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    EUROGRAPHICS 2016: Tutorials Frontmatter
    (Eurographics Association, 2016) Sousa, A. Augusto; Bouatouch, Kadi;
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    Bayesian and Quasi Monte Carlo Spherical Integration for Illumination Integrals
    (The Eurographics Association, 2014) Marques, Ricardo; Bouville, Christian; Bouatouch, Kadi; Nicolas Holzschuch and Karol Myszkowski
    The spherical sampling of the incident radiance function entails a high computational cost. Therefore the illumination integral must be evaluated using a limited set of samples. Such a restriction raises the question of how to obtain the most accurate approximation possible with such a limited set of samples. We need to ensure that sampling produces the highest amount of information possible by carefully placing the limited set of samples. Furthermore we want our integral evaluation to take into account not only the information produced by the sampling but also possible information available prior to sampling. In this tutorial we focus on the case of hemispherical sampling for spherical Monte Carlo (MC) integration. We will show that existing techniques can be improved by making a detailed analysis of the theory of MC spherical integration. We will then use this theory to identify and improve the weak points of current approaches, based on very recent advances in the fields of integration and spherical Quasi-Monte Carlo integration.
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    Two-Level Adaptive Sampling for Illumination Integrals using Bayesian Monte Carlo
    (The Eurographics Association, 2016) Marques, Ricardo; Bouville, Christian; Santos, Luis P.; Bouatouch, Kadi; T. Bashford-Rogers and L. P. Santos
    Bayesian Monte Carlo (BMC) is a promising integration technique which considerably broadens the theoretical tools that can be used to maximize and exploit the information produced by sampling, while keeping the fundamental property of data dimension independence of classical Monte Carlo (CMC). Moreover, BMC uses information that is ignored in the CMC method, such as the position of the samples and prior stochastic information about the integrand, which often leads to better integral estimates. Nevertheless, the use of BMC in computer graphics is still in an incipient phase and its application to more evolved and widely used rendering algorithms remains cumbersome. In this article we propose to apply BMC to a two-level adaptive sampling scheme for illumination integrals. We propose an efficient solution for the second level quadrature computation and show that the proposed method outperforms adaptive quasi-Monte Carlo in terms of image error and high frequency noise.