Zero-Variance Transmittance Estimation

We apply zero-variance theory to the Volterra integral formulation of volumetric transmittance. We solve for the guided sampling decisions in this framework that produce zero-variance ratio tracking and next-flight ratio tracking estimators. In both cases, a zero-variance estimate arises by colliding only with the null particles along the interval. For ratio tracking, this is equivalent to residual ratio tracking with a perfect control. The next-flight zero-variance estimator is of the collision type and can only produce zero-variance estimates if the random walk never terminates. In drawing these new connections, we enrich the theory of Monte Carlo transmittance estimation and provide a new rigorous path-stretching interpretation of residual ratio tracking.