PKCS: A Polynomial Kernel Family With Compact Support for Scale- Space Image Processing
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Bibliographic record
Abstract
In a scale-space framework, the Gaussian kernel has some properties that make it unique. However, because of its infinite support, exact implementation of this kernel is not possible. To avoid this drawback, there exist two different approaches: approximating the Gaussian kernel by a finite support kernel, or defining new kernels with properties closed to the Gaussian. In this paper, we propose a polynomial kernel family with compact support which overcomes the Gaussian practical drawbacks while preserving a large number of the useful Gaussian properties. The new kernels are not obtained by approximating the Gaussian, though they are derived from it. We show that, for a suitable choice of kernel parameters, this family provides an approximated solution of the diffusion equation and satisfies some other basic constraints of the linear scale-space theory. The construction and properties of the proposed kernel are described, and an application in which handwritten data are extracted from noisy document images is presented.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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