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Item EUROGRAPHICS 2016: Tutorials Frontmatter(Eurographics Association, 2016) Sousa, A. Augusto; Bouatouch, Kadi;Item An adaptive Discretization Method For Radiosity(Blackwell Science Ltd and the Eurographics Association, 1992) Languenou, Eric; Bouatouch, Kadi; Tellier, PierreWhen using radiosiiy, the visual quality of the rendered images strongly depends on the method employed for discretizing the scene into patches. A too fine discretization may give rise to artifacts, while with a coarse discretization areas with high radiosity gradient may appear. To overcome these problems, the discretization must adapt to the scene. That is, the interaction between two patches must account for the distance between them as well as their surface area. In other words, surfaces far away are discretized less finely than nearby surfaces. These aspects are considered by the new adaptive discretiration method described in this paper. It performs both discretization and system resolution at each iteration of the shooting process, allowing then interactivity.Item Bayesian and Quasi Monte Carlo Spherical Integration for Illumination Integrals(The Eurographics Association, 2014) Marques, Ricardo; Bouville, Christian; Bouatouch, Kadi; Nicolas Holzschuch and Karol MyszkowskiThe 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.Item 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. SantosBayesian 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.Item Computation of Higher Order Illumination with a Non-Deterministic Approach(Blackwell Science Ltd and the Eurographics Association, 1996) Bouatouch, Kadi; Pattanaik, S. N.; Zeghers, EricIn spite of the number of efforts made by the computer graphics researchers, till today the computation of view-independent global illumination in an environment containing non-diffusely reflecting objects is a non-resolved problem. In general, non-deterministic techniques seem to be capable of solving this problem. In this article we propose one such non-deterministic method which will permit such calculation by using a combined technique of higher order function approximation and particle tracing. We have used multi-wavelets as basis functions and have calculated the illumination function approximation coefficients by exploiting the adjointness between the radiance equation and the potential equation.Item Low Sampling Densities using a psychovisual approach(Eurographics Association, 1991) Bouville, Christian; Tellier, Pierre; Bouatouch, KadiIt has long been observed that the keenness of sight is lower for diagonal directions than for horizontal or vertical ones. This anisotropy of the human eye response can be exploited by using a non-orthogonal sampling pattern with a reduced sampling density. After an introduction to the two-dimensional sampling theory, it is shown that quincunx sampling is well suited to this characteristic. Then a sampling scheme based on this approach is described. This effectively leads to halving the sampling density and thereby the computing time of ray-traced pictures.Item Fast Wavelet Radiosity Method(Blackwell Science Ltd and the Eurographics Association, 1994) Pattanaik, Sumanta N.; Bouatouch, KadiWavelet analysis has been found [1] to be very useful for functional representation and accurate global solution of radiosity. In radiosity we deal with functions in 2D and 4D spaces. Under such conditions, the biggest bottleneck in applying this wavelet analysis seems to be the large number of multidimensional inner products. In this paper, we propose (i) the use of interpolating wavelets for fast inner product computation and consequently for faster wavelet radiosity solution (ii) the use of hierarchical decomposition technique for determining the smoothness of the radiosity function for optimal adaptive subdivision.