MEDIAL AXIS APPROXIMATION AND UNSTABLE FLOW COMPLEX
Bibliographic record
Abstract
The medial axis of a shape is known to carry a lot of information about the shape. In particular, a recent result of Lieutier establishes that every bounded open subset of ℝn has the same homotopy type as its medial axis. In this paper we provide an algorithm that computes a structure we call the core for the approximation of the medial axis of a shape with smooth boundary from a discrete sample of its boundary. The core is a piecewise linear cell complex that is guaranteed to capture the topology of the medial axis of the shape provided the sample of its boundary is sufficiently dense but not necessarily uniform. We also present a natural method for augmenting the core in order to extend it geometrically while maintaining the topological guarantees. The definition of the core and its extension are based on the steepest ascent flow map that results from the distance function induced by the sample point set. We also provide a geometric guarantee on the closeness of the core and the actual medial axis.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".