Analysis of Sample Correlations for Monte Carlo Rendering


Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.

Computer Graphics Forum (Proceedings of Eurographics)

Caption: * Different stratification techniques are summarized in 2D with their 1D projection along the vertical y-axis, where applicable. (a) Placing samples at the center of a grid gives visual banding artifacts during rendering. (b) By offsetting all samples within a pixel (jittering) by the same random amount, these artifacts can be avoided. (c) Random translation followed by a random rotation further helps to reduce variance. (d) Another variant involves perturbing each sample with a random offset from a radially symmetric Normal distribution within each stratum. (e) Random (and Gaussian) jittering does not have dense 1D stratification (1D projection contains more than one sample per stratum). (f) LH (or N-rooks) sampling does not preserve 2D stratification (empty strata in the top row and leftmost column). (g) Multi-jittered (MJ) sampling preserves both 1D and 2D stratifications, thereby combining LH and random jittering properties. (h) Correlated multi-jittered sampling further enforces points to be far apart from each other while preserving multi-jittered behavior. Bottom row shows their expected power spectra (exposure adjusted to highlight the spikes).*

      author = {Gurprit Singh and Cengiz Öztireli and Abdalla GM Ahmed and David Coeurjolly and Kartic Subr and Victor Ostromoukhov and Oliver Deussen and Ravi Ramamoorthi and Wojciech Jarosz},
      journal = {Computer Graphics Forum (Proceedings of Eurographics)},
      month = {June},
      number = {2},
      series = {State-of-the-art Report},
      title = {Analysis of Sample Correlations for Monte Carlo Rendering},
      volume = {38},
      year = {2019}