Abstract
As opposed to Monte Carlo integration the quasi-Monte Carlo method does not allow for an error estimate from the samples used for the integral approximation and the deterministic error bound is not accessible in the setting of computer graphics, since usually the integrands are of unbounded variation. We investigate the application of randomized quasi-Monte Carlo integration to bidirectional path tracing yielding much more efficient algorithms that exploit low-discrepancy sampling and at the same time allow for variance estimation.
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References
J. Beck and W. Chen, Irregularities of Distribution, Cambridge University Press, 1987.
R. Cook, Stochastic Sampling in Computer Graphics, ACM Transactions on Graphics 5 (1986), no. 1, 51–72.
R. Cranley and T. Patterson, Randomization of Number Theoretic Methods for Multiple Integration, SI AM Journal on Numerical Analysis 13 (1976), 904–914.
H. Faure, Good Permutations for Extreme Discrepancy, J. Number Theory 42 (1992), 47–56.
I. Friedel and A. Keller, Fast Generation of Randomized Low Discrepancy Point Sets, 2000, this volume.
A. Glassner, Principles of Digital Image Synthesis, Morgan Kaufmann, 1995.
E. Hlawka, Discrepancy and Riemann Integration, Studies in Pure Mathematics (L. Mirsky, ed.), Academic Press, New York, 1971, pp. 121–129.
A. Keller, Quasi-Monte Carlo Methods for Photorealistic Image Synthesis, Ph.D. thesis, Shaker, Aachen, 1998.
[Kel98b] —, The Quasi-Random Walk, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing 1996 (H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof, eds.), Lecture Notes in Statistics, vol. 127, Springer, 1998, pp. 277–291.
E. Lafortune and Y. Willems, Bidirectional Path Tracing, Proc. 3rd International Conference on Computational Graphics and Visualization Techniques (Compugraphics), 1993, pp. 145–153.
H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Pennsylvania, 1992.
H. Niederreiter and C. Xing, H. Niederreiter, eds.), Cambridge University Press, 1996, 269–29
A. Owen, Randomly Permuted (t,m,s)-Nets and (t,s)-Sequences, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P. Shiue, eds.), Lecture Notes in Statistics, vol. 106, Springer, 1995, pp. 299–317.
[Owe98a], Latin Supercube Sampling for Very High Dimensional Simulations, ACM Transactions on Modeling and Computer Simulation 8 (1998), 71–102.
[Owe98b]—, Monte Carlo Extension of Quasi-Monte Carlo, Winter Simulation Conference, IEEE Press, 1998, pp. 571–577.
A. Owen and Y. Zhou, Safe and Effective Importance Sampling, Tech. report, Stanford University, Goldman-Sachs, 1999.
G. Pirsic, A Soßware Implementation of Niederreit er-Xing Sequences, 2000, this volume.
P. Shirley, Physically Based Lighting Calculations for Computer Graphics, Ph.D. thesis, University of Illinois, Urbana-Champaign, 1990.
I. Sloan and S. Joe, Lattice Methods for Multiple Integration, Clarendon Press, Oxford, 1994.
I. Sobol, A Primer for the Monte Carlo Method, CRC Press, 1994.
B. Tuffin, On the Use of Low Discrepancy Sequences in Monte Carlo Methods, Monte Carlo Methods and Applications 2 (1996), no. 4, 295–320.
E. Veach, Robust Monte Carlo Methods for Light Transport Simulation, Ph.D. thesis, Stanford University, December 1997.
E. Veach and L. Guibas, Bidirectional Estimators for Light Transport, Proc. 5th Eurographics Workshop on Rendering (Darmstadt, Germany), June 1994, pp. 147–161.
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Kollig, T., Keller, A. (2002). Efficient Bidirectional Path Tracing by Randomized Quasi-Monte Carlo Integration. In: Fang, KT., Niederreiter, H., Hickernell, F.J. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56046-0_19
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DOI: https://doi.org/10.1007/978-3-642-56046-0_19
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