, Russian Federation
, Russian Federation
BISAC MAT008000 Discrete Mathematics
A Monte-Carlo ray tracing is nowadays standard approach for lighting simulation and generation of realistic images. A widely used method for noise reduction in Monte-Carlo ray tracing is combing different means of sampling, known as Multiple Importance Sampling (MIS). For bi-directional Monte-Carlo ray tracing with photon maps (BDPM) the join paths are obtained by merging camera and light sub-paths. Since several light paths are checked against the same camera path and vice versa, the join paths obtained are not statistically independent. Thus the noise in this method does not obey the laws which are correct in simple classic Monte-Carlo with independent samples. And, correspondingly, the MIS weights that minimize that noise must also be calculated differently. In this paper we calculate these weights for a simple model scene directly minimizing the noise of calculation. This is a pure direct numerical minimization that does not involve any doubtful hypothesis or approximations. We show that the weights obtained are qualitatively different from those calculated from classic “balance heuristic” for Monte-Carlo with independent samples. They depend on the scene distance, but not only on scattering properties of the surfaces and the distribution of light source emission.
Monte-Carlo ray tracing, bi-directional ray tracing, photon maps, reduction of noise, multiple importance sampling, weights
1. Matt Pharr and Greg Humphreys. 2010. Physically Based Rendering, Second Edition: From Theory to Implementation (2nd ed.). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.
2. H. W. Jensen, Global illumination using photon maps, in Proceedings of the Eurographics Workshop on Rendering Techniques '96, (London, UK, UK), pp. 21–30, Springer-Verlag, 1996.
3. Eric Veach. A dissertation: Robust Monte-Carlo methods for light transport simulation, 1997.
4. Jiri Vorba. Bidirectional photon mapping. In Proceedings of CESCG 2011: The 15th Central European Seminar on Computer Graphics, Prague, 2011.
5. I. Georgiev, J. Křivánek, T. Davidovič, and Ph. Slusallek. 2012. Light transport simulation with vertex connection and merging. ACM Trans. Graph. 31, 6, Article 192 (November 2012)
6. S. Ershov, D. Zhdanov, and A. Voloboy. Estimation of noise in calculation of scattering medium luminance by MCRT. Mathematica Montisnigri, XLV: 60–73, 2019.
7. S. Ershov, D. Zhdanov, A. Voloboy, M. Sorokin. Treating diffuse elements as quasi-specular to reduce noise in bi-directional ray tracing // Keldysh Institute Preprints. 2018. No. 122. 30 p. doi:10.20948/prepr-2018-122-e
8. S. Popov, R. Ramamoorthi, F. Durand, and G. Drettakis, Probabilistic Connections for Bidirectional Path Tracing, Computer Graphics Forum, 2015.
9. N. Dodik, Implementing probabilistic connections for bidirectional path tracing in the Mitsuba Renderer, Sept. 2017.