CPPM: Chi-squared Progressive Photon Mapping

摘要

We present a novel chi-squared progressive photon mapping algorithm(CPPM) that constructs an estimator by controlling the bandwidth to obtainsuperior image quality. Our estimator has parametric statistical advantagesover prior nonparametric methods. First, we show that when a probabilitydensity function of the photon distribution is subject to uniform distribution,the radiance estimation is unbiased under certain assumptions. Next,the local photon distribution is evaluated via a chi-squared test to determinewhether the photons follow the hypothesized distribution (uniformdistribution) or not. If the statistical test deems that the photons insidethe bandwidth are uniformly distributed, bandwidth reduction should besuspended. Finally, we present a pipeline with a bandwidth retention andconditional reduction scheme according to the test results. This pipeline not only accumulates sufficient photons for a reliable chi-squared test, but alsoguarantees that the estimate converges to the correct solution under ourassumptions. We evaluate our method on various benchmarks and observesignificant improvement in the running time and rendering quality in termsof mean squared error over prior progressive photon mapping methods.