A spatial target function for metropolis photon tracing

The human visual system is sensitive to relative differences in luminance, but light transport simulation algorithms based on Metropolis sampling often result in a highly nonuniform relative error distribution over the rendered image. Although this issue has previously been addressed in the context of the Metropolis light transport algorithm, our work focuses on Metropolis photon tracing. We present a new target function (TF) for Metropolis photon tracing that ensures good stratification of photons leading to pixel estimates with equalized relative error. We develop a hierarchical scheme for progressive construction of the TF from paths sampled during rendering. In addition to the approach taken in previous work, where the TF is defined in the image plane, ours can be associated with compact spatial regions. This allows us to take advantage of illumination coherence to more robustly estimate the TF while adapting to geometry discontinuities. To sample from this TF, we design a new replica exchange Metropolis scheme. We apply our algorithm in progressive photon mapping and show that it often outperforms alternative approaches in terms of image quality by a large margin.