Line Integration for Rendering Heterogeneous Emissive Volumes

Emissive media are often challenging to render: in thin regions where only few scattering events occur the emission is poorly sampled, while sampling events for emission can be disadvantageous due to absorption in dense regions. We extend the standard path space measurement contribution to also collect emission along path segments, not only at vertices. We apply this extension to two estimators: extending paths via scattering and distance sampling, and next event estimation. In order to do so, we unify the two approaches and derive the corresponding Monte Carlo estimators to interpret next event estimation as a solid angle sampling technique. We avoid connecting paths to vertices hidden behind dense absorbing layers of smoke by also including transmittance sampling into next event estimation. We demonstrate the advantages of our line integration approach which generates estimators with lower variance since entire segments are accounted for. Also, our novel forward next event estimation technique yields faster run times compared to previous next event estimation as it penetrates less deeply into dense volumes.     

A Survey on Gradient‐Domain Rendering

Monte 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.     

Bayesian Collaborative Denoising for Monte Carlo Rendering

The stochastic nature of Monte Carlo rendering algorithms inherently produces noisy images. Essentially, three approaches have been developed to solve this issue: improving the ray‐tracing strategies to reduce pixel variance, providing adaptive sampling by increasing the number of rays in regions needing so, and filtering the noisy image as a post‐process. Although the algorithms from the latter category introduce bias, they remain highly attractive as they quickly improve the visual quality of the images, are compatible with all sorts of rendering effects, have a low computational cost and, for some of them, avoid deep modifications of the rendering engine. In this paper, we build upon recent advances in both non‐local and collaborative filtering methods to propose a new efficient denoising operator for Monte Carlo rendering. Starting from the local statistics which emanate from the pixels sample distribution, we enrich the image with local covariance measures and introduce a nonlocal bayesian filter which is specifically designed to address the noise stemming from Monte Carlo rendering. The resulting algorithm only requires the rendering engine to provide for each pixel a histogram and a covariance matrix of its color samples. Compared to state‐of‐the‐art sample‐based methods, we obtain improved denoising results, especially in dark areas, with a large increase in speed and more robustness with respect to the main parameter of the algorithm. We provide a detailed mathematical exposition of our bayesian approach, discuss extensions to multiscale execution, adaptive sampling and animated scenes, and experimentally validate it on a collection of scenes.     

Quantifying the Error of Light Transport Algorithms

This paper proposes a new methodology for measuring the error of unbiased physically based rendering algorithms. The current state of the art includes mean squared error (MSE) based metrics and visual comparisons of equal‐time renderings of competing algorithms. Neither is satisfying as MSE does not describe behavior and can exhibit significant variance, and visual comparisons are inherently subjective. Our contribution is two‐fold: First, we propose to compute many short renderings instead of a single long run and use the short renderings to estimate MSE expectation and variance as well as per‐pixel standard deviation. An algorithm that achieves good results in most runs, but with occasional outliers is essentially unreliable, which we wish to quantify numerically. We use per‐pixel standard deviation to identify problematic lighting effects of rendering algorithms. The second contribution is the error spectrum ensemble (ESE), a tool for measuring the distribution of error over frequencies. The ESE serves two purposes: It reveals correlation between pixels and can be used to detect outliers, which offset the amount of error substantially.     

Spectral Gradient Sampling for Path Tracing

Spectral Monte‐Carlo methods are currently the most powerful techniques for simulating light transport with wavelength‐dependent phenomena (e.g., dispersion, colored particle scattering, or diffraction gratings). Compared to trichromatic rendering, sampling the spectral domain requires significantly more samples for noise‐free images. Inspired by gradient‐domain rendering, which estimates image gradients, we propose spectral gradient sampling to estimate the gradients of the spectral distribution inside a pixel. These gradients can be sampled with a significantly lower variance by carefully correlating the path samples of a pixel in the spectral domain, and we introduce a mapping function that shifts paths with wavelength‐dependent interactions. We compute the result of each pixel by integrating the estimated gradients over the spectral domain using a one‐dimensional screened Poisson reconstruction. Our method improves convergence and reduces chromatic noise from spectral sampling, as demonstrated by our implementation within a conventional path tracer.     

