Lossless Basis Expansion for Gradient‐Domain Rendering
Bibliographic record
Abstract
Abstract Gradient‐domain rendering utilizes difference estimates with shift mapping to reduce variance in Monte Carlo rendering. Such difference estimates are effective under the assumption that pixels for difference estimates have similar integrands. This assumption is often violated because it is common to have spatially varying BSDFs with material maps, which potentially result in a very different integrand per pixel. We introduce an extension of gradient‐domain rendering that effectively supports such per‐pixel variation in BSDFs based on basis expansion. Basis expansion for BSDFs has been used extensively in other problems in rendering, where the goal is to approximate a given BSDF by a weighted sum of predefined basis functions. We instead utilize lossless basis expansion, representing a BSDF without any approximation by adding the remaining difference in the original basis expansion. This lossless basis expansion allows us to cancel more terms via shift mapping, resulting in low variance difference estimates even with per‐pixel BSDF variation. We also extend the Poisson reconstruction process to support this basis expansion. Regular gradient‐domain rendering can be expressed as a special case of our extension, where the basis is simply the BSDF per pixel (i.e., no basis expansion). We provide proof‐of‐concept experiments and showcase the effectiveness of our method for scenes with highly varying material maps. Our results show noticeable improvement over regular gradient‐domain rendering under both L1 and L2 reconstructions. The resulting formulation via basis expansion essentially serves as a new way of path reuse among pixels in the presence of per‐pixel variation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".