Improved Stochastic Progressive Photon Mapping with Metropolis Sampling

This paper presents an improvement to the stochastic progressive photon mapping (SPPM), a method for robustly simulating complex global illumination with distributed ray tracing effects. Normally, similar to photon mapping and other particle tracing algorithms, SPPM would become inefficient when the photons are poorly distributed. An inordinate amount of photons are required to reduce the error caused by noise and bias to acceptable levels. In order to optimize the distribution of photons, we propose an extension of SPPM with a Metropolis‐Hastings algorithm, effectively exploiting local coherence among the light paths that contribute to the rendered image. A well‐designed scalar contribution function is introduced as our Metropolis sampling strategy, targeting at specific parts of image areas with large error to improve the efficiency of the radiance estimator. Experimental results demonstrate that the new Metropolis sampling based approach maintains the robustness of the standard SPPM method, while significantly improving the rendering efficiency for a wide range of scenes with complex lighting.     

Solid Angle Sampling of Disk and Cylinder Lights

A new unbiased sampling approach is presented, which allows the direct illumination from disk and cylinder light sources to be sampled with a uniform probability distribution within their solid angles, as seen from each illuminated point. This approach applies to any form of global illumination path tracing algorithm (forward or bidirectional), where the direct illumination integral from light sources needs to be estimated. We show that taking samples based on the solid angle of these two light sources leads to improved estimates and reduced variance of the Monte Carlo integral for direct illumination. This work follows from previously known unbiased methods for the solid angle sampling of triangular and rectangular light sources and extends the class of lights that can be rendered with these improved sampling algorithms.     

Guided Image Filtering for Interactive High‐quality Global Illumination

Interactive computation of global illumination is a major challenge in current computer graphics research. Global illumination heavily affects the visual quality of generated images. It is therefore a key attribute for the perception of photo‐realistic images. Path tracing is able to simulate the physical behaviour of light using Monte Carlo techniques. However, the computational burden of this technique prohibits interactive rendering times on standard commodity hardware in high‐quality. Trying to solve the Monte Carlo integration with fewer samples results in characteristic noisy images. Global illumination filtering methods take advantage of the fact that the integral for neighbouring pixels may be very similar. Averaging samples of similar characteristics in screen‐space may approximate the correct integral, but may result in visible outliers. In this paper, we present a novel path tracing pipeline based on an edge‐aware filtering method for the indirect illumination which produces visually more pleasing results without noticeable outliers. The key idea is not to filter the noisy path traced images but to use it as a guidance to filter a second image composed from characteristic scene attributes that do not contain noise by default. We show that our approach better approximates the Monte Carlo integral compared to previous methods. Since the computation is carried out completely in screen‐space it is therefore applicable to fully dynamic scenes, arbitrary lighting and allows for high‐quality path tracing at interactive frame rates on commodity hardware.     

Efficient Monte Carlo rendering with realistic lenses

In this paper we present a novel approach to simulate image formation for a wide range of real world lenses in the Monte Carlo ray tracing framework. Our approach sidesteps the overhead of tracing rays through a system of lenses and requires no tabulation. To this end we first improve the precision of polynomial optics to closely match ground‐truth ray tracing. Second, we show how the Jacobian of the optical system enables efficient importance sampling, which is crucial for difficult paths such as sampling the aperture which is hidden behind lenses on both sides. Our results show that this yields converged images significantly faster than previous methods and accurately renders complex lens systems with negligible overhead compared to simple models, e.g. the thin lens model. We demonstrate the practicality of our method by incorporating it into a bidirectional path tracing framework and show how it can provide information needed for sophisticated light transport algorithms.     

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.     

Bidirectional Rendering of Vector Light Transport

On 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.     

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.     

Robust Statistical Pixel Estimation

Robust statistical methods are employed to reduce the noise in Monte Carlo ray tracing. Through the use of resampling, the sample mean distribution is determined for each pixel. Because this distribution is uni‐modal and normal for a large sample size, robust estimates converge to the true mean of the pixel values. Compared to existing methods, less additional storage is required at each pixel because the sample mean distribution can be distilled down to a compact size, and fewer computations are necessary because the robust estimation process is sampling independent and needs a small input size to compute pixel values. The robust statistical pixel estimators are not only resistant to impulse noise, but they also remove general noise from fat‐tailed distributions. A substantial speedup in rendering can therefore be achieved by reducing the number of samples required for a desired image quality. The effectiveness of the proposed approach is demonstrated for path tracing simulations.     

