Stratified Markov Chain Monte Carlo Light Transport
Bibliographic record
Abstract
Abstract Markov chain Monte Carlo (MCMC) sampling is a powerful approach to generate samples from an arbitrary distribution. The application to light transport simulation allows us to efficiently handle complex light transport such as highly occluded scenes. Since light transport paths in MCMC methods are sampled according to the path contributions over the sampling domain covering the whole image, bright pixels receive more samples than dark pixels to represent differences in the brightness. This variation in the number of samples per pixel is a fundamental property of MCMC methods. This property often leads to uneven convergence over the image, which is a notorious and fundamental issue of any MCMC method to date. We present a novel stratification method of MCMC light transport methods. Our stratification method, for the first time, breaks the fundamental limitation that the number of samples per pixel is uncontrollable. Our method guarantees that every pixel receives a specified number of samples by running a single Markov chain per pixel. We rely on the fact that different MCMC processes should converge to the same result when the sampling domain and the integrand are the same. We thus subdivide an image into multiple overlapping tiles associated with each pixel, run an independent MCMC process in each of them, and then align all of the tiles such that overlapping regions match. This can be formulated as an optimization problem similar to the reconstruction step for gradient‐domain rendering. Further, our method can exploit the coherency of integrands among neighboring pixels via coherent Markov chains and replica exchange. Images rendered with our method exhibit much more predictable convergence compared to existing MCMC methods.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".