Representation
A real material’s surface reflectance function is a very complex function of 16 variables. It is currently unfeasible to measure or to mathematically model such a function. Practical applications thus require its simplification, namely, using additional a
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Representation
Abstract A real material’s surface reflectance function is a very complex function of 16 variables. It is currently unfeasible to measure or to mathematically model such a function. Practical applications thus require its simplification, namely, using additional assumptions. The general reflectance functions can primarily be categorized within the frameworks of textured models and homogeneous models. This chapter describes taxonomy of both of these representation subgroups, their mutual relationships, advantages, and drawbacks.
2.1 General Reflectance Function A real material’s surface reflectance (Fig. 2.1) is a very complex physical phenomenon, which, among other considerations, intricately depends on incident and reflected spherical angles, time, and light spectrum. The reflectance thus provides a rich source of information regarding any material’s surface. If we know the general reflectance function, we cannot only precisely predict how any material will appear under any possible illumination intensity, direction or spectrum, but we can also accurately recognize any such material on the basis of the visual scene’s lighting conditions. The general reflectance function (GRF) has 16 dimensions (16D): YrGRF = GRF(λi , xi , yi , zi , ti , θi , ϕi , λv , xv , yv , zv , tv , θv , ϕv , θt , ϕt ),
(2.1)
where r = [r1 , . . . , r16 ] is the multi-index with corresponding partial indices. All possible values of the index will be denoted by •, e.g., a color input spectrum in the RGB space Y•,r2 ,...,r16 = [YR,r2 ,...,r16 , YG,r2 ,...,r16 , YB,r2 ,...,r16 ] and the missing index by ∅, e.g., a monospectral input Y∅,r2 ,...,r16 . The GRF domain (for a pixel) is the d-vector space (YrGRF ∈ R d ) where the dimensionality d depends on the GRF type, i.e., YrSVBRDF , YrBTF are three-dimensional (d = 3) in the RGB representation, while YrBRTTF is six-dimensional in the same representation. GRF describes the incident light with spectral value λi ; illuminating surface location xi , yi , zi in time ti ; under spherical incidence angles ωi = [θi , ϕi ] and observed at time tv from surface location xv , yv , zv under spherical reflectance angles ωv = [θv , ϕv ] and spectrum λv ; here ωt = [θt , ϕt ] are the corresponding transmittance angles where ω = [θ, ϕ] are the elevation and azimuthal angles, respectively. M. Haindl, J. Filip, Visual Texture, Advances in Computer Vision and Pattern Recognition, DOI 10.1007/978-1-4471-4902-6_2, © Springer-Verlag London 2013
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Fig. 2.1 General reflectance model
The model height parameters zi , zv indicate that radiance along light rays is not constant but depends on the height. The GRF function (2.1) is too complex to be accurately measured or modeled, hence some simplifying assumptions are inevitable in any practical application. The taxonomy of simplifying assumptions can be divided into two subgroups based on the possibility of neglecting a surface texture. A visual texture is a resolution-based relative notion. Any natural surface material is texture
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