Bidirectional Path Tracing Research Articles

Two‐stage Resampling for Bidirectional Path Tracing with Multiple Light Sub‐paths

AbstractRecent advances in bidirectional path tracing (BPT) reveal that the use of multiple light sub‐paths and the resampling of a small number of these can improve the efficiency of BPT. By increasing the number of pre‐sampled light sub‐paths, the possibility of generating light paths that provide large contributions can be better explored and this can alleviate the correlation of light paths due to the reuse of pre‐sampled light sub‐paths by all eye sub‐paths. The increased number of pre‐sampled light subpaths, however, also incurs a high computational cost. In this paper, we propose a two‐stage resampling method for BPT to efficiently handle a large number of pre‐sampled light sub‐paths. We also derive a weighting function that can treat the changes in path probability due to the two‐stage resampling. Our method can handle a two orders of magnitude larger number of presampled light sub‐paths than previous methods in equal‐time rendering, resulting in stable and better noise reduction than state‐of‐the‐art methods.

Resampling-aware Weighting Functions for Bidirectional Path Tracing Using Multiple Light Sub-Paths

Bidirectional path tracing (BPT) with multiple importance sampling (MIS) is a popular technique for rendering realistic images. Recently, it has been shown that BPT can be improved by preparing multiple light sub-paths and by resampling a small number of light sub-paths from them to generate full paths with large contribution. Traditionally, for MIS weights, the balance heuristic has widely been used to minimize the upper bound of variance, where each full path is weighted in proportion to the probability of the path. Although the probability of the path can change due to the resampling process, the weighting functions used in the previous methods remain unaffected by the change in probability, resulting in less efficiency. To address this problem, we propose new weighting functions for BPT with multiple light sub-paths. Our main contribution is a precise formulation of the variance and the derivation of the weighting functions that can appropriately treat the change in probability. We demonstrate that our weighting functions significantly improve the image quality. We will release a simple version of our implementation as open source to ensure reproducibility.

Calculation of MIS weights for bidirectional path tracing with photon maps in presence of direct illumination

Calculation of MIS weights for bidirectional path tracing with photon maps in presence of direct illumination

Selectively metropolised Monte Carlo light transport simulation

Light transport is a complex problem with many solutions. Practitioners are now faced with the difficult task of choosing which rendering algorithm to use for any given scene. Simple Monte Carlo methods, such as path tracing, work well for the majority of lighting scenarios, but introduce excessive variance when they encounter transport they cannot sample (such as caustics). More sophisticated rendering algorithms, such as bidirectional path tracing, handle a larger class of light transport robustly, but have a high computational overhead that makes them inefficient for scenes that are not dominated by difficult transport. The underlying problem is that rendering algorithms can only be executed indiscriminately on all transport, even though they may only offer improvement for a subset of paths. In this paper, we introduce a new scheme for selectively combining different Monte Carlo rendering algorithms. We use a simple transport method (e.g. path tracing) as the base, and treat high variance "fireflies" as seeds for a Markov chain that locally uses a Metropolised version of a more sophisticated transport method for exploration, removing the firefly in an unbiased manner. We use a weighting scheme inspired by multiple importance sampling to partition the integrand into regions the base method can sample well and those it cannot, and only use Metropolis for the latter. This constrains the Markov chain to paths where it offers improvement, and keeps it away from regions already handled well by the base estimator. Combined with stratified initialization, short chain lengths and careful allocation of samples, this vastly reduces non-uniform noise and temporal flickering artifacts normally encountered with a global application of Metropolis methods. Through careful design choices, we ensure our algorithm never performs much worse than the base estimator alone, and usually performs significantly better, thereby reducing the need to experiment with different algorithms for each scene.

Hierarchical russian roulette for vertex connections

While bidirectional path tracing is a well-established light transport algorithm, many samples are required to obtain high-quality results for specular-diffuse-glossy or glossy-diffuse-glossy reflections especially when they are highly glossy. To improve the efficiency for such light path configurations, we propose a hierarchical Russian roulette technique for vertex connections. Our technique accelerates a huge number of Russian roulette operations according to an approximate scattering lobe at an eye-subpath vertex for many cached light-subpath vertices. Our method dramatically reduces the number of random number generations needed for Russian roulette by introducing a hierarchical rejection algorithm which assigns random numbers in a top-down fashion. To efficiently reject light vertices in each hierarchy, we also introduce an efficient approximation of anisotropic scattering lobes used for the probability of Russian roulette. Our technique is easy to integrate into some existing bidirectional path tracing-based algorithms which cache light-subpath vertices (e.g., probabilistic connections, and vertex connection and merging). In addition, unlike existing many-light methods, our method does not restrict multiple importance sampling strategies thanks to the simplicity of Russian roulette. Although the proposed technique does not support perfectly specular surfaces, it significantly improves the efficiency for caustics reflected on extremely glossy surfaces in an unbiased fashion.

