Regional Adaptive Metropolis Light Transport

TL;DR

This work tackles the sensitivity of MCMC rendering performance to kernel parameters by introducing regional adaptive path perturbations for Metropolis Light Transport. By partitioning the path space into low-dimensional regions in a canonical space and updating per-region mutation sizes, the method achieves state-dependent proposals via lens and multi-chain perturbations, with adaptive quadtree refinement to focus updates where needed. The approach outperforms fixed and globally adaptive kernels on several scenes, demonstrating reduced sampling correlation and better detail capture. Its plug-in nature and reliance on information from the sampling process make it a practically impactful enhancement for existing MLT renderers.

Abstract

The design of the proposal distributions, and most notably the kernel parameters, are crucial for the performance of Markov chain Monte Carlo (MCMC) rendering. A poor selection of parameters can increase the correlation of the Markov chain and result in bad rendering performance. We approach this problem by a novel path perturbation strategy for online-learning of state-dependent kernel parameters. We base our approach on the theoretical framework of regional adaptive MCMC which enables the adaptation of parameters depending on the region of the state space which contains the current sample, and on information collected from previous samples. For this, we define a partitioning of the path space on a low-dimensional canonical space to capture the characteristics of paths, with a focus on path segments closer to the sensor. Fast convergence is achieved by adaptive refinement of the partitions. Exemplarily, we present two novel regional adaptive path perturbation techniques akin to lens and multi-chain perturbations. Our approach can easily be used on top of existing path space MLT methods to improve rendering efficiency, while being agnostic to the initial choice of kernel parameters.

Figures (11)

• Figure 1: Path perturbations based on bidirectional path sampling (lens and multi-chain perturbations). The proposal process first splits the current path into the eye and light subpaths. Each subpath is perturbed by their respective transition kernels. The final proposal is generated by reconnecting the perturbed subpaths. The lens perturbation is moving the outgoing direction at $\boldsymbol{y}_1$, indicated with an orange lobe, and the multi-chain perturbation additionally mutates the outgoing direction at $\boldsymbol{y}_3$. The path is propagated deterministically through the specular interactions at $\boldsymbol{y}_2$ and $\boldsymbol{y}_4$, respectively.
• Figure 2: Path space partitioning for lens and multi-chain perturbations. For the lens perturbation, we use a 2d partition in screen space. For the multi-chain perturbation, we use a 4d partition in screen space and the ray direction from the first non-specular vertex from the camera.
• Figure 3: Grid and quadtree partitioning applied to the 2d canonical space $\mathcal{S}=\left[0,1\right]^{2}$. The grid partition split the space into the region with uniform sizes. On the other hand, quadtree partition slipts the space into the regions with different sizes.
• Figure 4: Refinement of quadtree partition. For each leaf node, it determines whether it is split or not according to the criterion based on the number of visit of the region.
• Figure 5: The plot on the left shows the error with different grid sizes used for partitioning for the regional adaptive multi-chain perturbation (Fireplace Room scene). We use the 4d partitioning with the same parameter $N$ for both top and bottom level grids corresponding to primary and secondary ray directions. We can observe that results with too small as well as too large grid sizes are suboptimal.