Efficient and Accurate Spherical Kernel Integrals Using Isotropic Decomposition
Why this work is in the frame
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Bibliographic record
Abstract
Spherical filtering is fundamental to many problems in image synthesis, such as computing the reflected light over a surface or anti-aliasing mirror reflections over a pixel. This operation is challenging since the profile of spherical filters (e.g., the view-evaluated BRDF or the geometry-warped pixel footprint, mentioned before) typically exhibits both spatial and rotational variation at each pixel, precluding precomputed solutions. We accelerate complex spherical filtering tasks using isotropic spherical decomposition (ISD), decomposing spherical filters into a linear combination of simpler isotropic kernels. Our general ISD is flexible to the choice of the isotropic kernels, and we demonstrate practical realizations of ISD on several problems in rendering: shading and prefiltering with spatially varying BRDFs, anti-aliasing-environment-mapped mirror reflections, and filtering of noisy reflectance data. Compared to previous basis-space rendering solutions, our shading solution generates ground-truth-quality results at interactive rates, avoiding costly reconstruction and large approximation errors.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it