Frequency Analysis and Sheared Filtering for Multidimensional Effects in Rendering

Many of the most expensive effects in rendering are those that require integrating complex multidimensional signals. Computation for a single pixel can require hundreds of samples, and standard methods do not provide a mathematically sound way to share samples between pixels with overlapping integrands. This thesis first analyzes the underlying signals for motion blur and occlusion and identifies the sparse structure of these signals in the Fourier domain. We then leverage this information to design a sheared filter that is customized to each pixel's frequency content. We finally present practical algorithms that share samples between pixels, reduce sampling requirements by an order of magnitude, and provide significant speedups for many of the most expensive computations in computer graphics

Factored axis-aligned filtering for rendering multiple distribution effects

Monte Carlo (MC) ray-tracing for photo-realistic rendering often requires hours to render a single image due to the large sampling rates needed for convergence. Previous methods have attempted to filter sparsely sampled MC renders but these methods have high reconstruction overheads. Recent work has shown fast performance for individual effects, like soft shadows and indirect illumination, using axis-aligned filtering. While some components of light transport such as indirect or area illumination are smooth, they are often multiplied by high-frequency components such as texture, which prevents their sparse sampling and reconstruction. We propose an approach to adaptively sample and filter for simultaneously rendering primary (defocus blur) and secondary (soft shadows and indirect illumination) distribution effects, based on a multi-dimensional frequency analysis of the direct and indirect illumination light fields. We describe a novel approach of factoring texture and irradiance in the presence of defocus blur, which allows for pre-filtering noisy irradiance when the texture is not noisy. Our approach naturally allows for different sampling rates for primary and secondary effects, further reducing the overall ray count. While the theory considers only Lambertian surfaces, we obtain promising results for moderately glossy surfaces. We demonstrate 30x sampling rate reduction compared to equal quality noise-free MC. Combined with a GPU implementation and low filtering over-head, we can render scenes with complex geometry and diffuse and glossy BRDFs in a few seconds.National Science Foundation (U.S.) (Grant CGV 1115242)National Science Foundation (U.S.) (Grant CGV 1116303)Intel Corporation (Science and Technology Center for Visual Computing

5D Covariance Tracing for Efficient Defocus and Motion Blur

The rendering of effects such as motion blur and depth-of-field requires costly 5D integrals. We dramatically accelerate their computation through adaptive sampling and reconstruction based on the prediction of the anisotropy and bandwidth of the integrand. For this, we develop a new frequency analysis of the 5D temporal light-field, and show that first-order motion can be handled through simple changes of coordinates in 5D. We further introduce a compact representation of the spectrum using the co- variance matrix and Gaussian approximations. We derive update equations for the 5 × 5 covariance matrices for each atomic light transport event, such as transport, occlusion, BRDF, texture, lens, and motion. The focus on atomic operations makes our work general, and removes the need for special-case formulas. We present a new rendering algorithm that computes 5D covariance matrices on the image plane by tracing paths through the scene, focusing on the single-bounce case. This allows us to reduce sampling rates when appropriate and perform reconstruction of images with complex depth-of-field and motion blur effects

Temporal light field reconstruction for rendering distribution effects

Traditionally, effects that require evaluating multidimensional integrals for each pixel, such as motion blur, depth of field, and soft shadows, suffer from noise due to the variance of the high-dimensional integrand. In this paper, we describe a general reconstruction technique that exploits the anisotropy in the temporal light field and permits efficient reuse of samples between pixels, multiplying the effective sampling rate by a large factor. We show that our technique can be applied in situations that are challenging or impossible for previous anisotropic reconstruction methods, and that it can yield good results with very sparse inputs. We demonstrate our method for simultaneous motion blur, depth of field, and soft shadows

Frequency Based Radiance Cache for Rendering Animations

International audienceWe propose a method to render animation sequences with direct distant lighting that only shades a fraction of the total pixels. We leverage frequency-based analyses of light transport to determine shading and image sampling rates across an animation using a samples cache. To do so, we derive frequency bandwidths that account for the complexity of distant lights, visibility, BRDF, and temporal coherence during animation. We finaly apply a cross-bilateral filter when rendering our final images from sparse sets of shading points placed according to our frequency-based oracles (generally < 25% of the pixels, per frame)

Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur

International audienceMotion blur is crucial for high-quality rendering but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes is usually contained in a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that tightly packs the wedge of frequencies in the Fourier domain, and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require

