Abstract
This paper considers the uniform separation technique of integration domain for Monte Carlo image creation. Uniform Separation technique is based on symmetrical separation into small equal size sub-domains to solve the rendering equation which describes the photons propagation in a virtual scene. It tries to reduce the variance at solving the rendering equation pixel by pixel in the image pixels matrix.
Our goal is to analyze and study the Monte Carlo estimators by Uniform Separation for numerical treatment of the rendering equation, as well as the influence over the total process of image creation. We develop our consideration on the base of mathematical theory for Monte Carlo estimations and the experience of image creation. New results for the symmetric separation of integration domain are obtained and presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arvo, J.: Stratifed sampling of spherical triangles. In: Proceedings of SIGGRAPH 1995, ACM SIGGRAPH, pp. 437–438 (1995)
Dimov, I.T.: Optimal Monte Carlo Algorithms. In: ISMC 2006, Proceedings of IEEE — John Vincent Atanasoff, pp. 125–131 (2006)
Dimov, I.T.: Monte-Carlo Methods for Applied Scientists. World Scientific Publishing, Singapore (2008)
Dimov, I.T., Penzov, A.A., Stoilova, S.S.: Parallel Monte Carlo Sampling Scheme for Sphere and Hemisphere. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds.) NMA 2006. LNCS, vol. 4310, pp. 148–155. Springer, Heidelberg (2007)
Dimov, I.T., Penzov, A.A., Stoilova, S.S.: Parallel Monte Carlo Approach for Integration of the Rendering Equation. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds.) NMA 2006. LNCS, vol. 4310, pp. 140–147. Springer, Heidelberg (2007)
Kajiya, J.T.: The Rendering Equation. In: Proceedings of SIGGRAPH 1986 (1986); ACM SIGGRAPH Computer Graphics 20(4), 143–150 (1986)
Mitchell, D.P.: Consequences of stratified sampling in computer graphics. In: Proceedings of SIGGRAPH 1996, ACM SIGGRAPH, pp. 277–280 (1996)
Penzov, A.A., Dimov, I.T., Koylazov, V.N.: A New Solution of the Rendering Equation with Stratified Monte Carlo Approach. In: ICNAAM 2008, AIP Conference Proceedings, vol. 1048, pp. 432–435 (2008)
Penzov, A.A., Stoilova, S.S., Dimov, I.T., Mitev, N.M.: Uniform Separation for Parallel Monte Carlo Image Creation. In: Fourth Hungarian Conference on Computer Graphics and Geometry, SZTAKI, Budapest, Hungary, pp. 117–124 (2007)
Sobol, I.M.: Monte Carlo Numerical Methods, Nauka, Moscow (1975) (in Russian)
Szirmay-Kalos, L., Purgathofer, W.: Analisis of the Quasi-Monte Carlo Integration of the Rendering Equation. In: Proccedings of WSCG 1999, pp. 281–288. University of West Bohemia, Plzen (1999)
Szirmay-Kalos, L.: Monte-Carlo Methods in Global Illumination — Photo-realistic Rendering with Randomization. VDM Verlag Dr. Mueller e.K., Saarbrücken (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Penzov, A.A., Dimov, I.T., Szirmay-Kalos, L., Koylazov, V.N. (2010). Analysis of the Monte Carlo Image Creation by Uniform Separation. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_49
Download citation
DOI: https://doi.org/10.1007/978-3-642-12535-5_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12534-8
Online ISBN: 978-3-642-12535-5
eBook Packages: Computer ScienceComputer Science (R0)