A Survey on Gradient‐Domain Rendering

AbstractMonte Carlo methods for physically‐based light transport simulation are broadly adopted in the feature film production, animation and visual effects industries. These methods, however, often result in noisy images and have slow convergence. As such, improving the convergence of Monte Carlo rendering remains an important open problem. Gradient‐domain light transport is a recent family of techniques that can accelerate Monte Carlo rendering by up to an order of magnitude, leveraging a gradient‐based estimation and a reformulation of the rendering problem as an image reconstruction. This state of the art report comprehensively frames the fundamentals of gradient‐domain rendering, as well as the pragmatic details behind practical gradient‐domain uniand bidirectional path tracing and photon density estimation algorithms. Moreover, we discuss the various image reconstruction schemes that are crucial to accurate and stable gradient‐domain rendering. Finally, we benchmark various gradient‐domain techniques against the state‐of‐the‐art in denoising methods before discussing open problems.

RenderMan

Pixar’s RenderMan renderer is used to render all of Pixar’s films and by many film studios to render visual effects for live-action movies. RenderMan started as a scanline renderer based on the Reyes algorithm, and it was extended over the years with ray tracing and several global illumination algorithms. This article describes the modern version of RenderMan, a new architecture for an extensible and programmable path tracer with many features that are essential to handle the fiercely complex scenes in movie production. Users can write their own materials using a bxdf interface and their own light transport algorithms using an integrator interface—or they can use the materials and light transport algorithms provided with RenderMan. Complex geometry and textures are handled with efficient multi-resolution representations, with resolution chosen using path differentials. We trace rays and shade ray hit points in medium-sized groups, which provides the benefits of SIMD execution without excessive memory overhead or data streaming. The path-tracing architecture handles surface, subsurface, and volume scattering. We show examples of the use of path tracing, bidirectional path tracing, VCM, and UPBP light transport algorithms. We also describe our progressive rendering for interactive use and our adaptation of denoising techniques.

Bidirectional Rendering of Vector Light Transport

AbstractOn the foundations of many rendering algorithms it is the symmetry between the path traversed by light and its adjoint path starting from the camera. However, several effects, including polarization or fluorescence, break that symmetry, and are defined only on the direction of light propagation. This reduces the applicability of bidirectional methods that exploit this symmetry for simulating effectively light transport. In this work, we focus on how to include these non‐symmetric effects within a bidirectional rendering algorithm. We generalize the path integral to support the constraints imposed by non‐symmetric light transport. Based on this theoretical framework, we propose modifications on two bidirectional methods, namely bidirectional path tracing and photon mapping, extending them to support polarization and fluorescence, in both steady and transient state.

Aether

Implementing Monte Carlo integration requires significant domain expertise. While simple samplers, such as unidirectional path tracing, are relatively forgiving, more complex algorithms, such as bidirectional path tracing or Metropolis methods, are notoriously difficult to implement correctly. We propose Aether, an embedded domain specific language for Monte Carlo integration, which offers primitives for writing concise and correct-by-construction sampling and probability code. The user is tasked with writing sampling code, while our compiler automatically generates the code necessary for evaluating PDFs as well as the book keeping and combination of multiple sampling strategies. Our language focuses on ease of implementation for rapid exploration, at the cost of run time performance. We demonstrate the effectiveness of the language by implementing several challenging rendering algorithms as well as a new algorithm, which would otherwise be prohibitively difficult.

Bidirectional sound transport

We present a new sound propagation algorithm, Bidirectional Sound Transport (BST), based on bidirectional path tracing. Current state-of-the-art geometric acoustic method handles diffuse reflection by backward path tracing and uses diffuse rain to improve the validity of generated paths. We show that this can be viewed as a special case of bidirectional path tracing. By allowing the connections to be established between any nodes of the subpaths, we are able to improve the sampling quality when sound sources locate near scene objects. This ensures more stable rendering quality and eases ray budget selection. We propose a new metric based on the signal-to-noise (SNR) of the energy response to evaluate the performance of Monte-Carlo path tracing method for sound. Based on the metric, we develop an iterative algorithm to redistribute the samples among bounce numbers according to the statistic characteristics of the sampling of previous frames. We show that the sample redistribution algorithm converges and better balances between early and late reverberation. We evaluate our approach on different benchmarks and demonstrate significant speedup over prior geometric acoustic algorithms. We also discuss clustering algorithms used to improve the scalability for bidirectional sound transport.

