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）通过简单调节参数即可灵活表示多种材质外观，因而被广泛应用。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切片的部分区域进行采样。此外，许多采样方法需与特定BSDF类型配对使用。本文探索了一种高效且通用的参数化BSDF重要性采样方法。我们发现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参数确定时，对BSDF切片执行重要性采样的映射可被记录为一张二维图像，我们将其命名为重要性图。基于此观察，我们利用称为最优传输的数学工具精确预计算重要性图，随后提出一种轻量级神经网络高效压缩预计算的重要性图。通过这种方式，我们将参数化BSDF重要性采样转移至预计算阶段，避免了运行时的高强度计算。由于该过程类似于预计算一组图像的烘焙流程，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（PDF）查询网络，我们的方法无需修改渲染管线即可实现完整的多重重要性采样（MIS）。本方法本质上实现了完美重要性采样。与现有方法相比，我们在丰富的材质外观渲染结果中展示了更低的噪声水平。