High-Order Signed Distance Transform of Sampled Signals
Bibliographic record
Abstract
Signed distance transforms of sampled signals can be constructed better than the traditional exact signed distance transform. Such a transform is termed the high-order signed distance transform and is defined as satisfying three conditions: the Eikonal equation, recovery by a Heaviside function, and has an order of accuracy greater than unity away from the medial axis. Such a transform is an improvement to the classic notion of an exact signed distance transform because it does not exhibit artifacts of quantization. A large constant, linear time complexity high-order signed distance transform for arbitrary dimensionality sampled signals is developed based on the high order fast sweeping method. The transform is initialized with an exact signed distance transform and quantization corrected through an upwind solver for the boundary value Eikonal equation. The proposed method cannot attain arbitrary order of accuracy and is limited by the initialization method and non-uniqueness of the problem. However, meshed surfaces are visually smoother and do not exhibit artifacts of quantization in local mean and Gaussian curvature.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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 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".