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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.