Error analysis of estimators that use combinations of stochastic sampling strategies for direct illumination

We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance‐reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. J...

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Published in:	Computer graphics forum Vol. 33; no. 4; pp. 93 - 102
Main Authors:	Subr, Kartic, Nowrouzezahrai, Derek, Jarosz, Wojciech, Kautz, Jan, Mitchell, Kenny
Format:	Journal Article
Language:	English
Published:	Oxford Blackwell Publishing Ltd 01.07.2014
Subjects:	Analysis Categories and Subject Descriptors (according to ACM CCS) Computer graphics Computer simulation Convergence Estimating techniques Estimators I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation Illumination Importance sampling Monte Carlo methods Monte Carlo simulation Multimedia computer applications Sampling Strategy Studies Telematics
ISSN:	0167-7055, 1467-8659
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Abstract	We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance‐reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. Jittered sampling (a type of stratified sampling), on the other hand is known to improve the convergence rate. Most rendering software optimistically combine importance sampling with jittered sampling, hoping to achieve both. We derive the exact error of the combination of multiple importance sampling with jittered sampling. In addition, we demonstrate a further benefit of introducing negative correlations (antithetic sampling) between estimates to the convergence rate. As with importance sampling, antithetic sampling is known to reduce error for certain classes of integrands without affecting the convergence rate. In this paper, our analysis and experiments reveal that importance and antithetic sampling, if used judiciously and in conjunction with jittered sampling, may improve convergence rates. We show the impact of such combinations of strategies on the convergence rate of estimators for direct illumination.
AbstractList	We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance-reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. Jittered sampling (a type of stratified sampling), on the other hand is known to improve the convergence rate. Most rendering software optimistically combine importance sampling with jittered sampling, hoping to achieve both. We derive the exact error of the combination of multiple importance sampling with jittered sampling. In addition, we demonstrate a further benefit of introducing negative correlations (antithetic sampling) between estimates to the convergence rate. As with importance sampling, antithetic sampling is known to reduce error for certain classes of integrands without affecting the convergence rate. In this paper, our analysis and experiments reveal that importance and antithetic sampling, if used judiciously and in conjunction with jittered sampling, may improve convergence rates. We show the impact of such combinations of strategies on the convergence rate of estimators for direct illumination. We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance-reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. Jittered sampling (a type of stratified sampling), on the other hand is known to improve the convergence rate. Most rendering software optimistically combine importance sampling with jittered sampling, hoping to achieve both. We derive the exact error of the combination of multiple importance sampling with jittered sampling. In addition, we demonstrate a further benefit of introducing negative correlations (antithetic sampling) between estimates to the convergence rate. As with importance sampling, antithetic sampling is known to reduce error for certain classes of integrands without affecting the convergence rate. In this paper, our analysis and experiments reveal that importance and antithetic sampling, if used judiciously and in conjunction with jittered sampling, may improve convergence rates. We show the impact of such combinations of strategies on the convergence rate of estimators for direct illumination. [PUBLICATION ABSTRACT]