Gradient-Domain Photon Density Estimation

The most common solutions to the light transport problem rely on either Monte Carlo MC integration or density estimation methods, such as uni- & bi-directional path tracing or photon mapping. Recent gradient-domain extensions of MC approaches show great promise; here, gradients of the final image are estimated numerically instead of the image intensities themselves with coherent paths generated from a deterministic shift mapping. We extend gradient-domain approaches to light transport simulation based on density estimation. As with previous gradient-domain methods, we detail important considerations that arise when moving from a primal- to gradient-domain estimator. We provide an efficient and straightforward solution to these problems. Our solution supports stochastic progressive density estimation, so it is robust to complex transport effects. We show that gradient-domain photon density estimation converges faster than its primal-domain counterpart, as well as being generally more robust than gradient-domain uni- & bi-directional path tracing for scenes dominated by complex transport.

Gradient-Domain Vertex Connection and Merging

Recently, gradient-domain rendering techniques have shown great promise in reducing Monte Carlo noise and improving overall rendering efficiency. However, all existing gradient-domain methods are built exclusively on top of Monte Carlo integration or density estimation. While these methods can be effective, combining Monte Carlo integration and density estimation has been shown (in the primal domain) to more robustly handle a wider variety of light paths from arbitrarily complex scenes. We present gradient-domain vertex connection and merging (G-VCM), a new gradient-domain technique motivated by primal domain VCM. Our method enables robust gradient sampling in the presence of complex transport, such as specular-diffuse-specular paths, while retaining the denoising power and fast convergence of gradient-domain bidirectional path tracing. We show that G-VCM is able to handle a variety of scenes that exhibit slow convergence when rendered with previous gradient-domain methods.

Interactive sound propagation with bidirectional path tracing

We introduce Bidirectional Sound Transport (BST) , a new algorithm that simulates sound propagation by bidirectional path tracing using multiple importance sampling. Our approach can handle multiple sources in large virtual environments with complex occlusion, and can produce plausible acoustic effects at an interactive rate on a desktop PC. We introduce a new metric based on the signal-to-noise ratio (SNR) of the energy response and use this metric to evaluate the performance of ray-tracing-based acoustic simulation methods. Our formulation exploits temporal coherence in terms of using the resulting sample distribution of the previous frame to guide the sample distribution of the current one. We show that our sample redistribution algorithm converges and better balances between early and late reflections. We evaluate our approach on different benchmarks and demonstrate significant speedup over prior geometric acoustic algorithms.

Estimating the daily solar irradiation on building roofs and facades using Blender Cycles path tracing algorithm

The paper presents the development of an daily solar irradiation algorithm with application of the free software Blender. Considerable attention was paid to the possibilities of simulation of reflections of direct and diffuse solar radiation. For this purpose, the rendering algorithm “Cycles” was used, based on the principle of bi-directional path tracing – tracing random paths of light beams. The value of global radiation in this study is the sum of four components: direct beam radiation, reflected beam radiation, diffuse radiation and reflected diffuse radiation. The developed algorithm allows calculation of solar irradiation for all elements of the 3D model created in Blender, or imported from an external source. One minute is the highest possible time resolution of the analysis, while the accuracy is dependent on the resolution of textures defined for each element of a 3D object. The analysed data is stored in the form of textures that in the algorithm are converted to the value of solar radiance. The result of the analysis is visualization, which shows the distribution of daily solar irradiation on all defined elements of the 3D model.

Unbiased photon gathering for light transport simulation

Photon mapping (PM) has been widely regarded as an efficient solution for light transport simulation, including challenging caustics paths and many-bounce indirect lighting. The efficiency of PM comes from reusing traced photons. However, the handling of photon gathering in existing PM algorithms is universally biased -- the expected value of their results does not necessarily agree with the true solution of the rendering equation. We present a novel photon gathering method to efficiently achieve unbiased rendering with photon mapping. Instead of aggregating the gathered photons into an estimated density as in classical photon mapping, we process each photon individually and connect the corresponding light sub-path with the eye sub-path that generates the gather point, creating an unbiased path sample. The Monte Carlo estimate for such a path sample is calculated by evaluating all relevant terms in a strict and unbiased way, leading to a self-contained unbiased sampling technique. We further develop a set of multiple importance sampling (MIS) weights that allow our method to be optimally combined with bidirectional path tracing (BDPT), resulting in an unbiased rendering algorithm that can efficiently handle a wide variety of light paths and that compares favorably with previous algorithms. Experiments demonstrate the efficacy and robustness of our method.