A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes

The numerical calculation of integrals is central to many computer graphics algorithms such as Monte-Carlo Ray Tracing. We show that such methods can be studied using Fourier analysis. Numerical error is shown to correspond to aliasing and the link between properties of the sampling pattern and the integrand is studied. The approach also permits the unified study of image aliasing and numerical integration, by considering a multidimensional domain where some dimensions are integrated while others are sampled

Une approche fréquentielle pratique pour l'échantillonnage adaptatif en espace image

En synthèse d'images réalistes, l'intensité finale d'un pixel est calculée en estimant une intégrale de rendu multi-dimensionnelle. Une large portion de la recherche menée dans ce domaine cherche à trouver de nouvelles techniques afin de réduire le coût de calcul du rendu tout en préservant la fidelité et l'exactitude des images résultantes. En tentant de réduire les coûts de calcul afin d'approcher le rendu en temps réel, certains effets réalistes complexes sont souvent laissés de côté ou remplacés par des astuces ingénieuses mais mathématiquement incorrectes. Afin d'accélerer le rendu, plusieurs avenues de travail ont soit adressé directement le calcul de pixels individuels en améliorant les routines d'intégration numérique sous-jacentes; ou ont cherché à amortir le coût par région d'image en utilisant des méthodes adaptatives basées sur des modèles prédictifs du transport de la lumière. L'objectif de ce mémoire, et de l'article résultant, est de se baser sur une méthode de ce dernier type[Durand2005], et de faire progresser la recherche dans le domaine du rendu réaliste adaptatif rapide utilisant une analyse du transport de la lumière basée sur la théorie de Fourier afin de guider et prioriser le lancer de rayons. Nous proposons une approche d'échantillonnage et de reconstruction adaptative pour le rendu de scènes animées illuminées par cartes d'environnement, permettant la reconstruction d'effets tels que les ombres et les réflexions de tous les niveaux fréquentiels, tout en préservant la cohérence temporelle.In realistic image synthesis, a pixel's final intensity is computed by estimating a multi-dimensional shading integral. A large part of the research in this domain is thus aimed at finding new techniques to reduce the computational cost of rendering while preserving the fidelity and correctness of the resulting images. When trying to reduce rendering costs to approach real-time computation, complex realistic effects are often left aside or replaced by clever but mathematically incorrect tricks. To accelerate rendering, previous directions of work have either addressed the computation of individual pixels by improving the underlying numerical integration routines; or have sought to amortize the computation across regions of an image using adaptive methods based on predictive models of light transport. This thesis' - and resulting paper's - objective is to build upon the latter of the aforementioned classes of methods[Durand2005], and foray into fast adaptive rendering techniques using frequency-based light transport analysis to efficiently guide and prioritize ray tracing. We thus propose an adaptive sampling and reconstruction approach to render animated scenes lit by environment lighting and faithfully reconstruct all-frequency shading effects such as shadows and reflections while preserving temporal coherency

Logarithmic perspective shadow maps

The shadow map algorithm is a popular approach for generating shadows for real-time applications. Shadow maps are flexible and easy to implement, but they are prone to aliasing artifacts. To reduce aliasing artifacts we introduce logarithmic perspective shadow maps (LogPSMs). LogPSMs are based on a novel shadow map parameterization that consists of a perspective projection and a logarithmic transformation. They can be used for both point and directional light sources to produce hard shadows. To establish the benefits of LogPSMs, we perform an in-depth analysis of shadow map aliasing error and the error characteristics of existing algorithms. Using this analysis we compute a parameterization that produces near-optimal perspective aliasing error. This parameterization has high arithmetical complexity which makes it less practical than existing methods. We show, however, that over all light positions, the simpler LogPSM parameterization produces the same maximum error as the near-optimal parameterization. We also show that compared with competing algorithms, LogPSMs produce significantly less aliasing error. Equivalently, for the same error as competing algorithms, LogPSMs require significantly less storage and bandwidth. We demonstrate difference in shadow quality achieved with LogPSMs on several models of varying complexity. LogPSMs are rendered using logarithmic rasterization. We show how current GPU architectures can be modified incrementally to perform logarithmic rasterization at current GPU fill rates. Specifically, we modify the rasterizer to support rendering to a nonuniform grid with the same watertight rasterization properties as current rasterizers. We also describe a novel depth compression scheme to handle the nonlinear primitives produced by logarithmic rasterization. Our proposed architecture enhancements align with current trends of decreasing cost for on-chip computation relative to off-chip bandwidth and storage. For only a modest increase in computation, logarithmic rasterization can greatly reduce shadow map bandwidth and storage costs