Multiple-bounce Smith Microfacet BRDFs using the Invariance Principle

TL;DR

This paper introduces a novel, unbiased multiple-bounce Smith microfacet BRDF model using the invariance principle, reducing noise and bias in rendering rough surfaces compared to previous methods.

Contribution

It presents a simple derivation of multiple-bounce BRDFs with the invariance principle, ensuring unbiasedness and improved noise performance, along with a new PDF for better importance sampling.

Findings

The proposed model produces less noise than previous methods.

It maintains unbiasedness while simplifying the derivation.

The new PDF improves importance sampling accuracy.

Abstract

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.