Delayed Rejection Metropolis Light Transport

Abstract

Designing robust mutation strategies for primary sample space Metropolis light transport is a challenging problem: poorly tuned mutations both hinder state space exploration and introduce structured image artifacts. Scenes with complex materials, lighting, and geometry make hand-designing strategies that remain optimal over the entire state space infeasible. Moreover, these difficult regions are often sparse in state space, and so relying exclusively on intricate—and often expensive—proposal mechanisms can be wasteful, whereas simpler inexpensive mechanisms are more sample efficient. We generalize Metropolis–Hastings light transport to employ a flexible two-stage mutation strategy based on delayed rejection Markov chain Monte Carlo. Our approach generates multiple proposals based on the failure of previous ones, all while preserving Markov chain ergodicity. This allows us to reduce error while maintaining fast global exploration and low correlation across chains. Direct application of delayed rejection to light transport leads to low acceptance probabilities, and so we also propose a novel transition kernel to alleviate this issue. We benchmark our approach on several applications including bold-then-timid and cheap-then-expensive proposals across different light transport algorithms. Our method is applicable to any primary sample space algorithm with minimal implementation effort, producing consistently better results on a variety of challenging scenes.

Ensemble Metropolis Light Transport

“…[Kelemen et al 2002] introduced mutations to light paths in PSS (PSSMLT). These mutations were improved by [Hachisuka et al 2014] who combined PSSMLT with Multiple Importance Sampling [Veach and Guibas 1995], [Bitterli and Jarosz 2019] who detected and perturbed high variance paths in PSS, the use of delayed rejection by [Rioux-Lavoie et al 2020], the use of Hamiltonian Monte Carlo applied to rendering by [Li et al 2015] who used anisotropic Gaussian kernels generated from a path gradient, and [Luan et al 2020] who used the Metropolis-adjusted Langevin algorithm also based on the gradients of the path. Integration in both path space and PSS have been proposed [Bitterli et al 2018;Otsu et al 2017;Pantaleoni 2017] which allows path space mutations to be combined with PSS mutations.…”

“…Perturbation strategies such as Manifold Perturbations Marschner 2012], Multiple Try Metropolis [Nimier-David et al 2019;Segovia et al 2007], selectively choosing paths to perturb [Bitterli and Jarosz 2019] and Delayed Rejection MLT [Rioux-Lavoie et al 2020] could all be combined with our approach into a larger set of possible strategies. Manifold perturbations are especially effective at locally perturbing specular paths, thus complementary to our approach which perturbs paths in a wider region.…”

The current state of the methods for calculating global illumination in tasks of realistic computer graphics

“…The numbered rectangles in the upper left figure denote the image areas shown in Fig. 15 Мы полагаем, что для сложного освещения наиболее эффективными могут быть признаны методы на основе современных работ: VCM и аналоги [24,25,27], HMC [94,96,102], MMLT [78,84], RJMLT [88][89][90]…”

“…Таким образом, за последние 10 лет появилось много новых расчётных методов, и некоторые из них можно считать чрезвычайно интересными в плане эффективности решения фудаментально трудной задачи. Заявка, сделанная методами на основе HMC [94,96,102], выглядит многообещающе. В этом смысле по сравнению с 2010 годом в науке расчёта глобального освещения произошёл настоящий прорыв.…”

Unbiased warped-area sampling for differentiable rendering

“…In light transport simulation, derivatives with respect to light path parameters are often used by rendering algorithms to guide sampling and reconstruction [Arvo 1994;Chen and Arvo 2000;Mitchell and Hanrahan 1992;Ramamoorthi et al 2007;Shinya et al 1987;Ward and Heckbert 1992;Wu et al 2020]. In more recent work, derivatives are used in Markov chain Monte Carlo algorithms for guiding the mutation [Hanika et al 2015;Jakob and Marschner 2012;Kaplanyan et al 2014;Li et al 2015;Luan et al 2020;Rioux-Lavoie et al 2020]. In contrast, we are interested in computing derivatives of light transport contributions with respect to arbitrary parameters, including scene parameters such as camera pose and triangle vertex positions.…”