Fourier analysis of numerical integration in Monte Carlo rendering
Kartic Subr, Gurprit Singh, Wojciech Jarosz · 2016
Since being introduced to graphics in the 1980s, Monte Carlo sampling and integration has become the cornerstone of most modern rendering algorithms. Originally introduced to combat the effect of aliasing when estimating pixels values, Monte Carlo has since become a more general tool for solving complex, multi-dimensional integration problems in rendering. In this context, MC integration involves sampling a function at various stochastically placed points to approximate an integral, e.g. the radiance through a pixel integrated across the multi-dimensional space of possible light transport paths. Unfortunately, this estimation is error-prone, and the visual manifestation of this error depends critically on the properties of the integrand, placement of the stochastic sample points used, and the type of problem (integration vs. reconstruction) that is being solved with these samples.