Name
Abstract | ||
|---|---|---|
Traditional Monte Carlo (MC) integration methods use point samples to numerically approximate the underlying integral. This approximation introduces variance in the integrated result, and this error can depend critically on the sampling patterns used during integration. Most of the well-known samplers used for MC integration in graphics---e.g. jittered, Latin-hypercube (N-rooks), multijittered---are anisotropic in nature. However, there are currently no tools available to analyze the impact of such anisotropic samplers on the variance convergence behavior of Monte Carlo integration. In this work, we develop a Fourier-domain mathematical tool to analyze the variance, and subsequently the convergence rate, of Monte Carlo integration using any arbitrary (anisotropic) sampling power spectrum. We also validate and leverage our theoretical analysis, demonstrating that judicious alignment of anisotropic sampling and integrand spectra can improve variance and convergence rates in MC rendering, and that similar improvements can apply to (anisotropic) deterministic samplers. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1145/3072959.3073656 | ACM Trans. Graph. |
Keywords | Field | DocType |
Monte Carlo,stochastic sampling,signal processing | Monte Carlo method in statistical physics,Monte Carlo method,Mathematical optimization,Control variates,Hybrid Monte Carlo,Quasi-Monte Carlo method,Monte Carlo integration,Dynamic Monte Carlo method,Monte Carlo molecular modeling,Mathematics | Journal |
Volume | Issue | ISSN |
36 | 4 | 0730-0301 |
Citations | PageRank | References |
2 | 0.37 | 28 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gurprit Singh | 1 | 27 | 6.11 |
| Wojciech Jarosz | 2 | 1041 | 60.39 |