Variance Analysis and Adaptive Sampling for Indirect Light Path Reuse

In this paper, we study the estimation variance of a set of global illumination algorithms based on indirect light path reuse. These algorithms usually contain two passes — in the first pass, a small number of indirect light samples are generated and evaluated, and they are then reused by a large number of reconstruction samples in the second pass. Our analysis shows that the covariance of the reconstruction samples dominates the estimation variance under high reconstruction rates and increasing the reconstruction rate cannot effectively reduce the covariance. We also find that the covariance represents to what degree the indirect light samples are reused during reconstruction. This analysis motivates us to design a heuristic approximating the covariance as well as an adaptive sampling scheme based on this heuristic to reduce the rendering variance. We validate our analysis and adaptive sampling scheme in the indirect light field reconstruction algorithm and the axis-aligned filtering algorithm for indirect lighting. Experiments are in accordance with our analysis and show that rendering artifacts can be greatly reduced at a similar computational cost.