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.