“Homomorphic factorization of BRDFs for high-performance rendering” by McCool, Ang and Ahmad

A bidirectional reflectance distribution function (BRDF) describes how a material reflects light from its surface. To use arbitrary BRDFs in real-time rendering, a compression technique must be used to represent BRDFs using the available texture-mapping and computational capabilities of an accelerated graphics pipeline. We present a numerical technique, homomorphic factorization, that can decompose arbitrary BRDFs into products of two or more factors of lower dimensionality, each factor dependent on a different interpolated geometric parameter. Compared to an earlier factorization technique based on the singular value decomposition, this new technique generates a factorization with only positive factors (which makes it more suitable for current graphics hardware accelerators), provides control over the smoothness of the result, minimizes relative rather than absolute error, and can deal with scattered, sparse data without a separate resampling and interpolation algorithm.

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