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We propose a set of techniques to efficiently importance sample the derivatives of a wide range of Bidirectional Reflectance Distribution Function (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 58× 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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An Adaptive BRDF Fitting Metric
Abstract We propose a novel image‐driven fitting strategy for isotropic BRDFs. Whereas existing BRDF fitting methods minimize a cost function directly on the error between the fitted analytical BRDF and the measured isotropic BRDF samples, we also take into account the resulting material appearance in visualizations of the BRDF. This change of fitting paradigm improves the appearance reproduction fidelity, especially for analytical BRDF models that lack the expressiveness to reproduce the measured surface reflectance. We formulate BRDF fitting as a two‐stage process that first generates a series of candidate BRDF fits based only on the BRDF error with measured BRDF samples. Next, from these candidates, we select the BRDF fit that minimizes the visual error. We demonstrate qualitatively and quantitatively improved fits for the Cook‐Torrance and GGX microfacet BRDF models. Furthermore, we present an analysis of the BRDF fitting results, and show that the image‐driven isotropic BRDF fits generalize well to other light conditions, and that depending on the measured material, a different weighting of errors with respect to the measured BRDF is necessary.
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- Award ID(s):
- 1909028
- PAR ID:
- 10173616
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Computer Graphics Forum
- Volume:
- 39
- Issue:
- 4
- ISSN:
- 0167-7055
- Page Range / eLocation ID:
- p. 59-74
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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