Analysis of geometrical distortion and statistical variance in length, area, and volume in a linearly scanned 3-D ultrasound image
Bibliographic record
Abstract
A linearly scanned three-dimensional (3-D) ultrasound imaging system is considered. The transducer array is initially oriented along the x axis and aimed in the y direction. After being tilted by an angle theta about the x axis, and then swiveled by an angle phi about the y axis, it is translated in the z direction, in steps of size d, to acquire a series of parallel two-dimendional (2-D) images. From these, the 3-D image is reconstructed, using the nominal values of the parameters (phi, theta, d). Thus, any systematic or random errors in these, relative to their actual values (phi0, theta0, d0), will respectively cause distortions or variances in length, area, and volume in the reconstructed 3-D image, relative to the 3-D object. Here, we analyze these effects. Compact linear approximations are derived for the relative distortions as functions of the parameter errors, and hence, for the relative variances as functions of the parameter variances. Also, exact matrix formulas for the relative distortions are derived for arbitrary values of (phi, theta, d) and (phi0, theta0, d0). These were numerically compared to the linear approximations and to measurements from simulated 3-D images of a cubical object and real 3-D images of a wire phantom. In every case tested, the theory was confirmed within experimental error (0.5%).
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 teacher head, 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".