BRDF s and Relighting Topics in Image Based Modeling and Rendering CSE291 J00 Lecture 12 David Kriegman 2003 CS291 J00 Winter 2003 Environment Matte Basic Assumption Single ray into object single ray out CS291 J00 Winter 2003 David Kriegman 2003 1 Background textures w foreground object Background Textures Note Complex O log k David Kriegman 2003 CS291 J00 Winter 2003 Explanation of R M T A m i i i i 1 Ri Reflectance coefficient M Texture mapping operator for axis aligned rectangle Ai of texture T i CS291 J00 Winter 2003 David Kriegman 2003 2 Environment Matte Example Alpha Matte Environment Matte Photograph David Kriegman 2003 CS291 J00 Winter 2003 A composited object CS291 J00 Winter 2003 David Kriegman 2003 3 BRDF David Kriegman 2003 CS291 J00 Winter 2003 Surface Reflectance Models Common Models Arbitrary Reflectance Lambertian Phong Physics based Specular Blinn 1977 Cook Torrance 1982 Ward 1992 Diffuse Hanrahan Kreuger 1993 Generalized Lambertian Oren Nayar 1995 Thoroughly Pitted Surfaces Non parametric model Anisotropic Non uniform over surface BRDF Measurement Dana et al 1999 Koenderink et al 1999 Phenomenological Koenderink Van Doorn 1996 CS291 J00 Winter 2003 David Kriegman 2003 4 BRDF CS291 J00 Winter 2003 Adapted from DavidSteve Kriegman Marschner 2003 Isotropic BRDF Function of Three variables fr i e e fi i e i e CS291 J00 Winter 2003 Adapted from DavidSteve Kriegman Marschner 2003 5 BSSRDF Bidirectional Subsurface Scattering Reflectance Distribution Function CS291 J00 Winter 2003 Adapted from DavidSteve Kriegman Marschner 2003 Off Specular Reflection CS291 J00 Winter 2003 Adapted from DavidSteve Kriegman Marschner 2003 6 Backscatter Adapted from DavidSteve Kriegman Marschner 2003 CS291 J00 Winter 2003 BRDF CS291 J00 Winter 2003 Adapted from DavidSteve Kriegman Marschner 2003 7 BSSRDF Bidirectional Subsurface Scattering Reflectance Distribution Function Adapted from DavidSteve Kriegman Marschner 2003 CS291 J00 Winter 2003 Materials Conductor Conductor CS291 J00 Winter 2003 Conductor Microgeometry David Kriegman 2003 8 Material Insulator Adapted from DavidSteve Kriegman Marschner 2003 CS291 J00 Winter 2003 Measured BRDFs BRDF cross sections CS291 J00 Winter 2003 Surface microstructure David Kriegman 2003 9 Ward reflectance model A physically realizable variant of the Phong model satisfies energy conservation and reciprocity f i i r r diffuse component d s 1 exp tan2 2 4 2 cos i cos r specular component d proportion of incident radiation reflected diffusely s proportion of incident radiation reflected specularly surface roughness or blur in specular component From David RonKriegman Dror s slides 2003 CS291 J00 Winter 2003 Cook Torrance Model 1982 Diffuse Lambertian and Specular and Fresnel reflection Microfacet model surface is modeled as a collection of parallel symmetric V groves called microfacets facets are large w r t wavelength small w r t pixel size a n da f F i G i r D h 4cos i cos r dA Facet distribution is given by a specific distribution e g Gaussian D kexp m 2 Facets are purely specular CS291 J00 Winter 2003 David Kriegman 2003 10 Geometric Attenuation Masking and Shadowing Geometric Attenuation G 1 L1 L2 Geoemtric A L2 CS291 J00 Winter 2003 Gm 2 N H N V V H Gs 2 N H N L V H L1 David Kriegman 2003 Fresnel Equation for Polished Copper CS291 J00 Winter 2003 David Kriegman 2003 11 Reflectance as Function of Angle of Incidence for Copper Blue Green Red David Kriegman 2003 CS291 J00 Winter 2003 Generalized Lambertian Model Oren Nayar 1994 Like Torrance Sparrow but with Lambertian facets Intensity doesn t fall of as quickly as function of incident illumination CS291 J00 Winter 2003 Rough Cylindrical Clay Vase David Kriegman 2003 12 Velvet A general BRDF Portrait of Sir Thomas More Hans Holbein the Younger 1527 CS291 J00 Winter 2003 After Koenderink et al 1998 David Kriegman 2003 Measuring Isotropic BRDF s CS291 J00 Winter 2003 Adapted from Steve Marschner David Kriegman 2003 13 Image based Marschner Known Geometry of Sample From single image one obtains 2 D slice of BRDF CS291 J00 Winter 2003 Adapted from DavidSteve Kriegman Marschner 2003 Known illumination inverse rendering If one assumes that illumination and surface geometry are known in advance one can recover samples of the BRDF from an image Marschner Sato Ikeuchi CS291 J00 Winter 2003 From David RonKriegman Dror s slides 2003 14 Empirical BRDF s Consider a collection of basis functions bj i i e e Represent an arbitrary BRDF as i i r r w j b j i i r r j Given measurements estimate wj to fit BRDF to data What is a good set of basis functions 1 Product of spherical harmonics 2 Wavelets 3 Zernike polynomials David Kriegman 2003 CS291 J00 Winter 2003 Spherical Harmonics Basri Jacobs 01 Ramamoorthi Hanrahan 01 Y A set of orthonormal basis functions defined first nine harmoncs lm on the unit sphere 1 l Definition of SPHERICAL HARMONICS Y00 0 2821 Y11 Y10 Y1 1 0 4886 x y z l lThe l 0 Yl 1 xzz cos yz xy e x 1 N P 21 Y2 1 Y2 2 y 093 im m lm lm l 2 l m are Y20 0 3154 3 zindices 1 l 0 and l m l N normalization factor lm Y22l 2 0 5462 x 2 y 2 2 m yz xyPl Legendre 3functions z 1 zx CS291 J00 Winter 2003 m 2 m 1 m 0 m 1 x2 y 2 m 2 Borrowed from Ramamoorthi Hanrahan SIGGRAPH 01 David Kriegman 2003 15 Phenomenological BRDF model Zernike Polynomials Koenderink van Doorn Doorn 1996 A problem with spherical harmonics half of sphere should be zero General compact representation defined on disk Preserve Helmholtz Reciprocity Preserve reciprocity isotropy if desired Domain is product of hemispheres Same topology as unit disk adapt basis David Kriegman 2003 CS291 J00 Winter 2003 Zernike Polynomials Optics complete orthogonal basis on unit disk using polynomials of radius Z m n n 1 m Rn e im n m even m n R has terms of degree at least m Even or odd depending on m even or odd Orthonormal using measure d d Cool Demo http wyant opt sci arizona edu zernikes zernikes htm CS291 J00 Winter 2003 David Kriegman 2003 16 m n 0 1 m n 0 2 m n n m must be even m n 1 n m must be even n m must be even n m must be even 2 David Kriegman 2003 CS291 J00 Winter 2003 Relighting 1 Steerable lighting 2 Lambertian Surfaces and linear subspaces 3 Arbitrary BRDF arbitrary lighting CS291 J00 Winter 2003 David Kriegman 2003 17 Superposition of lighting An important point If I1 R S L1 is the image of a scene S under lighting L1 and if I2 R S L2 is the image of a scene S under lighting L2 then the image of the scene under lighting L1 L2 is simply I1 I2 David
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