Author	Subr, Kartic Jarosz, Wojciech Nowrouzezahrai, Derek Mitchell, Kenny Kautz, Jan
Author_xml	– sequence: 1 givenname: Kartic surname: Subr fullname: Subr, Kartic organization: Disney Research, Zurich – sequence: 2 givenname: Derek surname: Nowrouzezahrai fullname: Nowrouzezahrai, Derek organization: University of Montreal – sequence: 3 givenname: Wojciech surname: Jarosz fullname: Jarosz, Wojciech organization: Disney Research, Zurich – sequence: 4 givenname: Jan surname: Kautz fullname: Kautz, Jan organization: University College London – sequence: 5 givenname: Kenny surname: Mitchell fullname: Mitchell, Kenny organization: Disney Research, Zurich
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References	Hammersley J.M., Mauldon J.G.: General Principles of Antithetic Variates. Proc. Cambridge Philos. Soc. 52 (1956), 476-481. 2 Owen A., Zhou Y.: Safe and Effective Importance Sampling. Journal of the American Statistical Association 95, 449 (2000), 135-143. 2 Niederreiter H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, 1992. 3 Owen A.B.: Local Antithetic Sampling with Scrambled Nets. The Annals of Statistics 36, 5 (2008), 2319-2343. 2, 3, 6 Agarwal S., Ramamoorthi R., Belongie S., Jensen H.W.: Structured Importance Sampling of Environment Maps. ACM Transactions on Graphics 22, 3 (2003), 605-612. 2 Neyman J.: On the two different aspects of the representative method: the method of stratified sampling and of purposive selection. J. of the Royal Stat. Society 97, 4 (1934), 558-625. 3 Haber, S.: Numerical Evaluation of Multiple Integrals. SIAM Review 12 (1970), 481-526. 3 Bishop C.M.: Pattern Recognition and Machine Learning. Springer, 2006. 2 Křivánek J., Colbert M.: Real-time Shading with Filtered Importance Sampling. Computer Graphics Forum (EGSR '08) 27, 4 (2008), 1147-1154. 3 Ramamoorthi R., Anderson J., Meyer M., Nowrouzezahrai D.: A Theory of Monte Carlo Visibility Sampling. ACM Trans. Graph. 31, 5 (2012), 121:1-121:16. 3, 6 Cook R.L.: Stochastic Sampling in Computer Graphics. ACM Transactions on Graphics 5, 1 (Jan. 1986), 51-72. 2 Hesterberg T.C.: Advances in Importance Sampling. PhD thesis, Stanford University, 2003. 2 Georgiev I., Křivánek J., Hachisuka T., Nowrouzezahrai D., Jarosz W.: Joint Importance Sampling of Low-order Volumetric Scattering. ACM Transactions on Graphics 32, 6 (2013), 164:1-164:14. 2 Dick J., Pillichshammer F.: Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration. Cambridge University Press, New York, NY, USA, 2010. 3 Clarberg P., Jarosz W., Akenine-Möller T., Jensen H.W.: Wavelet Importance Sampling: Efficiently Evaluating Products of Complex Functions. ACM Transactions on Graphics 24, 3 (2005). 2 Hammersley J.M., Morton K.W.: A New Monte Carlo Technique: Antithetic Variates. Proc. Cambridge Philos. Soc. 52 (1956), 449-475. 2 Saliby E., Paul R.J.: A farewell to the use of antithetic variates in Monte Carlo simulation. JORS 60, 7 (2009), 1026-1035. 2 Keller A., Heinrich S., Niederreiter H.: Monte Carlo and Quasi-Monte Carlo methods. Springer, 2006. 3 Veach E.: Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University, 1997. 1, 2 Keller A.: Quasi-Monte Carlo methods in computer graphics: the global illumination problem. Lectures in Applied Mathematics. 32 (1996), 455-470. 3 2012 2010 1956; 52 2009; 60 1970; 12 2008; 36 2000; 95 1997 1996 2006 1995 2005 2004 2003 1992 1996; 32 2012; 31 2005; 24 2013; 32 1986; 5 2008; 27 1934; 97 1983 2013 2003; 22 e_1_2_8_27_2 e_1_2_8_28_2 e_1_2_8_29_2 Veach E. (e_1_2_8_33_2) 1995 e_1_2_8_23_2 e_1_2_8_24_2 e_1_2_8_25_2 Veach E. (e_1_2_8_32_2) 1997 e_1_2_8_26_2 e_1_2_8_9_2 Hesterberg T.C. (e_1_2_8_10_2) 2003 e_1_2_8_2_2 e_1_2_8_4_2 e_1_2_8_3_2 e_1_2_8_6_2 e_1_2_8_5_2 e_1_2_8_8_2 e_1_2_8_7_2 e_1_2_8_20_2 e_1_2_8_22_2 Keller A. (e_1_2_8_15_2) 1996; 32 NELSEN R.B. (e_1_2_8_21_2) 2006 e_1_2_8_17_2 e_1_2_8_19_2 e_1_2_8_12_2 e_1_2_8_13_2 e_1_2_8_14_2 Keller A. (e_1_2_8_16_2) 2006 e_1_2_8_31_2 e_1_2_8_30_2 e_1_2_8_11_2 Lemieux C. (e_1_2_8_18_2) 2010
