Efficiency Investigation of Langevin Monte Carlo Ray Tracing

Sergey Ershov, Vladimir Frolov, Alexander Nikolaev, Vladimir Galaktionov and Alexey Voloboy ()
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Sergey Ershov: Department of Computer Graphics and Computational Optics, Keldysh Institute of Applied Mathematics RAS, 125047 Moscow, Russia
Vladimir Frolov: Department of Computer Graphics and Computational Optics, Keldysh Institute of Applied Mathematics RAS, 125047 Moscow, Russia
Alexander Nikolaev: Laboratory of Computer Graphics and Multimedia, Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991 Moscow, Russia
Vladimir Galaktionov: Department of Computer Graphics and Computational Optics, Keldysh Institute of Applied Mathematics RAS, 125047 Moscow, Russia
Alexey Voloboy: Department of Computer Graphics and Computational Optics, Keldysh Institute of Applied Mathematics RAS, 125047 Moscow, Russia

Mathematics, 2024, vol. 12, issue 21, 1-24

Abstract: The main computationally expensive task of realistic computer graphics is the calculation of global illumination. Currently, most of the lighting simulation methods are based on various types of Monte Carlo ray tracing. One of them, the Langevin Monte Carlo ray tracing, generates samples using the time series of a system of the Langevin dynamics. The method seems to be very promising for calculating the global illumination. However, it remains poorly studied, while its analysis could significantly speed up the calculations without losing the quality of the result. In our work, we analyzed the most computationally expensive operations of this method and also conducted the computational experiments demonstrating the contribution of a particular operation to the convergence speed. One of our main conclusions is that the computationally expensive drift term can be dropped because it does not improve convergence. Another important conclution is that the preconditioning matrix makes the greatest contribution to the improvement of convergence. At the same time, calculation of this matrix is not so expensive, because it does not require calculating the gradient of the potential. The results of our study allow to significantly speed up the method.

Keywords: global illumination; monte carloray tracing; Markov chain; Langevin dynamics; preconditioning matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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