brdf/bv/‡Ward reflection model: For calculating an image from a description of the shape, the illumination, and the BRDFThe Ward model is a physically realizable cousin of the Phong model.Le(qe,fe)=ŸŸLi(qi,fi)r(qi,fi,qe,fe)cosqisinfidqidfir(qi,fi,qe,fe)=rdp+rse-tan2HdLëa24 pa2 cosqi cosqe20.SurfaceMaterial.nb 5d is the angle between the viewer and the vector defining the mirror reflection of the incident ray (i.e. where the angle of reflection equals the angle of incidence). a can be thought of is a measure of "roughness", and rd and rsgive the amounts of diffuse to reflected contributions.‡Other linkshttp://www.cs.princeton.edu/~smr/cs348c-97/surveypaper.htmlhttp://www.nps.navy.mil/cs/sullivan/MV4470/resources/BRDFIntro.pdfhttp://www.ciks.nist.gov/appmain.htmhttp://www.graphics.cornell.edu/research/measure/For examples using BRDF measurements of human skin see:http://www.graphics.cornell.edu/online/measurements/Textured materialsNote: "texture" sometimes refers to low-level cues or statistics useful for inferring properties like slant and shape, but it is also used to refer to surface material properties that are useful to estimate because they represent view-invariant object properties. In other words, sometimes it refers to a cue (measurement to support an estimate) and other times to an esti-mate itself. Thus, sometimes "texture" refers to an image features, and other times to 3D surface properties.In this lecture, we focus on texture as a material property.Textures can be:regular ("herringbone pattern") or stochastic ("fur")"coherence" e.g. sand & gravel, vs. asphaltTextures can be due to:reflectance/pigment variations or bump (small geometric) variationsperceptually it isn't always easy to tell the difference, and may not matter depending on visual function.(Note that image texture can also result from a completely uniform (shiny) material reflecting a textured environment)6 20.SurfaceMaterial.nbTextures can be:regular ("herringbone pattern") or stochastic ("fur")"coherence" e.g. sand & gravel, vs. asphaltTextures can be due to:reflectance/pigment variations or bump (small geometric) variationsperceptually it isn't always easy to tell the difference, and may not matter depending on visual function.(Note that image texture can also result from a completely uniform (shiny) material reflecting a textured environment)Key ideas: spatial variations are small with respect to the global scale of the surface structurespatial homogeneity‡Appearance-based measurementsHow can one characterize the generative model? Much more complicated because of small-, but not micro-scale surface non-uniformity.http://www1.cs.columbia.edu/CAVE/projects/btf/‡Random synthesis and