References_xml	– reference: Hammersley J.M., Morton K.W.: A New Monte Carlo Technique: Antithetic Variates. Proc. Cambridge Philos. Soc. 52 (1956), 449-475. 2 – reference: Bishop C.M.: Pattern Recognition and Machine Learning. Springer, 2006. 2 – reference: Haber, S.: Numerical Evaluation of Multiple Integrals. SIAM Review 12 (1970), 481-526. 3 – reference: Owen A., Zhou Y.: Safe and Effective Importance Sampling. Journal of the American Statistical Association 95, 449 (2000), 135-143. 2 – reference: Hesterberg T.C.: Advances in Importance Sampling. PhD thesis, Stanford University, 2003. 2 – reference: Clarberg P., Jarosz W., Akenine-Möller T., Jensen H.W.: Wavelet Importance Sampling: Efficiently Evaluating Products of Complex Functions. ACM Transactions on Graphics 24, 3 (2005). 2 – reference: Georgiev I., Křivánek J., Hachisuka T., Nowrouzezahrai D., Jarosz W.: Joint Importance Sampling of Low-order Volumetric Scattering. ACM Transactions on Graphics 32, 6 (2013), 164:1-164:14. 2 – reference: Ramamoorthi R., Anderson J., Meyer M., Nowrouzezahrai D.: A Theory of Monte Carlo Visibility Sampling. ACM Trans. Graph. 31, 5 (2012), 121:1-121:16. 3, 6 – reference: Hammersley J.M., Mauldon J.G.: General Principles of Antithetic Variates. Proc. Cambridge Philos. Soc. 52 (1956), 476-481. 2 – reference: Veach E.: Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University, 1997. 1, 2 – reference: Cook R.L.: Stochastic Sampling in Computer Graphics. ACM Transactions on Graphics 5, 1 (Jan. 1986), 51-72. 2 – reference: Saliby E., Paul R.J.: A farewell to the use of antithetic variates in Monte Carlo simulation. JORS 60, 7 (2009), 1026-1035. 2 – reference: Niederreiter H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, 1992. 3 – reference: Agarwal S., Ramamoorthi R., Belongie S., Jensen H.W.: Structured Importance Sampling of Environment Maps. ACM Transactions on Graphics 22, 3 (2003), 605-612. 2 – reference: Dick J., Pillichshammer F.: Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration. Cambridge University Press, New York, NY, USA, 2010. 3 – reference: Neyman J.: On the two different aspects of the representative method: the method of stratified sampling and of purposive selection. J. of the Royal Stat. Society 97, 4 (1934), 558-625. 3 – reference: Keller A.: Quasi-Monte Carlo methods in computer graphics: the global illumination problem. Lectures in Applied Mathematics. 32 (1996), 455-470. 3 – reference: Křivánek J., Colbert M.: Real-time Shading with Filtered Importance Sampling. Computer Graphics Forum (EGSR '08) 27, 4 (2008), 1147-1154. 3 – reference: Owen A.B.: Local Antithetic Sampling with Scrambled Nets. The Annals of Statistics 36, 5 (2008), 2319-2343. 2, 3, 6 – reference: Keller A., Heinrich S., Niederreiter H.: Monte Carlo and Quasi-Monte Carlo methods. Springer, 2006. 3 – start-page: 277 year: 1996 end-page: 280 – volume: 32 start-page: 455 year: 1996 end-page: 470 article-title: Quasi‐Monte Carlo methods in computer graphics: the global illumination problem publication-title: Lectures in Applied Mathematics. – year: 1983 – volume: 27 start-page: 1147 issue: 4 year: 2008 end-page: 1154 article-title: Real‐time Shading with Filtered Importance Sampling publication-title: Computer Graphics Forum (EGSR '08) – volume: 24 issue: 3 year: 2005 article-title: Wavelet Importance Sampling: Efficiently Evaluating Products of Complex Functions publication-title: ACM Transactions on Graphics – volume: 52 start-page: 449 year: 1956 end-page: 475 article-title: A New Monte Carlo Technique: Antithetic Variates publication-title: Proc. Cambridge Philos. Soc. – start-page: 183 end-page: 194 – volume: 5 issue: 1 year: 1986 article-title: Stochastic Sampling in Computer Graphics publication-title: ACM Transactions on Graphics – year: 2003 – volume: 12 start-page: 481 year: 1970 end-page: 526 article-title: Numerical Evaluation of Multiple Integrals publication-title: SIAM Review – year: 1992 – volume: 97 start-page: 558 issue: 4 year: 1934 end-page: 625 article-title: On the two