S. Des-contributions-passe-en-utilisant-un-faible-taux-d-'échantillonnage, puis de détecter les zones de l'image pour lesquelles le niveau de bruit n'est pas acceptable et enfin suréchantillonner ces dernières jusqu'à ce qu'un certain critère de qualité soit atteint. Notre objectif est d'appliquer BMC avec une approche adaptative pour évaluer l'intégrale de l'éclairement. L'idée consiste à calculer une première estimation avec BMC (en utilisant un premier ensemble d'échantillons) puis, si le critère de qualité n'est pas satisfait, d'injecter directement le résultat comme connaissance a priori dans une nouvelle estimation

. [. Bibliography, J. S. Aistleitner, J. Brauchart, and . Dick, Point sets on the sphere S 2 with small spherical cap discrepancy, Discrete & Computational Geometry, vol.15, pp.1-35

J. Brouillat, C. Bouville, B. Loos, C. Hansen, K. Bouatouch et al., A Bayesian Monte Carlo Approach to Global Illumination, Computer Graphics Forum, vol.19, issue.1, pp.2315-2329, 2009.
DOI : 10.1111/j.1467-8659.2009.01537.x
URL : https://hal.archives-ouvertes.fr/inria-00479654

]. J. Bec84 and . Beck, Sums of distances between points on a sphere ? An application of the theory of irregularities of distribution to discrete geometry, Mathematika, vol.31, issue.1, pp.33-41, 1984.

J. S. Brauchart, E. B. Saff, I. H. Sloan, and R. S. Womersley, QMC designs: optimal order Quasi Monte Carlo Integration schemes on the sphere. ArXiv e-prints, 2012.

T. Caelli, Visual Perception, Theory and Practice, p.62, 1981.

R. L. Cook, T. Porter, and L. Carpenter, Distributed ray tracing, Proceedings of the 11th annual conference on Computer graphics and interactive techniques, SIGGRAPH '84, pp.137-145, 1984.

Z. Chen, Y. Yuan, L. Choi, W. Liu, and . Wang, Variational Blue Noise Sampling, IEEE Transactions on Visualization and Computer Graphics, vol.18, issue.10, pp.1784-1796, 2012.
DOI : 10.1109/TVCG.2012.94

]. F. De-goes, K. Breeden, V. Ostromoukhov, and M. Desbrun, Blue noise through optimal transport, ACM Transactions on Graphics, vol.31, issue.6, pp.31-46, 2012.
DOI : 10.1145/2366145.2366190
URL : https://hal.archives-ouvertes.fr/hal-01353135

B. Dutré, P. Heckbert, V. Ma, F. Pel-lacini, R. Porschka et al., Global illumination compendium, p.12, 2001.

M. S. Ebeida, A. Patney, S. A. Mitchell, A. Davidson, P. M. Knupp et al., Efficient maximal Poisson-disk sampling, ACM Transactions on Graphics, vol.30, issue.10, pp.49-64, 2011.

A. Geiger, Gaussian process for machine learning, ACM SIGGRAPH 2011 papers, pp.1-10, 2007.

. M. Ghb-+-05-]-k, E. Gorski, A. J. Hivon, B. D. Banday, F. K. Wandelt et al., HEALPix -A framework for high resolution discretization, and fast analysis of data distributed on the sphere, Astrophys. J, vol.622, issue.12, pp.759-771, 2005.

L. Grünschloß, J. Hanika, R. Schwede, and A. Keller, (t, m, s)-nets and maximized minimum distance, Monte Carlo and Quasi-Monte Carlo Methods, Proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, p.77, 2006.

L. Grünschloß and A. Keller, (t, m, s)-nets and maximized minimum distance, part ii, Monte Carlo and Quasi-Monte Carlo Methods , Proceedings of the Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, p.11, 2008.

R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science [Gon10] Álvaro González. Measurement of areas on a sphere using Fibonacci and Latitude?Longitude lattices, Mathematical Geosciences, vol.42, issue.15, pp.1549-64, 1994.

