A study of the anisotropically weighted procrustes problem [optical image-guided surgery application]
Bibliographic record
Abstract
The authors studied the problem of finding an optimal rigid-body transformation that maps one configuration of points to a corresponding configuration when the alignment errors are anisotropically weighted. Such a problem arises in point-to-point registration, in particular when an optical device (e.g. microscope or video camera) is involved, as in image-guided surgery. The authors review the existing literature and algorithms and study the mathematical difficulties. After stating a symmetry condition for critical points, they use it to establish some results. In particular, they show that the starting configuration and weight matrices can have a special form (orthogonal columns), they show that the rotational part can be computed from configurations translated so that their centroids lie at the origin, and they give an estimate for the total number of critical points. The authors then compare the 2 existing algorithms, studying carefully their dependence on the different parameters, and propose an independent technique in order to validate them. This technique reduces the problem to the problem of finding the roots of a system of 3 polynomials in 3 variables.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".