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Hartmann, K. (2020):

Theoretical study of photon mapping with stratification

In the last decades computer-generated images have become indispensable. From product design over the game and film industry until medical analysis - computer graphics plays a significant role in all of these sectors. The photon mapping algorithm is a relevant method used for generating especially photo realistic images. In this work the bias of photon mapping in combination with stratified sampling is examined. For this purpose three types of scenes are considered: a one dimensional setup, surface illumination and volumetric effects. The theoretical study of all three setups detects an overestimation bias similar to the bias described in "Describing and Solution of an Unreported Intrinsic Bias in Photon Mapping Density Estimation with Constant Kernel" by Garcìa et al. This overestimation bias is verified afterwards with an experimental study of stratified photon mapping. With different estimates for calculating the irradiance that were used in other theoretical studies of photon mapping it is investigated how the detected overestimation bias for stratified photon mapping behaves. The estimate proposed by Garcìa et al. leads to a small underestimation bias while the another estimate presented in "A Practical Guide to Global Illumination using Photon Mapping" by Jensen et al. reduces the absolute value of the bias, showing a mixture between over- and underestimation. In the end it is presented scientific research that applies the theoretical concept behind photon mapping and it is proposed a study of variance in combination with stratified photon mapping for a future research area.