[. Huszár and D. Duvenaud, Optimally-weighted herding is Bayesian quadrature, In Uncertainty in Artificial Intelligence, p.66, 2012.

]. Hachisuka, W. Jarosz, R. Peter-weistroffer, K. Dale, G. Humphreys et al., Multidimensional adaptive sampling and reconstruction for ray tracing, ACM Trans. Graph, vol.2733, issue.3, pp.1-3310, 2008.
DOI : 10.1145/1399504.1360632
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.7536

J. Hannay and J. Nye, Fibonacci numerical integration on a sphere, Proceedings of the eurographics workshop on Rendering techniques '96, pp.11591-11607, 1996.
DOI : 10.1088/0305-4470/37/48/005

J. T. Kajiya, The rendering equation, ACM SIGGRAPH Computer Graphics, vol.20, issue.4, pp.143-150, 1986.
DOI : 10.1145/15886.15902

[. K?ivánek and M. Colbert, Real-time Shading with Filtered Importance Sampling, Computer Graphics Forum, vol.24, issue.3, pp.1147-1154, 2008.
DOI : 10.1111/j.1467-8659.2008.01252.x

A. Keller, Quasi-Monte Carlo image synthesis in a nutshell, 2012. https://sites.google.com/site, p.76

A. Kensler, Correlated multi-jittered sampling

J. K?ivánek, P. Gautron, S. Pattanaik, and K. Bouatouch, Radiance Caching for Efficient Global Illumination Computation, Kuipers and H. Niederreiter. Uniform Distribution of Sequences. Dover Books on Mathematics, pp.550-561, 2002.
DOI : 10.1109/TVCG.2005.83

[. Keller, S. Premoze, and M. Raab, Advanced (quasi) Monte Carlo methods for image synthesis, ACM SIGGRAPH 2012 Posters on, SIGGRAPH '12, pp.1-46
DOI : 10.1145/2343483.2343502

A. Lagae and P. Dutré, A Comparison of Methods for Generating Poisson Disk Distributions, Computer Graphics Forum, vol.5, issue.1, pp.114-129, 2008.
DOI : 10.1145/1015706.1015750

L. Pierre and . Ecuyer, Quasi-monte carlo methods with applications in finance, Finance and Stochastics, vol.13, issue.3 7, pp.307-349, 2009.

F. [. Larcher and . Pillichshammer, Walsh series analysis of the L2- discrepancy of symmetrisized point sets, Monatshefte für Mathematik, pp.1-18, 2001.

R. [. Lubotzky, P. Phillips, and . Sarnak, Hecke operators and distributing points on the sphere I Statistically optimized sampling for distributed ray tracing, Communications on Pure and Applied Mathematics, pp.149-186, 1985.

P. Eric, Y. Lafortune, and . Willems, Bi-directional path tracing Eric Lafortune and Yves Willems. A 5D tree to reduce the variance of Monte Carlo ray tracing, Compugraphics '93 Rendering Techniques '95 (Proceedings of the Sixth Eurographics Workshop on Rendering) Àlex Méndez-Feliu and Mateu Sbert. Comparing hemisphere sampling techniques for obscurance computation 3IA 04: Proceedings of the International Conference on Computer Graphics and Artificial Intelligence, pp.145-153, 1993.

P. Mit87-]-don and . Mitchell, Generating antialiased images at low sampling densities, SIGGRAPH Comput. Graph, vol.21, issue.4, pp.65-72, 1987.

H. Niederreiter, Low-discrepancy and low-dispersion sequences, Journal of Number Theory, vol.30, issue.1, pp.51-70, 1988.
DOI : 10.1016/0022-314X(88)90025-X
URL : http://doi.org/10.1016/0022-314x(88)90025-x

H. Niederreiter, Random number generation and quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics, vol.10, p.11, 1992.
DOI : 10.1137/1.9781611970081

]. J. Nye03 and . Nye, A simple method of spherical near-field scanning to measure the far fields of antennas or passive scatterers. Antennas and Propagation, IEEE Transactions on, vol.51, issue.8, pp.2091-2098, 2003.

