Optimizing Path Termination for Radiance Caching Through Explicit Variance Trading

Radiance caching allows to amortize the cost of path tracing by sharing contributions of path suffices in a spatial data structure. This sharing generally introduces bias, but it can be traded with variance by terminating into the cache at deeper path vertices. We develop a framework to implicitly reduce bias by optimizing path termination towards a chosen variance bound. Importantly, this bound can be chosen large enough while still being amenable to denoising. This results in longer paths being sampled with unbiased path tracing as permitted by the estimator variance and variance bound. To that end, we reformulate the variance of a path tracing estimator as a quantity that can be expressed locally for a path, relying on auxiliary statistics that are shared through the radiance cache structure independently of the path prefix. This allows to perform the optimization locally during path construction, while still translating to a global bound. Our method is capable of maintaining the variance bound in complex scenes, resulting in lower bias compared to other techniques such as heuristics based on ray differentials. We additionally present first findings on directly optimizing the bias-variance tradeoff based on local bias estimates of individual cache records, although the optimization is only approximate, resulting in suboptimal termination decisions.