2023/02/07 by Yuang Cui, Cui, Yuang, Gaole Pan +9 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algorithm #Artificial intelligence #Bidirectional reflectance distribution function #Computer Graphics and Visualization Techniques #Computer science #Computer vision #FOS: Computer and information sciences #Function (biology) #Graphics (cs.GR) #Image (mathematics) #Masking (illustration) #Mathematics #Noise (video) #Optics #Physics #Position (finance) #Probability density function #Reflectivity #Simple (philosophy) #Statistics #Surface Roughness and Optical Measurements
paper · pdf · doi:10.48550/arxiv.2302.03408
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Smith microfacet models are widely used in computer graphics to represent materials. Traditional microfacet models do not consider the multiple bounces on microgeometries, leading to visible energy missing, especially on rough surfaces. Later, as the equivalence between the microfacets and volume has been revealed, random walk solutions have been proposed to introduce multiple bounces, but at the cost of high variance. Recently, the position-free property has been introduced into the multiple-bounce model, resulting in much less noise, but also bias or a complex derivation. In this paper, we propose a simple way to derive the multiple-bounce Smith microfacet bidirectional reflectance distribution functions (BRDFs) using the invariance principle. At the core of our model is a shadowing-masking function for a path consisting of direction collections, rather than separated bounces. Our model ensures unbiasedness and can produce less noise compared to the previous work with equal time, thanks to the simple formulation. Furthermore, we also propose a novel probability density function (PDF) for BRDF multiple importance sampling, which has a better match with the multiple-bounce BRDFs, producing less noise than previous naive approximations.