Determination of 3D PSFs from computed tomography reconstructed x‐ray images of spherical objects and the effects of sphere radii
Bibliographic record
Abstract
PURPOSE: A method was developed to obtain three-dimensional (3D) point spread functions (PSFs) of reconstructed x-ray volumetric images using spheres of known diameters. The algorithm consists of a sphere localization step using template matching applied to the entire volume. Richardson Lucy (RL) deconvolution is used atypically to determine the PSF from the reconstructed x-ray image and a model of the sphere. The resulting PSF is arbitrary, that is, there are no assumptions of separability or symmetry. Oversampling is not used, and sample spacing matches the image. The effect of sphere radius on PSF estimate reproducibility is investigated. METHODS: Phantoms were constructed by suspending five polytetrafluoroethylene (PTFE) spheres having known radii equal to 4.77, 7.95, 9.52, 12.68, and 19.53 mm in an agar solution. The phantom included a 25 μm steel wire to calculate a line spread function (LSF). The phantom was imaged and reconstructed with a Medtronic surgical O-Arm 23 times and a Toshiba Aquilion One computed tomography (CT) 20 times. A sharp reconstruction kernel exhibiting a nonmonotonic PSF was used with the Toshiba CT. PSFs and LSFs were computed for all of the images and repeated estimates were used to compute mean and standard deviation values for every point of the PSFs and LSFs. The PSFs from spheres were converted to LSFs and compared to the wire LSF. RESULTS: The standard deviations of the PSF estimates exhibit a decreasing trend as the sphere radius is increased. The PSF from the smallest 4.77 mm sphere is the least reproducible. The normalized root mean square difference between the mean LSF derived from the 4.77 mm radius sphere and the mean wire LSF is 2.0% for the O-arm and 1.2% for the CT. CONCLUSION: Richardson Lucy (RL) deconvolution provides a method to estimate generalized (no separability or other simplifying assumptions) 3D PSFs from spheres. X-ray noise in images acquired with typical clinical protocols cause noticeable variations in PSF estimates which can be mitigated by selecting larger spheres and combining PSF estimates from different images.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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".