Robust Fourier‐based slanted‐edge method to measure scatter ratio
Bibliographic record
Abstract
BACKGROUND: Patient scatter incident on an x-ray detector reduces radiographic contrast and adds quantum noise, and minimizing scatter is critical in some specialized techniques such as dual-energy and energy-subtraction methods. Existing methods to measure scatter are either labor-intensive (multiple disks) or not appropriate to use in radiography where scatter often exceeds the width of the x-ray beam. PURPOSE: Develop a method to measure the scatter-to-primary ratio (SPR) that can be used for a wide range of radiographic and mammographic conditions, both with scatter equilibrium (scatter function does not exceed primary-beam width) and without. METHODS: Fourier theory is used to show the SPR can be measured from the low-frequency drop (LFD) of the Fourier transform of the derivative of a normalized edge profile. The method was validated both experimentally and by simulation for radiography and mammography under scatter equilibrium and nonequilibrium conditions. RESULTS: The theoretical derivation showed that by normalizing an edge profile with a profile without the edge, scatter equilibrium is not required and the method accommodates a nonuniform primary beam from beam divergence and Heel effect. The method was validated by a simulation study for a range of scatter-LSF widths, primary-beam widths, and image regions of interest used in the analysis. Experimental scatter measurements agreed with a similar edge-method published by Cooper when scatter equilibrium is achieved. CONCLUSIONS: A simple and direct method of measuring the SPR obtained with both uniform and nonuniform test phantoms is described. Validated both experimentally and theoretically, it uses the Fourier LFD obtained from a normalized slanted-edge profile and works for a wide range of practical mammographic and radiographic conditions.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".