Higher Order Ray Marching

Rendering participating media is still a challenging and time consuming task. In such media light interacts at every differential point of its path. Several rendering algorithms are based on ray marching: dividing the path of light into segments and calculating interactions at each of them. In this work, we revisit and analyze ray marching both as a quadrature integrator and as an initial value problem solver, and apply higher order adaptive solvers that ensure several interesting properties, such as faster convergence, adaptiveness to the mathematical definition of light transport and robustness to singularities. We compare several numerical methods, including standard ray marching and Monte Carlo integration, and illustrate the benefits of different solvers for a variety of scenes. Any participating media rendering algorithm that is based on ray marching may benefit from the application of our approach by reducing the number of needed samples (and therefore, rendering time) and increasing accuracy.     

Visualization of Coherent Structures of Light Transport

Inspired by vector field topology, an established tool for the extraction and identification of important features of flows and vector fields, we develop means for the analysis of the structure of light transport. For that, we derive an analogy to vector field topology that defines coherent structures in light transport. We also introduce Finite‐Time Path Deflection (FTPD), a scalar quantity that represents the deflection characteristic of all light transport paths passing through a given point in space. For virtual scenes, the FTPD can be computed directly using path‐space Monte Carlo integration. We visualize the FTPD field for several example scenes and discuss the revealed structures. Lastly, we show that the coherent regions visualized by the FTPD are closely related to the coherent regions in our new topologically‐motivated analysis of light transport. FTPD visualizations are thus also visualizations of the structure of light transport.     

Table‐driven Adaptive Importance Sampling

Monte Carlo rendering algorithms generally rely on some form of importance sampling to evaluate the measurement equation. Most of these importance sampling methods only take local information into account, however, so the actual importance function used may not closely resemble the light distribution in the scene. In this paper, we present Table‐driven Adaptive Importance Sampling (TAIS), a sampling technique that augments existing importance functions with tabular importance maps that direct sampling towards undersampled regions of path space. The importance maps are constructed lazily, relying on information gathered during the course of sampling. During sampling the importance maps act either in parallel with or as a preprocess to existing importance sampling methods. We show that our adaptive importance maps can be effective at reducing variance in a number of rendering situations.     

Bidirectional Importance Sampling for Unstructured Direct Illumination

Recent research in bidirectional importance sampling has focused primarily on structured illumination sources such as distant environment maps, while unstructured illumination has received little attention. In this paper, we present a method for bidirectional importance sampling of unstructured illumination, allowing us to use the same method for sampling both distant as well as local/indirect sources. Building upon recent work in [ WFA*05 ], we model complex illumination as a large set of point lights. The subsequent sampling process draws samples only from this point set. We start by constructing a piecewise constant approximation for the lighting using an illumination cut [ CPWAP08 ]. We show that this cut can be used directly for illumination importance sampling. We then use BRDF importance sampling followed by sample counting to update the cut, resulting in a bidirectional distribution that closely approximates the product of the illumination and BRDF. Drawing visibility samples from this new distribution significantly reduces the sampling variance. As a main advance over previous work, our method allows for unstructured sources, including arbitrary local direct lighting and one-bounce of indirect lighting.     

ISHair: Importance Sampling for Hair Scattering

We present an importance sampling method for the bidirectional scattering distribution function (bsdf) of hair. Our method is based on the multi‐lobe hair scattering model presented by Sadeghi et al. [ [SPJT10] ]. We reduce noise by drawing samples from a distribution that approximates the bsdf well. Our algorithm is efficient and easy to implement, since the sampling process requires only the evaluation of a few analytic functions, with no significant memory overhead or need for precomputation. We tested our method in a research raytracer and a production renderer based on micropolygon rasterization. We show significant improvements for rendering direct illumination using multiple importance sampling and for rendering indirect illumination using path tracing.     

Toward Optimal Space Partitioning for Unbiased,Adaptive Free Path Sampling of Inhomogeneous Participating Media

Photo‐realistic rendering of inhomogeneous participating media with light scattering in consideration is important in computer graphics, and is typically computed using Monte Carlo based methods. The key technique in such methods is the free path sampling, which is used for determining the distance (free path) between successive scattering events. Recently, it has been shown that efficient and unbiased free path sampling methods can be constructed based on Woodcock tracking. The key concept for improving the efficiency is to utilize space partitioning (e.g., kd‐tree or uniform grid), and a better space partitioning scheme is important for better sampling efficiency. Thus, an estimation framework for investigating the gain in sampling efficiency is important for determining how to partition the space. However, currently, there is no estimation framework that works in 3D space. In this paper, we propose a new estimation framework to overcome this problem. Using our framework, we can analytically estimate the sampling efficiency for any typical partitioned space. Conversely, we can also use this estimation framework for determining the optimal space partitioning. As an application, we show that new space partitioning schemes can be constructed using our estimation framework. Moreover, we show that the differences in the performances using different schemes can be predicted fairly well using our estimation framework.     

