End-to-end Sampling Patterns

Sample patterns have many uses in Computer Graphics, ranging from procedural object placement over Monte Carlo image synthesis to non-photorealistic depiction. Their properties such as discrepancy, spectra, anisotropy, or progressiveness have been analyzed extensively. However, designing methods to produce sampling patterns with certain properties can require substantial hand-crafting effort, both in coding, mathematical derivation and compute time. In particular, there is no systematic way to derive the best sampling algorithm for a specific end-task. Tackling this issue, we suggest another level of abstraction: a toolkit to end-to-end optimize over all sampling methods to find the one producing user-prescribed properties such as discrepancy or a spectrum that best fit the end-task. A user simply implements the forward losses and the sampling method is found automatically -- without coding or mathematical derivation -- by making use of back-propagation abilities of modern deep learning frameworks. While this optimization takes long, at deployment time the sampling method is quick to execute as iterated unstructured non-linear filtering using radial basis functions (RBFs) to represent high-dimensional kernels. Several important previous methods are special cases of this approach, which we compare to previous work and demonstrate its usefulness in several typical Computer Graphics applications. Finally, we propose sampling patterns with properties not shown before, such as high-dimensional blue noise with projective properties

Analysis of Sample Correlations for Monte Carlo Rendering

Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.publishe

Um ambiente para desevonvoimento de algoritmos de amostragem e remoção de ruído

In the context of Monte Carlo rendering, although many sampling and denoising techniques have been proposed in the last few years, the case for which one should be used for a specific scene is still to be made. Moreover, developing a new technique has required selecting a particular rendering system, which makes the technique tightly coupled to the chosen renderer and limits the amount of scenes it can be tested on. In this work, we propose a renderer-agnostic framework for developing and benchmarking sampling and denoising techniques for Monte Carlo rendering. It decouples techniques from rendering systems by hiding the renderer details behind a general API. This improves productivity and allows for direct comparisons among techniques using scenes from different rendering systems. The proposed framework contains two main parts: a software development kit that helps users to develop and and test their techniques locally, and an online system that allows users to submit their techniques and have them automatically benchmarked on our servers. We demonstrate its effectiveness by using our API to instrument four rendering systems and a variety of Monte Carlo denoising techniques — including recent learning-based ones — and performing a benchmark across different rendering systems.No contexto de Monte Carlo rendering, apesar de diversas técnicas de amostragem e remoção de ruído tenham sido propostas nos últimos anos, aportar qual técnica deve ser usada para uma cena específica ainda é uma tarefa difícil. Além disso, desenvolver uma nova técnica requer escolher um renderizador em particular, o que torna a técnica dependente do renderizador escolhido e limita a quantidade de cenas disponíveis para testar a técnica. Neste trabalho, um framework para desenvolvimento e avaliação de técnicas de amostragem e remoção de ruído para Monte Carlo rendering é proposto. Ele permite desacoplar as técnicas dos renderizadores por meio de uma API genérica, promovendo a reprodutibilidade e permitindo comparações entre técnicas utilizando-se cenas de diferentes renderizadores. O sistema proposto contém duas partes principais: um kit de desenvolvimento de software que ajuda os usuários a desenvolver e testar suas técnicas localmente, e um sistema online que permite que usuários submetam técnicas para que as mesmas sejam automaticamente avaliadas no nosso servidor. Para demonstramos a efetividade do ambiante proposto, modificamos quatro renderizadores e várias técnicas de remoção de ruído — incluindo técnicas recentes baseadas em aprendizado de máquina — e efetuamos uma avaliação utilizando cenas de diferentes renderizadores

Sequences with Low-Discrepancy Blue-Noise 2-D Projections

International audienceStaged local optimized permutations Our optimized scrambled sequence Sobol sequence Our sequence Ground truth Figure 1: Left: our staged per-tile optimized scrambling, applied to a Sobol sequence of sampling points, produces a power spectrum close to Blue Noise. Right: Rendering of a challenging scene featuring depth of field and high specularity (jewels). The sampling was done with the Sobol sequence (top) and our sampler (bottom); both use 256 samples per pixel and 3 light bounces. Note the improvement in aliasing when using our method in comparison to the original Sobol sequence. Abstract Distributions of samples play a very important role in rendering, affecting variance, bias and aliasing in Monte-Carlo and Quasi-Monte Carlo evaluation of the rendering equation. In this paper, we propose an original sampler which inherits many important features of classical low-discrepancy sequences (LDS): a high degree of uniformity of the achieved distribution of samples, computational efficiency and progressive sampling capability. At the same time, we purposely tailor our sampler in order to improve its spectral characteristics, which in turn play a crucial role in variance reduction, anti-aliasing and improving visual appearance of rendering. Our sampler can efficiently generate sequences of multidimensional points, whose power spectra approach so-called Blue-Noise (BN) spectral property while preserving low discrepancy (LD) in certain 2-D projections. In our tile-based approach, we perform permutations on subsets of the original Sobol LDS. In a large space of all possible permutations, we select those which better approach the target BN property, using pair-correlation statistics. We pre-calculate such " good " permutations for each possible Sobol pattern, and store them in a lookup table efficiently accessible in runtime. We provide a complete and rigorous proof that such permutations preserve dyadic partitioning and thus the LDS properties of the point set in 2-D projections. Our construction is computationally efficient, has a relatively low memory footprint and supports adaptive sampling. We validate our method by performing spectral/discrepancy/aliasing analysis of the achieved distributions, and provide variance analysis for several target integrands of theoretical and practical interest

Sequences with Low-Discrepancy Blue-Noise 2-D Projections

International audienceStaged local optimized permutations Our optimized scrambled sequence Sobol sequence Our sequence Ground truth Figure 1: Left: our staged per-tile optimized scrambling, applied to a Sobol sequence of sampling points, produces a power spectrum close to Blue Noise. Right: Rendering of a challenging scene featuring depth of field and high specularity (jewels). The sampling was done with the Sobol sequence (top) and our sampler (bottom); both use 256 samples per pixel and 3 light bounces. Note the improvement in aliasing when using our method in comparison to the original Sobol sequence. Abstract Distributions of samples play a very important role in rendering, affecting variance, bias and aliasing in Monte-Carlo and Quasi-Monte Carlo evaluation of the rendering equation. In this paper, we propose an original sampler which inherits many important features of classical low-discrepancy sequences (LDS): a high degree of uniformity of the achieved distribution of samples, computational efficiency and progressive sampling capability. At the same time, we purposely tailor our sampler in order to improve its spectral characteristics, which in turn play a crucial role in variance reduction, anti-aliasing and improving visual appearance of rendering. Our sampler can efficiently generate sequences of multidimensional points, whose power spectra approach so-called Blue-Noise (BN) spectral property while preserving low discrepancy (LD) in certain 2-D projections. In our tile-based approach, we perform permutations on subsets of the original Sobol LDS. In a large space of all possible permutations, we select those which better approach the target BN property, using pair-correlation statistics. We pre-calculate such " good " permutations for each possible Sobol pattern, and store them in a lookup table efficiently accessible in runtime. We provide a complete and rigorous proof that such permutations preserve dyadic partitioning and thus the LDS properties of the point set in 2-D projections. Our construction is computationally efficient, has a relatively low memory footprint and supports adaptive sampling. We validate our method by performing spectral/discrepancy/aliasing analysis of the achieved distributions, and provide variance analysis for several target integrands of theoretical and practical interest