different aspects of the representative method: the method of stratified sampling and of purposive selection publication-title: J. of the Royal Stat. Society – volume: 31 start-page: 121:1 issue: 5 year: 2012 end-page: 121:16 article-title: A Theory of Monte Carlo Visibility Sampling publication-title: ACM Trans. Graph – year: 2010 – volume: 36 start-page: 2319 issue: 5 year: 2008 end-page: 2343 article-title: Local Antithetic Sampling with Scrambled Nets publication-title: The Annals of Statistics – volume: 60 start-page: 1026 issue: 7 year: 2009 end-page: 1035 article-title: A farewell to the use of antithetic variates in Monte Carlo simulation publication-title: JORS – start-page: 496 year: 2004 end-page: 505 – volume: 22 start-page: 605 issue: 3 year: 2003 end-page: 612 article-title: Structured Importance Sampling of Environment Maps publication-title: ACM Transactions on Graphics – start-page: 147 year: 2005 end-page: 156 – volume: 52 start-page: 476 year: 1956 end-page: 481 article-title: General Principles of Antithetic Variates publication-title: Proc. Cambridge Philos. Soc. – year: 2006 – year: 1997 – volume: 95 start-page: 135 issue: 449 year: 2000 end-page: 143 article-title: Safe and Effective Importance Sampling publication-title: Journal of the American Statistical Association – start-page: 21:1 year: 2012 end-page: 21:46 – volume: 32 start-page: 164:1 issue: 6 year: 2013 end-page: 164:14 article-title: Joint Importance Sampling of Low‐order Volumetric Scattering publication-title: ACM Transactions on Graphics – start-page: 419 year: 1995 end-page: 428 – year: 2013 – volume-title: Springer Series in Statistics year: 2006 ident: e_1_2_8_21_2 – volume-title: Springer Series in Statistics year: 2010 ident: e_1_2_8_18_2 – ident: e_1_2_8_27_2 – ident: e_1_2_8_24_2 doi: 10.1214/07-AOS548 – ident: e_1_2_8_9_2 doi: 10.1137/1012102 – ident: e_1_2_8_17_2 doi: 10.1145/2343483.2343502 – ident: e_1_2_8_7_2 doi: 10.1017/CBO9780511761188 – ident: e_1_2_8_19_2 doi: 10.1145/1015706.1015751 – ident: e_1_2_8_2_2 doi: 10.1145/882262.882314 – ident: e_1_2_8_4_2 doi: 10.1007/978-0-387-45528-0 – volume-title: Monte Carlo and Quasi‐Monte Carlo methods year: 2006 ident: e_1_2_8_16_2 – volume-title: Robust Monte Carlo Methods for Light Transport Simulation year: 1997 ident: e_1_2_8_32_2 – ident: e_1_2_8_5_2 doi: 10.1145/1073204.1073328 – ident: e_1_2_8_11_2 doi: 10.1017/S0305004100031467 – ident: e_1_2_8_29_2 – ident: e_1_2_8_3_2 doi: 10.1145/1187112.1187241 – ident: e_1_2_8_8_2 doi: 10.1145/2508363.2508411 – ident: e_1_2_8_28_2 doi: 10.1145/2231816.2231819 – ident: e_1_2_8_31_2 – volume: 32 start-page: 455 year: 1996 ident: e_1_2_8_15_2 article-title: Quasi‐Monte Carlo methods in computer graphics: the global illumination problem publication-title: Lectures in Applied Mathematics. – ident: e_1_2_8_20_2 – start-page: 419 volume-title: 22Nd Annual Conference on Computer Graphics and Interactive Techniques year: 1995 ident: e_1_2_8_33_2 – ident: e_1_2_8_25_2 – volume-title: Advances in Importance Sampling year: 2003 ident: e_1_2_8_10_2 – ident: e_1_2_8_12_2 doi: 10.1017/S0305004100031455 – ident: e_1_2_8_23_2 doi: 10.1137/1.9781611970081 – ident: e_1_2_8_30_2 doi: 10.1057/palgrave.jors.2602645 – ident: e_1_2_8_6_2 doi: 10.1145/7529.8927 – ident: e_1_2_8_14_2 doi: 10.1111/j.1467-8659.2008.01252.x – ident: e_1_2_8_22_2 doi: 10.1111/j.2397-2335.1934.tb04184.x – ident: e_1_2_8_13_2 – ident: e_1_2_8_26_2 doi: 10.1080/01621459.2000.10473909
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SubjectTerms	Analysis Categories and Subject Descriptors (according to ACM CCS) Computer graphics Computer simulation Convergence Estimating techniques Estimators I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation Illumination Importance sampling Monte Carlo methods Monte Carlo simulation Multimedia computer applications Sampling Strategy Studies Telematics
Title	Error analysis of estimators that use combinations of stochastic sampling strategies for direct illumination
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