A General BRDF Representation Based on Tensor Decomposition

Generating photo‐realistic images through Monte Carlo rendering requires efficient representation of light–surface interaction and techniques for importance sampling. Various models with good representation abilities have been developed but only a few of them have their importance sampling procedure. In this paper, we propose a method which provides a good bidirectional reflectance distribution function (BRDF) representation and efficient importance sampling procedure. Our method is based on representing BRDF as a function of tensor products. Four‐dimensional measured BRDF tensor data are factorized using Tucker decomposition. A large data set is used for comparing the proposed BRDF model with a number of well‐known BRDF models. It is shown that the underlying model provides good approximation to BRDFs.     

A Significance Cache for Accelerating Global Illumination

Rendering using physically based methods requires substantial computational resources. Most methods that are physically based use straightforward techniques that may excessively compute certain types of light transport, while ignoring more important ones. Importance sampling is an effective and commonly used technique to reduce variance in such methods. Most current approaches for physically based rendering based on Monte Carlo methods sample the BRDF and cosine term, but are unable to sample the indirect illumination as this is the term that is being computed. Knowledge of the incoming illumination can be especially useful in the case of hard to find light paths, such as caustics or scenes which rely primarily on indirect illumination. To facilitate the determination of such paths, we propose a caching scheme which stores important directions, and is analytically sampled to calculate important paths. Results show an improvement over BRDF sampling and similar illumination importance sampling.     

Combinatorial Bidirectional Path‐Tracing for Efficient Hybrid CPU/GPU Rendering

This paper presents a reformulation of bidirectional path‐tracing that adequately divides the algorithm into processes efficiently executed in parallel on both the CPU and the GPU. We thus benefit from high‐level optimization techniques such as double buffering, batch processing, and asyncronous execution, as well as from the exploitation of most of the CPU, GPU, and memory bus capabilities. Our approach, while avoiding pure GPU implementation limitations (such as limited complexity of shaders, light or camera models, and processed scene data sets), is more than ten times faster than standard bidirectional path‐tracing implementations, leading to performance suitable for production‐oriented rendering engines.     

Sample‐Based Manifold Filtering for Interactive Global Illumination and Depth of Field

We present a fast reconstruction filtering method for images generated with Monte Carlo–based rendering techniques. Our approach specializes in reducing global illumination noise in the presence of depth‐of‐field effects at very low sampling rates and interactive frame rates. We employ edge‐aware filtering in the sample space to locally improve outgoing radiance of each sample. The improved samples are then distributed in the image plane using a fast, linear manifold‐based approach supporting very large circles of confusion. We evaluate our filter by applying it to several images containing noise caused by Monte Carlo–simulated global illumination, area light sources and depth of field. We show that our filter can efficiently denoise such images at interactive frame rates on current GPUs and with as few as 4–16 samples per pixel. Our method operates only on the colour and geometric sample information output of the initial rendering process. It does not make any assumptions on the underlying rendering technique and sampling strategy and can therefore be implemented completely as a post‐process filter.     

Flux‐Limited Diffusion for Multiple Scattering in Participating Media

For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions, classical diffusion approximation suffers from non‐physical radiative fluxes which leads to a poor match to correct light transport. In particular, this prevents the application of classical diffusion approximation to heterogeneous media, where opaque material is embedded within transparent regions. To address this limitation, we introduce flux‐limited diffusion, a technique from the astrophysics domain. This method provides a better approximation to light transport than classical diffusion approximation, particularly when applied to heterogeneous media, and hence broadens the applicability of diffusion‐based techniques. We provide an algorithm for flux‐limited diffusion, which is validated using the transport theory for a point light source in an infinite homogeneous medium. We further demonstrate that our implementation of flux‐limited diffusion produces more accurate renderings of multiple scattering in various heterogeneous datasets than classical diffusion approximation, by comparing both methods to ground truth renderings obtained via volumetric path tracing.     

Product Importance Sampling for Light Transport Path Guiding

The efficiency of Monte Carlo algorithms for light transport simulation is directly related to their ability to importance‐sample the product of the illumination and reflectance in the rendering equation. Since the optimal sampling strategy would require knowledge about the transport solution itself, importance sampling most often follows only one of the known factors – BRDF or an approximation of the incident illumination. To address this issue, we propose to represent the illumination and the reflectance factors by the Gaussian mixture model (GMM), which we fit by using a combination of weighted expectation maximization and non‐linear optimization methods. The GMM representation then allows us to obtain the resulting product distribution for importance sampling on‐the‐fly at each scene point. For its efficient evaluation and sampling we preform an up‐front adaptive decimation of both factor mixtures. In comparison to state‐of‐the‐art sampling methods, we show that our product importance sampling can lead to significantly better convergence in scenes with complex illumination and reflectance.