Importance Sampling BRDF Derivatives
We propose a set of techniques to efficiently importance sample the derivatives of several BRDF models. In differentiable rendering, BRDFs are replaced by their differential BRDF counterparts which are real-valued and can have negative values. This leads to a new source of variance arising from thei...
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Zusammenfassung: | We propose a set of techniques to efficiently importance sample the
derivatives of several BRDF models. In differentiable rendering, BRDFs are
replaced by their differential BRDF counterparts which are real-valued and can
have negative values. This leads to a new source of variance arising from their
change in sign. Real-valued functions cannot be perfectly importance sampled by
a positive-valued PDF and the direct application of BRDF sampling leads to high
variance. Previous attempts at antithetic sampling only addressed the
derivative with the roughness parameter of isotropic microfacet BRDFs. Our work
generalizes BRDF derivative sampling to anisotropic microfacet models, mixture
BRDFs, Oren-Nayar, Hanrahan-Krueger, among other analytic BRDFs.
Our method first decomposes the real-valued differential BRDF into a sum of
single-signed functions, eliminating variance from a change in sign. Next, we
importance sample each of the resulting single-signed functions separately. The
first decomposition, positivization, partitions the real-valued function based
on its sign, and is effective at variance reduction when applicable. However,
it requires analytic knowledge of the roots of the differential BRDF, and for
it to be analytically integrable too. Our key insight is that the single-signed
functions can have overlapping support, which significantly broadens the ways
we can decompose a real-valued function. Our product and mixture decompositions
exploit this property, and they allow us to support several BRDF derivatives
that positivization could not handle. For a wide variety of BRDF derivatives,
our method significantly reduces the variance (up to 58x in some cases) at
equal computation cost and enables better recovery of spatially varying
textures through gradient-descent-based inverse rendering. |
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DOI: | 10.48550/arxiv.2304.04088 |