Deep Adaptive Sampling for Low Sample Count Rendering

Recently, deep learning approaches have proven successful at removing noise from Monte Carlo (MC) rendered images at extremely low sampling rates, e.g., 1–4 samples per pixel (spp). While these methods provide dramatic speedups, they operate on uniformly sampled MC rendered images. However, the full promise of low sample counts requires both adaptive sampling and reconstruction/denoising. Unfortunately, the traditional adaptive sampling techniques fail to handle the cases with low sampling rates, since there is insufficient information to reliably calculate their required features, such as variance and contrast. In this paper, we address this issue by proposing a deep learning approach for joint adaptive sampling and reconstruction of MC rendered images with extremely low sample counts. Our system consists of two convolutional neural networks (CNN), responsible for estimating the sampling map and denoising, separated by a renderer. Specifically, we first render a scene with one spp and then use the first CNN to estimate a sampling map, which is used to distribute three additional samples per pixel on average adaptively. We then filter the resulting render with the second CNN to produce the final denoised image. We train both networks by minimizing the error between the denoised and ground truth images on a set of training scenes. To use backpropagation for training both networks, we propose an approach to effectively compute the gradient of the renderer. We demonstrate that our approach produces better results compared to other sampling techniques. On average, our 4 spp renders are comparable to 6 spp from uniform sampling with deep learning‐based denoising. Therefore, 50% more uniformly distributed samples are required to achieve equal quality without adaptive sampling.     

Ray Tracing Generalized Tube Primitives: Method and Applications

We present a general high‐performance technique for ray tracing generalized tube primitives. Our technique efficiently supports tube primitives with fixed and varying radii, general acyclic graph structures with bifurcations, and correct transparency with interior surface removal. Such tube primitives are widely used in scientific visualization to represent diffusion tensor imaging tractographies, neuron morphologies, and scalar or vector fields of 3D flow. We implement our approach within the OSPRay ray tracing framework, and evaluate it on a range of interactive visualization use cases of fixed‐ and varying‐radius streamlines, pathlines, complex neuron morphologies, and brain tractographies. Our proposed approach provides interactive, high‐quality rendering, with low memory overhead.     

Scalable Ray Tracing Using the Distributed FrameBuffer

Image‐ and data‐parallel rendering across multiple nodes on high‐performance computing systems is widely used in visualization to provide higher frame rates, support large data sets, and render data in situ. Specifically for in situ visualization, reducing bottlenecks incurred by the visualization and compositing is of key concern to reduce the overall simulation runtime. Moreover, prior algorithms have been designed to support either image‐ or data‐parallel rendering and impose restrictions on the data distribution, requiring different implementations for each configuration. In this paper, we introduce the Distributed FrameBuffer, an asynchronous image‐processing framework for multi‐node rendering. We demonstrate that our approach achieves performance superior to the state of the art for common use cases, while providing the flexibility to support a wide range of parallel rendering algorithms and data distributions. By building on this framework, we extend the open‐source ray tracing library OSPRay with a data‐distributed API, enabling its use in data‐distributed and in situ visualization applications.     

Adaptive BRDF‐Oriented Multiple Importance Sampling of Many Lights

Many‐light rendering is becoming more common and important as rendering goes into the next level of complexity. However, to calculate the illumination under many lights, state of the art algorithms are still far from efficient, due to the separate consideration of light sampling and BRDF sampling. To deal with the inefficiency of many‐light rendering, we present a novel light sampling method named BRDF‐oriented light sampling, which selects lights based on importance values estimated using the BRDF's contributions. Our BRDF‐oriented light sampling method works naturally with MIS, and allows us to dynamically determine the number of samples allocated for different sampling techniques. With our method, we can achieve a significantly faster convergence to the ground truth results, both perceptually and numerically, as compared to previous many‐light rendering algorithms.     

A new microflake model with microscopic self‐shadowing for accurate volume downsampling

Naïve linear methods for downsampling high‐resolution microflake volumes often produce inaccurate appearance, especially when input voxels are very opaque. Preserving correct appearance at all resolutions requires taking into account maskingshadowing effects that occur between and inside dense input voxels. We introduce a new microflake model whose additional parameters characterize self‐shadowing effects at a microscopic scale. We provide an anisotropic self‐shadowing function and microflake distributions for which the scattering coefficients and the phase functions of our model have closed‐form expressions. We use this model in a new downsampling approach in which scattering parameters are computed from local estimations of self‐shadowing probabilities in the input volume. Unlike previous work, our method handles datasets with spatially varying scattering parameters, semi‐transparent volumes and datasets with intricate silhouettes. We show that our method generates LoDs with correct transparency and consistent appearance through scales for a wide range of challenging datasets, allowing for huge memory savings and efficient distant rendering without loss of quality.     

