Fourier Analysis of Correlated Monte Carlo Importance Sampling

International audienceFourier analysis is gaining popularity in image synthesis, as a tool for the analysis of error in Monte Carlo (MC) integration. Still, existing tools are only able to analyze convergence under simplifying assumptions (such as randomized shifts) which are not applied in practice during rendering. We reformulate the expressions for bias and variance of sampling-based integrators to unify non-uniform sample distributions (importance sampling) as well as correlations between samples while respecting finite sampling domains. Our unified formulation hints at fundamental limitations of Fourier-based tools in performing variance analysis for MC integration. This non-trivial exercise also provides exciting insight into the effects of importance sampling on the convergence rate of estimators because of the introduction or removal of discontinuities. Specifically, we demonstrate that the convergence of multiple importance sampling (MIS) is determined by the strategy that converges slowest. We propose two simple and practical approaches to limit the impact of discontinuities on the convergence rate of estimators: The first one involves mirroring the integrand to cancel out the effect of boundary discontinuities. This is followed by two novel mirror sampling techniques for MC estimation in this mirrored domain. The second approach improves direct illumination light sampling by smoothing out discontinuities within the domain at the cost of introducing a small amount of bias. Our approaches are simple, practical and can be easily incorporated in production renderers

How natural forest conversion affects insect biodiversity in the Peruvian Amazon : can agroforestry help?

The Amazonian rainforest is a unique ecosystem that comprises habitat for thousands of animal species. Over the last decades, the ever-increasing human population has caused forest conversion to agricultural land with concomitant high biodiversity losses, mainly near a number of fast-growing cities in the Peruvian Amazon. In this research, we evaluated insect species richness and diversity in five ecosystems: natural forests, multistrata agroforests, cocoa agroforests, annual cropping monoculture and degraded grasslands. We determined the relationship between land use intensity and insect diversity changes. Collected insects were taxonomically determined to morphospecies and data evaluated using standardized biodiversity indices. The highest species richness and abundance were found in natural forests, followed by agroforestry systems. Conversely, monocultures and degraded grasslands were found to be biodiversity-poor ecosystems. Diversity indices were relatively high for all ecosystems assessed with decreasing values along the disturbance gradient. An increase in land use disturbance causes not only insect diversity decreases but also complete changes in species composition. As agroforests, especially those with cocoa, currently cover many hectares of tropical land and show a species composition similar to natural forest sites, we can consider them as biodiversity reservoirs for some of the rainforest insect species

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

A PVM-based parallel implementation of the REYES image rendering architecture

In this paper a PVM-based distributed platform of the well known REYES rendering architecture developed byPix ar is presented. This work effectivelyt ackles issues related to load balancing and memory allocation by a master-slave paradigm. In particular, the rendering is distributed performing both an image and an object space subdivision; in this way, low memory resources are necessary to the slave side. Examples show the effectiveness of the proposed work