Browsing by Author "Jarosz, Wojciech"

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    A Bidirectional Formulation for Walk on Spheres
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Qi, Yang; Seyb, Dario; Bitterli, Benedikt; Jarosz, Wojciech; Ghosh, Abhijeet; Wei, Li-Yi
    Numerically solving partial differential equations (PDEs) is central to many applications in computer graphics and scientific modeling. Conventional methods for solving PDEs often need to discretize the space first, making them less efficient for complex geometry. Unlike conventional methods, the walk on spheres (WoS) algorithm recently introduced to graphics is a grid-free Monte Carlo method that can provide numerical solutions of Poisson equations without discretizing space. We draw analogies between WoS and classical rendering algorithms, and find that the WoS algorithm is conceptually equivalent to forward path tracing. Inspired by similar approaches in light transport, we propose a novel WoS reformulation that operates in the reverse direction, starting at source points and estimating the Green's function at ''sensor'' points. Implementations of this algorithm show improvement over classical WoS in solving Poisson equation with sparse sources. Our approach opens exciting avenues for future algorithms for PDE estimation which, analogous to light transport, connect WoS walks starting from sensors and sources and combine different strategies for robust solution algorithms in all cases.
  • Thumbnail Image
    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, 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.
  • Thumbnail Image
    Item
    Impulse Responses for Precomputing Light from Volumetric Media
    (The Eurographics Association, 2019) Dubouchet, Adrien; Sloan, Peter-Pike; Jarosz, Wojciech; Nowrouzezahrai, Derek; Boubekeur, Tamy and Sen, Pradeep
    Modern interactive rendering can rely heavily on precomputed static lighting on surfaces and in volumes. Scattering from volumetric media can be similarly treated using precomputation, but transport from volumes onto surfaces is typically ignored here. We propose a compact, efficient method to simulate volume-to-surface transport during lighting precomputation . We leverage a novel model of the spherical impulse response of light scattered (and attenuated) in volumetric media to simulate light transport from volumes onto surfaces with simple precomputed lookup tables. These tables model the impulse response as a function of distance and angle to the light and surfaces. We then remap the impulse responses to media with arbitrary, potentially heterogeneous scattering parameters and various phase functions. Moreover, we can compose our impulse response model to treat multiple scattering events in the volume (arriving at surfaces). We apply our method to precomputed volume-to-surface light transport in complex scenes, generating results indistinguishable from ground truth simulations. Our tables allow us to precompute volume-to-surface transport orders of magnitude faster than even an optimized path tracing-based solution would.
  • Thumbnail Image
    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, 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.
  • Thumbnail Image
    Item
    Scalable Virtual Ray Lights Rendering for Participating Media
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Vibert, Nicolas; Gruson, Adrien; Stokholm, Heine; Mortensen, Troels; Jarosz, Wojciech; Hachisuka, Toshiya; Nowrouzezahrai, Derek; Boubekeur, Tamy and Sen, Pradeep
    Virtual ray lights (VRL) are a powerful representation for multiple-scattered light transport in volumetric participating media. While efficient Monte Carlo estimators can importance sample the contribution of a VRL along an entire sensor subpath, render time still scales linearly in the number of VRLs. We present a new scalable hierarchial VRL method that preferentially samples VRLs according to their image contribution. Similar to Lightcuts-based approaches, we derive a tight upper bound on the potential contribution of a VRL that is efficient to compute. Our bound takes into account the sampling probability densities used when estimating VRL contribution. Ours is the first such upper bound formulation, leading to an efficient and scalable rendering technique with only a few intuitive user parameters. We benchmark our approach in scenes with many VRLs, demonstrating improved scalability compared to existing state-of-the-art techniques.
  • Thumbnail Image
    Item
    Temporally Sliced Photon Primitives for Time-of-flight Rendering
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Liu, Yang; Jiao, Shaojie; Jarosz, Wojciech; Ghosh, Abhijeet; Wei, Li-Yi
    We derive a class of new Monte Carlo estimators for volumetric time-of-flight rendering, generalizing prior work on transient photon points and beams. Conceptually, our method starts with any steady-state photon primitive – like a photon plane, parallelepiped, or parallelotope – and slices it with a temporal wavefront, producing a primitive of one dimension lower. We show how different unbiased temporally sliced primitives arise by analytically integrating any four dimensions within a novel extended spatio-temporal path space formulation. The differences between these estimators reduce to the determinant of a 4×4 Jacobian matrix, with columns dictated by the chosen dimensions. We then show how to combine the relative strengths of different sliced primitives using multiple importance sampling. Finally, we implement several of the new estimators enabled by our theory and compare them to each other as well as previous techniques.