Type-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Saddle-Shaped Articular Surfaces
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Bibliographic record
Abstract
The scope of this paper is the guaranteed fitting of specified types of quadratic surfaces to scattered 3D point clouds. Since we chose quadrics to account for articular surfaces of various shapes in medical images, the models thus estimated usefully extract global symmetry-related intrinsic features in human joints: centers, axes, extremal curvatures. The unified type-enforcing method is based on a constrained weighted least-squares minimization of algebraic residuals which uses a robust and bias- corrected metric. Provided that at most one quadratic constraint is involved, every step produces closed-form eigenvector solutions. In this framework, guaranteeing the occurrence of 3D primitives of certain types among this eigendecomposition is not a straightforward transcription of the priorly handled 2D case. To explore possibilities, we re-exploit a mapping to a 2D space called the quadric shape map (QSM) where the influence of any constraint on shape and type can in fact be studied visually. As a result, we provide a new enforceable quadratic constraint that practically ensures types such as hyperboloids, which helps characterize saddle-like articular surfaces. Application to a database shows how this guarantee is needed to coherently extract the center and axes of the ankle joint.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it