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Parallel Iteration to the Radiative Transport in Inhomogeneous Media with Bootstrapping
February 2011 (vol. 17 no. 2)
pp. 146-158
László Szirmay-Kalos, Budapest University of Technology and Economics, Magyar Tudósok
Gábor Liktor, Budapest University of Technology and Economics, Magyar Tudósok
Tamás Umenhoffer, Budapest University of Technology and Economics, Magyar Tudósok
Balázs Tóth, Budapest University of Technology and Economics, Magyar Tudósok
Shree Kumar, Hewlett-Packard India Software Operations, Bangalore
Glenn Lupton, Hewlett-Packard USA, Hollis
This paper presents a fast parallel method to solve the radiative transport equation in inhomogeneous participating media. We apply a novel approximation scheme to find a good initial guess for both the direct and scattered components. Then, the initial approximation is used to bootstrap an iterative multiple scattering solver, i.e., we let the iteration concentrate just on the residual problem. This kind of bootstrapping makes the volumetric source approximation more uniform, thus it helps to reduce the discretization artifacts and improves the efficiency of the parallel implementation. The iterative refinement is executed on a face-centered cubic grid. The implementation is based on CUDA and runs on the GPU. For large volumes that do not fit into the GPU memory, we also consider the implementation on a GPU cluster, where the volume is decomposed to blocks according to the available GPU nodes. We show how the communication bottleneck can be avoided in the cluster implementation by not exchanging the boundary conditions in every iteration step. In addition to light photons, we also discuss the generalization of the method to \gamma-photons that are relevant in medical simulation.

[1] L. Szirmay-Kalos, G. Liktor, T. Umenhoffer, B. Tóth, S. Kumar, and G. Lupton, "Parallel Solution to the Radiative Transport," Proc. Eurographics Symp. Parallel Graphics and Visualization, J. Comba, K. Debattista, and D. Weiskopf, eds., pp. 95-102, 2009.
[2] C.N. Yang, "The Klein-Nishina Formula & Quantum Electrodynamics," Lecture Notes in Physics, pp. 393-397, Springer, 2008.
[3] E. Cerezo, F. Pérez, X. Pueyo, F.J. Seron, and F.X. Sillion, "A Survey on Participating Media Rendering Techniques," The Visual Computer, vol. 21, no. 5, pp. 303-328, 2005.
[4] J.F. Blinn, "Light Reflection Functions for Simulation of Clouds and Dusty Surfaces," Proc. ACM SIGGRAPH '82, pp. 21-29, 1982.
[5] B. Sun, R. Ramamoorthi, S.G. Narasimhan, and S.K. Nayar, "A Practical Analytic Single Scattering Model for Real Time Rendering," ACM Trans. Graphics, vol. 24, no. 3, pp. 1040-1049, 2005.
[6] V. Pegoraro and S.G. Parker, "An Analytical Solution to Single Scattering in Homogeneous Participating Media," Computer Graphics Forum, vol. 28, no. 2, pp. 329-335, 2009.
[7] M. Harris and A. Lastra, "Real-Time Cloud Rendering," Computer Graphics Forum, vol. 20, no. 3, pp. 76-84, 2001.
[8] J. Kniss, S. Premoze, C. Hansen, and D. Ebert, "Interactive Translucent Volume Rendering and Procedural Modeling," Proc. IEEE Conf. Visualization (VIS '02), pp. 109-116, 2002.
[9] J. Stam, "Multiple Scattering as a Diffusion Process," Proc. Eurographics Rendering Workshop, pp. 41-50, 1995.
[10] H.W. Jensen, S.R. Marschner, M. Levoy, and P. Hanrahan, "A Practical Model for Subsurface Light Transport," Proc. ACM SIGGRAPH '01, pp. 511-518, 2001.
[11] X. Tong, J. Wang, S. Lin, B. Guo, and H.-Y. Shum, "Modeling and Rendering of Quasi-Homogeneous Materials," Proc. ACM SIGGRAPH '05 Papers, pp. 1054-1061, 2005.
[12] R. Geist, K. Rasche, J. Westall, and R.J. Schalkoff, "Lattice-Boltzmann Lighting," Proc. Workshop Rendering Techniques, pp. 355-362, 2004.
[13] T. Haber, T. Mertens, P. Bekaert, and F. Van Reeth, "A Computational Approach to Simulate Subsurface Light Diffusion in Arbitrarily Shaped Objects," Proc. Graphics Interface (GI '05) Conf., pp. 79-86, 2005.
[14] J. Wang, S. Zhao, X. Tong, S. Lin, Z. Lin, Y. Dong, B. Guo, and H.-Y. Shum, "Modeling and Rendering of Heterogeneous Translucent Materials Using the Diffusion Equation," ACM Trans. Graphics, vol. 27, no. 1, pp. 1-18, 2008.
[15] H.W. Jensen and P.H. Christensen, "Efficient Simulation of Light Transport in Scenes with Participating Media Using Photon Maps," Proc. ACM SIGGRAPH '98, pp. 311-320, 1998.
[16] F. Qiu, F. Xu, Z. Fan, and N. Neophytos, "Lattice-Based Volumetric Global Illumination," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, pp. 1576-1583, Nov. 2007.
[17] K. Zhou, Z. Ren, S. Lin, H. Bao, B. Guo, and H.-Y. Shum, "Real-Time Smoke Rendering Using Compensated Ray Marching," ACM Trans. Graphics, vol. 27, no. 3, p. 36, 2008.
[18] L. Szirmay-Kalos, M. Sbert, and T. Umenhoffer, "Real-Time Multiple Scattering in Participating Media with Illumination Networks," Proc. Eurographics Symp. Rendering, pp. 277-282, 2005.
[19] J. Kajiya and B.V. Herzen, "Ray Tracing Volume Densities," Proc. ACM SIGGRAPH '84, pp. 165-174, 1984.
[20] H.E. Rushmeier and K.E. Torrance, "The Zonal Method for Calculating Light Intensities in the Presence of a Participating Medium," Proc. ACM SIGGRAPH '87, pp. 293-302, 1987.
[21] R. Fattal, "Participating Media Illumination Using Light Propagation Maps," ACM Trans. Graphics, vol. 28, no. 1, pp. 1-11, 2009.
[22] M. Strengert, M. Magallon, D. Weiskopf, S. Guthe, and T. Ertl, "Hierarchical Visualization and Compression of Large Volume Datasets Using GPU Clusters," Proc. Eurographics Symp. Parallel Graphics and Visualization, pp. 41-48, 2004.
[23] B. Csébfalvi, "Prefiltered Gaussian Reconstruction for High-Quality Rendering of Volumetric Data Sampled on a Body-Centered Cubic Grid," Proc. IEEE Visualization (VIS '05) Conf. pp. 311-318, 2005.
[24] Paracomp, "Hp Scalable Visualization Array Version 2.1," technical report, Hewlett-Packard, , 2007.

Index Terms:
Radiative transport equation, multiple scattering, diffusion approximation, FCC grid, parallel computation, Monte Carlo method, iteration, GPU, CUDA.
László Szirmay-Kalos, Gábor Liktor, Tamás Umenhoffer, Balázs Tóth, Shree Kumar, Glenn Lupton, "Parallel Iteration to the Radiative Transport in Inhomogeneous Media with Bootstrapping," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 2, pp. 146-158, Feb. 2011, doi:10.1109/TVCG.2010.97
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