Schaller, S. (2021):
Variance of Photon Mapping with Stratification
This thesis studies the theoretical aspect of the photon mapping algorithm based on the framework laid out in the paper from Rubén Jesús García-Hernández ``Description and Solution of an Unreported Intrinsic Bias in Photon Mapping Density Estimation with Constant Kernel'' by applying order statistics to the algorithm to derive theoretical results. We start by recapping the previous results while deriving a first-order approximation to the results. We explain how to reduce the over bias while keeping the variance the same. Furthermore, to reduce variance, we apply stratification to our model and look at the results. We are building upon the previous works: Kathrin Hartmann, in her bachelor thesis -- ``Theoretical study of photon mapping with stratiﬁcation'' -- calculates the expectation values of the irradiance. Zhiming Gan, in his bachelor thesis -- "Variance of photon mapping density estimation" -- calculates the variances for different filtering kernels. We extend this work by calculating the variance and derive an approximation to expectation values and variance. In the last part of the work, we provide a proof of concept. We show that our theoretical results are in good agreement with experimental values from our simulation.