Metropolis Light Transport Research Articles

Temporally Stable Metropolis Light Transport Denoising using Recurrent Transformer Blocks

Metropolis Light Transport (MLT) is a global illumination algorithm that is well-known for rendering challenging scenes with intricate light paths. However, MLT methods tend to produce unpredictable correlation artifacts in images, which can introduce visual inconsistencies for animation rendering. This drawback also makes it challenging to denoise MLT renderings while maintaining temporal stability. We tackle this issue with modern learning-based methods and build a sequence denoiser combining the recurrent connections with the cutting-edge vision transformer architecture. We demonstrate that our sophisticated denoiser can consistently improve the quality and temporal stability of MLT renderings with difficult light paths. Our method is efficient and scalable for complex scene renderings that require high sample counts.

Specular Manifold Bisection Sampling for Caustics Rendering

AbstractWe propose Specular Manifold Bisection Sampling (SMBS), an improved version of Specular Manifold Sampling (SMS) [ZGJ20]. SMBS is inspired by the small and large mutations in Metropolis Light Transport (MLT) [VG97]. While the Jacobian Matrix of the original SMS method performs well in local convergence (the small mutation), it might fail to find a valid manifold path when the ray deviates too much from the light or bounces from a complex surface. Our proposed SMBS method adds a large mutation step to avoid such a problematic convergence to the local minimum. The results show SMBS can find valid manifold paths in fewer iterations and also find more valid manifold paths. In scenes with complex reflective or refractive surfaces, our method achieves nearly twice or more improvement when measured in manifold walk success rate (SR) and root mean square error (RMSE).

Next Event Estimation++: Visibility Mapping for Efficient Light Transport Simulation

AbstractMonte‐Carlo rendering requires determining the visibility between scene points as the most common and compute intense operation to establish paths between camera and light source. Unfortunately, many tests reveal occlusions and the corresponding paths do not contribute to the final image. In this work, we present next event estimation++ (NEE++): a visibility mapping technique to perform visibility tests in a more informed way by caching voxel to voxel visibility probabilities. We show two scenarios: Russian roulette style rejection of visibility tests and direct importance sampling of the visibility. We show applications to next event estimation and light sampling in a uni‐directional path tracer, and light‐subpath sampling in Bi‐Directional Path Tracing. The technique is simple to implement, easy to add to existing rendering systems, and comes at almost no cost, as the required information can be directly extracted from the rendering process itself. It discards up to 80% of visibility tests on average, while reducing variance by ∼20% compared to other state‐of‐the‐art light sampling techniques with the same number of samples. It gracefully handles complex scenes with efficiency similar to Metropolis light transport techniques but with a more uniform convergence.

Delayed Rejection Metropolis Light Transport

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.

Improved multiplexed Metropolis light transport based on fusion mutation strategy

Improved multiplexed Metropolis light transport based on fusion mutation strategy

Precomputed Multiple Scattering for Rapid Light Simulation in Participating Media.

Rendering translucent materials is costly: light transport algorithms need to simulate a large number of scattering events inside the material before reaching convergence. The cost is especially high for materials with a large albedo or a small mean-free-path, where higher-order scattering effects dominate. We present a new method for fast computation of global illumination with participating media. Our method uses precomputed multiple scattering effects, stored in two compact tables. These precomputed multiple scattering tables are easy to integrate with any illumination simulation algorithm. We give examples for virtual ray lights (VRL), photon mapping with beams and paths (UPBP), Metropolis Light Transport with Manifold Exploration (MEMLT). The original algorithms are in charge of low-order scattering, combined with multiple scattering computed using our table. Our results show significant improvements in convergence speed and memory costs, with negligible impact on accuracy.

Geometry-aware metropolis light transport

Markov chain Monte Carlo (MCMC) rendering utilizes a sequence of correlated path samples which is obtained by iteratively mutating the current state to the next. The efficiency of MCMC rendering depends on how well the mutation strategy is designed to adapt to the local structure of the state space. We present a novel MCMC rendering method that automatically adapts the step sizes of the mutations to the geometry of the rendered scene. Our geometry-aware path space perturbation largely avoids tentative samples with zero contribution due to occlusion. Our method limits the mutation step size by estimating the maximum opening angle of a cone, centered around a segment of a light transport path, where no geometry obstructs visibility. This geometry-aware mutation increases the acceptance rates, while not degrading the sampling quality. As this cone estimation introduces a considerable overhead if done naively, to make our approach efficient, we discuss and analyze fast approximate methods for cone angle estimation which utilize the acceleration structure already present for the ray-geometry intersection. Our new approach, integrated into the framework of Metropolis light transport, can achieve results with lower error and less artifact in equal time compared to current path space mutation techniques.

