A Stable Transport-Mechanism Descriptor for Per-Pixel Rendering Difficulty

<jats:p>Per-pixel rendering difficulty is conventionally measured by the sample variance ˆσ2(p) of a Monte Carlo estimator, yet this signal is least reliable exactly where difficulty concentrates: under heavytailed transport its relative error is governed by the integrand’s kurtosis, and the split-half reliability of variance-derived evaluation targets reaches only ρ = 0.23–0.29 even at 40,000 samples per pixel. We propose a complementary discrete transport-mechanism descriptor: every contribution event is classified by its end-vertex BSDF lobe and the presence of a delta-specular event, yielding seven mutually exclusive labels whose six named mechanisms receive all observed energy on the tested scenes, with continuous side-channels retaining the per-pixel mechanism mixture. Across seven scenes, the dominant label agrees 87–99.6% between 64 and 4096 samples per pixel — where quantile-binned ˆσ2 agrees as little as 21% — and is robust to restoring the estimator’s MIS half. The descriptor exposes cross-scene structure that a scalar variance cannot represent, including a geometrycontrolled sign reversal of the caustic–glossy correlation. Finally, we demonstrate operational value: using the label to correct a noisy pilot ˆσ2 consistently improves on pilot-variance sample allocation at equal budget, exactly on the scenes where the pilot is least reliable — narrowing, though not yet closing, its gap to uniform sampling on the scenes where the raw pilot loses even to uniform — while acting only where heavy-tailed buckets exist, with gains that survive a random-partition placebo control and persist on top of a robust (median-of-means) pilot baseline.</jats:p>