38-Issue 4

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https://diglib.eg.org/handle/10.2312/2632794

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Browsing 38-Issue 4 by Subject "Mathematics of computing"

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    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, Pradeep
    We 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.
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    Microfacet Model Regularization for Robust Light Transport
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Jendersie, Johannes; Grosch, Thorsten; Boubekeur, Tamy and Sen, Pradeep
    Today, 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.
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    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, Pradeep
    We 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.