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Item Global Illumination Shadow Layers(The Eurographics Association and John Wiley & Sons Ltd., 2019) DESRICHARD, François; Vanderhaeghe, David; PAULIN, Mathias; Boubekeur, Tamy and Sen, PradeepComputer graphics artists often resort to compositing to rework light effects in a synthetic image without requiring a new render. Shadows are primary subjects of artistic manipulation as they carry important stylistic information while our perception is tolerant with their editing. In this paper we formalize the notion of global shadow, generalizing direct shadow found in previous work to a global illumination context. We define an object's shadow layer as the difference between two altered renders of the scene. A shadow layer contains the radiance lost on the camera film because of a given object. We translate this definition in the theoretical framework of Monte-Carlo integration, obtaining a concise expression of the shadow layer. Building on it, we propose a path tracing algorithm that renders both the original image and any number of shadow layers in a single pass: the user may choose to separate shadows on a per-object and per-light basis, enabling intuitive and decoupled edits.Item Orthogonal Array Sampling for Monte Carlo Rendering(The Eurographics Association and John Wiley & Sons Ltd., 2019) Jarosz, Wojciech; Enayet, Afnan; Kensler, Andrew; Kilpatrick, Charlie; Christensen, Per; Boubekeur, Tamy and Sen, PradeepWe generalize N-rooks, jittered, and (correlated) multi-jittered sampling to higher dimensions by importing and improving upon a class of techniques called orthogonal arrays from the statistics literature. Renderers typically combine or ''pad'' a collection of lower-dimensional (e.g. 2D and 1D) stratified patterns to form higher-dimensional samples for integration. This maintains stratification in the original dimension pairs, but looses it for all other dimension pairs. For truly multi-dimensional integrands like those in rendering, this increases variance and deteriorates its rate of convergence to that of pure random sampling. Care must therefore be taken to assign the primary dimension pairs to the dimensions with most integrand variation, but this complicates implementations. We tackle this problem by developing a collection of practical, in-place multi-dimensional sample generation routines that stratify points on all t-dimensional and 1-dimensional projections simultaneously. For instance, when t=2, any 2D projection of our samples is a (correlated) multi-jittered point set. This property not only reduces variance, but also simplifies implementations since sample dimensions can now be assigned to integrand dimensions arbitrarily while maintaining the same level of stratification. Our techniques reduce variance compared to traditional 2D padding approaches like PBRT's (0,2) and Stratified samplers, and provide quality nearly equal to state-of-the-art QMC samplers like Sobol and Halton while avoiding their structured artifacts as commonly seen when using a single sample set to cover an entire image. While in this work we focus on constructing finite sampling point sets, we also discuss potential avenues for extending our work to progressive sequences (more suitable for incremental rendering) in the future.Item Adaptive BRDF-Oriented Multiple Importance Sampling of Many Lights(The Eurographics Association and John Wiley & Sons Ltd., 2019) Liu, Yifan; Xu, Kun; Yan, Ling-Qi; Boubekeur, Tamy and Sen, PradeepMany-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.Item Quantifying the Error of Light Transport Algorithms(The Eurographics Association and John Wiley & Sons Ltd., 2019) Celarek, Adam; Jakob, Wenzel; Wimmer, Michael; Lehtinen, Jaakko; Boubekeur, Tamy and Sen, PradeepThis 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.Item Combining Point and Line Samples for Direct Illumination(The Eurographics Association and John Wiley & Sons Ltd., 2019) Salesin, Katherine; Jarosz, Wojciech; Boubekeur, Tamy and Sen, PradeepWe develop a unified framework for combining point and line samples in direct lighting calculations. While line samples have proven beneficial in a variety of rendering contexts, their application in direct lighting has been limited due to a lack of formulas for evaluating advanced BRDFs along a line and performance tied to the orientation of occluders in the scene. We lift these limitations by elevating line samples to a shared higher-dimensional space with point samples. Our key insight is to separate the probability distribution functions of line samples and points that lie along a line sample. This simple conceptual change allows us to apply multiple importance sampling (MIS) between points and lines, and lines with each other, in order to leverage their respective strengths. We also show how to improve the convergence rate of MIS between points and lines in an unbiased way using a novel discontinuity-smoothing balance heuristic. We verify through a set of rendering experiments that our proposed MISing of points and lines, and lines with each other, reduces variance of the direct lighting estimate while supporting an increased range of BSDFs compared to analytic line integration.Item Microfacet Model Regularization for Robust Light Transport(The Eurographics Association and John Wiley & Sons Ltd., 2019) Jendersie, Johannes; Grosch, Thorsten; Boubekeur, Tamy and Sen, PradeepToday, Monte Carlo light transport algorithms are used in many applications to render realistic images. Depending on the complexity of the used methods, several light effects can or cannot be found by the sampling process. Especially, specular and smooth glossy surfaces often lead to high noise and missing light effects. Path space regularization provides a solution, improving any sampling algorithm, by modifying the material evaluation code. Previously, Kaplanyan and Dachsbacher [KD13] introduced the concept for pure specular interactions. We extend this idea to the commonly used microfacet models by manipulating the roughness parameter prior to the evaluation. We also show that this kind of regularization requires a change in the MIS weight computation and provide the solution. Finally, we propose two heuristics to adaptively reduce the introduced bias. Using our method, many complex light effects are reproduced and the fidelity of smooth objects is increased. Additionally, if a path was sampleable before, the variance is partially reduced.Item Adaptive Temporal Sampling for Volumetric Path Tracing of Medical Data(The Eurographics Association and John Wiley & Sons Ltd., 2019) Martschinke, Jana; Hartnagel, Stefan; Keinert, Benjamin; Engel, Klaus; Stamminger, Marc; Boubekeur, Tamy and Sen, PradeepMonte-Carlo path tracing techniques can generate stunning visualizations of medical volumetric data. In a clinical context, such renderings turned out to be valuable for communication, education, and diagnosis. Because a large number of computationally expensive lighting samples is required to converge to a smooth result, progressive rendering is the only option for interactive settings: Low-sampled, noisy images are shown while the user explores the data, and as soon as the camera is at rest the view is progressively refined. During interaction, the visual quality is low, which strongly impedes the user's experience. Even worse, when a data set is explored in virtual reality, the camera is never at rest, leading to constantly low image quality and strong flickering. In this work we present an approach to bring volumetric Monte-Carlo path tracing to the interactive domain by reusing samples over time. To this end, we transfer the idea of temporal antialiasing from surface rendering to volume rendering. We show how to reproject volumetric ray samples even though they cannot be pinned to a particular 3D position, present an improved weighting scheme that makes longer history trails possible, and define an error accumulation method that downweights less appropriate older samples. Furthermore, we exploit reprojection information to adaptively determine the number of newly generated path tracing samples for each individual pixel. Our approach is designed for static, medical data with both volumetric and surface-like structures. It achieves good-quality volumetric Monte-Carlo renderings with only little noise, and is also usable in a VR context.