RayPortals: a light transport editing framework

Physically based rendering, using path-space formulation of global illumination, has become a standard technique for high-quality computer-generated imagery. Nonetheless, being able to control and edit the resulting picture so that it corresponds to the artist vision is still a tedious trial-and-error process. We show how the manipulation of light transport translates into the path-space integral formulation of the rendering equation. We introduce portals as a path-space manipulation tool to edit and control renderings and show how our editing tool unifies and extends previous work on lighting editing. Portals allow the artist to precisely control the final aspect of the image without modifying neither scene geometry nor lighting setup. According to the setup of two geometric handles and a simple path selection filter, portals capture specific lightpaths and teleport them through 3D space. We implement portals in major path-based algorithms (Photon Mapping, Progressive Photon Mapping and Bi-directional Path Tracing) and demonstrate the wide range of control this technique allows on various lighting effects, from low-frequency color bleeding to high-frequency caustics as well as view-dependent reflections.

Skeleton based Vertex Connection Resampling for Bidirectional Path Tracing

Bidirectional path tracing is known to perform poorly for the rendering of highly occluded scenes. Indeed, the connection strategy between light and eye subpaths does not take into account the visibility factor, presenting no contribution for many sampled paths. To improve the efficiency of bidirectional path tracing, we propose a new method for adaptive resampling of connections between light and eye subpaths. Aiming for this objective, we build discrete probability distributions of light subpaths based on a skeleton of the empty space of the scene. In order to demonstrate the efficiency of our algorithm, we compare our method to both standard bidirectional path tracing and a recent important caching method.

Probabilistic Connections for Bidirectional Path Tracing

Bidirectional path tracing BDPT with Multiple Importance Sampling is one of the most versatile unbiased rendering algorithms today. BDPT repeatedly generates sub-paths from the eye and the lights, ...

Probabilistic Connections for Bidirectional Path Tracing

AbstractBidirectional path tracing (BDPT) with Multiple Importance Sampling is one of the most versatile unbiased rendering algorithms today. BDPT repeatedly generates sub‐paths from the eye and the lights, which are connected for each pixel and then discarded. Unfortunately, many such bidirectional connections turn out to have low contribution to the solution. Our key observation is that we can importance sample connections to an eye sub‐path by considering multiple light sub‐paths at once and creating connections probabilistically. We do this by storing light paths, and estimating probability mass functions of the discrete set of possible connections to all light paths. This has two key advantages: we efficiently create connections with low variance by Monte Carlo sampling, and we reuse light paths across different eye paths. We also introduce a caching scheme by deriving an approximation to sub‐path contribution which avoids high‐dimensional path distance computations. Our approach builds on caching methods developed in the different context of VPLs. Our Probabilistic Connections for Bidirectional Path Tracing approach raises a major challenge, since reuse results in high variance due to correlation between paths. We analyze the problem of path correlation and derive a conservative upper bound of the variance, with computationally tractable sample weights. We present results of our method which shows significant improvement over previous unbiased global illumination methods, and evaluate our algorithmic choices.

Wavelet Point‐Based Global Illumination

AbstractPoint‐Based Global Illumination (PBGI) is a popular rendering method in special effects and motion picture productions. This algorithm provides a diffuse global illumination solution by caching radiance in a mesh‐less hierarchical data structure during a preprocess, while solving for visibility over this cache, at rendering time and for each receiver, using microbuffers, which are localized depth and color buffers inspired from real time rendering environments. As a result, noise free ambient occlusion, indirect soft shadows and color bleeding effects are computed efficiently for high resolution image output and in a temporally coherent fashion. We propose an evolution of this method to address the case of non‐diffuse inter‐reflections and refractions. While the original PBGI algorithm models radiance using spherical harmonics, we propose to use wavelets parameterized on the direction space to better localize the radiance representation in the presence of highly directional reflectance. We also propose a new importance‐driven adaptive microbuffer model to capture accurately incoming radiance at a point. Furthermore, we evaluate outgoing radiance using a fast wavelet radiance product and contain the induced larger memory footprint by encoding hierarchically the wavelets in the PBGI tree. As a result, our algorithm can handle non‐lambertian BSDF in the light transport simulation, reproducing caustics and multiple reflections/refractions bounces with a similar quality to bidirectional path tracing in a large number of cases and for only a fraction of its computation time. Our approach is simple to implement and easy to integrate into any existing PBGI framework, with an intuitive control on the approximation error. We evaluate it on a collection of example scenes.