Исследование алгоритма Multiplexed Metropolis Light Transport на графических процессорах

Исследование алгоритма Multiplexed Metropolis Light Transport на графических процессорах

An Improved Multiplexed Metropolis Light Transport Algorithm Based on Variance Filtering

An Improved Multiplexed Metropolis Light Transport Algorithm Based on Variance Filtering

Reversible Jump Metropolis Light Transport Using Inverse Mappings

We study Markov Chain Monte Carlo (MCMC) methods operating in primary sample space and their interactions with multiple sampling techniques. We observe that incorporating the sampling technique into the state of the Markov Chain, as done in Multiplexed Metropolis Light Transport, impedes the ability of the chain to properly explore the path space, as transitions between sampling techniques lead to disruptive alterations of path samples. To address this issue, we reformulate Multiplexed MLT in the Reversible Jump MCMC framework (RJMCMC) and introduce inverse sampling techniques that turn light paths into the random numbers that would produce them. This allows us to formulate a novel perturbation that can locally transition between sampling techniques without changing the geometry of the path, and we derive the correct acceptance probability using RJMCMC. We investigate how to generalize this concept to non-invertible sampling techniques commonly found in practice, and introduce probabilistic inverses that extend our perturbation to cover most sampling methods found in light transport simulations. Our theory reconciles the inverses with RJMCMC yielding an unbiased algorithm, which we call Reversible Jump MLT . We verify the correctness of our implementation in canonical and practical scenarios and demonstrate improved temporal coherence, decrease in structured artifacts, and faster convergence on a wide variety of scenes.

Improved stratification for Metropolis light transport

The approximation error of Monte Carlo methods depends on two factors, how accurately the target density of the samples mimics the integrand and how well the finite number of samples are distributed with the target density. The first factor can be reduced by importance sampling, the second by stratification. The Metropolis algorithm is particularly effective in importance sampling, but is poor concerning stratification if mutation strategies are not carefully designed. This means that although the asymptotic distribution of the samples well mimics most of the factors of the integrand, the empirical distribution of the finite number of samples can be far from the desired distribution. This paper examines this issue and proposes a simple mutation scheme for Primary Sample Space Metropolis Light Transport (PSSMLT), which improves the stratum of samples and thus reduces the integration error. Unlike other approaches, the proposed method does not sacrifice importance sampling for better stratification and uses only the local importance value without requiring derivatives that would be problematic for discontinuous integrands caused by occlusions and texture patterns. The method is simple to implement and to integrate into photo-realistic renderers.

Charted metropolis light transport

In this manuscript, inspired by a simpler reformulation of primary sample space Metropolis light transport, we derive a novel family of general Markov chain Monte Carlo algorithms called charted Metropolis-Hastings , that introduces the notion of sampling charts to extend a given sampling domain and make it easier to sample the desired target distribution and escape from local maxima through coordinate changes. We further apply the novel algorithms to light transport simulation, obtaining a new type of algorithm called charted Metropolis light transport , that can be seen as a bridge between primary sample space and path space Metropolis light transport. The new algorithms require to provide only right inverses of the sampling functions, a property that we believe crucial to make them practical in the context of light transport simulation.

Fusing state spaces for markov chain Monte Carlo rendering

Rendering algorithms using Markov chain Monte Carlo (MCMC) currently build upon two different state spaces. One of them is the path space, where the algorithms operate on the vertices of actual transport paths. The other state space is the primary sample space, where the algorithms operate on sequences of numbers used for generating transport paths. While the two state spaces are related by the sampling procedure of transport paths, all existing MCMC rendering algorithms are designed to work within only one of the state spaces. We propose a first framework which provides a comprehensive connection between the path space and the primary sample space. Using this framework, we can use mutation strategies designed for one space with mutation strategies in the respective other space. As a practical example, we take a combination of manifold exploration and multiplexed Metropolis light transport using our framework. Our results show that the simultaneous use of the two state spaces improves the robustness of MCMC rendering. By combining efficient local exploration in the path space with global jumps in primary sample space, our method achieves more uniform convergence as compared to using only one space.

A Spatial Target Function for Metropolis Photon Tracing

The human visual system is sensitive to relative differences in luminance, but light transport simulation algorithms based on Metropolis sampling often result in a highly nonuniform relative error distribution over the rendered image. Although this issue has previously been addressed in the context of the Metropolis light transport algorithm, our work focuses on Metropolis photon tracing. We present a new target function (TF) for Metropolis photon tracing that ensures good stratification of photons leading to pixel estimates with equalized relative error. We develop a hierarchical scheme for progressive construction of the TF from paths sampled during rendering. In addition to the approach taken in previous work, where the TF is defined in the image plane, ours can be associated with compact spatial regions. This allows us to take advantage of illumination coherence to more robustly estimate the TF while adapting to geometry discontinuities. To sample from this TF, we design a new replica exchange Metropolis scheme. We apply our algorithm in progressive photon mapping and show that it often outperforms alternative approaches in terms of image quality by a large margin.

