Parametric Bidirectional Scattering Distribution Functions (BSDFs) are pervasively used because of their flexibility to represent a large variety of material appearances by simply tuning the parameters. While efficient evaluation of parametric BSDFs has been well-studied, high-quality importance sampling techniques for parametric BSDFs are still scarce. Existing sampling strategies either heavily rely on approximations, resulting in high variance, or solely perform sampling on a portion of the whole BSDF slice. Moreover, many of the sampling approaches are specifically paired with certain types of BSDFs. In this paper, we seek an efficient and general way for importance sampling parametric BSDFs. We notice that the nature of importance sampling is the mapping between a uniform distribution and the target distribution. Specifically, when BSDF parameters are given, the mapping that performs importance sampling on a BSDF slice can be simply recorded as a 2D image that we name as importance map. Following this observation, we accurately precompute the importance maps using a mathematical tool named optimal transport. Then we propose a lightweight neural network to efficiently compress the precomputed importance maps. In this way, we have brought parametric BSDF important sampling to the precomputation stage, avoiding heavy runtime computation. Since this process is similar to light baking where a set of images are precomputed, we name our method importance baking. Together with a BSDF evaluation network and a PDF (probability density function) query network, our method enables full multiple importance sampling (MIS) without any revision to the rendering pipeline. Our method essentially performs perfect importance sampling. Compared with previous methods, we demonstrate reduced noise levels on rendering results with a rich set of appearances.

翻译：参数化双向散射分布函数（BSDF）因其仅需调节参数即可灵活表示多种材质外观而被广泛应用。尽管参数化BSDF的高效求值已得到充分研究，但其高质量重要性采样技术仍较为稀缺。现有采样策略要么严重依赖近似方法导致高方差，要么仅对BSDF切面的部分区域进行采样。此外，许多采样方法专门与特定类型的BSDF配对。本文旨在寻找一种高效且通用的参数化BSDF重要性采样方法。我们注意到重要性采样的本质是均匀分布与目标分布之间的映射。具体而言，当BSDF参数给定时，对BSDF切面进行重要性采样的映射可简单记录为二维图像（我们称之为重要性图）。基于此观察，我们利用最优传输这一数学工具精确预计算重要性图，随后提出轻量级神经网络高效压缩预计算的重要性图。由此将参数化BSDF重要性采样迁移至预计算阶段，避免运行时大量计算。由于该过程类似于预先计算一组图像的轻量级烘焙技术，我们将此方法命名为重要性烘焙。结合BSDF求值网络与概率密度函数查询网络，本方法无需修改渲染管线即可实现完整的多重重要性采样。我们的方法本质上实现了完美重要性采样。相较于先前方法，我们在涵盖丰富材质外观的渲染结果中验证了噪声水平的显著降低。