(The Eurographics Association, 2025) Yu, Rui; Sun, Guangzhong; Zhao, Shuang; Dong, Yue; Wang, Beibei; Wilkie, Alexander
We present a theoretical framework for estimating the convergence of Markov-Chain Monte Carlo (MCMC) rendering algorithms. Our theory considers both the variance and the correlation between samples, allowing for quantitative analyses of the convergence properties of MCMC estimators. With our theoretical framework, we devise a Monte Carlo (MC) algorithm capable of accurately estimating the expected MSE of an MCMC rendering algorithm. By adopting an efficient rejection sampling scheme, our MC-based MSE estimator yields a lower standard deviation compared to directly measuring the MSE by running the MCMC rendering algorithm multiple times. Moreover, we demonstrate that modifying the target distribution of the Markov chain by roughening the specular BRDF might lead to faster convergence on some scenarios. This finding suggests that our estimator can serve as a potential guide for selecting the target distribution.