Geometric Sample Reweighting for Monte Carlo Integration

Numerical integration is fundamental in multiple Monte Carlo rendering problems. We present a sample reweighting scheme, including underlying theory, and analysis of numerical performance for the integration of an unknown one-dimensional function. Our method is simple to implement and builds upon the insight to link the weights to a function reconstruction process during integration. We provide proof that our solution is unbiased in one-dimensional cases and consistent in multi-dimensional cases. We illustrate its effectiveness in several use cases.

@Article { GE21,
  author       = "Guo, Jerry and Eisemann, Elmar",
  title        = "Geometric Sample Reweighting for Monte Carlo Integration",
  journal      = "Computer Graphics Forum (Proc. of Pacific Graphics)",
  number       = "7",
  volume       = "40",
  pages        = "109-119",
  month        = "Oct",
  year         = "2021",
  note         = "doi: 10.1111:cgf.14405",
  url          = "http://graphics.tudelft.nl/Publications-new/2021/GE21"
}