Herschel-Bulkley diffusion filtering: non-Newtonian fluid mechanics in image processing
Bibliographic record
Abstract
We consider certain nonlinear diffusion filters of TV-type, which have a physical analogy as a visco-plastic fluid model. By separating timescales and spatial scales of the image and noise, we develop an energy inequality that governs the evolution of the noise on a local sub-domain of 4k2 pixels. Subtracting the local mean of the noise we derive an inequality that bounds the decay of the L2 norm of the noise, minus its local mean. We thus produce estimates for the decay of the noise to its local mean. We show that the noise decays to its local mean in a finite time and give an expression for this stopping time. We show that our stopping time estimate is valid for a range of filter parameters and show how to properly select filter parameters in a consistent way. Finally, we show how the noise decay can be improved by making our filter parameters locally defined, according to the underlying image.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".