Gradient Outlier Removal for Gradient‐Domain Path Tracing

We present a new outlier removal technique for a gradient‐domain path tracing (G‐PT) that computes image gradients as well as colors. Our approach rejects gradient outliers whose estimated errors are much higher than those of the other gradients for improving reconstruction quality for the G‐PT. We formulate our outlier removal problem as a least trimmed squares optimization, which employs only a subset of gradients so that a final image can be reconstructed without including the gradient outliers. In addition, we design this outlier removal process so that the chosen subset of gradients maintains connectivity through gradients between pixels, preventing pixels from being isolated. Lastly, the optimal number of inlier gradients is estimated to minimize our reconstruction error. We have demonstrated that our reconstruction with robustly rejecting gradient outliers produces visually and numerically improved results, compared to the previous screened Poisson reconstruction that uses all the gradients.     

Handling Fluorescence in a Uni‐directional Spectral Path Tracer

We present two separate improvements to the handling of fluorescence effects in modern uni‐directional spectral rendering systems. The first is the formulation of a new distance tracking scheme for fluorescent volume materials which exhibit a pronounced wavelength asymmetry. Such volumetric materials are an important and not uncommon corner case of wavelength‐shifting media behaviour, and have not been addressed so far in rendering literature. The second one is that we introduce an extension of Hero wavelength sampling which can handle fluorescence events, both on surfaces, and in volumes. Both improvements are useful by themselves, and can be used separately: when used together, they enable the robust inclusion of arbitrary fluorescence effects in modern uni‐directional spectral MIS path tracers. Our extension of Hero wavelength sampling is generally useful, while our proposed technique for distance tracking in strongly asymmetric media is admittedly not very efficient. However, it makes the most of a rather difficult situation, and at least allows the inclusion of such media in uni‐directional path tracers, albeit at comparatively high cost. Which is still an improvement since up to now, their inclusion was not really possible at all, due to the inability of conventional tracking schemes to generate sampling points in such volume materials.     

On‐the‐Fly Power‐Aware Rendering

Power saving is a prevailing concern in desktop computers and, especially, in battery‐powered devices such as mobile phones. This is generating a growing demand for power‐aware graphics applications that can extend battery life, while preserving good quality. In this paper, we address this issue by presenting a real‐time power‐efficient rendering framework, able to dynamically select the rendering configuration with the best quality within a given power budget. Different from the current state of the art, our method does not require precomputation of the whole camera‐view space, nor Pareto curves to explore the vast power‐error space; as such, it can also handle dynamic scenes. Our algorithm is based on two key components: our novel power prediction model, and our runtime quality error estimation mechanism. These components allow us to search for the optimal rendering configuration at runtime, being transparent to the user. We demonstrate the performance of our framework on two different platforms: a desktop computer, and a mobile device. In both cases, we produce results close to the maximum quality, while achieving significant power savings.     

Distortion‐Free Displacement Mapping

Displacement mapping is routinely used to add geometric details in a fast and easy‐to‐control way, both in offline rendering as well as recently in interactive applications such as games. However, it went largely unnoticed (with the exception of McGuire and Whitson [MW08]) that, when applying displacement mapping to a surface with a low‐distortion parametrization, this parametrization is distorted as the geometry was changed by the displacement mapping. Typical resulting artifacts are “rubber band”‐like distortion patterns in areas of strong displacement change where a small isotropic area in texture space is mapped to a large anisotropic area in world space. We describe a fast, fully GPU‐based two‐step procedure to resolve this problem. First, a correction deformation is computed from the displacement map. Second, two variants to apply this correction when computing displacement mapping are proposed. The first variant is backward‐compatible and can resolve the artifact in any rendering pipeline without modifying it and without requiring additional computation at render time, but only works for bijective parametrizations. The second variant works for more general parametrizations, but requires to modify the rendering code and incurs a very small computational overhead.     