. [. Hagan, Bayes???Hermite quadrature, Ost07] Victor Ostromoukhov. Sampling with polyominoes. Proceedings of ACM SIGGRAPH 2007, pp.245-260, 1991.
DOI : 10.1016/0378-3758(91)90002-V

M. Pharr and G. Humphreys, Physically Based Rendering, Second Edition: From Theory To Implementation, 2010.

D. [. Pfingsten, C. E. Herrmann, and . Rasmussen, Model-based design analysis and yield optimization. Semiconductor Manufacturing, IEEE Trans. on, vol.19, issue.4, pp.475-486, 2006.
DOI : 10.1109/tsm.2006.883589
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.8647

W. Purgathofer, A statistical method for adaptive stochastic sampling, Computers & Graphics, vol.11, issue.2, pp.157-162, 1987.
DOI : 10.1016/0097-8493(87)90029-X

J. Rigau, M. Feixas, and M. Sbert, New Contrast Measures for Pixel Supersampling, Proceedings of CGI 02, pp.439-451, 2002.
DOI : 10.1007/978-1-4471-0103-1_28

J. Rigau, M. Feixas, and M. Sbert, Entropy-based adaptive sampling, Graphics Interface, pp.149-158, 2003.

C. Edward-rasmussen and Z. Ghahramani, Bayesian Monte Carlo, Neural Information Processing Systems, pp.489-496, 2002.

C. [. Rasmussen and . Williams, Gaussian Process for Machine Learning, p.42, 2006.

P. Shirley, K. Shirley, D. Edwards, and S. Boulos, A Low Distortion Map Between Disk and Square, Journal of Graphics Tools, vol.2, issue.3, pp.45-52, 1997.
DOI : 10.1080/10867651.1997.10487479

]. C. Sha48, . Shannonsk97-]-e, A. Saff, and . Kuijlaars, A mathematical theory of communication Distributing many points on a sphere [Sob67] I. M. Sobol. On the distribution of points in a cube and the approximate evaluation of integrals, Bell System Technical Journal The Mathematical Intelligencer USSR Computational Math. and Math. Phys, vol.27, issue.15, pp.625-636, 1948.

R. Swinbank and J. Purser, Fibonacci grids: A novel approach to global modelling, Quarterly Journal of the Royal Meteorological Society, vol.102, issue.619, pp.1769-1793, 2006.
DOI : 10.1256/qj.05.227

]. D. Sve94 and . Svergun, Solution scattering from biopolymers: advanced contrastvariation data analysis, Acta Crystallographica Section A, vol.50, issue.3, pp.391-402, 1994.

E. Veach, Robust Monte Carlo Methods for Light Transport Simulation, p.76, 1998.

E. Veach and L. Guibas, Bidirectional Estimators for Light Transport, Proceedings of Eurographics Rendering Workshop, p.76, 1994.
DOI : 10.1007/978-3-642-87825-1_11

H. Vogel, A better way to construct the sunflower head, Mathematical Biosciences, vol.44, issue.3-4, pp.3-4179, 1979.
DOI : 10.1016/0025-5564(79)90080-4

G. J. Ward, F. M. Rubinstein, and R. D. Clear, A ray tracing solution for diffuse interreflection, ACM SIGGRAPH Computer Graphics, vol.22, issue.4, pp.85-92, 1988.
DOI : 10.1145/378456.378490

P. Wang, M. Ren, J. Gong, B. Snyder, and . Guo, All-frequency rendering of dynamic, spatially-varying reflectance, ACM Trans. Graph, vol.28, pp.133-134, 2009.

Q. Xu, S. Bao, R. Zhang, R. Hu, M. Sbert-feixas et al., Adaptive Sampling for Monte Carlo Global Illumination Using Tsallis Entropy, Computational Intelligence and Security, International Conference, Proceedings , Part II CAD/Graphics Industrial Electronics (ISIE), 2010 IEEE International Symposium on, pp.989-994, 2005.
DOI : 10.1007/11596981_147