Characterising Per-Pixel Rendering Difficulty by Transport Mechanism

Abstract

Per-pixel rendering difficulty is conventionally characterised by one noisy scalar: the sample variance of a Monte Carlo estimator. We argue that it should instead be characterised through \emph{transport structure} --- a discrete description of how each contribution's energy reaches the sensor, deterministic under stated renderer conventions --- with variance treated as a measurement whose reliability that structure helps predict. We make this concrete with a seven-class transport-mechanism descriptor assigned per contribution event, evaluate it on eleven scenes, and measure variance reliability on the seven first-party ones. The dominant label agrees $87$--$99.6\%$ between 64 and 4096 samples per pixel, where quantile-binned variance agrees as little as $21\%$; its stability on unseen scenes is predicted from their pilots. Conditioning a pilot variance on the label improves equal-budget sample allocation wherever heavy-tailed buckets carry appreciable population, reduces to the incumbent where they are absent or negligible, and is neither reproduced by a random partition nor absorbed by a median-of-means estimator; where the pilot fails for other reasons, as on the classical ajar-door scene ($6.8$~dB below uniform), the label says so from the pilot alone.