Fast Hardware Construction and Refitting of Quantized Bounding Volume Hierarchies

There is recent interest in GPU architectures designed to accelerate ray tracing, especially on mobile systems with limited memory bandwidth. A promising recent approach is to store and traverse Bounding Volume Hierarchies (BVHs), used to accelerate ray tracing, in low arithmetic precision. However, so far there is no research on refitting or construction of such compressed BVHs, which is necessary for any scenes with dynamic content. We find that in a hardware‐accelerated tree update, significant memory traffic and runtime savings are available from streaming, bottom‐up compression. Novel algorithmic techniques of modulo encoding and treelet‐based compression are proposed to reduce backtracking inherent in bottom‐up compression. Together, these techniques reduce backtracking to a small fraction. Compared to a separate top‐down compression pass, streaming bottom‐up compression with the proposed optimizations saves on average 42% of memory accesses for LBVH construction and 56% for refitting of compressed BVHs, over 16 test scenes. In architectural simulation, the proposed streaming compression reduces LBVH runtime by 20% compared to a single‐precision build, and 41% compared to a single‐precision build followed by top‐down compression. Since memory traffic dominates the energy cost of refitting and LBVH construction, energy consumption is expected to fall by a similar fraction.     

Global Texture Mapping for Dynamic Objects

We propose a novel framework to generate a global texture atlas for a deforming geometry. Our approach distinguishes from prior arts in two aspects. First, instead of generating a texture map for each timestamp to color a dynamic scene, our framework reconstructs a global texture atlas that can be consistently mapped to a deforming object. Second, our approach is based on a single RGB‐D camera, without the need of a multiple‐camera setup surrounding a scene. In our framework, the input is a 3D template model with an RGB‐D image sequence, and geometric warping fields are found using a state‐of‐the‐art non‐rigid registration method [GXW*15] to align the template mesh to noisy and incomplete input depth images. With these warping fields, our multi‐scale approach for texture coordinate optimization generates a sharp and clear texture atlas that is consistent with multiple color observations over time. Our approach is accelerated by graphical hardware and provides a handy configuration to capture a dynamic geometry along with a clean texture atlas. We demonstrate our approach with practical scenarios, particularly human performance capture. We also show that our approach is resilient on misalignment issues caused by imperfect estimation of warping fields and inaccurate camera parameters.     

Practical Foldover‐Free Volumetric Mapping Construction

In this paper, we present a practically robust method for computing foldover‐free volumetric mappings with hard linear constraints. Central to this approach is a projection algorithm that monotonically and efficiently decreases the distance from the mapping to the bounded conformal distortion mapping space. After projection, the conformal distortion of the updated mapping tends to be below the given bound, thereby significantly reducing foldovers. Since it is non‐trivial to define an optimal bound, we introduce a practical conformal distortion bound generation scheme to facilitate subsequent projections. By iteratively generating conformal distortion bounds and trying to project mappings into bounded conformal distortion spaces monotonically, our algorithm achieves high‐quality foldover‐free volumetric mappings with strong practical robustness and high efficiency. Compared with existing methods, our method computes mesh‐based and meshless volumetric mappings with no prescribed conformal distortion bounds. We demonstrate the efficacy and efficiency of our method through a variety of geometric processing tasks.     

Adaptive Matrix Completion for Fast Visibility Computations with Many Lights Rendering

Several fast global illumination algorithms rely on the Virtual Point Lights framework. This framework separates illumination into two steps: first, propagate radiance in the scene and store it in virtual lights, then gather illumination from these virtual lights. To accelerate the second step, virtual lights and receiving points are grouped hierarchically, for example using Multi-Dimensional Lightcuts. Computing visibility between clusters of virtual lights and receiving points is a bottleneck. Separately, matrix completion algorithms reconstruct completely a low-rank matrix from an incomplete set of sampled elements. In this paper, we use adaptive matrix completion to approximate visibility information after an initial clustering step. We reconstruct visibility information using as little as 10 % to 20 % samples for most scenes, and combine it with shading information computed separately, in parallel on the GPU. Overall, our method computes global illumination 3 or more times faster than previous state-of-the-art methods.     

Area‐Preserving Parameterizations for Spherical Ellipses

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area‐preserving mappings from the unit square [0,1]² to a spherical ellipse (i.e. the projection of the disk onto the unit sphere). These mappings allow for low‐variance stratified sampling of direct illumination from disk‐shaped light sources. We discuss how to efficiently incorporate our methods into a production renderer and demonstrate the quality of our maps, showing significantly lower variance than previous work.