Memory-compact Metropolis light transport on GPUs

Solutions to the key problems of Metropolis light transport implementation on GPUs are proposed. A "burn-in" method relying on the ordinary Monte Carlo method, owing to which the "startup bias" is significantly reduced, is suggested. Memory optimizations methods (including multiple proposal Metropolis light transport) are proposed, and technical aspects of efficient Metropolis light transport implementation on GPUs are discussed.

A spatial target function for metropolis photon tracing

The human visual system is sensitive to relative differences in luminance, but light transport simulation algorithms based on Metropolis sampling often result in a highly nonuniform relative error distribution over the rendered image. Although this issue has previously been addressed in the context of the Metropolis light transport algorithm, our work focuses on Metropolis photon tracing. We present a new target function (TF) for Metropolis photon tracing that ensures good stratification of photons leading to pixel estimates with equalized relative error. We develop a hierarchical scheme for progressive construction of the TF from paths sampled during rendering. In addition to the approach taken in previous work, where the TF is defined in the image plane, ours can be associated with compact spatial regions. This allows us to take advantage of illumination coherence to more robustly estimate the TF while adapting to geometry discontinuities. To sample from this TF, we design a new replica exchange Metropolis scheme. We apply our algorithm in progressive photon mapping and show that it often outperforms alternative approaches in terms of image quality by a large margin.

Избирательное применение Metropolis Light Transport для трудновычислимых феноменов освещённости

Избирательное применение Metropolis Light Transport для трудновычислимых феноменов освещённости

A Spatial Target Function for Metropolis Photon Tracing

The human visual system is sensitive to relative differences in luminance, but light transport simulation algorithms based on Metropolis sampling often result in a highly nonuniform relative error distribution over the rendered image. Although this issue has previously been addressed in the context of the Metropolis light transport algorithm, our work focuses on Metropolis photon tracing. We present a new target function (TF) for Metropolis photon tracing that ensures good stratification of photons leading to pixel estimates with equalized relative error. We develop a hierarchical scheme for progressive construction of the TF from paths sampled during rendering. In addition to the approach taken in previous work, where the TF is defined in the image plane, ours can be associated with compact spatial regions. This allows us to take advantage of illumination coherence to more robustly estimate the TF while adapting to geometry discontinuities. To sample from this TF, we design a new replica exchange Metropolis scheme. We apply our algorithm in progressive photon mapping and show that it often outperforms alternative approaches in terms of image quality by a large margin.

Исследование масштабируемости распределённых рендер-систем на основе алгоритмов адаптивной трассировки путей и Metropolis Light Transport в гетерогенных сетях

Исследование масштабируемости распределённых рендер-систем на основе алгоритмов адаптивной трассировки путей и Metropolis Light Transport в гетерогенных сетях

Anisotropic Gaussian mutations for metropolis light transport through Hessian-Hamiltonian dynamics

The simulation of light transport in the presence of multi-bounce glossy effects and motion is challenging because the integrand is high dimensional and areas of high-contribution tend to be narrow and hard to sample. We present a Markov Chain Monte Carlo (MCMC) rendering algorithm that extends Metropolis Light Transport by automatically and explicitly adapting to the local shape of the integrand, thereby increasing the acceptance rate. Our algorithm characterizes the local behavior of throughput in path space using its gradient as well as its Hessian. In particular, the Hessian is able to capture the strong anisotropy of the integrand. We obtain the derivatives using automatic differentiation, which makes our solution general and easy to extend to additional sampling dimensions such as time. However, the resulting second order Taylor expansion is not a proper distribution and cannot be used directly for importance sampling. Instead, we use ideas from Hamiltonian Monte-Carlo and simulate the Hamiltonian dynamics in a flipped version of the Taylor expansion where gravity pulls particles towards the high-contribution region. Whereas such methods usually require numerical integration, we show that our quadratic landscape leads to a closed-form anisotropic Gaussian distribution for the final particle positions, and it results in a standard Metropolis-Hastings algorithm. Our method excels at rendering glossy-to-glossy reflections on small and highly curved surfaces. Furthermore, unlike previous work that derives sampling anisotropy with pen and paper and only considers specific effects such as specular BSDFs, we characterize the local shape of throughput through automatic differentiation. This makes our approach very general. In particular, our method is the first MCMC rendering algorithm that is able to resolve the anisotropy in the time dimension and render difficult moving caustics.