This paper presents an analysis of the overestimation bias in common used filtering kernels in the context of photon mapping density estimation. We use the joint distribution of order statistics to calculate the expected value of the estimators of irradiance, and show that the estimator provided by the cone filter is not consistent unless the slope is one (yielding the triangular kernel), and that the Epanechnikov and Silverman kernels are consistent. The Gaussian filter has two different estimation biases: the original normalization constant α underestimates radiance by 46.9 percent, and the use of the kth nearest photon reduces this underestimation slightly. We also show that a new normalization constant for the Gaussian filter together with discarding the contribution of the kth nearest photon in the Gaussian and cone filter estimators produces new, consistent estimators. The specialized differential filter also benefits from the new estimate.

Abstract This paper presents an analysis of the irradiance estimator often used in photon mapping algorithms and concludes that the classical approach with a constant kernel overestimates the correct value. We propose a new estimator that solves this problem and provide both theoretical and empirical studies to verify it.

This paper describes an approach to obtain interactive recalculation of global illumination for scenes with small moving objects (with respect to the complete geometry), on a standard PC, using density estimation techniques